| Home | Libraries | People | FAQ | More

## Special Function Error Rates Report

Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

## beta

Table 1. Error rates for beta

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Beta Function: Small Values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = +INFε (Mean = +INFε) And other failures.) (Rmath 3.2.3: Max = 1.14ε (Mean = 0.574ε)) | Max = 2.86ε (Mean = 1.22ε) (<cmath>: Max = 364ε (Mean = 76.2ε)) | Max = 2.86ε (Mean = 1.22ε) | Max = 2.23ε (Mean = 1.14ε)
Beta Function: Medium Values | Max = 0.978ε (Mean = 0.0595ε) (GSL 2.1: Max = 1.18e+03ε (Mean = 238ε)) (Rmath 3.2.3: Max = 1.09e+03ε (Mean = 265ε)) | Max = 61.4ε (Mean = 19.4ε) (<cmath>: Max = 1.07e+03ε (Mean = 264ε)) | Max = 107ε (Mean = 24.5ε) | Max = 96.5ε (Mean = 22.4ε)
Beta Function: Divergent Values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 12.1ε (Mean = 1.99ε)) (Rmath 3.2.3: Max = 176ε (Mean = 28ε)) | Max = 8.99ε (Mean = 2.44ε) (<cmath>: Max = 128ε (Mean = 23.8ε)) | Max = 18.8ε (Mean = 2.71ε) | Max = 11.4ε (Mean = 2.19ε)

## beta (incomplete)

Table 2. Error rates for beta (incomplete)

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Incomplete Beta Function: Small Values | Max = 0ε (Mean = 0ε) | Max = 11.1ε (Mean = 2.32ε) | Max = 18.7ε (Mean = 3.19ε) | Max = 9.94ε (Mean = 2.17ε)
Incomplete Beta Function: Medium Values | Max = 0.568ε (Mean = 0.0254ε) | Max = 69.2ε (Mean = 13.4ε) | Max = 174ε (Mean = 25ε) | Max = 90ε (Mean = 12.7ε)
Incomplete Beta Function: Large and Diverse Values | Max = 0.999ε (Mean = 0.0325ε) | Max = 6.84e+04ε (Mean = 2.76e+03ε) | Max = 6.86e+04ε (Mean = 2.79e+03ε) | Max = 633ε (Mean = 29.7ε)
Incomplete Beta Function: Small Integer Values | Max = 0.786ε (Mean = 0.0323ε) | Max = 11.6ε (Mean = 3.6ε) | Max = 51.8ε (Mean = 11ε) | Max = 26ε (Mean = 6.28ε)

## betac

Table 3. Error rates for betac

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Incomplete Beta Function: Small Values | Max = 0.676ε (Mean = 0.0302ε) | Max = 9.92ε (Mean = 2.3ε) | Max = 11.2ε (Mean = 2.94ε) | Max = 8.94ε (Mean = 2.06ε)
Incomplete Beta Function: Medium Values | Max = 0.949ε (Mean = 0.098ε) | Max = 63.5ε (Mean = 13.5ε) | Max = 97.6ε (Mean = 24.3ε) | Max = 90.6ε (Mean = 14.8ε)
Incomplete Beta Function: Large and Diverse Values | Max = 1.12ε (Mean = 0.0458ε) | Max = 1.05e+05ε (Mean = 5.45e+03ε) | Max = 1.04e+05ε (Mean = 5.46e+03ε) | Max = 3.72e+03ε (Mean = 113ε)
Incomplete Beta Function: Small Integer Values | Max = 0.586ε (Mean = 0.0314ε) | Max = 11.1ε (Mean = 3.65ε) | Max = 103ε (Mean = 17.4ε) | Max = 26.2ε (Mean = 6.36ε)

## binomial_coefficient

Table 4. Error rates for binomial_coefficient

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Binomials: small arguments | Max = 1ε (Mean = 0.369ε) | Max = 1.5ε (Mean = 0.339ε) | Max = 1.5ε (Mean = 0.339ε) | Max = 1ε (Mean = 0.369ε)
Binomials: large arguments | Max = 0.939ε (Mean = 0.314ε) | Max = 26.6ε (Mean = 6.13ε) | Max = 53.2ε (Mean = 10.8ε) | Max = 37.2ε (Mean = 7.4ε)

## boost::math::powm1

Table 5. Error rates for boost::math::powm1

| GNU C++ version 7.1.0 linux long double | GNU C++ version 7.1.0 linux double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
powm1 | (<math.h>: Max = 2.04ε (Mean = 0.493ε)) Max = 2.04ε (Mean = 0.493ε) (<cmath>: Max = 2.04ε (Mean = 0.493ε)) | (Rmath 3.2.3: Max = 1.06ε (Mean = 0.425ε)) (GSL 2.1: Max = 1.06ε (Mean = 0.425ε)) Max = 1.06ε (Mean = 0.425ε) | Max = 1.88ε (Mean = 0.49ε) (<math.h>: Max = 1.88ε (Mean = 0.49ε)) | (<math.h>: Max = 1.84ε (Mean = 0.486ε)) Max = 1.84ε (Mean = 0.486ε)

## cbrt

Table 6. Error rates for cbrt

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
cbrt Function | Max = 0ε (Mean = 0ε) | Max = 1.34ε (Mean = 0.471ε) (<cmath>: Max = 1.34ε (Mean = 0.471ε)) (<math.h>: Max = 1.34ε (Mean = 0.471ε)) | Max = 1.34ε (Mean = 0.471ε) (<math.h>: Max = 1.34ε (Mean = 0.471ε)) | Max = 1.7ε (Mean = 0.565ε) (<math.h>: Max = 1.7ε (Mean = 0.565ε))

## cos_pi

Table 7. Error rates for cos_pi

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
sin_pi and cos_pi | Max = 0ε (Mean = 0ε) | Max = 0.991ε (Mean = 0.302ε) | Max = 0.991ε (Mean = 0.302ε) | Max = 0.996ε (Mean = 0.284ε)
sin_pi and cos_pi near integers and half integers | Max = 0ε (Mean = 0ε) | Max = 0.976ε (Mean = 0.28ε) | Max = 0.976ε (Mean = 0.28ε) | Max = 0.996ε (Mean = 0.298ε)

## cyl_bessel_i

Table 8. Error rates for cyl_bessel_i

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Bessel I0: Mathworld Data | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 270ε (Mean = 91.6ε) And other failures.) (Rmath 3.2.3: Max = 1.52ε (Mean = 0.622ε) And other failures.) | Max = 1.95ε (Mean = 0.738ε) (<cmath>: Max = 8.49ε (Mean = 3.46ε) And other failures.) | Max = 1.95ε (Mean = 0.661ε) | Max = 0.762ε (Mean = 0.329ε)
Bessel I1: Mathworld Data | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 128ε (Mean = 41ε) And other failures.) (Rmath 3.2.3: Max = 1.53ε (Mean = 0.483ε) And other failures.) | Max = 0.64ε (Mean = 0.202ε) (<cmath>: Max = 5ε (Mean = 2.15ε) And other failures.) | Max = 0.64ε (Mean = 0.202ε) | Max = 0.767ε (Mean = 0.398ε)
Bessel In: Mathworld Data | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 2.31ε (Mean = 0.838ε) And other failures.) (Rmath 3.2.3: Max = 1.73ε (Mean = 0.601ε) And other failures.) | Max = 1.8ε (Mean = 1.33ε) (<cmath>: Max = 430ε (Mean = 163ε) And other failures.) | Max = 463ε (Mean = 140ε) | Max = 3.46ε (Mean = 1.32ε)
Bessel Iv: Mathworld Data | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 5.95ε (Mean = 2.08ε) And other failures.) (Rmath 3.2.3: Max = 3.53ε (Mean = 1.39ε)) | Max = 4.12ε (Mean = 1.85ε) (<cmath>: Max = 616ε (Mean = 221ε) And other failures.) | Max = 4.12ε (Mean = 1.95ε) | Max = 2.97ε (Mean = 1.24ε)
Bessel In: Random Data | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 261ε (Mean = 53.2ε) And other failures.) (Rmath 3.2.3: Max = 7.37ε (Mean = 2.4ε)) | Max = 4.62ε (Mean = 1.06ε) (<cmath>: Max = 645ε (Mean = 132ε)) | Max = 176ε (Mean = 39.1ε) | Max = 9.67ε (Mean = 1.88ε)
Bessel Iv: Random Data | Max = 0.661ε (Mean = 0.0441ε) (GSL 2.1: Max = 6.18e+03ε (Mean = 1.55e+03ε) And other failures.) (Rmath 3.2.3: Max = 4.28e+08ε (Mean = 2.85e+07ε)) | Max = 8.35ε (Mean = 1.62ε) (<cmath>: Max = 1.05e+03ε (Mean = 224ε) And other failures.) | Max = 283ε (Mean = 88.4ε) | Max = 7.46ε (Mean = 1.71ε)
Bessel Iv: Mathworld Data (large values) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 37ε (Mean = 18ε) And other failures.) (Rmath 3.2.3: Max = 3.77e+168ε (Mean = 2.39e+168ε) And other failures.) | Max = 14.7ε (Mean = 6.66ε) (<cmath>: Max = 118ε (Mean = 57.2ε) And other failures.) | Max = 14.7ε (Mean = 6.59ε) | Max = 3.67ε (Mean = 1.64ε)

## cyl_bessel_i (integer orders)

Table 9. Error rates for cyl_bessel_i (integer orders)

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Bessel I0: Mathworld Data (Integer Version) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 0.79ε (Mean = 0.482ε)) (Rmath 3.2.3: Max = 1.52ε (Mean = 0.622ε) And other failures.) | Max = 1.95ε (Mean = 0.738ε) (<cmath>: Max = 8.49ε (Mean = 3.46ε) And other failures.) | Max = 1.95ε (Mean = 0.661ε) | Max = 0.762ε (Mean = 0.329ε)
Bessel I1: Mathworld Data (Integer Version) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 0.82ε (Mean = 0.456ε)) (Rmath 3.2.3: Max = 1.53ε (Mean = 0.483ε) And other failures.) | Max = 0.64ε (Mean = 0.202ε) (<cmath>: Max = 5ε (Mean = 2.15ε) And other failures.) | Max = 0.64ε (Mean = 0.202ε) | Max = 0.767ε (Mean = 0.398ε)
Bessel In: Mathworld Data (Integer Version) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 5.15ε (Mean = 2.13ε) And other failures.) (Rmath 3.2.3: Max = 1.73ε (Mean = 0.601ε) And other failures.) | Max = 1.8ε (Mean = 1.33ε) (<cmath>: Max = 430ε (Mean = 163ε) And other failures.) | Max = 463ε (Mean = 140ε) | Max = 3.46ε (Mean = 1.32ε)

## cyl_bessel_i_prime

Table 10. Error rates for cyl_bessel_i_prime

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Bessel I'0: Mathworld Data | Max = 0ε (Mean = 0ε) | Max = 0.82ε (Mean = 0.259ε) | Max = 0.82ε (Mean = 0.259ε) | Max = 0.82ε (Mean = 0.354ε)
Bessel I'1: Mathworld Data | Max = 0ε (Mean = 0ε) | Max = 1.97ε (Mean = 0.757ε) | Max = 1.97ε (Mean = 0.757ε) | Max = 1.36ε (Mean = 0.782ε)
Bessel I'n: Mathworld Data | Max = 0ε (Mean = 0ε) | Max = 2.31ε (Mean = 1.41ε) | Max = 701ε (Mean = 212ε) | Max = 3.61ε (Mean = 1.22ε)
Bessel I'v: Mathworld Data | Max = 1.62ε (Mean = 0.512ε) | Max = 2.89e+03ε (Mean = 914ε) | Max = 2.89e+03ε (Mean = 914ε) | Max = 3.76e+03ε (Mean = 1.19e+03ε)
Bessel I'n: Random Data | Max = 0ε (Mean = 0ε) | Max = 3.95ε (Mean = 1.06ε) | Max = 195ε (Mean = 37.1ε) | Max = 9.85ε (Mean = 1.82ε)
Bessel I'v: Random Data | Max = 0ε (Mean = 0ε) | Max = 14.1ε (Mean = 2.93ε) | Max = 336ε (Mean = 68.5ε) | Max = 14ε (Mean = 2.5ε)
Bessel I'v: Mathworld Data (large values) | Max = 0ε (Mean = 0ε) | Max = 42.6ε (Mean = 20.2ε) | Max = 42.6ε (Mean = 20.2ε) | Max = 59.5ε (Mean = 26.6ε)

## cyl_bessel_i_prime (integer orders)

Table 11. Error rates for cyl_bessel_i_prime (integer orders)

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Bessel I'0: Mathworld Data (Integer Version) | Max = 0ε (Mean = 0ε) | Max = 0.82ε (Mean = 0.259ε) | Max = 0.82ε (Mean = 0.259ε) | Max = 0.82ε (Mean = 0.354ε)
Bessel I'1: Mathworld Data (Integer Version) | Max = 0ε (Mean = 0ε) | Max = 1.97ε (Mean = 0.757ε) | Max = 1.97ε (Mean = 0.757ε) | Max = 1.36ε (Mean = 0.782ε)
Bessel I'n: Mathworld Data (Integer Version) | Max = 0ε (Mean = 0ε) | Max = 2.31ε (Mean = 1.41ε) | Max = 701ε (Mean = 212ε) | Max = 3.61ε (Mean = 1.22ε)

## cyl_bessel_j

Table 12. Error rates for cyl_bessel_j

| GNU C++ version 7.1.0 linux long double | GNU C++ version 7.1.0 linux double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Bessel J0: Mathworld Data | Max = 6.55ε (Mean = 2.86ε) (<cmath>: Max = 5.04ε (Mean = 1.78ε) And other failures.) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 0.629ε (Mean = 0.223ε) And other failures.) (Rmath 3.2.3: Max = 0.629ε (Mean = 0.223ε) And other failures.) | Max = 6.55ε (Mean = 2.86ε) | Max = 2.52ε (Mean = 1.2ε)
Bessel J0: Mathworld Data (Tricky cases) | Max = 1.64e+08ε (Mean = 6.69e+07ε) (<cmath>: Max = 4.79e+08ε (Mean = 1.96e+08ε)) | Max = 8e+04ε (Mean = 3.27e+04ε) (GSL 2.1: Max = 6.5e+07ε (Mean = 2.66e+07ε)) (Rmath 3.2.3: Max = 1.04e+07ε (Mean = 4.29e+06ε)) | Max = 1.64e+08ε (Mean = 6.69e+07ε) | Max = 1e+07ε (Mean = 4.09e+06ε)
Bessel J1: Mathworld Data | Max = 3.59ε (Mean = 1.33ε) (<cmath>: Max = 6.1ε (Mean = 2.95ε) And other failures.) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 6.62ε (Mean = 2.35ε) And other failures.) (Rmath 3.2.3: Max = 0.946ε (Mean = 0.39ε) And other failures.) | Max = 1.44ε (Mean = 0.637ε) | Max = 1.73ε (Mean = 0.976ε)
Bessel J1: Mathworld Data (tricky cases) | Max = 2.18e+05ε (Mean = 9.76e+04ε) (<cmath>: Max = 2.15e+06ε (Mean = 1.58e+06ε)) | Max = 106ε (Mean = 47.5ε) (GSL 2.1: Max = 8.75e+05ε (Mean = 5.32e+05ε)) (Rmath 3.2.3: Max = 2.93e+06ε (Mean = 1.7e+06ε)) | Max = 2.18e+05ε (Mean = 9.76e+04ε) | Max = 3.23e+04ε (Mean = 1.45e+04ε)
Bessel JN: Mathworld Data | Max = 6.85ε (Mean = 3.35ε) (<cmath>: Max = 2.13e+19ε (Mean = 5.16e+18ε) And other failures.) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 6.9e+05ε (Mean = 2.15e+05ε) And other failures.) (Rmath 3.2.3: Max = +INFε (Mean = +INFε) And other failures.) | Max = 463ε (Mean = 112ε) | Max = 14.7ε (Mean = 5.4ε)
Bessel J: Mathworld Data | Max = 14.7ε (Mean = 4.11ε) (<cmath>: Max = 3.49e+05ε (Mean = 8.09e+04ε) And other failures.) | Max = 10ε (Mean = 2.24ε) (GSL 2.1: Max = 2.39e+05ε (Mean = 5.37e+04ε) And other failures.) (Rmath 3.2.3: Max = +INFε (Mean = +INFε) And other failures.) | Max = 14.7ε (Mean = 4.22ε) | Max = 14.9ε (Mean = 3.89ε)
Bessel J: Mathworld Data (large values) | Max = 607ε (Mean = 305ε) (<cmath>: Max = 34.9ε (Mean = 17.4ε) And other failures.) | Max = 0.536ε (Mean = 0.268ε) (GSL 2.1: Max = 4.91e+03ε (Mean = 2.46e+03ε) And other failures.) (Rmath 3.2.3: Max = 5.9ε (Mean = 3.76ε)) | Max = 607ε (Mean = 305ε) | Max = 9.31ε (Mean = 5.52ε)
Bessel JN: Random Data | Max = 50.8ε (Mean = 3.69ε) (<cmath>: Max = 1.12e+03ε (Mean = 88.7ε)) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 75.7ε (Mean = 5.36ε)) (Rmath 3.2.3: Max = 3.93ε (Mean = 1.22ε)) | Max = 99.6ε (Mean = 22ε) | Max = 17.5ε (Mean = 1.46ε)
Bessel J: Random Data | Max = 11.4ε (Mean = 1.68ε) (<cmath>: Max = 501ε (Mean = 52.3ε)) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 15.5ε (Mean = 3.33ε) And other failures.) (Rmath 3.2.3: Max = 6.74ε (Mean = 1.3ε)) | Max = 260ε (Mean = 34ε) | Max = 9.24ε (Mean = 1.17ε)
Bessel J: Random Data (Tricky large values) | Max = 785ε (Mean = 94.2ε) (<cmath>: Max = 5.01e+17ε (Mean = 6.23e+16ε)) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 2.48e+05ε (Mean = 5.11e+04ε)) (Rmath 3.2.3: Max = 71.6ε (Mean = 11.7ε)) | Max = 785ε (Mean = 97.4ε) | Max = 59.2ε (Mean = 8.67ε)

## cyl_bessel_j (integer orders)

Table 13. Error rates for cyl_bessel_j (integer orders)

| GNU C++ version 7.1.0 linux long double | GNU C++ version 7.1.0 linux double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Bessel J0: Mathworld Data (Integer Version) | Max = 6.55ε (Mean = 2.86ε) (<cmath>: Max = 5.04ε (Mean = 1.78ε) And other failures.) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 1.12ε (Mean = 0.488ε)) (Rmath 3.2.3: Max = 0.629ε (Mean = 0.223ε) And other failures.) | Max = 6.55ε (Mean = 2.86ε) | Max = 2.52ε (Mean = 1.2ε) (<math.h>: Max = 1.89ε (Mean = 0.988ε))
Bessel J0: Mathworld Data (Tricky cases) (Integer Version) | Max = 1.64e+08ε (Mean = 6.69e+07ε) (<cmath>: Max = 4.79e+08ε (Mean = 1.96e+08ε)) | Max = 8e+04ε (Mean = 3.27e+04ε) (GSL 2.1: Max = 1e+07ε (Mean = 4.11e+06ε)) (Rmath 3.2.3: Max = 1.04e+07ε (Mean = 4.29e+06ε)) | Max = 1.64e+08ε (Mean = 6.69e+07ε) | Max = 1e+07ε (Mean = 4.09e+06ε) (<math.h>: Max = 2.54e+08ε (Mean = 1.04e+08ε))
Bessel J1: Mathworld Data (Integer Version) | Max = 3.59ε (Mean = 1.33ε) (<cmath>: Max = 6.1ε (Mean = 2.95ε) And other failures.) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 1.89ε (Mean = 0.721ε)) (Rmath 3.2.3: Max = 0.946ε (Mean = 0.39ε) And other failures.) | Max = 1.44ε (Mean = 0.637ε) | Max = 1.73ε (Mean = 0.976ε) (<math.h>: Max = 11.4ε (Mean = 4.15ε))
Bessel J1: Mathworld Data (tricky cases) (Integer Version) | Max = 2.18e+05ε (Mean = 9.76e+04ε) (<cmath>: Max = 2.15e+06ε (Mean = 1.58e+06ε)) | Max = 106ε (Mean = 47.5ε) (GSL 2.1: Max = 1.26e+06ε (Mean = 6.28e+05ε)) (Rmath 3.2.3: Max = 2.93e+06ε (Mean = 1.7e+06ε)) | Max = 2.18e+05ε (Mean = 9.76e+04ε) | Max = 3.23e+04ε (Mean = 1.45e+04ε) (<math.h>: Max = 1.44e+07ε (Mean = 6.5e+06ε))
Bessel JN: Mathworld Data (Integer Version) | Max = 6.85ε (Mean = 3.35ε) (<cmath>: Max = 2.13e+19ε (Mean = 5.16e+18ε) And other failures.) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 6.9e+05ε (Mean = 2.53e+05ε) And other failures.) (Rmath 3.2.3: Max = +INFε (Mean = +INFε) And other failures.) | Max = 463ε (Mean = 112ε) | Max = 14.7ε (Mean = 5.4ε) (<math.h>: Max = +INFε (Mean = +INFε) And other failures.)

## cyl_bessel_j_prime

Table 14. Error rates for cyl_bessel_j_prime

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Bessel J0': Mathworld Data | Max = 0ε (Mean = 0ε) | Max = 18.9ε (Mean = 6.82ε) | Max = 18.9ε (Mean = 6.72ε) | Max = 6.62ε (Mean = 2.55ε)
Bessel J0': Mathworld Data (Tricky cases) | Max = 0ε (Mean = 0ε) | Max = 7.44ε (Mean = 3.34ε) | Max = 7.44ε (Mean = 3.31ε) | Max = 3.67ε (Mean = 1.74ε)
Bessel J1': Mathworld Data | Max = 0ε (Mean = 0ε) | Max = 7.9ε (Mean = 3.37ε) | Max = 7.9ε (Mean = 3.37ε) | Max = 0.999ε (Mean = 0.627ε)
Bessel J1': Mathworld Data (tricky cases) | Max = 287ε (Mean = 129ε) | Max = 5.88e+05ε (Mean = 2.63e+05ε) | Max = 5.88e+05ε (Mean = 2.63e+05ε) | Max = 288ε (Mean = 129ε)
Bessel JN': Mathworld Data | Max = 0.527ε (Mean = 0.128ε) | Max = 1.29e+03ε (Mean = 312ε) | Max = 1.29e+03ε (Mean = 355ε) | Max = 14ε (Mean = 6.13ε)
Bessel J': Mathworld Data | Max = 21.5ε (Mean = 4.7ε) | Max = 42.5ε (Mean = 9.31ε) | Max = 42.5ε (Mean = 9.32ε) | Max = 23.7ε (Mean = 8ε)
Bessel J': Mathworld Data (large values) | Max = 0ε (Mean = 0ε) | Max = 989ε (Mean = 495ε) | Max = 989ε (Mean = 495ε) | Max = 2.9ε (Mean = 1.61ε)
Bessel JN': Random Data | Max = 0.593ε (Mean = 0.0396ε) | Max = 11.3ε (Mean = 1.85ε) | Max = 79.4ε (Mean = 16.2ε) | Max = 6.34ε (Mean = 0.999ε)
Bessel J': Random Data | Max = 0.885ε (Mean = 0.033ε) | Max = 139ε (Mean = 6.47ε) | Max = 279ε (Mean = 27.2ε) | Max = 176ε (Mean = 9.75ε)
Bessel J': Random Data (Tricky large values) | Max = 0ε (Mean = 0ε) | Max = 474ε (Mean = 62.2ε) | Max = 474ε (Mean = 64.5ε) | Max = 379ε (Mean = 45.4ε)

## cyl_bessel_j_prime (integer orders)

Table 15. Error rates for cyl_bessel_j_prime (integer orders)

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Bessel J0': Mathworld Data (Integer Version) | Max = 0ε (Mean = 0ε) | Max = 18.9ε (Mean = 6.82ε) | Max = 18.9ε (Mean = 6.72ε) | Max = 6.62ε (Mean = 2.55ε)
Bessel J0': Mathworld Data (Tricky cases) (Integer Version) | Max = 0ε (Mean = 0ε) | Max = 7.44ε (Mean = 3.34ε) | Max = 7.44ε (Mean = 3.31ε) | Max = 3.67ε (Mean = 1.74ε)
Bessel J1': Mathworld Data (Integer Version) | Max = 0ε (Mean = 0ε) | Max = 7.9ε (Mean = 3.37ε) | Max = 7.9ε (Mean = 3.37ε) | Max = 0.999ε (Mean = 0.627ε)
Bessel J1': Mathworld Data (tricky cases) (Integer Version) | Max = 287ε (Mean = 129ε) | Max = 5.88e+05ε (Mean = 2.63e+05ε) | Max = 5.88e+05ε (Mean = 2.63e+05ε) | Max = 288ε (Mean = 129ε)
Bessel JN': Mathworld Data (Integer Version) | Max = 0.527ε (Mean = 0.128ε) | Max = 1.29e+03ε (Mean = 312ε) | Max = 1.29e+03ε (Mean = 355ε) | Max = 14ε (Mean = 6.13ε)

## cyl_bessel_k

Table 16. Error rates for cyl_bessel_k

| GNU C++ version 7.1.0 linux long double | GNU C++ version 7.1.0 linux double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Bessel K0: Mathworld Data | Max = 0.833ε (Mean = 0.436ε) (<cmath>: Max = 9.33ε (Mean = 3.25ε)) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 6.04ε (Mean = 2.16ε)) (Rmath 3.2.3: Max = 0.833ε (Mean = 0.601ε)) | Max = 0.833ε (Mean = 0.436ε) | Max = 0.833ε (Mean = 0.552ε)
Bessel K1: Mathworld Data | Max = 0.786ε (Mean = 0.329ε) (<cmath>: Max = 8.94ε (Mean = 3.19ε)) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 6.26ε (Mean = 2.21ε)) (Rmath 3.2.3: Max = 0.894ε (Mean = 0.516ε)) | Max = 0.786ε (Mean = 0.329ε) | Max = 0.786ε (Mean = 0.39ε)
Bessel Kn: Mathworld Data | Max = 2.6ε (Mean = 1.21ε) (<cmath>: Max = 12.9ε (Mean = 4.91ε) And other failures.) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 3.36ε (Mean = 1.43ε) And other failures.) (Rmath 3.2.3: Max = 8.48ε (Mean = 2.98ε)) | Max = 2.6ε (Mean = 1.21ε) | Max = 3.63ε (Mean = 1.46ε)
Bessel Kv: Mathworld Data | Max = 3.58ε (Mean = 2.39ε) (<cmath>: Max = 13ε (Mean = 4.81ε) And other failures.) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 5.47ε (Mean = 2.04ε) And other failures.) (Rmath 3.2.3: Max = 3.15ε (Mean = 1.35ε)) | Max = 5.21ε (Mean = 2.53ε) | Max = 4.78ε (Mean = 2.19ε)
Bessel Kv: Mathworld Data (large values) | Max = 42.3ε (Mean = 21ε) (<cmath>: Max = 42.3ε (Mean = 19.8ε) And other failures.) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 308ε (Mean = 142ε) And other failures.) (Rmath 3.2.3: Max = 84.6ε (Mean = 37.8ε)) | Max = 42.3ε (Mean = 21ε) | Max = 59.8ε (Mean = 26.9ε)
Bessel Kn: Random Data | Max = 4.55ε (Mean = 1.12ε) (<cmath>: Max = 13.9ε (Mean = 2.91ε)) | Max = 0.764ε (Mean = 0.0348ε) (GSL 2.1: Max = 8.71ε (Mean = 1.76ε) And other failures.) (Rmath 3.2.3: Max = 7.47ε (Mean = 1.34ε)) | Max = 4.55ε (Mean = 1.12ε) | Max = 9.34ε (Mean = 1.7ε)
Bessel Kv: Random Data | Max = 7.88ε (Mean = 1.48ε) (<cmath>: Max = 13.6ε (Mean = 2.68ε) And other failures.) | Max = 0.507ε (Mean = 0.0313ε) (GSL 2.1: Max = 9.71ε (Mean = 1.47ε) And other failures.) (Rmath 3.2.3: Max = 7.37ε (Mean = 1.49ε)) | Max = 7.88ε (Mean = 1.47ε) | Max = 8.33ε (Mean = 1.62ε)

## cyl_bessel_k (integer orders)

Table 17. Error rates for cyl_bessel_k (integer orders)

| GNU C++ version 7.1.0 linux long double | GNU C++ version 7.1.0 linux double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Bessel K0: Mathworld Data (Integer Version) | Max = 0.833ε (Mean = 0.436ε) (<cmath>: Max = 9.33ε (Mean = 3.25ε)) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 1.2ε (Mean = 0.733ε)) (Rmath 3.2.3: Max = 0.833ε (Mean = 0.601ε)) | Max = 0.833ε (Mean = 0.436ε) | Max = 0.833ε (Mean = 0.552ε)
Bessel K1: Mathworld Data (Integer Version) | Max = 0.786ε (Mean = 0.329ε) (<cmath>: Max = 8.94ε (Mean = 3.19ε)) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 0.626ε (Mean = 0.333ε)) (Rmath 3.2.3: Max = 0.894ε (Mean = 0.516ε)) | Max = 0.786ε (Mean = 0.329ε) | Max = 0.786ε (Mean = 0.39ε)
Bessel Kn: Mathworld Data (Integer Version) | Max = 2.6ε (Mean = 1.21ε) (<cmath>: Max = 12.9ε (Mean = 4.91ε) And other failures.) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 168ε (Mean = 59.5ε)) (Rmath 3.2.3: Max = 8.48ε (Mean = 2.98ε)) | Max = 2.6ε (Mean = 1.21ε) | Max = 3.63ε (Mean = 1.46ε)

## cyl_bessel_k_prime

Table 18. Error rates for cyl_bessel_k_prime

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Bessel K'0: Mathworld Data | Max = 0ε (Mean = 0ε) | Max = 0.786ε (Mean = 0.329ε) | Max = 0.786ε (Mean = 0.329ε) | Max = 0.786ε (Mean = 0.39ε)
Bessel K'1: Mathworld Data | Max = 0ε (Mean = 0ε) | Max = 0.736ε (Mean = 0.389ε) | Max = 0.736ε (Mean = 0.389ε) | Max = 0.761ε (Mean = 0.444ε)
Bessel K'n: Mathworld Data | Max = 0ε (Mean = 0ε) | Max = 2.16ε (Mean = 1.08ε) | Max = 2.16ε (Mean = 1.08ε) | Max = 4.17ε (Mean = 1.75ε)
Bessel K'v: Mathworld Data | Max = 0ε (Mean = 0ε) | Max = 3.94ε (Mean = 2.44ε) | Max = 3.94ε (Mean = 2.34ε) | Max = 3.94ε (Mean = 1.47ε)
Bessel K'v: Mathworld Data (large values) | Max = 0ε (Mean = 0ε) | Max = 59.2ε (Mean = 42.9ε) | Max = 58.7ε (Mean = 42.6ε) | Max = 18.6ε (Mean = 11.8ε)
Bessel K'n: Random Data | Max = 0ε (Mean = 0ε) | Max = 4.45ε (Mean = 1.19ε) | Max = 4.45ε (Mean = 1.19ε) | Max = 9.67ε (Mean = 1.73ε)
Bessel K'v: Random Data | Max = 0ε (Mean = 0ε) | Max = 7.95ε (Mean = 1.53ε) | Max = 7.95ε (Mean = 1.52ε) | Max = 8.32ε (Mean = 1.65ε)

## cyl_bessel_k_prime (integer orders)

Table 19. Error rates for cyl_bessel_k_prime (integer orders)

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Bessel K'0: Mathworld Data (Integer Version) | Max = 0ε (Mean = 0ε) | Max = 0.786ε (Mean = 0.329ε) | Max = 0.786ε (Mean = 0.329ε) | Max = 0.786ε (Mean = 0.39ε)
Bessel K'1: Mathworld Data (Integer Version) | Max = 0ε (Mean = 0ε) | Max = 0.736ε (Mean = 0.389ε) | Max = 0.736ε (Mean = 0.389ε) | Max = 0.761ε (Mean = 0.444ε)
Bessel K'n: Mathworld Data (Integer Version) | Max = 0ε (Mean = 0ε) | Max = 2.16ε (Mean = 1.08ε) | Max = 2.16ε (Mean = 1.08ε) | Max = 4.17ε (Mean = 1.75ε)

## cyl_neumann

Table 20. Error rates for cyl_neumann

| GNU C++ version 7.1.0 linux long double | GNU C++ version 7.1.0 linux double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Y0: Mathworld Data | Max = 5.53ε (Mean = 2.4ε) (<cmath>: Max = 2.05e+05ε (Mean = 6.87e+04ε)) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 60.9ε (Mean = 20.4ε)) (Rmath 3.2.3: Max = 167ε (Mean = 56.5ε)) | Max = 5.53ε (Mean = 2.4ε) | Max = 4.61ε (Mean = 2.29ε)
Y1: Mathworld Data | Max = 6.33ε (Mean = 2.25ε) (<cmath>: Max = 9.71e+03ε (Mean = 4.08e+03ε)) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 23.4ε (Mean = 8.1ε)) (Rmath 3.2.3: Max = 193ε (Mean = 64.4ε)) | Max = 6.33ε (Mean = 2.29ε) | Max = 4.75ε (Mean = 1.72ε)
Yn: Mathworld Data | Max = 55.2ε (Mean = 17.8ε) (<cmath>: Max = 2.2e+20ε (Mean = 6.97e+19ε) And other failures.) | Max = 0.993ε (Mean = 0.314ε) (GSL 2.1: Max = 2.41e+05ε (Mean = 7.62e+04ε) And other failures.) (Rmath 3.2.3: Max = 1.24e+04ε (Mean = 4e+03ε)) | Max = 55.2ε (Mean = 17.8ε) | Max = 35ε (Mean = 11.9ε)
Yv: Mathworld Data | Max = 10.7ε (Mean = 4.93ε) (<cmath>: Max = 3.49e+15ε (Mean = 1.05e+15ε) And other failures.) | Max = 10ε (Mean = 3.02ε) (GSL 2.1: Max = 1.07e+05ε (Mean = 3.22e+04ε) And other failures.) (Rmath 3.2.3: Max = 243ε (Mean = 73.9ε)) | Max = 10.7ε (Mean = 5.1ε) | Max = 7.89ε (Mean = 3.27ε)
Yv: Mathworld Data (large values) | Max = 1.7ε (Mean = 1.33ε) (<cmath>: Max = 43.2ε (Mean = 16.3ε) And other failures.) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 60.8ε (Mean = 23ε) And other failures.) (Rmath 3.2.3: Max = 0.682ε (Mean = 0.335ε)) | Max = 1.7ε (Mean = 1.33ε) | Max = 0.682ε (Mean = 0.423ε)
Y0 and Y1: Random Data | Max = 10.8ε (Mean = 3.04ε) (<cmath>: Max = 2.59e+03ε (Mean = 500ε)) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 34.4ε (Mean = 8.9ε)) (Rmath 3.2.3: Max = 83ε (Mean = 14.2ε)) | Max = 10.8ε (Mean = 3.04ε) | Max = 4.17ε (Mean = 1.24ε)
Yn: Random Data | Max = 338ε (Mean = 27.5ε) (<cmath>: Max = 4.01e+03ε (Mean = 348ε)) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 500ε (Mean = 47.8ε)) (Rmath 3.2.3: Max = 691ε (Mean = 67.9ε)) | Max = 338ε (Mean = 27.5ε) | Max = 117ε (Mean = 10.2ε)
Yv: Random Data | Max = 2.08e+03ε (Mean = 149ε) (<cmath>: Max = +INFε (Mean = +INFε) And other failures.) | Max = 1.53ε (Mean = 0.102ε) (GSL 2.1: Max = 1.41e+06ε (Mean = 7.67e+04ε)) (Rmath 3.2.3: Max = 1.79e+05ε (Mean = 9.64e+03ε)) | Max = 2.08e+03ε (Mean = 149ε) | Max = 1.23e+03ε (Mean = 69.9ε)

## cyl_neumann (integer orders)

Table 21. Error rates for cyl_neumann (integer orders)

| GNU C++ version 7.1.0 linux long double | GNU C++ version 7.1.0 linux double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Y0: Mathworld Data (Integer Version) | Max = 5.53ε (Mean = 2.4ε) (<cmath>: Max = 2.05e+05ε (Mean = 6.87e+04ε)) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 6.46ε (Mean = 2.38ε)) (Rmath 3.2.3: Max = 167ε (Mean = 56.5ε)) | Max = 5.53ε (Mean = 2.4ε) | Max = 4.61ε (Mean = 2.29ε) (<math.h>: Max = 5.37e+03ε (Mean = 1.81e+03ε))
Y1: Mathworld Data (Integer Version) | Max = 6.33ε (Mean = 2.25ε) (<cmath>: Max = 9.71e+03ε (Mean = 4.08e+03ε)) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 1.51ε (Mean = 0.839ε)) (Rmath 3.2.3: Max = 193ε (Mean = 64.4ε)) | Max = 6.33ε (Mean = 2.29ε) | Max = 4.75ε (Mean = 1.72ε) (<math.h>: Max = 1.86e+04ε (Mean = 6.2e+03ε))
Yn: Mathworld Data (Integer Version) | Max = 55.2ε (Mean = 17.8ε) (<cmath>: Max = 2.2e+20ε (Mean = 6.97e+19ε) And other failures.) | Max = 0.993ε (Mean = 0.314ε) (GSL 2.1: Max = 2.41e+05ε (Mean = 7.62e+04ε)) (Rmath 3.2.3: Max = 1.24e+04ε (Mean = 4e+03ε)) | Max = 55.2ε (Mean = 17.8ε) | Max = 35ε (Mean = 11.9ε) (<math.h>: Max = 2.49e+05ε (Mean = 8.14e+04ε))

## cyl_neumann_prime

Table 22. Error rates for cyl_neumann_prime

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Y'0: Mathworld Data | Max = 0ε (Mean = 0ε) | Max = 6.33ε (Mean = 3.12ε) | Max = 6.33ε (Mean = 3.14ε) | Max = 4.75ε (Mean = 1.75ε)
Y'1: Mathworld Data | Max = 0.58ε (Mean = 0.193ε) | Max = 37.1ε (Mean = 12.8ε) | Max = 34ε (Mean = 11.8ε) | Max = 3.08ε (Mean = 1.2ε)
Y'n: Mathworld Data | Max = 2.05ε (Mean = 0.677ε) | Max = 56ε (Mean = 18.2ε) | Max = 56ε (Mean = 21.3ε) | Max = 563ε (Mean = 178ε)
Y'v: Mathworld Data | Max = 21.5ε (Mean = 6.49ε) | Max = 42.5ε (Mean = 13.4ε) | Max = 42.5ε (Mean = 13.6ε) | Max = 23.7ε (Mean = 10.1ε)
Y'v: Mathworld Data (large values) | Max = 0ε (Mean = 0ε) | Max = 1.57ε (Mean = 1.24ε) | Max = 1.57ε (Mean = 1.24ε) | Max = 0.627ε (Mean = 0.237ε)
Y'0 and Y'1: Random Data | Max = 0ε (Mean = 0ε) | Max = 23.8ε (Mean = 3.69ε) | Max = 23.8ε (Mean = 3.69ε) | Max = 5.95ε (Mean = 1.36ε)
Y'n: Random Data | Max = 1.53ε (Mean = 0.0885ε) | Max = 2.35e+03ε (Mean = 136ε) | Max = 2.35e+03ε (Mean = 136ε) | Max = 621ε (Mean = 36ε)
Y'v: Random Data | Max = 56.8ε (Mean = 2.59ε) | Max = 1.16e+05ε (Mean = 5.28e+03ε) | Max = 1.16e+05ε (Mean = 5.28e+03ε) | Max = 3.23e+04ε (Mean = 1.13e+03ε)

## cyl_neumann_prime (integer orders)

Table 23. Error rates for cyl_neumann_prime (integer orders)

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Y'0: Mathworld Data (Integer Version) | Max = 0ε (Mean = 0ε) | Max = 6.33ε (Mean = 3.12ε) | Max = 6.33ε (Mean = 3.14ε) | Max = 4.75ε (Mean = 1.75ε)
Y'1: Mathworld Data (Integer Version) | Max = 0.58ε (Mean = 0.193ε) | Max = 37.1ε (Mean = 12.8ε) | Max = 34ε (Mean = 11.8ε) | Max = 3.08ε (Mean = 1.2ε)
Y'n: Mathworld Data (Integer Version) | Max = 2.05ε (Mean = 0.677ε) | Max = 56ε (Mean = 18.2ε) | Max = 56ε (Mean = 21.3ε) | Max = 563ε (Mean = 178ε)

## digamma

Table 24. Error rates for digamma

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Digamma Function: Large Values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 1.84ε (Mean = 0.71ε)) (Rmath 3.2.3: Max = 1.18ε (Mean = 0.331ε)) | Max = 1.39ε (Mean = 0.413ε) | Max = 1.39ε (Mean = 0.413ε) | Max = 0.98ε (Mean = 0.369ε)
Digamma Function: Near the Positive Root | Max = 0.891ε (Mean = 0.0995ε) (GSL 2.1: Max = 135ε (Mean = 11.9ε)) (Rmath 3.2.3: Max = 2.02e+03ε (Mean = 256ε)) | Max = 1.37ε (Mean = 0.477ε) | Max = 1.31ε (Mean = 0.471ε) | Max = 0.997ε (Mean = 0.527ε)
Digamma Function: Near Zero | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 0.953ε (Mean = 0.348ε)) (Rmath 3.2.3: Max = 1.17ε (Mean = 0.564ε)) | Max = 0.984ε (Mean = 0.361ε) | Max = 0.984ε (Mean = 0.361ε) | Max = 0.953ε (Mean = 0.337ε)
Digamma Function: Negative Values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 4.56e+04ε (Mean = 3.91e+03ε)) (Rmath 3.2.3: Max = 4.6e+04ε (Mean = 3.94e+03ε)) | Max = 180ε (Mean = 13ε) | Max = 180ε (Mean = 13ε) | Max = 214ε (Mean = 16.1ε)
Digamma Function: Values near 0 | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 0.866ε (Mean = 0.387ε)) (Rmath 3.2.3: Max = 3.58e+05ε (Mean = 1.6e+05ε)) | Max = 1ε (Mean = 0.592ε) | Max = 1ε (Mean = 0.592ε) | Max = 0ε (Mean = 0ε)
Digamma Function: Integer arguments | Max = 0.992ε (Mean = 0.215ε) (GSL 2.1: Max = 1.18ε (Mean = 0.607ε)) (Rmath 3.2.3: Max = 4.33ε (Mean = 0.982ε)) | Max = 0.888ε (Mean = 0.403ε) | Max = 0.888ε (Mean = 0.403ε) | Max = 0.992ε (Mean = 0.452ε)
Digamma Function: Half integer arguments | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 1.09ε (Mean = 0.531ε)) (Rmath 3.2.3: Max = 46.2ε (Mean = 7.24ε)) | Max = 0.906ε (Mean = 0.409ε) | Max = 0.906ε (Mean = 0.409ε) | Max = 0.78ε (Mean = 0.314ε)

## ellint_1

Table 25. Error rates for ellint_1

| GNU C++ version 7.1.0 linux long double | GNU C++ version 7.1.0 linux double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Elliptic Integral F: Mathworld Data | Max = 0.94ε (Mean = 0.509ε) (<cmath>: Max = +INFε (Mean = +INFε) And other failures.) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 0.919ε (Mean = 0.544ε)) | Max = 0.94ε (Mean = 0.509ε) | Max = 0.919ε (Mean = 0.542ε)
Elliptic Integral F: Random Data | Max = 1.57ε (Mean = 0.56ε) (<cmath>: Max = 2.56ε (Mean = 0.816ε)) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 2.99ε (Mean = 0.797ε)) | Max = 1.57ε (Mean = 0.561ε) | Max = 2.26ε (Mean = 0.631ε)

## ellint_1 (complete)

Table 26. Error rates for ellint_1 (complete)

| GNU C++ version 7.1.0 linux long double | GNU C++ version 7.1.0 linux double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Elliptic Integral K: Mathworld Data | Max = 0.887ε (Mean = 0.296ε) (<cmath>: Max = 1.19ε (Mean = 0.765ε)) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 0.623ε (Mean = 0.393ε)) | Max = 0.887ε (Mean = 0.296ε) | Max = 0.915ε (Mean = 0.547ε)
Elliptic Integral K: Random Data | Max = 1.27ε (Mean = 0.473ε) (<cmath>: Max = 2.19ε (Mean = 0.694ε)) | Max = 0.851ε (Mean = 0.0851ε) (GSL 2.1: Max = 2.32ε (Mean = 0.688ε)) | Max = 1.27ε (Mean = 0.473ε) | Max = 0.958ε (Mean = 0.408ε)

## ellint_2

Table 27. Error rates for ellint_2

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Elliptic Integral E: Mathworld Data | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 0.63ε (Mean = 0.325ε)) | Max = 0.656ε (Mean = 0.317ε) (<cmath>: Max = +INFε (Mean = +INFε) And other failures.) | Max = 0.656ε (Mean = 0.317ε) | Max = 1.31ε (Mean = 0.727ε)
Elliptic Integral E: Random Data | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 4.4ε (Mean = 1.16ε)) | Max = 2.05ε (Mean = 0.632ε) (<cmath>: Max = 3.08e+04ε (Mean = 3.84e+03ε)) | Max = 2.05ε (Mean = 0.632ε) | Max = 2.23ε (Mean = 0.639ε)
Elliptic Integral E: Small Angles | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 0.5ε (Mean = 0.118ε)) | Max = 1ε (Mean = 0.283ε) (<cmath>: Max = 2ε (Mean = 0.333ε)) | Max = 1ε (Mean = 0.283ε) | Max = 1ε (Mean = 0.421ε)

## ellint_2 (complete)

Table 28. Error rates for ellint_2 (complete)

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Elliptic Integral E: Mathworld Data | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 3.09ε (Mean = 1.04ε) And other failures.) | Max = 0.836ε (Mean = 0.469ε) (<cmath>: Max = 170ε (Mean = 55.1ε)) | Max = 0.836ε (Mean = 0.469ε) | Max = 1.3ε (Mean = 0.615ε)
Elliptic Integral E: Random Data | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 4.34ε (Mean = 1.18ε)) | Max = 1.97ε (Mean = 0.629ε) (<cmath>: Max = 2.49e+04ε (Mean = 3.39e+03ε)) | Max = 1.97ε (Mean = 0.629ε) | Max = 1.71ε (Mean = 0.553ε)

## ellint_3

Table 29. Error rates for ellint_3

| GNU C++ version 7.1.0 linux long double | GNU C++ version 7.1.0 linux double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Elliptic Integral PI: Mathworld Data | Max = 475ε (Mean = 86.3ε) (<cmath>: Max = +INFε (Mean = +INFε) And other failures.) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 1.48e+05ε (Mean = 2.54e+04ε) And other failures.) | Max = 475ε (Mean = 86.3ε) | Max = 565ε (Mean = 102ε)
Elliptic Integral PI: Random Data | Max = 4.54ε (Mean = 0.895ε) (<cmath>: Max = 3.37e+20ε (Mean = 3.47e+19ε) And other failures.) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 633ε (Mean = 50.1ε)) | Max = 4.49ε (Mean = 0.885ε) | Max = 8.33ε (Mean = 0.971ε)
Elliptic Integral PI: Large Random Data | Max = 3.7ε (Mean = 0.893ε) (<cmath>: Max = 2.52e+18ε (Mean = 4.83e+17ε) And other failures.) | Max = 0.557ε (Mean = 0.0389ε) (GSL 2.1: Max = 40.1ε (Mean = 7.77ε)) | Max = 3.7ε (Mean = 0.892ε) | Max = 2.86ε (Mean = 0.944ε)

## ellint_3 (complete)

Table 30. Error rates for ellint_3 (complete)

| GNU C++ version 7.1.0 linux long double | GNU C++ version 7.1.0 linux double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Complete Elliptic Integral PI: Mathworld Data | Max = 1.4ε (Mean = 0.575ε) (<cmath>: Max = 6.31e+20ε (Mean = 1.53e+20ε) And other failures.) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 6.33e+04ε (Mean = 1.54e+04ε) And other failures.) | Max = 1.4ε (Mean = 0.575ε) | Max = 0.971ε (Mean = 0.464ε)
Complete Elliptic Integral PI: Random Data | Max = 2.45ε (Mean = 0.696ε) (<cmath>: Max = 8.78e+20ε (Mean = 1.02e+20ε) And other failures.) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 24ε (Mean = 2.99ε)) | Max = 2.4ε (Mean = 0.677ε) | Max = 2.46ε (Mean = 0.657ε)

## ellint_d

Table 31. Error rates for ellint_d

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Elliptic Integral E: Mathworld Data | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 0.862ε (Mean = 0.568ε)) | Max = 1.3ε (Mean = 0.813ε) | Max = 1.3ε (Mean = 0.813ε) | Max = 0.862ε (Mean = 0.457ε)
Elliptic Integral D: Random Data | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 3.01ε (Mean = 0.928ε)) | Max = 2.51ε (Mean = 0.883ε) | Max = 2.51ε (Mean = 0.883ε) | Max = 2.87ε (Mean = 0.805ε)

## ellint_d (complete)

Table 32. Error rates for ellint_d (complete)

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Elliptic Integral E: Mathworld Data | Max = 0.637ε (Mean = 0.368ε) | Max = 1.27ε (Mean = 0.735ε) | Max = 1.27ε (Mean = 0.735ε) | Max = 0.637ε (Mean = 0.368ε)
Elliptic Integral D: Random Data | Max = 0ε (Mean = 0ε) | Max = 1.27ε (Mean = 0.334ε) | Max = 1.27ε (Mean = 0.334ε) | Max = 1.27ε (Mean = 0.355ε)

## ellint_rc

Table 33. Error rates for ellint_rc

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | ---
RC: Random data | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 2.4ε (Mean = 0.624ε)) | Max = 0.995ε (Mean = 0.433ε) | Max = 0.962ε (Mean = 0.407ε)

## ellint_rd

Table 34. Error rates for ellint_rd

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | ---
RD: Random data | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 2.59ε (Mean = 0.878ε)) | Max = 2.73ε (Mean = 0.831ε) | Max = 2.16ε (Mean = 0.803ε)
RD: y = z | Max = 0.896ε (Mean = 0.022ε) (GSL 2.1: Max = 2.88ε (Mean = 0.839ε)) | Max = 2.65ε (Mean = 0.82ε) | Max = 16.5ε (Mean = 0.843ε)
RD: x = y | Max = 0.824ε (Mean = 0.0272ε) (GSL 2.1: Max = 3.74ε (Mean = 0.84ε)) | Max = 2.85ε (Mean = 0.865ε) | Max = 3.51ε (Mean = 0.816ε)
RD: x = 0, y = z | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 2ε (Mean = 0.656ε)) | Max = 1.19ε (Mean = 0.522ε) | Max = 1.16ε (Mean = 0.497ε)
RD: x = y = z | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 1.03ε (Mean = 0.418ε)) | Max = 0.998ε (Mean = 0.387ε) | Max = 1.03ε (Mean = 0.418ε)
RD: x = 0 | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 2.85ε (Mean = 0.781ε)) | Max = 2.79ε (Mean = 0.883ε) | Max = 2.64ε (Mean = 0.894ε)

## ellint_rf

Table 35. Error rates for ellint_rf

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | ---
RF: Random data | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 2.73ε (Mean = 0.804ε)) | Max = 2.54ε (Mean = 0.674ε) | Max = 2.02ε (Mean = 0.677ε)
RF: x = y = z | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 0.999ε (Mean = 0.34ε)) | Max = 0.991ε (Mean = 0.345ε) | Max = 0.999ε (Mean = 0.34ε)
RF: x = y or y = z or x = z | Max = 0.536ε (Mean = 0.00658ε) (GSL 2.1: Max = 2.89ε (Mean = 0.749ε)) | Max = 1.95ε (Mean = 0.418ε) | Max = 1.21ε (Mean = 0.394ε)
RF: x = 0, y = z | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 1.29ε (Mean = 0.527ε)) | Max = 0.894ε (Mean = 0.338ε) | Max = 0.999ε (Mean = 0.407ε)
RF: z = 0 | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 2.54ε (Mean = 0.781ε)) | Max = 1.7ε (Mean = 0.539ε) | Max = 1.89ε (Mean = 0.587ε)

## ellint_rg

Table 36. Error rates for ellint_rg

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | ---
RG: Random Data | Max = 0.983ε (Mean = 0.0172ε) (GSL 2.1: Max = 0.983ε (Mean = 0.0172ε)) | Max = 3.95ε (Mean = 0.951ε) | Max = 3.65ε (Mean = 0.929ε)
RG: two values 0 | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 0ε (Mean = 0ε)) | Max = 0ε (Mean = 0ε) | Max = 0ε (Mean = 0ε)
RG: All values the same or zero | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 0ε (Mean = 0ε)) | Max = 0.992ε (Mean = 0.288ε) | Max = 1.06ε (Mean = 0.348ε)
RG: two values the same | Max = 0.594ε (Mean = 0.0103ε) (GSL 2.1: Max = 0.594ε (Mean = 0.0103ε)) | Max = 1.51ε (Mean = 0.404ε) | Max = 1.96ε (Mean = 0.374ε)
RG: one value zero | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 0ε (Mean = 0ε)) | Max = 2.14ε (Mean = 0.722ε) | Max = 1.96ε (Mean = 0.674ε)

## ellint_rj

Table 37. Error rates for ellint_rj

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | ---
RJ: Random data | Max = 0.52ε (Mean = 0.0184ε) (GSL 2.1: Max = 3.57ε (Mean = 0.704ε) And other failures.) | Max = 186ε (Mean = 6.67ε) | Max = 215ε (Mean = 7.66ε)
RJ: 4 Equal Values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 1.03ε (Mean = 0.418ε)) | Max = 0.998ε (Mean = 0.387ε) | Max = 1.03ε (Mean = 0.418ε)
RJ: 3 Equal Values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 3.96ε (Mean = 1.06ε)) | Max = 20.8ε (Mean = 0.986ε) | Max = 39.9ε (Mean = 1.17ε)
RJ: 2 Equal Values | Max = 0.6ε (Mean = 0.0228ε) (GSL 2.1: Max = 2.57ε (Mean = 0.754ε)) | Max = 220ε (Mean = 6.64ε) | Max = 214ε (Mean = 5.28ε)
RJ: Equal z and p | Max = 0.742ε (Mean = 0.0166ε) (GSL 2.1: Max = 2.62ε (Mean = 0.699ε)) | Max = 17.2ε (Mean = 1.16ε) | Max = 16.1ε (Mean = 1.14ε)

## erf

Table 38. Error rates for erf

| GNU C++ version 7.1.0 linux long double | GNU C++ version 7.1.0 linux double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Erf Function: Small Values | Max = 0.925ε (Mean = 0.193ε) (<cmath>: Max = 0.944ε (Mean = 0.191ε)) (<math.h>: Max = 0.944ε (Mean = 0.191ε)) | Max = 0.841ε (Mean = 0.0687ε) (GSL 2.1: Max = 2.06ε (Mean = 0.319ε)) | Max = 0.925ε (Mean = 0.193ε) (<math.h>: Max = 0.944ε (Mean = 0.194ε)) | Max = 0.996ε (Mean = 0.182ε) (<math.h>: Max = 1.57ε (Mean = 0.317ε))
Erf Function: Medium Values | Max = 1.5ε (Mean = 0.193ε) (<cmath>: Max = 0.921ε (Mean = 0.0723ε)) (<math.h>: Max = 0.921ε (Mean = 0.0723ε)) | Max = 1ε (Mean = 0.119ε) (GSL 2.1: Max = 2.31ε (Mean = 0.368ε)) | Max = 1.5ε (Mean = 0.197ε) (<math.h>: Max = 0.921ε (Mean = 0.071ε)) | Max = 1ε (Mean = 0.171ε) (<math.h>: Max = 1.19ε (Mean = 0.244ε))
Erf Function: Large Values | Max = 0ε (Mean = 0ε) (<cmath>: Max = 0ε (Mean = 0ε)) (<math.h>: Max = 0ε (Mean = 0ε)) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 0ε (Mean = 0ε)) | Max = 0ε (Mean = 0ε) (<math.h>: Max = 0ε (Mean = 0ε)) | Max = 0ε (Mean = 0ε) (<math.h>: Max = 0ε (Mean = 0ε))

## erf_inv

Table 39. Error rates for erf_inv

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Inverse Erf Function | Max = 0ε (Mean = 0ε) | Max = 0.996ε (Mean = 0.389ε) | Max = 1.08ε (Mean = 0.395ε) | Max = 1.09ε (Mean = 0.502ε)

## erfc

Table 40. Error rates for erfc

| GNU C++ version 7.1.0 linux long double | GNU C++ version 7.1.0 linux double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Erf Function: Small Values | Max = 0ε (Mean = 0ε) (<cmath>: Max = 0ε (Mean = 0ε)) (<math.h>: Max = 0ε (Mean = 0ε)) | Max = 0.658ε (Mean = 0.0537ε) (GSL 2.1: Max = 1.01ε (Mean = 0.485ε)) | Max = 0ε (Mean = 0ε) (<math.h>: Max = 0ε (Mean = 0ε)) | Max = 0ε (Mean = 0ε) (<math.h>: Max = 0ε (Mean = 0ε))
Erf Function: Medium Values | Max = 1.76ε (Mean = 0.365ε) (<cmath>: Max = 1.35ε (Mean = 0.307ε)) (<math.h>: Max = 1.35ε (Mean = 0.307ε)) | Max = 0.983ε (Mean = 0.213ε) (GSL 2.1: Max = 2.64ε (Mean = 0.662ε)) | Max = 1.76ε (Mean = 0.38ε) (<math.h>: Max = 2.81ε (Mean = 0.739ε)) | Max = 1.65ε (Mean = 0.373ε) (<math.h>: Max = 2.36ε (Mean = 0.539ε))
Erf Function: Large Values | Max = 1.57ε (Mean = 0.542ε) (<cmath>: Max = 1.26ε (Mean = 0.441ε)) (<math.h>: Max = 1.26ε (Mean = 0.441ε)) | Max = 0.868ε (Mean = 0.147ε) (GSL 2.1: Max = 3.9ε (Mean = 0.472ε)) | Max = 1.57ε (Mean = 0.564ε) (<math.h>: Max = 4.91ε (Mean = 1.54ε)) | Max = 1.14ε (Mean = 0.248ε) (<math.h>: Max = 1.84ε (Mean = 0.331ε))

## erfc_inv

Table 41. Error rates for erfc_inv

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Inverse Erfc Function | Max = 0ε (Mean = 0ε) | Max = 0.996ε (Mean = 0.397ε) | Max = 1.08ε (Mean = 0.403ε) | Max = 1ε (Mean = 0.491ε)
Inverse Erfc Function: extreme values |  | Max = 1.62ε (Mean = 0.383ε) | Max = 1.62ε (Mean = 0.383ε) |

## expint (Ei)

Table 42. Error rates for expint (Ei)

| GNU C++ version 7.1.0 linux long double | GNU C++ version 7.1.0 linux double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Exponential Integral Ei | Max = 5.05ε (Mean = 0.821ε) (<cmath>: Max = 14.1ε (Mean = 2.43ε) And other failures.) | Max = 0.994ε (Mean = 0.142ε) (GSL 2.1: Max = 8.96ε (Mean = 0.703ε)) | Max = 5.05ε (Mean = 0.835ε) | Max = 1.43ε (Mean = 0.54ε)
Exponential Integral Ei: double exponent range | Max = 1.72ε (Mean = 0.593ε) (<cmath>: Max = 3.11ε (Mean = 1.13ε)) | Max = 0.998ε (Mean = 0.156ε) (GSL 2.1: Max = 1.5ε (Mean = 0.612ε)) | Max = 1.72ε (Mean = 0.607ε) | Max = 1.7ε (Mean = 0.66ε)
Exponential Integral Ei: long exponent range | Max = 1.98ε (Mean = 0.595ε) (<cmath>: Max = 1.93ε (Mean = 0.855ε)) |  | Max = 1.98ε (Mean = 0.575ε) |

## expint (En)

Table 43. Error rates for expint (En)

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Exponential Integral En | Max = 0.589ε (Mean = 0.0331ε) (GSL 2.1: Max = 58.5ε (Mean = 17.1ε)) | Max = 9.97ε (Mean = 2.13ε) | Max = 9.97ε (Mean = 2.13ε) | Max = 7.16ε (Mean = 1.85ε)
Exponential Integral En: small z values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 115ε (Mean = 23.6ε)) | Max = 1.99ε (Mean = 0.559ε) | Max = 1.99ε (Mean = 0.559ε) | Max = 2.62ε (Mean = 0.531ε)
Exponential Integral E1 | Max = 0.556ε (Mean = 0.0625ε) (GSL 2.1: Max = 0.988ε (Mean = 0.469ε)) | Max = 0.965ε (Mean = 0.414ε) | Max = 0.965ε (Mean = 0.408ε) | Max = 0.988ε (Mean = 0.486ε)

## expm1

Table 44. Error rates for expm1

| GNU C++ version 7.1.0 linux long double | GNU C++ version 7.1.0 linux double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Random test data | Max = 0.992ε (Mean = 0.402ε) (<cmath>: Max = 0.992ε (Mean = 0.402ε)) (<math.h>: Max = 0.992ε (Mean = 0.402ε)) | Max = 0.793ε (Mean = 0.126ε) (Rmath 3.2.3: Max = 0.793ε (Mean = 0.126ε)) | Max = 1.31ε (Mean = 0.428ε) (<math.h>: Max = 0.996ε (Mean = 0.426ε)) | Max = 1.31ε (Mean = 0.496ε) (<math.h>: Max = 1.31ε (Mean = 0.496ε))

## gamma_p

Table 45. Error rates for gamma_p

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
tgamma(a, z) medium values | Max = 0.955ε (Mean = 0.05ε) (GSL 2.1: Max = 342ε (Mean = 45.8ε)) (Rmath 3.2.3: Max = 389ε (Mean = 44ε)) | Max = 41.6ε (Mean = 8.09ε) | Max = 239ε (Mean = 30.2ε) | Max = 35.1ε (Mean = 6.98ε)
tgamma(a, z) small values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 4.82ε (Mean = 0.758ε)) (Rmath 3.2.3: Max = 1.01ε (Mean = 0.306ε)) | Max = 2ε (Mean = 0.464ε) | Max = 2ε (Mean = 0.461ε) | Max = 1.54ε (Mean = 0.439ε)
tgamma(a, z) large values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 1.02e+03ε (Mean = 105ε)) (Rmath 3.2.3: Max = 1.11e+03ε (Mean = 67.5ε)) | Max = 3.08e+04ε (Mean = 1.86e+03ε) | Max = 3.02e+04ε (Mean = 1.91e+03ε) | Max = 243ε (Mean = 20.2ε)
tgamma(a, z) integer and half integer values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 128ε (Mean = 22.6ε)) (Rmath 3.2.3: Max = 66.2ε (Mean = 12.2ε)) | Max = 11.8ε (Mean = 2.66ε) | Max = 71.6ε (Mean = 9.47ε) | Max = 13ε (Mean = 2.97ε)

## gamma_p_inv

Table 46. Error rates for gamma_p_inv

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
incomplete gamma inverse(a, z) medium values | Max = 0.993ε (Mean = 0.15ε) (Rmath 3.2.3: Max = 4.88ε (Mean = 0.868ε)) | Max = 1.8ε (Mean = 0.406ε) | Max = 1.89ε (Mean = 0.466ε) | Max = 1.71ε (Mean = 0.34ε)
incomplete gamma inverse(a, z) large values | Max = 0ε (Mean = 0ε) (Rmath 3.2.3: Max = 0.816ε (Mean = 0.0874ε)) | Max = 0.509ε (Mean = 0.0447ε) | Max = 0.509ε (Mean = 0.0447ε) | Max = 0.924ε (Mean = 0.108ε)
incomplete gamma inverse(a, z) small values | Max = 441ε (Mean = 53.9ε) (Rmath 3.2.3: Max = 547ε (Mean = 61.6ε)) | Max = 9.17e+03ε (Mean = 1.45e+03ε) | Max = 1.09e+04ε (Mean = 1.3e+03ε) | Max = 1.1e+03ε (Mean = 131ε)

## gamma_p_inva

Table 47. Error rates for gamma_p_inva

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Incomplete gamma inverses. | Max = 0ε (Mean = 0ε) | Max = 7.87ε (Mean = 1.15ε) | Max = 4.08ε (Mean = 1.12ε) | Max = 4.92ε (Mean = 1.03ε)

## gamma_q

Table 48. Error rates for gamma_q

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
tgamma(a, z) medium values | Max = 0.927ε (Mean = 0.035ε) (GSL 2.1: Max = 201ε (Mean = 13.5ε)) (Rmath 3.2.3: Max = 131ε (Mean = 12.7ε)) | Max = 32.3ε (Mean = 6.61ε) | Max = 199ε (Mean = 26.6ε) | Max = 23.7ε (Mean = 4ε)
tgamma(a, z) small values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 1.38e+10ε (Mean = 1.05e+09ε)) (Rmath 3.2.3: Max = 65.6ε (Mean = 11ε)) | Max = 2.45ε (Mean = 0.885ε) | Max = 2.45ε (Mean = 0.819ε) | Max = 2.26ε (Mean = 0.74ε)
tgamma(a, z) large values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 2.71e+04ε (Mean = 2.16e+03ε)) (Rmath 3.2.3: Max = 1.02e+03ε (Mean = 62.7ε)) | Max = 6.82e+03ε (Mean = 414ε) | Max = 1.15e+04ε (Mean = 733ε) | Max = 469ε (Mean = 31.5ε)
tgamma(a, z) integer and half integer values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 118ε (Mean = 12.5ε)) (Rmath 3.2.3: Max = 138ε (Mean = 16.9ε)) | Max = 11.1ε (Mean = 2.07ε) | Max = 54.7ε (Mean = 6.16ε) | Max = 8.72ε (Mean = 1.48ε)

## gamma_q_inv

Table 49. Error rates for gamma_q_inv

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
incomplete gamma inverse(a, z) medium values | Max = 0.912ε (Mean = 0.154ε) (Rmath 3.2.3: Max = 4.66ε (Mean = 0.792ε)) | Max = 6.2ε (Mean = 0.627ε) | Max = 6.2ε (Mean = 0.683ε) | Max = 2.88ε (Mean = 0.469ε)
incomplete gamma inverse(a, z) large values | Max = 0.894ε (Mean = 0.0915ε) (Rmath 3.2.3: Max = 0.894ε (Mean = 0.106ε)) | Max = 0ε (Mean = 0ε) | Max = 0ε (Mean = 0ε) | Max = 0.814ε (Mean = 0.0856ε)
incomplete gamma inverse(a, z) small values | Max = 292ε (Mean = 36.4ε) (Rmath 3.2.3: Max = 415ε (Mean = 48.7ε)) | Max = 8.28e+03ε (Mean = 1.09e+03ε) | Max = 8.98e+03ε (Mean = 877ε) | Max = 451ε (Mean = 64.7ε)

## gamma_q_inva

Table 50. Error rates for gamma_q_inva

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Incomplete gamma inverses. | Max = 0ε (Mean = 0ε) | Max = 8.42ε (Mean = 1.3ε) | Max = 7.86ε (Mean = 1.24ε) | Max = 5.05ε (Mean = 1.08ε)

## hermite

Table 51. Error rates for hermite

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Hermite Polynomials | Max = 0ε (Mean = 0ε) | Max = 6.24ε (Mean = 2.07ε) | Max = 6.24ε (Mean = 2.07ε) | Max = 4.46ε (Mean = 1.41ε)

## heuman_lambda

Table 52. Error rates for heuman_lambda

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Elliptic Integral Jacobi Zeta: Mathworld Data | Max = 0ε (Mean = 0ε) | Max = 1.89ε (Mean = 0.887ε) | Max = 1.89ε (Mean = 0.887ε) | Max = 1.08ε (Mean = 0.734ε)
Elliptic Integral Heuman Lambda: Random Data | Max = 0ε (Mean = 0ε) | Max = 3.82ε (Mean = 0.609ε) | Max = 3.82ε (Mean = 0.608ε) | Max = 2.12ε (Mean = 0.588ε)

## ibeta

Table 53. Error rates for ibeta

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Incomplete Beta Function: Small Values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 682ε (Mean = 32.6ε)) (Rmath 3.2.3: Max = 22.9ε (Mean = 3.35ε)) | Max = 8.97ε (Mean = 2.09ε) | Max = 21.3ε (Mean = 2.75ε) | Max = 8.4ε (Mean = 1.93ε)
Incomplete Beta Function: Medium Values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 690ε (Mean = 151ε)) (Rmath 3.2.3: Max = 232ε (Mean = 27.9ε)) | Max = 50ε (Mean = 12.1ε) | Max = 124ε (Mean = 18.4ε) | Max = 106ε (Mean = 16.3ε)
Incomplete Beta Function: Large and Diverse Values | Max = 1.26ε (Mean = 0.063ε) (GSL 2.1: Max = 3.9e+05ε (Mean = 1.82e+04ε) And other failures.) (Rmath 3.2.3: Max = 574ε (Mean = 49.4ε)) | Max = 1.96e+04ε (Mean = 997ε) | Max = 4.98e+04ε (Mean = 2.07e+03ε) | Max = 1.32e+03ε (Mean = 68.5ε)
Incomplete Beta Function: Small Integer Values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 254ε (Mean = 50.9ε)) (Rmath 3.2.3: Max = 62.2ε (Mean = 8.95ε)) | Max = 4.45ε (Mean = 0.814ε) | Max = 44.5ε (Mean = 10.1ε) | Max = 3.85ε (Mean = 0.791ε)

## ibeta_inv

Table 54. Error rates for ibeta_inv

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Inverse incomplete beta | Max = 11ε (Mean = 0.345ε) (Rmath 3.2.3: Max = 1.14e+121ε (Mean = 3.28e+119ε) And other failures.) | Max = 3.8e+04ε (Mean = 2.66e+03ε) | Max = 4.07e+04ε (Mean = 2.86e+03ε) | Max = 8.59e+03ε (Mean = 277ε)

## ibeta_inva

Table 55. Error rates for ibeta_inva

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Inverse incomplete beta | Max = 0.602ε (Mean = 0.0239ε) | Max = 377ε (Mean = 24.4ε) | Max = 438ε (Mean = 31.3ε) | Max = 242ε (Mean = 22.9ε)

## ibeta_invb

Table 56. Error rates for ibeta_invb

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Inverse incomplete beta | Max = 0.765ε (Mean = 0.0422ε) | Max = 407ε (Mean = 27.2ε) | Max = 407ε (Mean = 24.4ε) | Max = 409ε (Mean = 19.3ε)

## ibetac

Table 57. Error rates for ibetac

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Incomplete Beta Function: Small Values | Max = 0ε (Mean = 0ε) (Rmath 3.2.3: Max = 22.4ε (Mean = 3.67ε)) | Max = 10.6ε (Mean = 2.22ε) | Max = 13.8ε (Mean = 2.68ε) | Max = 6.94ε (Mean = 1.71ε)
Incomplete Beta Function: Medium Values | Max = 0ε (Mean = 0ε) (Rmath 3.2.3: Max = 204ε (Mean = 25.8ε)) | Max = 73.9ε (Mean = 11.2ε) | Max = 132ε (Mean = 19.8ε) | Max = 56.7ε (Mean = 14.3ε)
Incomplete Beta Function: Large and Diverse Values | Max = 0.981ε (Mean = 0.0573ε) (Rmath 3.2.3: Max = 889ε (Mean = 68.4ε)) | Max = 3.45e+04ε (Mean = 1.32e+03ε) | Max = 6.31e+04ε (Mean = 2.04e+03ε) | Max = 1.88e+03ε (Mean = 82.7ε)
Incomplete Beta Function: Small Integer Values | Max = 0ε (Mean = 0ε) (Rmath 3.2.3: Max = 84.6ε (Mean = 18ε)) | Max = 5.34ε (Mean = 1.11ε) | Max = 107ε (Mean = 17.1ε) | Max = 6.37ε (Mean = 1.03ε)

## ibetac_inv

Table 58. Error rates for ibetac_inv

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Inverse incomplete beta | Max = 0.977ε (Mean = 0.0976ε) (Rmath 3.2.3: Max = 3.01e+132ε (Mean = 8.65e+130ε) And other failures.) | Max = 4.88e+04ε (Mean = 3.16e+03ε) | Max = 5.05e+04ε (Mean = 3.33e+03ε) | Max = 2.93e+03ε (Mean = 198ε)

## ibetac_inva

Table 59. Error rates for ibetac_inva

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Inverse incomplete beta | Max = 0.683ε (Mean = 0.0314ε) | Max = 382ε (Mean = 22.2ε) | Max = 315ε (Mean = 23.7ε) | Max = 408ε (Mean = 26.7ε)

## ibetac_invb

Table 60. Error rates for ibetac_invb

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Inverse incomplete beta | Max = 0.724ε (Mean = 0.0303ε) | Max = 317ε (Mean = 19.8ε) | Max = 369ε (Mean = 22.6ε) | Max = 271ε (Mean = 16.4ε)

## jacobi_cn

Table 61. Error rates for jacobi_cn

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Jacobi Elliptic: Mathworld Data | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 17.3ε (Mean = 4.29ε) And other failures.) | Max = 71.6ε (Mean = 19.3ε) | Max = 71.6ε (Mean = 19.4ε) | Max = 45.8ε (Mean = 11.4ε)
Jacobi Elliptic: Random Data | Max = 0.816ε (Mean = 0.0563ε) (GSL 2.1: Max = 2.43ε (Mean = 0.803ε)) | Max = 1.68ε (Mean = 0.443ε) | Max = 1.68ε (Mean = 0.454ε) | Max = 1.83ε (Mean = 0.455ε)
Jacobi Elliptic: Random Small Values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 55.2ε (Mean = 1.64ε) And other failures.) | Max = 10.4ε (Mean = 0.594ε) | Max = 10.4ε (Mean = 0.602ε) | Max = 26.2ε (Mean = 1.17ε)
Jacobi Elliptic: Modulus near 1 | Max = 0.919ε (Mean = 0.127ε) (GSL 2.1: Max = 0ε (Mean = 0ε) And other failures.) | Max = 675ε (Mean = 87.1ε) | Max = 675ε (Mean = 86.8ε) | Max = 513ε (Mean = 126ε)
Jacobi Elliptic: Large Phi | Max = 14.2ε (Mean = 0.927ε) (GSL 2.1: Max = 5.92e+03ε (Mean = 477ε)) | Max = 2.97e+04ε (Mean = 1.9e+03ε) | Max = 2.97e+04ε (Mean = 1.9e+03ε) | Max = 3.27e+04ε (Mean = 1.93e+03ε)

## jacobi_dn

Table 62. Error rates for jacobi_dn

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Jacobi Elliptic: Mathworld Data | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 2.82ε (Mean = 1.18ε) And other failures.) | Max = 49ε (Mean = 14ε) | Max = 49ε (Mean = 14ε) | Max = 34.3ε (Mean = 8.71ε)
Jacobi Elliptic: Random Data | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 3ε (Mean = 0.61ε)) | Max = 1.53ε (Mean = 0.473ε) | Max = 1.53ε (Mean = 0.481ε) | Max = 1.52ε (Mean = 0.466ε)
Jacobi Elliptic: Random Small Values | Max = 0.5ε (Mean = 0.0122ε) (GSL 2.1: Max = 1.5ε (Mean = 0.391ε) And other failures.) | Max = 22.4ε (Mean = 0.777ε) | Max = 22.4ε (Mean = 0.763ε) | Max = 16.1ε (Mean = 0.685ε)
Jacobi Elliptic: Modulus near 1 | Max = 2.28ε (Mean = 0.194ε) (GSL 2.1: Max = 0ε (Mean = 0ε) And other failures.) | Max = 3.75e+03ε (Mean = 293ε) | Max = 3.75e+03ε (Mean = 293ε) | Max = 6.24e+03ε (Mean = 482ε)
Jacobi Elliptic: Large Phi | Max = 14.1ε (Mean = 0.897ε) (GSL 2.1: Max = 121ε (Mean = 22ε)) | Max = 2.82e+04ε (Mean = 1.79e+03ε) | Max = 2.82e+04ε (Mean = 1.79e+03ε) | Max = 1.67e+04ε (Mean = 1e+03ε)

## jacobi_sn

Table 63. Error rates for jacobi_sn

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Jacobi Elliptic: Mathworld Data | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 588ε (Mean = 146ε) And other failures.) | Max = 341ε (Mean = 80.7ε) | Max = 341ε (Mean = 80.7ε) | Max = 481ε (Mean = 113ε)
Jacobi Elliptic: Random Data | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 4.02ε (Mean = 1.07ε)) | Max = 2.01ε (Mean = 0.584ε) | Max = 2.01ε (Mean = 0.593ε) | Max = 1.92ε (Mean = 0.567ε)
Jacobi Elliptic: Random Small Values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 11.7ε (Mean = 1.65ε) And other failures.) | Max = 1.99ε (Mean = 0.347ε) | Max = 1.99ε (Mean = 0.347ε) | Max = 2.11ε (Mean = 0.385ε)
Jacobi Elliptic: Modulus near 1 | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 0ε (Mean = 0ε) And other failures.) | Max = 109ε (Mean = 7.35ε) | Max = 109ε (Mean = 7.38ε) | Max = 23.2ε (Mean = 1.85ε)
Jacobi Elliptic: Large Phi | Max = 12ε (Mean = 0.771ε) (GSL 2.1: Max = 4.54e+04ε (Mean = 2.63e+03ε)) | Max = 2.45e+04ε (Mean = 1.51e+03ε) | Max = 2.45e+04ε (Mean = 1.51e+03ε) | Max = 4.36e+04ε (Mean = 2.54e+03ε)

## jacobi_zeta

Table 64. Error rates for jacobi_zeta

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Elliptic Integral Jacobi Zeta: Mathworld Data | Max = 0ε (Mean = 0ε) | Max = 1.66ε (Mean = 0.48ε) | Max = 1.66ε (Mean = 0.48ε) | Max = 1.52ε (Mean = 0.357ε)
Elliptic Integral Jacobi Zeta: Random Data | Max = 0ε (Mean = 0ε) | Max = 2.99ε (Mean = 0.824ε) | Max = 3.96ε (Mean = 1.06ε) | Max = 3.89ε (Mean = 0.824ε)
Elliptic Integral Jacobi Zeta: Large Phi Values | Max = 0ε (Mean = 0ε) | Max = 2.92ε (Mean = 0.951ε) | Max = 3.05ε (Mean = 1.13ε) | Max = 2.52ε (Mean = 0.977ε)

## laguerre(n, m, x)

Table 65. Error rates for laguerre(n, m, x)

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Associated Laguerre Polynomials | Max = 0.84ε (Mean = 0.0358ε) (GSL 2.1: Max = 434ε (Mean = 10.7ε)) | Max = 167ε (Mean = 6.38ε) (<cmath>: Max = 206ε (Mean = 6.86ε)) | Max = 167ε (Mean = 6.38ε) | Max = 434ε (Mean = 11.1ε)

## laguerre(n, x)

Table 66. Error rates for laguerre(n, x)

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Laguerre Polynomials | Max = 6.82ε (Mean = 0.408ε) (GSL 2.1: Max = 3.1e+03ε (Mean = 185ε)) | Max = 1.39e+04ε (Mean = 828ε) (<cmath>: Max = 4.2e+03ε (Mean = 251ε)) | Max = 1.39e+04ε (Mean = 828ε) | Max = 3.1e+03ε (Mean = 185ε)

## legendre_p

Table 67. Error rates for legendre_p

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Legendre Polynomials: Small Values | Max = 0.732ε (Mean = 0.0619ε) (GSL 2.1: Max = 211ε (Mean = 20.4ε)) | Max = 69.2ε (Mean = 9.58ε) (<cmath>: Max = 124ε (Mean = 13.2ε)) | Max = 69.2ε (Mean = 9.58ε) | Max = 211ε (Mean = 20.4ε)
Legendre Polynomials: Large Values | Max = 0.632ε (Mean = 0.0693ε) (GSL 2.1: Max = 300ε (Mean = 33.2ε)) | Max = 699ε (Mean = 59.6ε) (<cmath>: Max = 343ε (Mean = 32.1ε)) | Max = 699ε (Mean = 59.6ε) | Max = 300ε (Mean = 33.2ε)

## legendre_p (associated)

Table 68. Error rates for legendre_p (associated)

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Associated Legendre Polynomials: Small Values | Max = 0.999ε (Mean = 0.05ε) (GSL 2.1: Max = 121ε (Mean = 6.75ε) And other failures.) | Max = 175ε (Mean = 9.88ε) (<cmath>: Max = 175ε (Mean = 9.36ε) And other failures.) | Max = 77.7ε (Mean = 5.59ε) | Max = 121ε (Mean = 7.14ε)

## legendre_q

Table 69. Error rates for legendre_q

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Legendre Polynomials: Small Values | Max = 0.612ε (Mean = 0.0517ε) (GSL 2.1: Max = 46.4ε (Mean = 7.46ε)) | Max = 50.9ε (Mean = 9ε) | Max = 50.9ε (Mean = 8.98ε) | Max = 46.4ε (Mean = 7.32ε)
Legendre Polynomials: Large Values | Max = 2.49ε (Mean = 0.202ε) (GSL 2.1: Max = 4.6e+03ε (Mean = 366ε)) | Max = 5.98e+03ε (Mean = 478ε) | Max = 5.98e+03ε (Mean = 478ε) | Max = 4.6e+03ε (Mean = 366ε)

## lgamma

Table 70. Error rates for lgamma

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
factorials | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 33.6ε (Mean = 2.78ε)) (Rmath 3.2.3: Max = 1.55ε (Mean = 0.592ε)) | Max = 0.991ε (Mean = 0.308ε) (<cmath>: Max = 1.67ε (Mean = 0.487ε)) (<math.h>: Max = 1.67ε (Mean = 0.487ε)) | Max = 0.991ε (Mean = 0.383ε) (<math.h>: Max = 1.36ε (Mean = 0.476ε)) | Max = 0.914ε (Mean = 0.175ε) (<math.h>: Max = 0.958ε (Mean = 0.38ε))
near 0 | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 5.21ε (Mean = 1.57ε)) (Rmath 3.2.3: Max = 0ε (Mean = 0ε)) | Max = 1.42ε (Mean = 0.566ε) (<cmath>: Max = 0.964ε (Mean = 0.543ε)) (<math.h>: Max = 0.964ε (Mean = 0.543ε)) | Max = 1.42ε (Mean = 0.566ε) (<math.h>: Max = 0.964ε (Mean = 0.543ε)) | Max = 0.964ε (Mean = 0.462ε) (<math.h>: Max = 0.962ε (Mean = 0.372ε))
near 1 | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 442ε (Mean = 88.8ε)) (Rmath 3.2.3: Max = 7.99e+04ε (Mean = 1.68e+04ε)) | Max = 0.948ε (Mean = 0.36ε) (<cmath>: Max = 0.615ε (Mean = 0.096ε)) (<math.h>: Max = 0.615ε (Mean = 0.096ε)) | Max = 0.948ε (Mean = 0.36ε) (<math.h>: Max = 1.71ε (Mean = 0.581ε)) | Max = 0.867ε (Mean = 0.468ε) (<math.h>: Max = 0.906ε (Mean = 0.565ε))
near 2 | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 1.17e+03ε (Mean = 274ε)) (Rmath 3.2.3: Max = 2.63e+05ε (Mean = 5.84e+04ε)) | Max = 0.878ε (Mean = 0.242ε) (<cmath>: Max = 0.741ε (Mean = 0.263ε)) (<math.h>: Max = 0.741ε (Mean = 0.263ε)) | Max = 0.878ε (Mean = 0.242ε) (<math.h>: Max = 0.598ε (Mean = 0.235ε)) | Max = 0.591ε (Mean = 0.159ε) (<math.h>: Max = 0.741ε (Mean = 0.473ε))
near -10 | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 24.9ε (Mean = 4.6ε)) (Rmath 3.2.3: Max = 4.22ε (Mean = 1.26ε)) | Max = 3.81ε (Mean = 1.01ε) (<cmath>: Max = 0.997ε (Mean = 0.412ε)) (<math.h>: Max = 0.997ε (Mean = 0.412ε)) | Max = 3.81ε (Mean = 1.01ε) (<math.h>: Max = 3.04ε (Mean = 1.01ε)) | Max = 4.22ε (Mean = 1.33ε) (<math.h>: Max = 0.997ε (Mean = 0.444ε))
near -55 | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 7.02ε (Mean = 1.47ε)) (Rmath 3.2.3: Max = 250ε (Mean = 60.9ε)) | Max = 0.821ε (Mean = 0.513ε) (<cmath>: Max = 1.58ε (Mean = 0.672ε)) (<math.h>: Max = 1.58ε (Mean = 0.672ε)) | Max = 1.59ε (Mean = 0.587ε) (<math.h>: Max = 0.821ε (Mean = 0.674ε)) | Max = 0.821ε (Mean = 0.419ε) (<math.h>: Max = 249ε (Mean = 43.1ε))

## log1p

Table 71. Error rates for log1p

| GNU C++ version 7.1.0 linux long double | GNU C++ version 7.1.0 linux double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Random test data | Max = 0.818ε (Mean = 0.227ε) (<cmath>: Max = 0.818ε (Mean = 0.227ε)) (<math.h>: Max = 0.818ε (Mean = 0.227ε)) | Max = 0.846ε (Mean = 0.153ε) (Rmath 3.2.3: Max = 0.846ε (Mean = 0.153ε)) | Max = 2.3ε (Mean = 0.66ε) (<math.h>: Max = 0.818ε (Mean = 0.249ε)) | Max = 0.509ε (Mean = 0.057ε) (<math.h>: Max = 0.509ε (Mean = 0.057ε))

## non central beta CDF

Table 72. Error rates for non central beta CDF

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Non Central Beta, medium parameters | Max = 0.998ε (Mean = 0.0649ε) (Rmath 3.2.3: Max = 1.46e+26ε (Mean = 3.5e+24ε) And other failures.) | Max = 824ε (Mean = 27.4ε) | Max = 832ε (Mean = 38.1ε) | Max = 242ε (Mean = 31ε)
Non Central Beta, large parameters | Max = 1.18ε (Mean = 0.175ε) (Rmath 3.2.3: Max = 1.01e+36ε (Mean = 1.19e+35ε) And other failures.) | Max = 2.5e+04ε (Mean = 3.78e+03ε) | Max = 2.57e+04ε (Mean = 4.45e+03ε) | Max = 3.66e+03ε (Mean = 500ε)

## non central beta CDF complement

Table 73. Error rates for non central beta CDF complement

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Non Central Beta, medium parameters | Max = 0.998ε (Mean = 0.0936ε) (Rmath 3.2.3: Max = 7.5e+97ε (Mean = 1.37e+96ε) And other failures.) | Max = 396ε (Mean = 50.7ε) | Max = 554ε (Mean = 57.2ε) | Max = 624ε (Mean = 62.7ε)
Non Central Beta, large parameters | Max = 0.986ε (Mean = 0.188ε) (Rmath 3.2.3: Max = +INFε (Mean = +INFε) And other failures.) | Max = 6.83e+03ε (Mean = 993ε) | Max = 3.56e+03ε (Mean = 707ε) | Max = 1.25e+04ε (Mean = 1.49e+03ε)

## non central chi squared CDF

Table 74. Error rates for non central chi squared CDF

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Non Central Chi Squared, medium parameters | Max = 0.99ε (Mean = 0.0544ε) (Rmath 3.2.3: Max = 727ε (Mean = 121ε)) | Max = 46.5ε (Mean = 10.3ε) | Max = 115ε (Mean = 13.9ε) | Max = 48.9ε (Mean = 10ε)
Non Central Chi Squared, large parameters | Max = 1.07ε (Mean = 0.102ε) (Rmath 3.2.3: Max = 3.27e+08ε (Mean = 2.23e+07ε)) | Max = 3.07e+03ε (Mean = 336ε) | Max = 6.17e+03ε (Mean = 677ε) | Max = 9.79e+03ε (Mean = 723ε)

## non central chi squared CDF complement

Table 75. Error rates for non central chi squared CDF complement

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Non Central Chi Squared, medium parameters | Max = 0.96ε (Mean = 0.0635ε) (Rmath 3.2.3: Max = +INFε (Mean = +INFε) And other failures.) | Max = 107ε (Mean = 17.2ε) | Max = 171ε (Mean = 22.8ε) | Max = 98.6ε (Mean = 15.8ε)
Non Central Chi Squared, large parameters | Max = 2.11ε (Mean = 0.278ε) (Rmath 3.2.3: Max = +INFε (Mean = +INFε) And other failures.) | Max = 5.02e+03ε (Mean = 630ε) | Max = 5.1e+03ε (Mean = 577ε) | Max = 5.43e+03ε (Mean = 705ε)

## non central t CDF

Table 76. Error rates for non central t CDF

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Non Central T | Max = 0.796ε (Mean = 0.0691ε) (Rmath 3.2.3: Max = 5.28e+15ε (Mean = 8.49e+14ε) And other failures.) | Max = 139ε (Mean = 31ε) | Max = 145ε (Mean = 30.9ε) | Max = 135ε (Mean = 32.1ε)
Non Central T (small non-centrality) | Max = 0ε (Mean = 0ε) (Rmath 3.2.3: Max = 2.09e+03ε (Mean = 244ε)) | Max = 3.86ε (Mean = 1.4ε) | Max = 9.15ε (Mean = 2.13ε) | Max = 6.17ε (Mean = 1.45ε)
Non Central T (large parameters) | Max = 257ε (Mean = 72.1ε) (Rmath 3.2.3: Max = 2.46ε (Mean = 0.657ε)) | Max = 5.26e+05ε (Mean = 1.48e+05ε) | Max = 5.24e+05ε (Mean = 1.47e+05ε) | Max = 286ε (Mean = 62.8ε)

## non central t CDF complement

Table 77. Error rates for non central t CDF complement

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Non Central T | Max = 0.707ε (Mean = 0.0497ε) (Rmath 3.2.3: Max = 6.19e+15ε (Mean = 6.72e+14ε) And other failures.) | Max = 201ε (Mean = 31.7ε) | Max = 340ε (Mean = 43.2ε) | Max = 154ε (Mean = 32.1ε)
Non Central T (small non-centrality) | Max = 0ε (Mean = 0ε) (Rmath 3.2.3: Max = 1.87e+03ε (Mean = 263ε)) | Max = 10.5ε (Mean = 2.13ε) | Max = 10.5ε (Mean = 2.39ε) | Max = 4.6ε (Mean = 1.63ε)
Non Central T (large parameters) | Max = 478ε (Mean = 96.3ε) (Rmath 3.2.3: Max = 2.24ε (Mean = 0.945ε)) | Max = 9.79e+05ε (Mean = 1.97e+05ε) | Max = 9.79e+05ε (Mean = 1.97e+05ε) | Max = 227ε (Mean = 50.4ε)

## owens_t

Table 78. Error rates for owens_t

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Owens T (medium small values) | Max = 0ε (Mean = 0ε) | Max = 3.34ε (Mean = 0.944ε) | Max = 3.34ε (Mean = 0.911ε) | Max = 4.37ε (Mean = 0.98ε)
Owens T (large and diverse values) | Max = 0ε (Mean = 0ε) | Max = 49ε (Mean = 2.16ε) | Max = 24.5ε (Mean = 1.39ε) | Max = 3.78ε (Mean = 0.621ε)

## polygamma

Table 79. Error rates for polygamma

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Mathematica Data | Max = 0.824ε (Mean = 0.0574ε) (GSL 2.1: Max = 62.9ε (Mean = 12.8ε)) (Rmath 3.2.3: Max = 108ε (Mean = 15.2ε)) | Max = 7.38ε (Mean = 1.84ε) | Max = 34.3ε (Mean = 7.65ε) | Max = 9.32ε (Mean = 1.95ε)
Mathematica Data - large arguments | Max = 0.998ε (Mean = 0.0592ε) (GSL 2.1: Max = 244ε (Mean = 32.8ε) And other failures.) (Rmath 3.2.3: Max = 1.71e+56ε (Mean = 1.01e+55ε) And other failures.) | Max = 2.23ε (Mean = 0.323ε) | Max = 11.1ε (Mean = 0.848ε) | Max = 150ε (Mean = 13.9ε)
Mathematica Data - negative arguments | Max = 0.516ε (Mean = 0.022ε) (GSL 2.1: Max = 36.6ε (Mean = 3.04ε) And other failures.) (Rmath 3.2.3: Max = 0ε (Mean = 0ε) And other failures.) | Max = 269ε (Mean = 87.7ε) | Max = 269ε (Mean = 88.4ε) | Max = 497ε (Mean = 129ε)
Mathematica Data - large negative arguments | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 1.79ε (Mean = 0.197ε) And other failures.) (Rmath 3.2.3: Max = 0ε (Mean = 0ε) And other failures.) | Max = 155ε (Mean = 96.4ε) | Max = 155ε (Mean = 96.4ε) | Max = 162ε (Mean = 101ε)
Mathematica Data - small arguments | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 15.2ε (Mean = 5.03ε)) (Rmath 3.2.3: Max = 106ε (Mean = 20ε)) | Max = 3.33ε (Mean = 0.75ε) | Max = 3.33ε (Mean = 0.75ε) | Max = 3ε (Mean = 0.496ε)
Mathematica Data - Large orders and other bug cases | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 151ε (Mean = 39.3ε) And other failures.) (Rmath 3.2.3: Max = +INFε (Mean = +INFε) And other failures.) | Max = 54.5ε (Mean = 13.3ε) | Max = 145ε (Mean = 55.9ε) | Max = 200ε (Mean = 57.2ε)

## powm1

Table 80. Error rates for powm1

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
powm1 | Max = 1.06ε (Mean = 0.425ε) | Max = 2.04ε (Mean = 0.493ε) | Max = 1.88ε (Mean = 0.49ε) | Max = 1.84ε (Mean = 0.486ε)

## sin_pi

Table 81. Error rates for sin_pi

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
sin_pi and cos_pi | Max = 0ε (Mean = 0ε) | Max = 0.996ε (Mean = 0.335ε) | Max = 0.996ε (Mean = 0.336ε) | Max = 0.99ε (Mean = 0.328ε)
sin_pi and cos_pi near integers and half integers | Max = 0ε (Mean = 0ε) | Max = 0.976ε (Mean = 0.293ε) | Max = 0.976ε (Mean = 0.293ε) | Max = 0.996ε (Mean = 0.343ε)

## sph_bessel

Table 82. Error rates for sph_bessel

| GNU C++ version 7.1.0 linux long double | GNU C++ version 7.1.0 linux double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Bessel j: Random Data | Max = 243ε (Mean = 13.3ε) (<cmath>: Max = 1.91e+06ε (Mean = 1.09e+05ε)) | Max = 0.978ε (Mean = 0.0445ε) (GSL 2.1: Max = 1.79e+03ε (Mean = 107ε)) | Max = 243ε (Mean = 33.7ε) | Max = 245ε (Mean = 16.3ε)

## sph_bessel_prime

Table 83. Error rates for sph_bessel_prime

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Bessel j': Random Data | Max = 0.753ε (Mean = 0.0343ε) | Max = 167ε (Mean = 12ε) | Max = 167ε (Mean = 33.2ε) | Max = 307ε (Mean = 25.2ε)

## sph_neumann

Table 84. Error rates for sph_neumann

| GNU C++ version 7.1.0 linux long double | GNU C++ version 7.1.0 linux double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
y: Random Data | Max = 234ε (Mean = 19.5ε) (<cmath>: Max = 1.6e+06ε (Mean = 1.4e+05ε)) | Max = 0.995ε (Mean = 0.0665ε) (GSL 2.1: Max = 8.5e+04ε (Mean = 5.33e+03ε)) | Max = 234ε (Mean = 19.8ε) | Max = 281ε (Mean = 31.1ε)

## sph_neumann_prime

Table 85. Error rates for sph_neumann_prime

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
y': Random Data | Max = 0.988ε (Mean = 0.0869ε) | Max = 158ε (Mean = 18.8ε) | Max = 158ε (Mean = 20.2ε) | Max = 296ε (Mean = 25.6ε)

## spherical_harmonic_i

Table 86. Error rates for spherical_harmonic_i

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Spherical Harmonics | Max = 1.36ε (Mean = 0.0765ε) | Max = 2.89e+03ε (Mean = 108ε) | Max = 1.03e+04ε (Mean = 327ε) | Max = 2.27e+04ε (Mean = 725ε)

## spherical_harmonic_r

Table 87. Error rates for spherical_harmonic_r

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Spherical Harmonics | Max = 1.58ε (Mean = 0.0707ε) | Max = 2.89e+03ε (Mean = 108ε) | Max = 1.03e+04ε (Mean = 327ε) | Max = 2.27e+04ε (Mean = 725ε)

## sqrt1pm1

Table 88. Error rates for sqrt1pm1

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
sqrt1pm1 | Max = 1.3ε (Mean = 0.404ε) | Max = 1.33ε (Mean = 0.404ε) | Max = 1.54ε (Mean = 0.563ε) | Max = 1.35ε (Mean = 0.497ε)

## tgamma

Table 89. Error rates for tgamma

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
factorials | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 3.95ε (Mean = 0.783ε)) (Rmath 3.2.3: Max = 314ε (Mean = 93.4ε)) | Max = 2.67ε (Mean = 0.617ε) (<cmath>: Max = 1.66ε (Mean = 0.584ε)) (<math.h>: Max = 1.66ε (Mean = 0.584ε)) | Max = 172ε (Mean = 41ε) (<math.h>: Max = 0ε (Mean = 0ε)) | Max = 1.85ε (Mean = 0.566ε) (<math.h>: Max = 3.17ε (Mean = 0.928ε))
near 0 | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 4.51ε (Mean = 1.92ε)) (Rmath 3.2.3: Max = 1ε (Mean = 0.335ε)) | Max = 2ε (Mean = 0.608ε) (<cmath>: Max = 1ε (Mean = 0.376ε)) (<math.h>: Max = 1ε (Mean = 0.376ε)) | Max = 2ε (Mean = 0.647ε) (<math.h>: Max = 0.5ε (Mean = 0.0791ε)) | Max = 1.5ε (Mean = 0.635ε) (<math.h>: Max = 1ε (Mean = 0.405ε))
near 1 | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 4.41ε (Mean = 1.81ε)) (Rmath 3.2.3: Max = 1ε (Mean = 0.32ε)) | Max = 2.51ε (Mean = 1.02ε) (<cmath>: Max = 0.918ε (Mean = 0.203ε)) (<math.h>: Max = 0.918ε (Mean = 0.203ε)) | Max = 3.01ε (Mean = 1.06ε) (<math.h>: Max = 1ε (Mean = 0.175ε)) | Max = 1.1ε (Mean = 0.59ε) (<math.h>: Max = 1ε (Mean = 0.4ε))
near 2 | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 7.95ε (Mean = 3.12ε)) (Rmath 3.2.3: Max = 1ε (Mean = 0.191ε)) | Max = 4.1ε (Mean = 1.55ε) (<cmath>: Max = 0.558ε (Mean = 0.298ε)) (<math.h>: Max = 0.558ε (Mean = 0.298ε)) | Max = 5.01ε (Mean = 1.89ε) (<math.h>: Max = 0ε (Mean = 0ε)) | Max = 2ε (Mean = 0.733ε) (<math.h>: Max = 0ε (Mean = 0ε))
near -10 | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 2.6ε (Mean = 1.05ε)) (Rmath 3.2.3: Max = 34.9ε (Mean = 9.2ε)) | Max = 1.75ε (Mean = 0.895ε) (<cmath>: Max = 2.26ε (Mean = 1.08ε)) (<math.h>: Max = 2.26ε (Mean = 1.08ε)) | Max = 1.75ε (Mean = 0.819ε) (<math.h>: Max = 0ε (Mean = 0ε)) | Max = 1.86ε (Mean = 0.881ε) (<math.h>: Max = 0.866ε (Mean = 0.445ε))
near -55 | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 1.8ε (Mean = 0.782ε)) (Rmath 3.2.3: Max = 3.89e+04ε (Mean = 9.52e+03ε)) | Max = 2.69ε (Mean = 1.09ε) (<cmath>: Max = 1.79ε (Mean = 0.75ε)) (<math.h>: Max = 1.79ε (Mean = 0.75ε)) | Max = 98.5ε (Mean = 53.4ε) (<math.h>: Max = 0ε (Mean = 0ε)) | Max = 2.7ε (Mean = 1.35ε) (<math.h>: Max = 3.87e+04ε (Mean = 6.71e+03ε))

## tgamma1pm1

Table 90. Error rates for tgamma1pm1

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
tgamma1pm1(dz) | Max = 0ε (Mean = 0ε) | Max = 1.12ε (Mean = 0.49ε) | Max = 6.61ε (Mean = 0.84ε) | Max = 3.31ε (Mean = 0.517ε)

## tgamma_delta_ratio

Table 91. Error rates for tgamma_delta_ratio

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
tgamma + small delta ratios | Max = 0ε (Mean = 0ε) | Max = 5.83ε (Mean = 1.3ε) | Max = 15.4ε (Mean = 2.09ε) | Max = 7.56ε (Mean = 1.31ε)
tgamma + small delta ratios (negative delta) | Max = 0ε (Mean = 0ε) | Max = 7.94ε (Mean = 1.4ε) | Max = 18.3ε (Mean = 2.03ε) | Max = 7.43ε (Mean = 1.42ε)
tgamma + small integer ratios | Max = 0ε (Mean = 0ε) | Max = 1.96ε (Mean = 0.677ε) | Max = 1.96ε (Mean = 0.677ε) | Max = 2.74ε (Mean = 0.736ε)
tgamma + small integer ratios (negative delta) | Max = 0ε (Mean = 0ε) | Max = 1.62ε (Mean = 0.451ε) | Max = 1.62ε (Mean = 0.451ε) | Max = 2.15ε (Mean = 0.685ε)
integer tgamma ratios | Max = 0ε (Mean = 0ε) | Max = 0.997ε (Mean = 0.4ε) | Max = 0.997ε (Mean = 0.4ε) | Max = 0.968ε (Mean = 0.386ε)
integer tgamma ratios (negative delta) | Max = 0ε (Mean = 0ε) | Max = 0.853ε (Mean = 0.176ε) | Max = 0.853ε (Mean = 0.176ε) | Max = 0.974ε (Mean = 0.175ε)

## tgamma (incomplete)

Table 92. Error rates for tgamma (incomplete)

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
tgamma(a, z) medium values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 200ε (Mean = 13.3ε)) | Max = 8.47ε (Mean = 1.9ε) | Max = 412ε (Mean = 95.5ε) | Max = 8.14ε (Mean = 1.76ε)
tgamma(a, z) small values | Max = 0.753ε (Mean = 0.0474ε) (GSL 2.1: Max = 1.38e+10ε (Mean = 1.05e+09ε)) | Max = 2.31ε (Mean = 0.775ε) | Max = 2.13ε (Mean = 0.717ε) | Max = 2.53ε (Mean = 0.66ε)
tgamma(a, z) integer and half integer values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 117ε (Mean = 12.5ε)) | Max = 5.52ε (Mean = 1.48ε) | Max = 79.6ε (Mean = 20.9ε) | Max = 5.16ε (Mean = 1.33ε)

## tgamma_lower

Table 93. Error rates for tgamma_lower

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
tgamma(a, z) medium values | Max = 0.833ε (Mean = 0.0315ε) (GSL 2.1: Max = 0.833ε (Mean = 0.0315ε)) | Max = 6.79ε (Mean = 1.46ε) | Max = 363ε (Mean = 63.8ε) | Max = 5.62ε (Mean = 1.49ε)
tgamma(a, z) small values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 0ε (Mean = 0ε)) | Max = 1.97ε (Mean = 0.555ε) | Max = 1.97ε (Mean = 0.558ε) | Max = 1.57ε (Mean = 0.525ε)
tgamma(a, z) integer and half integer values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 0ε (Mean = 0ε)) | Max = 4.83ε (Mean = 1.15ε) | Max = 84.7ε (Mean = 17.5ε) | Max = 2.69ε (Mean = 0.849ε)

## tgamma_ratio

Table 94. Error rates for tgamma_ratio

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
tgamma ratios | Max = 0.694ε (Mean = 0.0347ε) | Max = 2.99ε (Mean = 1.15ε) | Max = 174ε (Mean = 61.2ε) | Max = 3.28ε (Mean = 1.12ε)

## trigamma

Table 95. Error rates for trigamma

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Mathematica Data | Max = 0.998ε (Mean = 0.105ε) (GSL 2.1: Max = 1.34e+04ε (Mean = 1.49e+03ε)) (Rmath 3.2.3: Max = 1.34e+04ε (Mean = 1.51e+03ε)) | Max = 1.28ε (Mean = 0.449ε) | Max = 1.28ε (Mean = 0.449ε) | Max = 1ε (Mean = 0.382ε)

## zeta

Table 96. Error rates for zeta

| GNU C++ version 7.1.0 linux long double | GNU C++ version 7.1.0 linux double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Zeta: Random values greater than 1 | Max = 0.846ε (Mean = 0.0833ε) (<cmath>: Max = 5.45ε (Mean = 1ε)) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 8.69ε (Mean = 1.03ε)) | Max = 0.846ε (Mean = 0.0833ε) | Max = 0.836ε (Mean = 0.093ε)
Zeta: Random values less than 1 | Max = 7.03ε (Mean = 2.93ε) (<cmath>: Max = 538ε (Mean = 59.3ε)) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 137ε (Mean = 13.8ε)) | Max = 70.1ε (Mean = 17.1ε) | Max = 6.84ε (Mean = 3.12ε)
Zeta: Values close to and greater than 1 | Max = 0.995ε (Mean = 0.5ε) (<cmath>: Max = 1.9e+06ε (Mean = 5.11e+05ε)) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 7.73ε (Mean = 4.07ε)) | Max = 0.995ε (Mean = 0.5ε) | Max = 0.994ε (Mean = 0.421ε)
Zeta: Values close to and less than 1 | Max = 0.998ε (Mean = 0.508ε) (<cmath>: Max = 8.53e+06ε (Mean = 1.87e+06ε)) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 0.991ε (Mean = 0.28ε)) | Max = 0.998ε (Mean = 0.508ε) | Max = 0.991ε (Mean = 0.375ε)
Zeta: Integer arguments | Max = 9ε (Mean = 3.06ε) (<cmath>: Max = 70.3ε (Mean = 17.4ε)) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 3.75ε (Mean = 1.1ε)) | Max = 28ε (Mean = 5.62ε) | Max = 9ε (Mean = 3ε)

## Error Logs

##### Error Output For cyl_bessel_j (integer orders) with compiler Microsoft Visual C++ version 14.1 and library <math.h> and test data Bessel JN: Mathworld Data (Integer Version)

CAUTION: Found non-finite result, when a finite value was expected at entry 16
Found: -nan(ind) Expected 0 Error: 1.79769e+308
10, 1e-100, 0
CAUTION: Gross error found at entry 16.
Found: -nan(ind) Expected 0 Error: 1.79769e+308
10, 1e-100, 0

##### Error Output For legendre_p (associated) with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data Associated Legendre Polynomials: Small Values

domain error
3.75573, -3, 0.264719, 0.0186823
domain error
3.75573, -3, 0.670017, 0.0085227
domain error
3.75573, -3, 0.915014, 0.00136786
domain error
3.75573, -3, 0.93539, 0.000921218
domain error
3.75573, -2, -0.804919, -0.035427
domain error
3.75573, -2, -0.623236, -0.0476446
domain error
3.75573, -2, 0.629447, 0.0475072
domain error
3.75573, -2, 0.929777, 0.0157498
domain error
3.75573, -2, 0.985763, 0.0034837
domain error
3.75573, -1, 0.093763, -0.118979
domain error
4.28576, -4, 0.0944412, 0.00255792
domain error
4.28576, -4, 0.670017, 0.000790849
domain error
4.28576, -3, -0.746026, -0.00458957
domain error
4.28576, -2, -0.623236, 0.0219016
domain error
4.28576, -2, 0.629447, 0.0223081
domain error
4.28576, -2, 0.93539, 0.0133504
domain error
4.28576, -1, 0.915014, 0.132001
domain error
4.28576, -1, 0.985763, 0.0787743
domain error
4.43859, -4, 0.093763, 0.00255858
domain error
4.43859, -4, 0.811584, 0.000303404
domain error
4.43859, -4, 0.826752, 0.000260835
domain error
4.43859, -4, 0.929777, 4.78235e-05
domain error
4.43859, -3, -0.804919, -0.00350364
domain error
4.43859, -3, -0.729046, -0.00487043
domain error
4.43859, -3, -0.623236, -0.00620995
domain error
4.43859, -3, 0.93539, 0.000861698
domain error
4.43859, -2, -0.557932, 0.0169167
domain error
4.43859, -2, -0.443004, 0.0062586
domain error
4.43859, -2, 0.915014, 0.016481
domain error
4.43859, -1, 0.629447, -0.0138523
domain error
5.39088, -5, 0.0944412, 0.000254649
domain error
5.39088, -5, 0.264719, 0.000217164
domain error
5.39088, -5, 0.670017, 5.87083e-05
domain error
5.39088, -5, 0.915014, 2.78273e-06
domain error
5.39088, -3, 0.929777, 0.000880849
domain error
5.39088, -2, 0.629447, 0.00448021
domain error
5.39088, -2, 0.826752, 0.01718
domain error
5.39088, -2, 0.937736, 0.011583
domain error
5.39088, -1, -0.804919, 0.0276144
domain error
5.39088, -1, -0.746026, -0.0119425
domain error
5.39088, -1, -0.443004, -0.0525987
domain error
5.39088, -1, 0.811584, 0.032475
domain error
5.39088, -1, 0.985763, 0.0759289
domain error
5.97861, -5, -0.729046, 3.91223e-05
domain error
5.97861, -5, -0.383666, 0.000174899
domain error
5.97861, -5, 0.93539, 1.43993e-06
domain error
5.97861, -4, -0.623236, -0.000607048
domain error
5.97861, -4, 0.264719, 0.00059614
domain error
5.97861, -3, 0.629447, 0.00313497
domain error
5.97861, -3, 0.670017, 0.00323895
domain error
5.97861, -2, 0.915014, 0.0140705
domain error
5.97861, -2, 0.992923, 0.00171356
domain error
5.97861, -1, -0.746026, -0.0119425
domain error
5.97861, -1, 0.937736, 0.106972
domain error
7.01297, -6, -0.443004, -4.99177e-06
domain error
7.01297, -6, 0.629447, 3.00689e-06
domain error
7.01297, -6, 0.811584, 7.00407e-07
domain error
7.01297, -6, 0.985763, 4.83431e-10
domain error
7.01297, -3, 0.670017, 0.000233323
domain error
7.01297, -2, -0.804919, -0.0027739
domain error
7.01297, -1, -0.383666, 0.0397866
domain error
7.01297, -1, 0.929777, 0.0544549
domain error
7.54701, -7, 0.929777, 1.42008e-09
domain error
7.54701, -6, 0.992923, 6.04622e-11
domain error
7.54701, -5, -0.804919, 1.18502e-05
domain error
7.54701, -5, -0.623236, 2.57049e-05
domain error
7.54701, -5, -0.557932, 2.60266e-05
domain error
7.54701, -5, 0.826752, 9.64276e-06
domain error
7.54701, -4, -0.746026, -0.0001618
domain error
7.54701, -3, 0.0944412, 0.000622493
domain error
7.54701, -3, 0.985763, 9.14782e-05
domain error
7.54701, -1, 0.811584, -0.0376184
domain error
11.8439, -10, -0.557932, -2.32652e-11
domain error
11.8439, -10, 0.811584, 1.01194e-12
domain error
11.8439, -8, -0.746026, -1.34891e-09
domain error
11.8439, -8, -0.729046, -1.5428e-09
domain error
11.8439, -8, 0.985763, 5.90035e-14
domain error
11.8439, -4, 0.629447, -1.44723e-05
domain error
11.8439, -4, 0.929777, 1.98812e-05
domain error
11.8439, -3, 0.670017, -4.58296e-05
domain error
11.8439, -2, 0.826752, -0.00244759
domain error
11.8439, -2, 0.992923, 0.00151458
domain error
11.8439, -1, -0.383666, 0.00419108
domain error
11.85, -11, 0.093763, 1.16526e-11
domain error
11.85, -11, 0.929777, 2.05797e-16
domain error
11.85, -11, 0.93539, 1.32249e-16
domain error
*** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***

##### Error Output For legendre_p (associated) with compiler GNU C++ version 7.1.0 and library <cmath> and test data Associated Legendre Polynomials: Small Values

order parameters less than 0 not supported in TR1
3.75573, -3, 0.264719, 0.0186823
order parameters less than 0 not supported in TR1
3.75573, -3, 0.670017, 0.0085227
order parameters less than 0 not supported in TR1
3.75573, -3, 0.915014, 0.00136786
order parameters less than 0 not supported in TR1
3.75573, -3, 0.93539, 0.000921218
order parameters less than 0 not supported in TR1
3.75573, -2, -0.804919, -0.035427
order parameters less than 0 not supported in TR1
3.75573, -2, -0.623236, -0.0476446
order parameters less than 0 not supported in TR1
3.75573, -2, 0.629447, 0.0475072
order parameters less than 0 not supported in TR1
3.75573, -2, 0.929777, 0.0157498
order parameters less than 0 not supported in TR1
3.75573, -2, 0.985763, 0.0034837
order parameters less than 0 not supported in TR1
3.75573, -1, 0.093763, -0.118979
order parameters less than 0 not supported in TR1
4.28576, -4, 0.0944412, 0.00255792
order parameters less than 0 not supported in TR1
4.28576, -4, 0.670017, 0.000790849
order parameters less than 0 not supported in TR1
4.28576, -3, -0.746026, -0.00458957
order parameters less than 0 not supported in TR1
4.28576, -2, -0.623236, 0.0219016
order parameters less than 0 not supported in TR1
4.28576, -2, 0.629447, 0.0223081
order parameters less than 0 not supported in TR1
4.28576, -2, 0.93539, 0.0133504
order parameters less than 0 not supported in TR1
4.28576, -1, 0.915014, 0.132001
order parameters less than 0 not supported in TR1
4.28576, -1, 0.985763, 0.0787743
order parameters less than 0 not supported in TR1
4.43859, -4, 0.093763, 0.00255858
order parameters less than 0 not supported in TR1
4.43859, -4, 0.811584, 0.000303404
order parameters less than 0 not supported in TR1
4.43859, -4, 0.826752, 0.000260835
order parameters less than 0 not supported in TR1
4.43859, -4, 0.929777, 4.78235e-05
order parameters less than 0 not supported in TR1
4.43859, -3, -0.804919, -0.00350364
order parameters less than 0 not supported in TR1
4.43859, -3, -0.729046, -0.00487043
order parameters less than 0 not supported in TR1
4.43859, -3, -0.623236, -0.00620995
order parameters less than 0 not supported in TR1
4.43859, -3, 0.93539, 0.000861698
order parameters less than 0 not supported in TR1
4.43859, -2, -0.557932, 0.0169167
order parameters less than 0 not supported in TR1
4.43859, -2, -0.443004, 0.0062586
order parameters less than 0 not supported in TR1
4.43859, -2, 0.915014, 0.016481
order parameters less than 0 not supported in TR1
4.43859, -1, 0.629447, -0.0138523
order parameters less than 0 not supported in TR1
5.39088, -5, 0.0944412, 0.000254649
order parameters less than 0 not supported in TR1
5.39088, -5, 0.264719, 0.000217164
order parameters less than 0 not supported in TR1
5.39088, -5, 0.670017, 5.87083e-05
order parameters less than 0 not supported in TR1
5.39088, -5, 0.915014, 2.78273e-06
order parameters less than 0 not supported in TR1
5.39088, -3, 0.929777, 0.000880849
order parameters less than 0 not supported in TR1
5.39088, -2, 0.629447, 0.00448021
order parameters less than 0 not supported in TR1
5.39088, -2, 0.826752, 0.01718
order parameters less than 0 not supported in TR1
5.39088, -2, 0.937736, 0.011583
order parameters less than 0 not supported in TR1
5.39088, -1, -0.804919, 0.0276144
order parameters less than 0 not supported in TR1
5.39088, -1, -0.746026, -0.0119425
order parameters less than 0 not supported in TR1
5.39088, -1, -0.443004, -0.0525987
order parameters less than 0 not supported in TR1
5.39088, -1, 0.811584, 0.032475
order parameters less than 0 not supported in TR1
5.39088, -1, 0.985763, 0.0759289
order parameters less than 0 not supported in TR1
5.97861, -5, -0.729046, 3.91223e-05
order parameters less than 0 not supported in TR1
5.97861, -5, -0.383666, 0.000174899
order parameters less than 0 not supported in TR1
5.97861, -5, 0.93539, 1.43993e-06
order parameters less than 0 not supported in TR1
5.97861, -4, -0.623236, -0.000607048
order parameters less than 0 not supported in TR1
5.97861, -4, 0.264719, 0.00059614
order parameters less than 0 not supported in TR1
5.97861, -3, 0.629447, 0.00313497
*** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***

##### Error Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library Rmath 3.2.3 and test data Bessel Iv: Mathworld Data (large values)

CAUTION: Gross error found at entry 0.
Found: 0 Expected 1.86459e-155 Error: 8.37988e+152
-1, 3.72917e-155, 1.86459e-155
CAUTION: Gross error found at entry 1.
Found: 0 Expected 1.86459e-155 Error: 8.37988e+152
1, 3.72917e-155, 1.86459e-155
CAUTION: Gross error found at entry 3.
Found: 0 Expected 8.02269e-175 Error: 3.60559e+133
1.125, 3.72917e-155, 8.02269e-175

##### Error Output For cyl_bessel_i (integer orders) with compiler GNU C++ version 7.1.0 and library Rmath 3.2.3 and test data Bessel In: Mathworld Data (Integer Version)

Unsupported domain
-5, -1, -0.000271463
Unsupported domain
10, -5, 0.00458004
Unsupported domain
-100, -200, 4.35275e+74

##### Error Output For cyl_bessel_i (integer orders) with compiler GNU C++ version 7.1.0 and library Rmath 3.2.3 and test data Bessel I1: Mathworld Data (Integer Version)

Unsupported domain
1, -2, -1.59064
Unsupported domain
1, -8, -399.873
Unsupported domain
1, -10, -2670.99

##### Error Output For cyl_bessel_i (integer orders) with compiler GNU C++ version 7.1.0 and library Rmath 3.2.3 and test data Bessel I0: Mathworld Data (Integer Version)

Unsupported domain
0, -2, 2.27959
Unsupported domain
0, -7, 168.594
Unsupported domain
0, -1, 1.26607

##### Error Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library Rmath 3.2.3 and test data Bessel In: Mathworld Data

Unsupported domain
-5, -1, -0.000271463
Unsupported domain
10, -5, 0.00458004
Unsupported domain
-100, -200, 4.35275e+74

##### Error Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library Rmath 3.2.3 and test data Bessel I1: Mathworld Data

Unsupported domain
1, -2, -1.59064
Unsupported domain
1, -8, -399.873
Unsupported domain
1, -10, -2670.99

##### Error Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library Rmath 3.2.3 and test data Bessel I0: Mathworld Data

Unsupported domain
0, -2, 2.27959
Unsupported domain
0, -7, 168.594
Unsupported domain
0, -1, 1.26607

##### Error Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library Rmath 3.2.3 and test data Bessel J: Mathworld Data

CAUTION: Gross error found at entry 6.
Found: 0 Expected -0.000747424 Error: 3.3591e+304
5.5, 1e+06, -0.000747424
CAUTION: Gross error found at entry 7.
Found: 0 Expected -0.0007766 Error: 3.49022e+304
5.125, 1e+06, -0.0007766
CAUTION: Gross error found at entry 8.
Found: 0 Expected -0.000466323 Error: 2.09576e+304
5.875, 1e+06, -0.000466323

##### Error Output For cyl_bessel_j (integer orders) with compiler GNU C++ version 7.1.0 and library Rmath 3.2.3 and test data Bessel JN: Mathworld Data (Integer Version)

Unsupported domain
5, -10, 0.234062
CAUTION: Gross error found at entry 6.
Found: 0 Expected 0.000725964 Error: 3.26265e+304
-5, 1e+06, 0.000725964
CAUTION: Gross error found at entry 7.
Found: 0 Expected -0.000725964 Error: 3.26265e+304
5, 1e+06, -0.000725964
Unsupported domain
-5, -1, 0.000249758
Unsupported domain
10, -10, 0.207486
Unsupported domain
10, -5, 0.0014678
CAUTION: Gross error found at entry 12.
Found: 0 Expected -0.000331079 Error: 1.48795e+304
-10, 1e+06, -0.000331079
CAUTION: Gross error found at entry 13.
Found: 0 Expected -0.000331079 Error: 1.48795e+304
10, 1e+06, -0.000331079

##### Error Output For cyl_bessel_j (integer orders) with compiler GNU C++ version 7.1.0 and library Rmath 3.2.3 and test data Bessel J1: Mathworld Data (Integer Version)

Unsupported domain
1, -2, -0.576725
Unsupported domain
1, -8, -0.234636
Unsupported domain
1, -10, -0.0434727

##### Error Output For cyl_bessel_j (integer orders) with compiler GNU C++ version 7.1.0 and library Rmath 3.2.3 and test data Bessel J0: Mathworld Data (Integer Version)

Unsupported domain
0, -2, 0.223891
Unsupported domain
0, -8, 0.171651
Unsupported domain
0, -10, -0.245936

##### Error Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library Rmath 3.2.3 and test data Bessel JN: Mathworld Data

Unsupported domain
5, -10, 0.234062
CAUTION: Gross error found at entry 6.
Found: 0 Expected 0.000725964 Error: 3.26265e+304
-5, 1e+06, 0.000725964
CAUTION: Gross error found at entry 7.
Found: 0 Expected -0.000725964 Error: 3.26265e+304
5, 1e+06, -0.000725964
Unsupported domain
-5, -1, 0.000249758
Unsupported domain
10, -10, 0.207486
Unsupported domain
10, -5, 0.0014678
CAUTION: Gross error found at entry 12.
Found: 0 Expected -0.000331079 Error: 1.48795e+304
-10, 1e+06, -0.000331079
CAUTION: Gross error found at entry 13.
Found: 0 Expected -0.000331079 Error: 1.48795e+304
10, 1e+06, -0.000331079

##### Error Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library Rmath 3.2.3 and test data Bessel J1: Mathworld Data

Unsupported domain
1, -2, -0.576725
Unsupported domain
1, -8, -0.234636
Unsupported domain
1, -10, -0.0434727

##### Error Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library Rmath 3.2.3 and test data Bessel J0: Mathworld Data

Unsupported domain
0, -2, 0.223891
Unsupported domain
0, -8, 0.171651
Unsupported domain
0, -10, -0.245936

##### Error Output For ibetac_inv with compiler GNU C++ version 7.1.0 and library Rmath 3.2.3 and test data Inverse incomplete beta

CAUTION: Gross error found at entry 7.
Found: 3.8247e-302 Expected 0 Error: 1.71891e+06
1.38853e-05, 0.0497627, 0.632396, 0, 0
CAUTION: Gross error found at entry 71.
Found: 1.38362e-204 Expected 0 Error: 6.21832e+103
3.77931e-05, 0.0150073, 0.835025, 0, 0
CAUTION: Gross error found at entry 90.
Found: 1.09275e-303 Expected 0 Error: 49109.6
4.29383e-05, 0.0428761, 0.814742, 0, 0
CAUTION: Gross error found at entry 102.
Found: 3.8625e-304 Expected 0 Error: 17358
4.80089e-05, 0.0296236, 0.913384, 0, 0
CAUTION: Gross error found at entry 115.
Found: 1.51774e-303 Expected 0 Error: 68209.8
0.000130387, 0.0404969, 0.814742, 0, 0
CAUTION: Gross error found at entry 123.
Found: 1.28036e-303 Expected 0 Error: 57541.4
0.000149328, 0.0201182, 0.905801, 5.70765e-267, 0
CAUTION: Gross error found at entry 133.
Found: 1.96732e-302 Expected 0 Error: 884160
0.000173563, 0.0301908, 0.913384, 4.21662e-213, 0
CAUTION: Gross error found at entry 159.
Found: 1.48697e-191 Expected 0 Error: 6.68279e+116
0.000260723, 0.0252933, 0.632396, 0, 0
CAUTION: Gross error found at entry 256.
Found: 9.24166e-245 Expected 0 Error: 4.15342e+63
0.00246975, 0.016063, 0.913384, 1, 0

##### Error Output For ibeta_inv with compiler GNU C++ version 7.1.0 and library Rmath 3.2.3 and test data Inverse incomplete beta

CAUTION: Gross error found at entry 1.
Found: 1.90197e-247 Expected 0 Error: 8.54789e+60
1.12733e-05, 0.022662, 0.135563, 0, 0
CAUTION: Gross error found at entry 30.
Found: 1.36217e-301 Expected 0 Error: 6.12191e+06
2.10769e-05, 0.0448972, 0.221112, 0, 0
CAUTION: Gross error found at entry 152.
Found: 2.92621e-285 Expected 0 Error: 1.31511e+23
0.000240381, 0.017982, 0.221112, 0, 0
CAUTION: Gross error found at entry 184.
Found: 5.63355e-203 Expected 0 Error: 2.53185e+105
0.000348822, 0.0275467, 0.135563, 0, 1.88165e-166
CAUTION: Gross error found at entry 205.
Found: 5.52731e-303 Expected 0 Error: 248409
0.000441212, 0.0313573, 0.127074, 0, 9.07221e-121

##### Error Output For non central beta CDF complement with compiler GNU C++ version 7.1.0 and library Rmath 3.2.3 and test data Non Central Beta, large parameters

CAUTION: Gross error found at entry 10.
Found: 9.76918e-10 Expected 1.61248e-15 Error: 605846
290.682, 72.6705, 20005.4, 0.997663, 1, 1.61248e-15
CAUTION: Gross error found at entry 11.
Found: 9.94184e-10 Expected 3.0108e-42 Error: 3.30205e+32
290.682, 145.341, 53489.1, 0.998663, 1, 3.0108e-42
CAUTION: Gross error found at entry 16.
Found: 8.45406e-10 Expected 4.46652e-22 Error: 1.89276e+12
290.682, 1162.73, 2308.07, 0.656921, 1, 4.46652e-22
CAUTION: Gross error found at entry 17.
Found: 9.41971e-10 Expected 1.7241e-50 Error: 5.46356e+40
290.682, 1453.41, 8064.48, 0.832237, 1, 1.7241e-50
CAUTION: Gross error found at entry 18.
Found: 9.30663e-10 Expected 2.09803e-305 Error: 4.43589e+295
975.766, 731.824, 232.285, 0.919742, 1, 2.09803e-305
CAUTION: Gross error found at entry 27.
Found: 9.76918e-10 Expected 9.3474e-18 Error: 1.04512e+08
1879.05, 187.905, 20005.4, 0.992215, 1, 9.3474e-18
CAUTION: Gross error found at entry 28.
Found: 9.94184e-10 Expected 1.8122e-90 Error: 5.48607e+80
1879.05, 469.762, 53489.1, 0.994618, 1, 1.8122e-90
CAUTION: Gross error found at entry 32.
Found: 9.27224e-10 Expected 3.18255e-15 Error: 291345
1879.05, 3758.1, 1879.05, 0.480508, 1, 3.18255e-15
CAUTION: Gross error found at entry 33.
Found: 8.45406e-10 Expected 1.10218e-77 Error: 7.67029e+67
1879.05, 5637.15, 2308.07, 0.458181, 1, 1.10218e-77
CAUTION: Gross error found at entry 34.
Found: 9.30663e-10 Expected 0 Error: 4.18262e+298
2308.07, 1154.03, 232.285, 0.919371, 1, 0
CAUTION: Gross error found at entry 35.
Found: 8.93617e-10 Expected 0 Error: 4.01612e+298
2308.07, 1731.05, 290.682, 0.917262, 1, 0
CAUTION: Gross error found at entry 43.
Found: 9.94184e-10 Expected 3.57283e-70 Error: 2.78262e+60
8064.48, 806.448, 53489.1, 0.988678, 1, 3.57283e-70
CAUTION: Gross error found at entry 48.
Found: 8.45406e-10 Expected 8.78057e-74 Error: 9.62814e+63
8064.48, 16129, 2308.07, 0.421531, 1, 8.78057e-74
CAUTION: Gross error found at entry 49.
Found: 9.30663e-10 Expected 0 Error: 4.18262e+298
15674.4, 3918.59, 232.285, 0.933726, 1, 0
CAUTION: Gross error found at entry 50.
Found: 8.93617e-10 Expected 0 Error: 4.01612e+298
15674.4, 7837.19, 290.682, 0.917179, 1, 0
CAUTION: Gross error found at entry 51.
Found: 8.9318e-10 Expected 0 Error: 4.01416e+298
15674.4, 11755.8, 975.766, 0.915784, 1, 0
CAUTION: Gross error found at entry 63.
Found: 9.41971e-10 Expected 2.31296e-171 Error: 4.07258e+161
20005.4, 40010.8, 8064.48, 0.432094, 1, 2.31296e-171
CAUTION: Gross error found at entry 64.
Found: 9.30663e-10 Expected 0 Error: 4.18262e+298
53489.1, 5348.92, 232.285, 0.954635, 1, 0
CAUTION: Gross error found at entry 65.
Found: 8.93617e-10 Expected 0 Error: 4.01612e+298
53489.1, 13372.3, 290.682, 0.933478, 1, 0
CAUTION: Gross error found at entry 66.
Found: 8.9318e-10 Expected 0 Error: 4.01416e+298
53489.1, 26744.6, 975.766, 0.91717, 1, 0

##### Error Output For non central beta CDF with compiler GNU C++ version 7.1.0 and library Rmath 3.2.3 and test data Non Central Beta, large parameters

CAUTION: Gross error found at entry 0.
Found: 9.1136e-209 Expected 5.82279e-200 Error: 6.38913e+08
232.285, 209.056, 232.285, 0.062486, 5.82279e-200, 1
CAUTION: Gross error found at entry 1.
Found: 4.08108e-115 Expected 2.37643e-112 Error: 581.304
232.285, 229.962, 290.682, 0.155342, 2.37643e-112, 1
CAUTION: Gross error found at entry 2.
Found: 1.07549e-93 Expected 9.53431e-89 Error: 88650
232.285, 232.052, 975.766, 0.378086, 9.53431e-89, 1
CAUTION: Gross error found at entry 3.
Found: 2.58402e-54 Expected 8.27353e-53 Error: 31.0181
232.285, 232.285, 1879.05, 0.625865, 8.27353e-53, 1
CAUTION: Gross error found at entry 4.
Found: 1.93718e-19 Expected 6.64275e-16 Error: 3428.08
232.285, 232.308, 2308.07, 0.770774, 6.64275e-16, 1
CAUTION: Gross error found at entry 21.
Found: 8.12962e-240 Expected 1.82294e-219 Error: 2.24234e+20
975.766, 974.79, 1879.05, 0.331337, 1.82294e-219, 1
CAUTION: Gross error found at entry 22.
Found: 3.47274e-69 Expected 1.42183e-67 Error: 39.9426
975.766, 975.766, 2308.07, 0.514323, 1.42183e-67, 1
CAUTION: Gross error found at entry 23.
Found: 5.86885e-50 Expected 1.27896e-47 Error: 216.923
975.766, 975.863, 8064.48, 0.753209, 1.27896e-47, 1
CAUTION: Gross error found at entry 39.
Found: 4.82785e-230 Expected 1.25446e-213 Error: 2.59838e+16
2308.07, 2308.07, 8064.48, 0.54983, 1.25446e-213, 1
CAUTION: Gross error found at entry 40.
Found: 1.22971e-87 Expected 1.82618e-85 Error: 147.505
2308.07, 2308.3, 15674.4, 0.733174, 1.82618e-85, 1
CAUTION: Gross error found at entry 56.
Found: 2.97337e-127 Expected 2.56068e-124 Error: 860.205
15674.4, 15675.9, 20005.4, 0.55883, 2.56068e-124, 1

##### Error Output For non central beta CDF complement with compiler GNU C++ version 7.1.0 and library Rmath 3.2.3 and test data Non Central Beta, medium parameters

CAUTION: Gross error found at entry 296.
Found: 9.44166e-10 Expected 6.22975e-10 Error: 0.515577
22.9367, 114.683, 19.5081, 0.480981, 1, 6.22975e-10
CAUTION: Gross error found at entry 369.
Found: 2.52234e-10 Expected 1.40246e-10 Error: 0.79851
27.5277, 20.6457, 0.956697, 0.915111, 1, 1.40246e-10
CAUTION: Gross error found at entry 429.
Found: 1.18105e-09 Expected 7.45745e-10 Error: 0.58372
28.8063, 21.6047, 60.3826, 0.946143, 1, 7.45745e-10
CAUTION: Gross error found at entry 430.
Found: 2.44435e-09 Expected 1.60695e-09 Error: 0.521115
28.8063, 21.6047, 148.129, 0.965121, 1, 1.60695e-09
CAUTION: Gross error found at entry 477.
Found: 7.57435e-10 Expected 7.14133e-11 Error: 9.60635
28.8063, 144.032, 42.3849, 0.504845, 1, 7.14133e-11
CAUTION: Gross error found at entry 489.
Found: 4.8561e-10 Expected 5.62991e-11 Error: 7.62553
31.9438, 23.9579, 44.2068, 0.93835, 1, 5.62991e-11
CAUTION: Gross error found at entry 490.
Found: 8.35187e-10 Expected 1.87483e-10 Error: 3.45473
31.9438, 23.9579, 135.747, 0.961117, 1, 1.87483e-10
CAUTION: Gross error found at entry 491.
Found: 1.00174e-09 Expected 2.38491e-10 Error: 3.20032
31.9438, 23.9579, 191.501, 0.968273, 1, 2.38491e-10
CAUTION: Gross error found at entry 537.
Found: 7.29746e-10 Expected 1.31223e-12 Error: 555.111
31.9438, 159.719, 34.2373, 0.489796, 1, 1.31223e-12
CAUTION: Gross error found at entry 538.
Found: 2.49663e-09 Expected 1.54239e-09 Error: 0.618681
31.9438, 159.719, 126.472, 0.581861, 1, 1.54239e-09
CAUTION: Gross error found at entry 549.
Found: 4.16125e-10 Expected 4.8536e-13 Error: 856.353
38.0822, 28.5617, 34.773, 0.931853, 1, 4.8536e-13
CAUTION: Gross error found at entry 550.
Found: 9.69907e-10 Expected 2.87054e-12 Error: 336.883
38.0822, 28.5617, 127.953, 0.956104, 1, 2.87054e-12
CAUTION: Gross error found at entry 551.
Found: 5.90132e-10 Expected 4.08361e-12 Error: 143.512
38.0822, 28.5617, 183.147, 0.963764, 1, 4.08361e-12
CAUTION: Gross error found at entry 597.
Found: 4.67033e-10 Expected 9.82939e-16 Error: 475139
38.0822, 190.411, 27.0954, 0.475419, 1, 9.82939e-16
CAUTION: Gross error found at entry 598.
Found: 9.33207e-10 Expected 4.03465e-12 Error: 230.298
38.0822, 190.411, 100.733, 0.544491, 1, 4.03465e-12
CAUTION: Gross error found at entry 599.
Found: 7.4092e-10 Expected 9.53942e-11 Error: 6.76693
38.0822, 190.411, 169.826, 0.594614, 1, 9.53942e-11
CAUTION: Gross error found at entry 609.
Found: 5.71813e-10 Expected 1.17207e-14 Error: 48785.7
42.7789, 32.0842, 28.3773, 0.927814, 1, 1.17207e-14
CAUTION: Gross error found at entry 610.
Found: 5.16834e-10 Expected 9.62679e-14 Error: 5367.71
42.7789, 32.0842, 109.376, 0.950307, 1, 9.62679e-14
CAUTION: Gross error found at entry 611.
Found: 6.08012e-10 Expected 1.7454e-13 Error: 3482.51
42.7789, 32.0842, 175.686, 0.960431, 1, 1.7454e-13
CAUTION: Gross error found at entry 657.
Found: 5.59489e-10 Expected 2.86344e-18 Error: 1.95391e+08
42.7789, 213.895, 21.9724, 0.467166, 1, 2.86344e-18
CAUTION: Gross error found at entry 658.
Found: 5.14798e-10 Expected 2.50972e-14 Error: 20511.2
42.7789, 213.895, 84.4175, 0.522676, 1, 2.50972e-14
CAUTION: Gross error found at entry 659.
Found: 8.49991e-10 Expected 2.38005e-12 Error: 356.131
42.7789, 213.895, 160.056, 0.576191, 1, 2.38005e-12
CAUTION: Gross error found at entry 671.
Found: 3.03281e-10 Expected 2.22036e-15 Error: 136590
44.5963, 33.4472, 22.4929, 0.924976, 1, 2.22036e-15
CAUTION: Gross error found at entry 672.
Found: 8.40636e-10 Expected 2.22384e-14 Error: 37800.1
44.5963, 33.4472, 94.9517, 0.946545, 1, 2.22384e-14
CAUTION: Gross error found at entry 673.
Found: 8.15021e-10 Expected 4.75974e-14 Error: 17122.2
44.5963, 33.4472, 162.945, 0.95793, 1, 4.75974e-14
CAUTION: Gross error found at entry 716.
Found: 1.11988e-10 Expected 2.84965e-22 Error: 3.92989e+11
44.5963, 222.981, 0.956697, 0.445432, 1, 2.84965e-22
CAUTION: Gross error found at entry 717.
Found: 7.99524e-10 Expected 3.04552e-15 Error: 262523
44.5963, 222.981, 78.4454, 0.515267, 1, 3.04552e-15
CAUTION: Gross error found at entry 718.
Found: 8.0958e-10 Expected 5.89458e-13 Error: 1372.43
44.5963, 222.981, 158.441, 0.57107, 1, 5.89458e-13
*** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***

##### Error Output For non central beta CDF with compiler GNU C++ version 7.1.0 and library Rmath 3.2.3 and test data Non Central Beta, medium parameters

CAUTION: Gross error found at entry 14.
Found: 4.64669e-35 Expected 7.14875e-33 Error: 152.846
1.45431, 1.30887, 158.441, 0.0983847, 7.14875e-33, 1
CAUTION: Gross error found at entry 15.
Found: 4.66674e-46 Expected 3.13332e-40 Error: 671416
1.45431, 1.30887, 196.222, 0.09869, 3.13332e-40, 1
CAUTION: Gross error found at entry 18.
Found: 5.84342e-28 Expected 3.61559e-27 Error: 5.18745
1.45431, 1.43976, 159.586, 0.245596, 3.61559e-27, 1
CAUTION: Gross error found at entry 19.
Found: 1.72833e-34 Expected 1.76943e-33 Error: 9.2378
1.45431, 1.43976, 198.576, 0.246444, 1.76943e-33, 1
CAUTION: Gross error found at entry 22.
Found: 1.76915e-19 Expected 3.69506e-18 Error: 19.8861
1.45431, 1.45285, 159.621, 0.491116, 3.69506e-18, 1
CAUTION: Gross error found at entry 23.
Found: 2.52007e-25 Expected 2.00482e-22 Error: 794.544
1.45431, 1.45285, 199.292, 0.492849, 2.00482e-22, 1
CAUTION: Gross error found at entry 73.
Found: 2.04477e-34 Expected 2.45287e-33 Error: 10.9958
7.62448, 6.86203, 148.129, 0.0921776, 2.45287e-33, 1
CAUTION: Gross error found at entry 74.
Found: 2.36587e-46 Expected 7.32638e-42 Error: 30966
7.62448, 6.86203, 193.539, 0.093784, 7.32638e-42, 1
CAUTION: Gross error found at entry 76.
Found: 3.29122e-26 Expected 7.418e-25 Error: 21.5387
7.62448, 7.54824, 148.626, 0.228717, 7.418e-25, 1
CAUTION: Gross error found at entry 77.
Found: 1.70126e-32 Expected 1.07666e-31 Error: 5.32864
7.62448, 7.54824, 193.774, 0.23303, 1.07666e-31, 1
CAUTION: Gross error found at entry 79.
Found: 1.3478e-15 Expected 4.21836e-15 Error: 2.12982
7.62448, 7.61686, 151.548, 0.457773, 4.21836e-15, 1
CAUTION: Gross error found at entry 80.
Found: 8.78487e-21 Expected 3.41238e-19 Error: 37.8438
7.62448, 7.61686, 194.119, 0.465826, 3.41238e-19, 1
CAUTION: Gross error found at entry 132.
Found: 3.85783e-23 Expected 1.54142e-22 Error: 2.99555
19.9593, 17.9634, 44.2068, 0.0698905, 1.54142e-22, 1
CAUTION: Gross error found at entry 133.
Found: 8.6122e-39 Expected 3.94361e-38 Error: 3.5791
19.9593, 17.9634, 135.747, 0.0829178, 3.94361e-38, 1
CAUTION: Gross error found at entry 134.
Found: 3.61781e-52 Expected 3.98669e-48 Error: 11018.6
19.9593, 17.9634, 191.501, 0.0864897, 3.98669e-48, 1
CAUTION: Gross error found at entry 135.
Found: 2.07122e-15 Expected 7.08614e-15 Error: 2.42124
19.9593, 19.7597, 55.6996, 0.176444, 7.08614e-15, 1
CAUTION: Gross error found at entry 136.
Found: 2.28223e-27 Expected 2.16759e-25 Error: 93.977
19.9593, 19.7597, 136.272, 0.20393, 2.16759e-25, 1
CAUTION: Gross error found at entry 137.
Found: 6.4251e-34 Expected 4.0064e-33 Error: 5.23554
19.9593, 19.7597, 191.898, 0.213398, 4.0064e-33, 1
CAUTION: Gross error found at entry 139.
Found: 2.1734e-14 Expected 4.65637e-14 Error: 1.14243
19.9593, 19.9394, 145.168, 0.410858, 4.65637e-14, 1
CAUTION: Gross error found at entry 140.
Found: 2.18388e-19 Expected 5.1677e-18 Error: 22.663
19.9593, 19.9394, 192.978, 0.426523, 5.1677e-18, 1
CAUTION: Gross error found at entry 192.
Found: 3.29537e-23 Expected 8.29996e-23 Error: 1.51867
22.4174, 20.1757, 34.773, 0.0661999, 8.29996e-23, 1
CAUTION: Gross error found at entry 193.
Found: 7.86091e-39 Expected 2.77686e-38 Error: 2.5325
22.4174, 20.1757, 127.953, 0.0809614, 2.77686e-38, 1
CAUTION: Gross error found at entry 194.
Found: 3.0161e-51 Expected 4.5396e-48 Error: 1504.12
22.4174, 20.1757, 183.147, 0.0848857, 4.5396e-48, 1
CAUTION: Gross error found at entry 195.
Found: 3.08022e-14 Expected 1.42713e-13 Error: 3.6332
22.4174, 22.1932, 37.6764, 0.162145, 1.42713e-13, 1
CAUTION: Gross error found at entry 196.
Found: 8.89935e-28 Expected 2.56187e-25 Error: 286.871
22.4174, 22.1932, 131.096, 0.199361, 2.56187e-25, 1
CAUTION: Gross error found at entry 197.
Found: 9.34392e-34 Expected 6.14831e-33 Error: 5.58001
22.4174, 22.1932, 186.799, 0.209601, 6.14831e-33, 1
CAUTION: Gross error found at entry 199.
Found: 2.79341e-13 Expected 4.79277e-13 Error: 0.71574
22.4174, 22.395, 131.148, 0.398015, 4.79277e-13, 1
CAUTION: Gross error found at entry 200.
Found: 3.13989e-19 Expected 7.01608e-18 Error: 21.345
22.4174, 22.395, 191.433, 0.419933, 7.01608e-18, 1
*** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***

##### Error Output For non central chi squared CDF complement with compiler GNU C++ version 7.1.0 and library Rmath 3.2.3 and test data Non Central Chi Squared, large parameters

CAUTION: Gross error found at entry 12.
Found: 0 Expected 1.17655e-12 Error: 5.28771e+295
101.815, 5236.73, 6406.25, 1, 1.17655e-12
CAUTION: Gross error found at entry 13.
Found: 0 Expected 1.79374e-44 Error: 8.06149e+263
101.815, 9735.22, 12788.2, 1, 1.79374e-44
CAUTION: Gross error found at entry 35.
Found: 2.58682e-14 Expected 1.84404e-61 Error: 1.4028e+47
107.623, 122.456, 920.317, 1, 1.84404e-61
CAUTION: Gross error found at entry 36.
Found: 0 Expected 2.30757e-102 Error: 1.03707e+206
107.623, 156.292, 1319.58, 1, 2.30757e-102
CAUTION: Gross error found at entry 52.
Found: 0 Expected 6.40952e-24 Error: 2.88059e+284
114.68, 417.884, 1065.13, 1, 6.40952e-24
CAUTION: Gross error found at entry 53.
Found: 0 Expected 1.02366e-98 Error: 4.60058e+209
114.68, 669.781, 2353.38, 1, 1.02366e-98
CAUTION: Gross error found at entry 69.
Found: 0 Expected 6.55726e-39 Error: 2.94699e+269
118.032, 3168.71, 4930.11, 1, 6.55726e-39
CAUTION: Gross error found at entry 85.
Found: 0 Expected 7.30688e-22 Error: 3.28388e+286
163.004, 9735.22, 11877.9, 1, 7.30688e-22
CAUTION: Gross error found at entry 86.
Found: 0 Expected 1.17171e-111 Error: 5.26596e+196
163.004, 25344.1, 33159.2, 1, 1.17171e-111
CAUTION: Gross error found at entry 108.
Found: 1.12355e-13 Expected 2.67349e-61 Error: 4.20255e+47
256.292, 122.456, 1136.25, 1, 2.67349e-61
CAUTION: Gross error found at entry 109.
Found: 1.16462e-13 Expected 8.30595e-116 Error: 1.40216e+102
256.292, 156.292, 1650.34, 1, 8.30595e-116
CAUTION: Gross error found at entry 124.
Found: 1.05804e-13 Expected 1.01672e-15 Error: 103.064
517.884, 417.884, 1403.65, 1, 1.01672e-15
CAUTION: Gross error found at entry 125.
Found: 2.00728e-13 Expected 3.50192e-56 Error: 5.73194e+42
517.884, 669.781, 2375.33, 1, 3.50192e-56
CAUTION: Gross error found at entry 141.
Found: 0 Expected 1.36924e-20 Error: 6.15368e+287
769.781, 3168.71, 5120.04, 1, 1.36924e-20
CAUTION: Gross error found at entry 142.
Found: 0 Expected 3.19215e-72 Error: 1.43463e+236
769.781, 5236.73, 9009.76, 1, 3.19215e-72
CAUTION: Gross error found at entry 157.
Found: 0 Expected 7.26231e-08 Error: 3.26385e+300
1223.88, 9735.22, 12055, 1, 7.26231e-08
CAUTION: Gross error found at entry 158.
Found: 0 Expected 4.5906e-56 Error: 2.06312e+252
1223.88, 25344.1, 31881.6, 1, 4.5906e-56
CAUTION: Gross error found at entry 194.
Found: 0 Expected 5.34714e-12 Error: 2.40313e+296
9835.22, 122.456, 10953.4, 1, 5.34714e-12
CAUTION: Gross error found at entry 195.
Found: 0 Expected 4.84412e-40 Error: 2.17706e+268
9835.22, 156.292, 11989.8, 1, 4.84412e-40
CAUTION: Gross error found at entry 196.
Found: 0 Expected 5.50199e-83 Error: 2.47272e+225
9835.22, 417.884, 13329, 1, 5.50199e-83
CAUTION: Gross error found at entry 197.
Found: 0 Expected 1.28192e-205 Error: 5.76124e+102
9835.22, 669.781, 15757.5, 1, 1.28192e-205
CAUTION: Gross error found at entry 211.
Found: 0 Expected 3.83272e-28 Error: 1.72251e+280
25444.1, 1123.88, 29224.8, 1, 3.83272e-28
CAUTION: Gross error found at entry 212.
Found: 0 Expected 1.69815e-101 Error: 7.63188e+206
25444.1, 3168.71, 34335.4, 1, 1.69815e-101
CAUTION: Gross error found at entry 213.
Found: 0 Expected 1.09245e-217 Error: 4.90974e+90
25444.1, 5236.73, 39885.1, 1, 1.09245e-217

##### Error Output For non central chi squared CDF complement with compiler GNU C++ version 7.1.0 and library Rmath 3.2.3 and test data Non Central Chi Squared, medium parameters

CAUTION: Gross error found at entry 36.
Found: 1.11022e-14 Expected 1.30043e-26 Error: 8.53738e+11
1.95191, 109.376, 445.313, 1, 1.30043e-26
CAUTION: Gross error found at entry 37.
Found: 0 Expected 1.45478e-39 Error: 6.53812e+268
1.95191, 109.444, 556.98, 1, 1.45478e-39
CAUTION: Gross error found at entry 54.
Found: 2.91989e-14 Expected 4.25949e-21 Error: 6.85501e+06
1.95191, 159.586, 484.613, 1, 4.25949e-21
CAUTION: Gross error found at entry 55.
Found: 0 Expected 1.33424e-37 Error: 5.99639e+270
1.95191, 159.621, 646.292, 1, 1.33424e-37
CAUTION: Gross error found at entry 56.
Found: 1.25455e-14 Expected 1.95903e-56 Error: 6.40393e+41
1.95191, 160.056, 810.04, 1, 1.95903e-56
CAUTION: Gross error found at entry 73.
Found: 0 Expected 4.34735e-25 Error: 1.9538e+283
1.95191, 193.539, 586.473, 1, 4.34735e-25
CAUTION: Gross error found at entry 74.
Found: 0 Expected 4.66119e-45 Error: 2.09485e+263
1.95191, 193.774, 782.902, 1, 4.66119e-45
CAUTION: Gross error found at entry 75.
Found: 4.77396e-15 Expected 8.92248e-68 Error: 5.35048e+52
1.95191, 194.119, 980.352, 1, 8.92248e-68
CAUTION: Gross error found at entry 111.
Found: 0 Expected 3.1064e-15 Error: 1.39609e+293
20.4105, 84.4175, 314.484, 1, 3.1064e-15
CAUTION: Gross error found at entry 112.
Found: 0 Expected 7.50903e-29 Error: 3.37473e+279
20.4105, 94.9517, 461.449, 1, 7.50903e-29
CAUTION: Gross error found at entry 113.
Found: 3.77476e-15 Expected 1.74225e-43 Error: 2.1666e+28
20.4105, 97.0751, 587.428, 1, 1.74225e-43
CAUTION: Gross error found at entry 130.
Found: 8.88178e-16 Expected 4.13277e-23 Error: 2.14911e+07
20.4105, 151.548, 515.876, 1, 4.13277e-23
CAUTION: Gross error found at entry 131.
Found: 1.75415e-14 Expected 1.92146e-41 Error: 9.12928e+26
20.4105, 152.75, 692.642, 1, 1.92146e-41
CAUTION: Gross error found at entry 132.
Found: 1.38778e-14 Expected 7.09864e-64 Error: 1.95499e+49
20.4105, 158.441, 894.26, 1, 7.09864e-64
CAUTION: Gross error found at entry 149.
Found: 2.22045e-16 Expected 8.74501e-28 Error: 2.5391e+11
20.4105, 191.433, 635.532, 1, 8.74501e-28
CAUTION: Gross error found at entry 150.
Found: 0 Expected 6.94227e-50 Error: 3.12002e+258
20.4105, 191.501, 847.648, 1, 6.94227e-50
CAUTION: Gross error found at entry 151.
Found: 3.40838e-14 Expected 5.3889e-75 Error: 6.32482e+60
20.4105, 191.898, 1061.55, 1, 5.3889e-75
CAUTION: Gross error found at entry 206.
Found: 5.88418e-15 Expected 2.69136e-22 Error: 2.18632e+07
22.8625, 141.209, 492.215, 1, 2.69136e-22
CAUTION: Gross error found at entry 207.
Found: 3.60822e-14 Expected 1.64941e-40 Error: 2.18759e+26
22.8625, 145.168, 672.121, 1, 1.64941e-40
CAUTION: Gross error found at entry 208.
Found: 3.73035e-14 Expected 1.6094e-61 Error: 2.31784e+47
22.8625, 148.129, 854.96, 1, 1.6094e-61
CAUTION: Gross error found at entry 225.
Found: 0 Expected 3.73672e-27 Error: 1.67937e+281
22.8625, 182.675, 616.613, 1, 3.73672e-27
CAUTION: Gross error found at entry 226.
Found: 0 Expected 8.85688e-49 Error: 3.98049e+259
22.8625, 183.147, 824.038, 1, 8.85688e-49
CAUTION: Gross error found at entry 227.
Found: 0 Expected 2.29176e-74 Error: 1.02997e+234
22.8625, 186.799, 1048.31, 1, 2.29176e-74
CAUTION: Gross error found at entry 282.
Found: 0 Expected 2.18831e-21 Error: 9.8348e+286
23.3804, 132.721, 468.305, 1, 2.18831e-21
CAUTION: Gross error found at entry 283.
Found: 0 Expected 1.3071e-38 Error: 5.87439e+269
23.3804, 135.747, 636.51, 1, 1.3071e-38
CAUTION: Gross error found at entry 284.
Found: 1.84297e-14 Expected 8.27843e-58 Error: 2.22623e+43
23.3804, 136.272, 798.262, 1, 8.27843e-58
CAUTION: Gross error found at entry 301.
Found: 0 Expected 9.85282e-26 Error: 4.42808e+282
23.3804, 169.826, 579.619, 1, 9.85282e-26
CAUTION: Gross error found at entry 302.
Found: 0 Expected 4.8094e-47 Error: 2.16145e+261
23.3804, 174.486, 791.465, 1, 4.8094e-47
CAUTION: Gross error found at entry 303.
Found: 1.11022e-16 Expected 6.70476e-71 Error: 1.65587e+54
23.3804, 175.686, 995.333, 1, 6.70476e-71
CAUTION: Gross error found at entry 358.
Found: 0 Expected 3.9702e-21 Error: 1.7843e+287
26.2704, 126.472, 458.227, 1, 3.9702e-21
CAUTION: Gross error found at entry 359.
*** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***

##### Error Output For non central t CDF complement with compiler GNU C++ version 7.1.0 and library Rmath 3.2.3 and test data Non Central T

CAUTION: Gross error found at entry 56.
Found: 0.000186411 Expected 7.85192e-05 Error: 1.37408
61.6335, 46.2251, 68.8608, 0.999921, 7.85192e-05
CAUTION: Gross error found at entry 75.
Found: 0.00011439 Expected 5.05344e-05 Error: 1.26361
80.8418, 60.6313, 86.1278, 0.999949, 5.05344e-05
CAUTION: Gross error found at entry 93.
Found: 0.000655162 Expected 0.000423927 Error: 0.545458
100.733, 50.3663, 65.7619, 0.999576, 0.000423927
CAUTION: Gross error found at entry 112.
Found: 0.000518249 Expected 0.00034473 Error: 0.503348
127.953, 63.9764, 81.0824, 0.999655, 0.00034473

##### Error Output For non central t CDF with compiler GNU C++ version 7.1.0 and library Rmath 3.2.3 and test data Non Central T

CAUTION: Gross error found at entry 74.
Found: 0.000830062 Expected 0.000522858 Error: 0.587549
79.7478, -39.8739, -53.8066, 0.000522858, 0.999477
CAUTION: Gross error found at entry 94.
Found: 7.69292e-05 Expected 3.54024e-05 Error: 1.17299
101.191, -75.8936, -104.104, 3.54024e-05, 0.999965
CAUTION: Gross error found at entry 113.
Found: 5.07713e-05 Expected 2.4439e-05 Error: 1.07747
128.792, -96.5942, -128.112, 2.4439e-05, 0.999976
CAUTION: Gross error found at entry 132.
Found: 4.08612e-05 Expected 2.01542e-05 Error: 1.02743
146.56, -109.92, -143.392, 2.01542e-05, 0.99998
CAUTION: Gross error found at entry 151.
Found: 3.55146e-05 Expected 1.7803e-05 Error: 0.994869
159.586, -119.689, -154.522, 1.7803e-05, 0.999982
CAUTION: Gross error found at entry 170.
Found: 3.03671e-05 Expected 1.55023e-05 Error: 0.958873
175.686, -131.765, -168.211, 1.55023e-05, 0.999984
CAUTION: Gross error found at entry 189.
Found: 2.61339e-05 Expected 1.3581e-05 Error: 0.924298
192.978, -144.733, -182.834, 1.3581e-05, 0.999986

##### Error Output For polygamma with compiler GNU C++ version 7.1.0 and library Rmath 3.2.3 and test data Mathematica Data - Large orders and other bug cases

CAUTION: Found non-finite result, when a finite value was expected at entry 0
Found: -nan Expected 2.07309e+257 Error: 1.79769e+308
171, 2, 2.07309e+257
CAUTION: Gross error found at entry 0.
Found: -nan Expected 2.07309e+257 Error: 1.79769e+308
171, 2, 2.07309e+257
CAUTION: Found non-finite result, when a finite value was expected at entry 1
Found: -nan Expected 7.42912e+188 Error: 1.79769e+308
171, 5, 7.42912e+188
CAUTION: Gross error found at entry 1.
Found: -nan Expected 7.42912e+188 Error: 1.79769e+308
171, 5, 7.42912e+188
CAUTION: Found non-finite result, when a finite value was expected at entry 2
Found: -nan Expected -4.81295e+247 Error: 1.79769e+308
166, 2, -4.81295e+247
CAUTION: Gross error found at entry 2.
Found: -nan Expected -4.81295e+247 Error: 1.79769e+308
166, 2, -4.81295e+247
CAUTION: Found non-finite result, when a finite value was expected at entry 3
Found: -nan Expected -1.88439e+218 Error: 1.79769e+308
166, 3, -1.88439e+218
CAUTION: Gross error found at entry 3.
Found: -nan Expected -1.88439e+218 Error: 1.79769e+308
166, 3, -1.88439e+218
CAUTION: Found non-finite result, when a finite value was expected at entry 4
Found: -nan Expected 7.53144e+74 Error: 1.79769e+308
171, 23, 7.53144e+74
CAUTION: Gross error found at entry 4.
Found: -nan Expected 7.53144e+74 Error: 1.79769e+308
171, 23, 7.53144e+74
CAUTION: Found non-finite result, when a finite value was expected at entry 5
Found: -nan Expected -6.52661e-66 Error: 1.79769e+308
168, 150, -6.52661e-66
CAUTION: Gross error found at entry 5.
Found: -nan Expected -6.52661e-66 Error: 1.79769e+308
168, 150, -6.52661e-66
CAUTION: Found non-finite result, when a finite value was expected at entry 6
Found: -nan Expected 9.2734e-88 Error: 1.79769e+308
169, 202, 9.2734e-88
CAUTION: Gross error found at entry 6.
Found: -nan Expected 9.2734e-88 Error: 1.79769e+308
169, 202, 9.2734e-88
Outside supported domain
20, -9.5, -0.00103076
Outside supported domain
21, -9.5, 4.28582e+26
Outside supported domain
22, -9.5, -0.00419144
Outside supported domain
23, -9.5, 8.6745e+29
Outside supported domain
24, -9.5, -0.0204825
Outside supported domain
25, -9.5, 2.08188e+33
Outside supported domain
26, -9.5, -0.118403
Outside supported domain
27, -9.5, 5.84592e+36
Outside supported domain
28, -9.5, -0.798969
Outside supported domain
29, -9.5, 1.89875e+40
Outside supported domain
30, -9.5, -6.22245

##### Error Output For polygamma with compiler GNU C++ version 7.1.0 and library Rmath 3.2.3 and test data Mathematica Data - large negative arguments

Outside supported domain
124, -1.5, 7.63705e+240
Outside supported domain
124, -2.5, 7.63705e+240
Outside supported domain
124, -3.5, 7.63705e+240
Outside supported domain
124, -4.5, 7.63705e+240
Outside supported domain
124, -5.5, 7.63705e+240
Outside supported domain
124, -6.5, 7.63705e+240
Outside supported domain
124, -7.5, 7.63705e+240
Outside supported domain
124, -8.5, 7.63705e+240
Outside supported domain
124, -9.5, 7.63705e+240
Outside supported domain
124, -10.5, 7.63705e+240
Outside supported domain
124, -11.5, 7.63705e+240
Outside supported domain
124, -12.5, 7.63705e+240
Outside supported domain
124, -13.5, 7.63705e+240
Outside supported domain
124, -14.5, 7.63705e+240
Outside supported domain
124, -15.5, 7.63705e+240
Outside supported domain
124, -16.5, 7.63705e+240
Outside supported domain
124, -17.5, 7.63705e+240
Outside supported domain
124, -18.5, 7.63705e+240
Outside supported domain
124, -19.5, 7.63705e+240
Outside supported domain
124, -20.5, 7.63705e+240
Outside supported domain
124, -1.5, -7.63705e+240
Outside supported domain
124, -2.5, -7.63705e+240
Outside supported domain
124, -3.5, -7.63705e+240
Outside supported domain
124, -4.5, -7.63705e+240
Outside supported domain
124, -5.5, -7.63705e+240
Outside supported domain
124, -6.5, -7.63705e+240
Outside supported domain
124, -7.5, -7.63705e+240
Outside supported domain
124, -8.5, -7.63705e+240
Outside supported domain
124, -9.5, -7.63705e+240
Outside supported domain
124, -10.5, -7.63705e+240
Outside supported domain
124, -11.5, -7.63705e+240
Outside supported domain
124, -12.5, -7.63705e+240
Outside supported domain
124, -13.5, -7.63705e+240
Outside supported domain
124, -14.5, -7.63705e+240
Outside supported domain
124, -15.5, -7.63705e+240
Outside supported domain
124, -16.5, -7.63705e+240
Outside supported domain
124, -17.5, -7.63705e+240
Outside supported domain
124, -18.5, -7.63705e+240
Outside supported domain
124, -19.5, -7.63705e+240
Outside supported domain
124, -20.5, -7.63705e+240
Outside supported domain
1, -0.5, 8.9348
Outside supported domain
2, -0.5, -0.828797
Outside supported domain
3, -0.5, 193.409
Outside supported domain
4, -0.5, -3.47425
Outside supported domain
5, -0.5, 15371.1
Outside supported domain
6, -0.5, -43.4579
Outside supported domain
7, -0.5, 2.58068e+06
Outside supported domain
8, -0.5, -1059.96
Outside supported domain
9, -0.5, 7.43185e+08
Outside supported domain
10, -0.5, -42108.9
Outside supported domain
11, -0.5, 3.26999e+11
Outside supported domain
12, -0.5, -2.46448e+06
Outside supported domain
13, -0.5, 2.04047e+14
Outside supported domain
14, -0.5, -1.9918e+08
Outside supported domain
15, -0.5, 1.71399e+17
Outside supported domain
16, -0.5, -2.12394e+10
Outside supported domain
17, -0.5, 1.86483e+20
Outside supported domain
18, -0.5, -2.88824e+12
Outside supported domain
19, -0.5, 2.55108e+23
Outside supported domain
20, -0.5, -4.87773e+14
Outside supported domain
21, -0.5, 4.28582e+26
Outside supported domain
1, -0.5, 8.9348
Outside supported domain
2, -0.5, -0.828843
Outside supported domain
3, -0.5, 193.409
Outside supported domain
4, -0.5, -3.47791
Outside supported domain
5, -0.5, 15371.1
Outside supported domain
6, -0.5, -44.0732
Outside supported domain
7, -0.5, 2.58068e+06
Outside supported domain
8, -0.5, -1237.15
Outside supported domain
9, -0.5, 7.43185e+08
Outside supported domain
10, -0.5, -120071
Outside supported domain
11, -0.5, 3.26999e+11
Outside supported domain
12, -0.5, -5.11131e+07
Outside supported domain
13, -0.5, 2.04047e+14
Outside supported domain
14, -0.5, -4.1064e+10
Outside supported domain
15, -0.5, 1.71399e+17
Outside supported domain
16, -0.5, -4.44822e+13
Outside supported domain
17, -0.5, 1.86483e+20
Outside supported domain
18, -0.5, -6.08254e+16
Outside supported domain
19, -0.5, 2.55108e+23
Outside supported domain
20, -0.5, -1.02182e+20
Outside supported domain
21, -0.5, 4.28582e+26
Outside supported domain
1, -0.5, 8.9348
Outside supported domain
2, -0.5, -0.828751
Outside supported domain
3, -0.5, 193.409
Outside supported domain
4, -0.5, -3.47059
Outside supported domain
*** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***

##### Error Output For polygamma with compiler GNU C++ version 7.1.0 and library Rmath 3.2.3 and test data Mathematica Data - negative arguments

Outside supported domain
1, -12.75, 19.6638
Outside supported domain
1, -12.25, 19.6608
Outside supported domain
1, -11.75, 19.6576
Outside supported domain
1, -11.25, 19.6542
Outside supported domain
1, -10.75, 19.6504
Outside supported domain
1, -10.25, 19.6463
Outside supported domain
1, -9.75, 19.6417
Outside supported domain
1, -9.25, 19.6367
Outside supported domain
1, -8.75, 19.6312
Outside supported domain
1, -8.25, 19.625
Outside supported domain
1, -7.75, 19.6181
Outside supported domain
1, -7.25, 19.6104
Outside supported domain
1, -6.75, 19.6015
Outside supported domain
1, -6.25, 19.5913
Outside supported domain
1, -5.75, 19.5795
Outside supported domain
1, -5.25, 19.5657
Outside supported domain
1, -4.75, 19.5493
Outside supported domain
1, -4.25, 19.5294
Outside supported domain
1, -3.75, 19.505
Outside supported domain
1, -3.25, 19.4741
Outside supported domain
1, -2.75, 19.4339
Outside supported domain
1, -2.25, 19.3794
Outside supported domain
1, -1.75, 19.3016
Outside supported domain
1, -1.25, 19.1819
Outside supported domain
1, -0.75, 18.9751
Outside supported domain
1, -0.25, 18.5419
Outside supported domain
2, -12.75, -124.031
Outside supported domain
2, -12.25, 124.019
Outside supported domain
2, -11.75, -124.032
Outside supported domain
2, -11.25, 124.018
Outside supported domain
2, -10.75, -124.033
Outside supported domain
2, -10.25, 124.016
Outside supported domain
2, -9.75, -124.035
Outside supported domain
2, -9.25, 124.015
Outside supported domain
2, -8.75, -124.037
Outside supported domain
2, -8.25, 124.012
Outside supported domain
2, -7.75, -124.04
Outside supported domain
2, -7.25, 124.009
Outside supported domain
2, -6.75, -124.044
Outside supported domain
2, -6.25, 124.003
Outside supported domain
2, -5.75, -124.051
Outside supported domain
2, -5.25, 123.995
Outside supported domain
2, -4.75, -124.061
Outside supported domain
2, -4.25, 123.981
Outside supported domain
2, -3.75, -124.08
Outside supported domain
2, -3.25, 123.955
Outside supported domain
2, -2.75, -124.118
Outside supported domain
2, -2.25, 123.897
Outside supported domain
2, -1.75, -124.214
Outside supported domain
2, -1.25, 123.721
Outside supported domain
2, -0.75, -124.587
Outside supported domain
2, -0.25, 122.697
Outside supported domain
3, -12.75, 1558.54
Outside supported domain
3, -12.25, 1558.54
Outside supported domain
3, -11.75, 1558.54
Outside supported domain
3, -11.25, 1558.54
Outside supported domain
3, -10.75, 1558.54
Outside supported domain
3, -10.25, 1558.54
Outside supported domain
3, -9.75, 1558.54
Outside supported domain
3, -9.25, 1558.54
Outside supported domain
3, -8.75, 1558.54
Outside supported domain
3, -8.25, 1558.54
Outside supported domain
3, -7.75, 1558.54
Outside supported domain
3, -7.25, 1558.54
Outside supported domain
3, -6.75, 1558.54
Outside supported domain
3, -6.25, 1558.54
Outside supported domain
3, -5.75, 1558.54
Outside supported domain
3, -5.25, 1558.54
Outside supported domain
3, -4.75, 1558.53
Outside supported domain
3, -4.25, 1558.53
Outside supported domain
3, -3.75, 1558.52
Outside supported domain
3, -3.25, 1558.51
Outside supported domain
3, -2.75, 1558.49
Outside supported domain
3, -2.25, 1558.46
Outside supported domain
3, -1.75, 1558.38
Outside supported domain
3, -1.25, 1558.22
Outside supported domain
3, -0.75, 1557.75
Outside supported domain
3, -0.25, 1555.76
Outside supported domain
4, -12.75, -24481.6
Outside supported domain
4, -12.25, 24481.6
Outside supported domain
4, -11.75, -24481.6
Outside supported domain
4, -11.25, 24481.6
Outside supported domain
4, -10.75, -24481.6
Outside supported domain
4, -10.25, 24481.6
Outside supported domain
4, -9.75, -24481.6
Outside supported domain
4, -9.25, 24481.6
Outside supported domain
4, -8.75, -24481.6
Outside supported domain
4, -8.25, 24481.6
Outside supported domain
4, -7.75, -24481.6
Outside supported domain
4, -7.25, 24481.6
Outside supported domain
4, -6.75, -24481.6
Outside supported domain
4, -6.25, 24481.6
Outside supported domain
4, -5.75, -24481.6
Outside supported domain
4, -5.25, 24481.6
Outside supported domain
*** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***

##### Error Output For polygamma with compiler GNU C++ version 7.1.0 and library Rmath 3.2.3 and test data Mathematica Data - large arguments

CAUTION: Gross error found at entry 211.
Found: -0 Expected -8.44974e-268 Error: 3.79751e+40
30, 8.58993e+09, -8.44974e-268
CAUTION: Gross error found at entry 212.
Found: -0 Expected -7.86943e-277 Error: 3.5367e+31
30, 1.71799e+10, -7.86943e-277
CAUTION: Gross error found at entry 213.
Found: -0 Expected -7.32898e-286 Error: 3.29381e+22
30, 3.43597e+10, -7.32898e-286
CAUTION: Gross error found at entry 214.
Found: -0 Expected -6.82564e-295 Error: 3.0676e+13
30, 6.87195e+10, -6.82564e-295
CAUTION: Gross error found at entry 215.
Found: -0 Expected -6.35687e-304 Error: 28568.3
30, 1.37439e+11, -6.35687e-304

##### Error Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data Bessel Iv: Mathworld Data (large values)

domain error
-1, 3.72917e-155, 1.86459e-155
domain error
-1.125, 3.72917e-155, -1.34964e+173

##### Error Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data Bessel Iv: Random Data

domain error
-80.4919, 24.7501, 4.18698e+28
domain error
-80.4919, 63.7722, 2.03248e+06
domain error
-74.6026, 24.7501, 7.20977e+23
domain error
-74.6026, 63.7722, 8.7549e+08
domain error
-72.9046, 24.7501, 1.04535e+22
domain error
-72.9046, 63.7722, 4.7162e+09
domain error
-62.3236, 24.7501, 3.65147e+14
domain error
-62.3236, 63.7722, 8.56683e+13
domain error
-55.7932, 24.7501, -7.70364e+09
domain error
-55.7932, 63.7722, 1.95969e+16
domain error
-44.3004, 9.50706, 2.93478e+22
domain error
-44.3004, 24.7501, 640.568
domain error
-44.3004, 63.7722, 8.05557e+19
domain error
-38.3666, 5.11399, 2.89105e+27
domain error
-38.3666, 9.50706, 8.80632e+16
domain error
-38.3666, 24.7501, 0.389004
domain error
-38.3666, 63.7722, 3.06303e+21
underflow
81.1584, 0.00177219, 0
underflow
81.1584, 0.00221773, 0
underflow
81.1584, 0.0074445, 6.08857e-319
underflow
82.6752, 0.00177219, 0
underflow
82.6752, 0.00221773, 0
underflow
82.6752, 0.0074445, 0
underflow
91.5014, 0.00177219, 0
underflow
91.5014, 0.00221773, 0
underflow
91.5014, 0.0074445, 0
underflow
91.5014, 0.014336, 0
underflow
91.5014, 0.0176092, 0
underflow
92.9777, 0.00177219, 0
underflow
92.9777, 0.00221773, 0
underflow
92.9777, 0.0074445, 0
underflow
92.9777, 0.014336, 0
underflow
92.9777, 0.0176092, 0
underflow
93.539, 0.00177219, 0
underflow
93.539, 0.00221773, 0
underflow
93.539, 0.0074445, 0
underflow
93.539, 0.014336, 0
underflow
93.539, 0.0176092, 0
underflow
93.7736, 0.00177219, 0
underflow
93.7736, 0.00221773, 0
underflow
93.7736, 0.0074445, 0
underflow
93.7736, 0.014336, 0
underflow
93.7736, 0.0176092, 0
underflow
98.5763, 0.00177219, 0
underflow
98.5763, 0.00221773, 0
underflow
98.5763, 0.0074445, 0
underflow
98.5763, 0.014336, 0
underflow
98.5763, 0.0176092, 0
underflow
99.2923, 0.00177219, 0
underflow
99.2923, 0.00221773, 0
underflow
99.2923, 0.0074445, 0
underflow
99.2923, 0.014336, 0
underflow
99.2923, 0.0176092, 0

##### Error Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data Bessel In: Random Data

underflow
70, 0.00177219, 1.75887e-314
underflow
73, 0.00177219, 0
underflow
73, 0.00221773, 4.24896e-322
underflow
76, 0.00177219, 0
underflow
76, 0.00221773, 0
underflow
79, 0.00177219, 0
underflow
79, 0.00221773, 0
underflow
79, 0.0074445, 1.38676e-309
underflow
82, 0.00177219, 0
underflow
82, 0.00221773, 0
underflow
82, 0.0074445, 1.33398e-322
underflow
85, 0.00177219, 0
underflow
85, 0.00221773, 0
underflow
85, 0.0074445, 0
underflow
85, 0.014336, 1.81568e-311
underflow
88, 0.00177219, 0
underflow
88, 0.00221773, 0
underflow
88, 0.0074445, 0
underflow
88, 0.014336, 9.88131e-324
underflow
88, 0.0176092, 7.34647e-316

##### Error Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data Bessel Iv: Mathworld Data

domain error
-4.99902, 2.125, 0.0267921
domain error
-5.5, 10, 597.578
domain error
-5.5, 100, 9.22363e+41
domain error
-10.0003, 0.000976562, 1.41474e+35
domain error
-10.0003, 50, 1.07153e+20
domain error
-141.4, 100, 2066.28

##### Error Output For cyl_bessel_i (integer orders) with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data Bessel In: Mathworld Data (Integer Version)

underflow
10, 1e-100, 0

##### Error Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data Bessel In: Mathworld Data

domain error
-2, 0, 0
domain error
-5, 100, 9.47009e+41
domain error
-5, -1, -0.000271463
domain error
10, -5, 0.00458004
domain error
-100, -200, 4.35275e+74
underflow
10, 1e-100, 0

##### Error Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data Bessel I1: Mathworld Data

domain error
1, -2, -1.59064
domain error
1, -8, -399.873
domain error
1, -10, -2670.99

##### Error Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data Bessel I0: Mathworld Data

domain error
0, -2, 2.27959
domain error
0, -7, 168.594
domain error
0, -1, 1.26607

##### Error Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library <cmath> and test data Bessel Iv: Mathworld Data (large values)

Bad argument in __cyl_bessel_i.
-1, 3.72917e-155, 1.86459e-155
Bad argument in __cyl_bessel_i.
-1.125, 3.72917e-155, -1.34964e+173

##### Error Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library <cmath> and test data Bessel Iv: Random Data

Bad argument in __cyl_bessel_i.
-80.4919, 24.7501, 4.18698e+28
Bad argument in __cyl_bessel_i.
-80.4919, 63.7722, 2.03248e+06
Bad argument in __cyl_bessel_i.
-74.6026, 24.7501, 7.20977e+23
Bad argument in __cyl_bessel_i.
-74.6026, 63.7722, 8.7549e+08
Bad argument in __cyl_bessel_i.
-72.9046, 24.7501, 1.04535e+22
Bad argument in __cyl_bessel_i.
-72.9046, 63.7722, 4.7162e+09
Bad argument in __cyl_bessel_i.
-62.3236, 24.7501, 3.65147e+14
Bad argument in __cyl_bessel_i.
-62.3236, 63.7722, 8.56683e+13
Bad argument in __cyl_bessel_i.
-55.7932, 24.7501, -7.70364e+09
Bad argument in __cyl_bessel_i.
-55.7932, 63.7722, 1.95969e+16
Bad argument in __cyl_bessel_i.
-44.3004, 9.50706, 2.93478e+22
Bad argument in __cyl_bessel_i.
-44.3004, 24.7501, 640.568
Bad argument in __cyl_bessel_i.
-44.3004, 63.7722, 8.05557e+19
Bad argument in __cyl_bessel_i.
-38.3666, 5.11399, 2.89105e+27
Bad argument in __cyl_bessel_i.
-38.3666, 9.50706, 8.80632e+16
Bad argument in __cyl_bessel_i.
-38.3666, 24.7501, 0.389004
Bad argument in __cyl_bessel_i.
-38.3666, 63.7722, 3.06303e+21

##### Error Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library <cmath> and test data Bessel Iv: Mathworld Data

Bad argument in __cyl_bessel_i.
-4.99902, 2.125, 0.0267921
Bad argument in __cyl_bessel_i.
-5.5, 10, 597.578
Bad argument in __cyl_bessel_i.
-5.5, 100, 9.22363e+41
Bad argument in __cyl_bessel_i.
-10.0003, 0.000976562, 1.41474e+35
Bad argument in __cyl_bessel_i.
-10.0003, 50, 1.07153e+20
Bad argument in __cyl_bessel_i.
-141.4, 100, 2066.28

##### Error Output For cyl_bessel_i (integer orders) with compiler GNU C++ version 7.1.0 and library <cmath> and test data Bessel In: Mathworld Data (Integer Version)

Bad argument in __cyl_bessel_i.
-2, 0, 0
Bad argument in __cyl_bessel_i.
-5, 100, 9.47009e+41
Bad argument in __cyl_bessel_i.
-5, -1, -0.000271463
Bad argument in __cyl_bessel_i.
10, -5, 0.00458004
Bad argument in __cyl_bessel_i.
-100, -200, 4.35275e+74

##### Error Output For cyl_bessel_i (integer orders) with compiler GNU C++ version 7.1.0 and library <cmath> and test data Bessel I1: Mathworld Data (Integer Version)

Bad argument in __cyl_bessel_i.
1, -2, -1.59064
Bad argument in __cyl_bessel_i.
1, -8, -399.873
Bad argument in __cyl_bessel_i.
1, -10, -2670.99

##### Error Output For cyl_bessel_i (integer orders) with compiler GNU C++ version 7.1.0 and library <cmath> and test data Bessel I0: Mathworld Data (Integer Version)

Bad argument in __cyl_bessel_i.
0, -2, 2.27959
Bad argument in __cyl_bessel_i.
0, -7, 168.594
Bad argument in __cyl_bessel_i.
0, -1, 1.26607

##### Error Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library <cmath> and test data Bessel In: Mathworld Data

Bad argument in __cyl_bessel_i.
-2, 0, 0
Bad argument in __cyl_bessel_i.
-5, 100, 9.47009e+41
Bad argument in __cyl_bessel_i.
-5, -1, -0.000271463
Bad argument in __cyl_bessel_i.
10, -5, 0.00458004
Bad argument in __cyl_bessel_i.
-100, -200, 4.35275e+74

##### Error Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library <cmath> and test data Bessel I1: Mathworld Data

Bad argument in __cyl_bessel_i.
1, -2, -1.59064
Bad argument in __cyl_bessel_i.
1, -8, -399.873
Bad argument in __cyl_bessel_i.
1, -10, -2670.99

##### Error Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library <cmath> and test data Bessel I0: Mathworld Data

Bad argument in __cyl_bessel_i.
0, -2, 2.27959
Bad argument in __cyl_bessel_i.
0, -7, 168.594
Bad argument in __cyl_bessel_i.
0, -1, 1.26607

##### Error Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data Bessel J: Random Data

underflow
63.8868, 5.5381e-05, 0
underflow
63.8868, 6.9304e-05, 0
underflow
63.8868, 0.000232641, 0
underflow
63.8868, 0.000448, 8.39912e-323
underflow
63.8868, 0.000550287, 4.32897e-317

##### Error Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data Bessel J: Mathworld Data (large values)

domain error
-0.5, 1.2459e-206, 7.14823e+102
domain error
-256, 8, 0
domain error
-2.5, 4, -0.0145679

##### Error Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data Bessel J: Mathworld Data

domain error
-5.5, 3.1416, -2.5582
domain error
-5.5, 10000, 0.00244984
domain error
-5.5, 10000, 0.00244984
domain error
-5.5, 1e+06, 0.000279243
domain error
-0.5, 101, 0.0708185
domain error
-10.0003, 0.000976562, 1.41474e+35
domain error
-10.0003, 15, -0.0902239
domain error
-10.0003, 100, -0.0547614
domain error
-10.0003, 20000, -0.00556869
domain error
-8.5, 12.5664, -0.257087

##### Error Output For cyl_bessel_j (integer orders) with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data Bessel JN: Mathworld Data (Integer Version)

underflow
10, 1e-100, 0

##### Error Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data Bessel JN: Mathworld Data

domain error
-1, 1.25, -0.510623
domain error
-2, 0, 0
domain error
5, -10, 0.234062
domain error
-5, 1e+06, 0.000725964
domain error
-5, -1, 0.000249758
domain error
10, -10, 0.207486
domain error
10, -5, 0.0014678
domain error
-10, 1e+06, -0.000331079
underflow
10, 1e-100, 0

##### Error Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data Bessel J1: Mathworld Data

domain error
1, -2, -0.576725
domain error
1, -8, -0.234636
domain error
1, -10, -0.0434727

##### Error Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data Bessel J0: Mathworld Data

domain error
0, -2, 0.223891
domain error
0, -8, 0.171651
domain error
0, -10, -0.245936

##### Error Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library <cmath> and test data Bessel J: Mathworld Data (large values)

Bad argument in __cyl_bessel_j.
-0.5, 1.2459e-206, 7.14823e+102
Bad argument in __cyl_bessel_j.
-256, 8, 1.46866e-353
Bad argument in __cyl_bessel_j.
-2.5, 4, -0.0145679

##### Error Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library <cmath> and test data Bessel J: Mathworld Data

Bad argument in __cyl_bessel_j.
-5.5, 3.1416, -2.5582
Bad argument in __cyl_bessel_j.
-5.5, 10000, 0.00244984
Bad argument in __cyl_bessel_j.
-5.5, 10000, 0.00244984
Bad argument in __cyl_bessel_j.
-5.5, 1e+06, 0.000279243
Bad argument in __cyl_bessel_j.
-0.5, 101, 0.0708185
Bad argument in __cyl_bessel_j.
-10.0003, 0.000976562, 1.41474e+35
Bad argument in __cyl_bessel_j.
-10.0003, 15, -0.0902239
Bad argument in __cyl_bessel_j.
-10.0003, 100, -0.0547614
Bad argument in __cyl_bessel_j.
-10.0003, 20000, -0.00556869
Bad argument in __cyl_bessel_j.
-8.5, 12.5664, -0.257087

##### Error Output For cyl_bessel_j (integer orders) with compiler GNU C++ version 7.1.0 and library <cmath> and test data Bessel JN: Mathworld Data (Integer Version)

Bad argument in __cyl_bessel_j.
-1, 1.25, -0.510623
Bad argument in __cyl_bessel_j.
-2, 0, 0
Bad argument in __cyl_bessel_j.
5, -10, 0.234062
Bad argument in __cyl_bessel_j.
-5, 1e+06, 0.000725964
Bad argument in __cyl_bessel_j.
-5, -1, 0.000249758
Bad argument in __cyl_bessel_j.
10, -10, 0.207486
Bad argument in __cyl_bessel_j.
10, -5, 0.0014678
Bad argument in __cyl_bessel_j.
-10, 1e+06, -0.000331079
CAUTION: Gross error found at entry 15.
Found: 0.0042409 Expected 0.00128318 Error: 2.305
1000, 100000, 0.00128318

##### Error Output For cyl_bessel_j (integer orders) with compiler GNU C++ version 7.1.0 and library <cmath> and test data Bessel J1: Mathworld Data (Integer Version)

Bad argument in __cyl_bessel_j.
1, -2, -0.576725
Bad argument in __cyl_bessel_j.
1, -8, -0.234636
Bad argument in __cyl_bessel_j.
1, -10, -0.0434727

##### Error Output For cyl_bessel_j (integer orders) with compiler GNU C++ version 7.1.0 and library <cmath> and test data Bessel J0: Mathworld Data (Integer Version)

Bad argument in __cyl_bessel_j.
0, -2, 0.223891
Bad argument in __cyl_bessel_j.
0, -8, 0.171651
Bad argument in __cyl_bessel_j.
0, -10, -0.245936

##### Error Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library <cmath> and test data Bessel JN: Mathworld Data

Bad argument in __cyl_bessel_j.
-1, 1.25, -0.510623
Bad argument in __cyl_bessel_j.
-2, 0, 0
Bad argument in __cyl_bessel_j.
5, -10, 0.234062
Bad argument in __cyl_bessel_j.
-5, 1e+06, 0.000725964
Bad argument in __cyl_bessel_j.
-5, -1, 0.000249758
Bad argument in __cyl_bessel_j.
10, -10, 0.207486
Bad argument in __cyl_bessel_j.
10, -5, 0.0014678
Bad argument in __cyl_bessel_j.
-10, 1e+06, -0.000331079
CAUTION: Gross error found at entry 15.
Found: 0.0042409 Expected 0.00128318 Error: 2.305
1000, 100000, 0.00128318

##### Error Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library <cmath> and test data Bessel J1: Mathworld Data

Bad argument in __cyl_bessel_j.
1, -2, -0.576725
Bad argument in __cyl_bessel_j.
1, -8, -0.234636
Bad argument in __cyl_bessel_j.
1, -10, -0.0434727

##### Error Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library <cmath> and test data Bessel J0: Mathworld Data

Bad argument in __cyl_bessel_j.
0, -2, 0.223891
Bad argument in __cyl_bessel_j.
0, -8, 0.171651
Bad argument in __cyl_bessel_j.
0, -10, -0.245936

##### Error Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data Bessel Kv: Random Data

domain error
-80.4919, 24.7501, 6.57902e+28
domain error
-80.4919, 63.7722, 2.39552e-09
domain error
-80.4919, 125.28, 3.06904e-45
domain error
-80.4919, 255.547, 2.30343e-107
domain error
-80.4919, 503.011, 1.20315e-217
domain error
-80.4919, 1007.46, 0
domain error
-80.4919, 1185.4, 0
domain error
-80.4919, 3534.52, 0
domain error
-80.4919, 8071.55, 0
domain error
-80.4919, 16229.2, 0
domain error
-80.4919, 32066.2, 0
domain error
-80.4919, 36367.9, 0
domain error
-74.6026, 24.7501, 1.19405e+24
domain error
-74.6026, 63.7722, 5.81897e-12
domain error
-74.6026, 125.28, 9.89214e-47
domain error
-74.6026, 255.547, 3.9726e-108
domain error
-74.6026, 503.011, 4.87462e-218
domain error
-74.6026, 1007.46, 0
domain error
-74.6026, 1185.4, 0
domain error
-74.6026, 3534.52, 0
domain error
-74.6026, 8071.55, 0
domain error
-74.6026, 16229.2, 0
domain error
-74.6026, 32066.2, 0
domain error
-74.6026, 36367.9, 0
domain error
-72.9046, 24.7501, 5.5618e+22
domain error
-72.9046, 63.7722, 1.09452e-12
domain error
-72.9046, 125.28, 3.8393e-47
domain error
-72.9046, 255.547, 2.45173e-108
domain error
-72.9046, 503.011, 3.80454e-218
domain error
-72.9046, 1007.46, 0
domain error
-72.9046, 1185.4, 0
domain error
-72.9046, 3534.52, 0
domain error
-72.9046, 8071.55, 0
domain error
-72.9046, 16229.2, 0
domain error
-72.9046, 32066.2, 0
domain error
-72.9046, 36367.9, 0
domain error
-62.3236, 24.7501, 6.74518e+14
domain error
-62.3236, 63.7722, 6.54531e-17
domain error
-62.3236, 125.28, 1.65653e-49
domain error
-62.3236, 255.547, 1.54767e-109
domain error
-62.3236, 503.011, 9.22721e-219
domain error
-62.3236, 1007.46, 0
domain error
-62.3236, 1185.4, 0
domain error
-62.3236, 3534.52, 0
domain error
-62.3236, 8071.55, 0
domain error
-62.3236, 16229.2, 0
domain error
-62.3236, 32066.2, 0
domain error
-62.3236, 36367.9, 0
domain error
-55.7932, 24.7501, 2.00028e+10
domain error
-55.7932, 63.7722, 3.01107e-19
domain error
-55.7932, 125.28, 8.54693e-51
domain error
-55.7932, 255.547, 3.47666e-110
domain error
-55.7932, 503.011, 4.29705e-219
domain error
-55.7932, 1007.46, 0
domain error
-55.7932, 1185.4, 0
domain error
-55.7932, 3534.52, 0
domain error
-55.7932, 8071.55, 0
domain error
-55.7932, 16229.2, 0
domain error
-55.7932, 32066.2, 0
domain error
-55.7932, 36367.9, 0
domain error
-44.3004, 9.50706, 5.6936e+22
domain error
-44.3004, 24.7501, 1242.73
domain error
-44.3004, 63.7722, 7.99341e-23
domain error
-44.3004, 125.28, 9.88149e-53
domain error
-44.3004, 255.547, 3.73007e-111
domain error
-44.3004, 503.011, 1.37367e-219
domain error
-44.3004, 1007.46, 0
domain error
-44.3004, 1185.4, 0
domain error
-44.3004, 3534.52, 0
domain error
-44.3004, 8071.55, 0
domain error
-44.3004, 16229.2, 0
domain error
-44.3004, 32066.2, 0
domain error
-44.3004, 36367.9, 0
domain error
-38.3666, 5.11399, 4.97154e+27
domain error
-38.3666, 9.50706, 1.51436e+17
domain error
-38.3666, 24.7501, 0.639495
domain error
-38.3666, 63.7722, 2.19334e-24
domain error
-38.3666, 125.28, 1.45351e-53
domain error
-38.3666, 255.547, 1.43713e-111
domain error
-38.3666, 503.011, 8.44445e-220
domain error
-38.3666, 1007.46, 0
domain error
-38.3666, 1185.4, 0
domain error
-38.3666, 3534.52, 0
domain error
-38.3666, 8071.55, 0
domain error
-38.3666, 16229.2, 0
domain error
-38.3666, 32066.2, 0
domain error
-38.3666, 36367.9, 0
underflow
9.3763, 1007.46, 0
underflow
9.3763, 1185.4, 0
underflow
9.3763, 3534.52, 0
underflow
9.3763, 8071.55, 0
underflow
9.3763, 16229.2, 0
underflow
9.3763, 32066.2, 0
underflow
9.3763, 36367.9, 0
underflow
9.44412, 1007.46, 0
underflow
9.44412, 1185.4, 0
underflow
9.44412, 3534.52, 0
underflow
9.44412, 8071.55, 0
underflow
9.44412, 16229.2, 0
underflow
9.44412, 32066.2, 0
underflow
9.44412, 36367.9, 0
underflow
26.4719, 1007.46, 0
underflow
26.4719, 1185.4, 0
underflow
26.4719, 3534.52, 0
underflow
26.4719, 8071.55, 0
underflow
26.4719, 16229.2, 0
underflow
26.4719, 32066.2, 0
underflow
26.4719, 36367.9, 0
underflow
62.9447, 1007.46, 0
underflow
62.9447, 1185.4, 0
underflow
62.9447, 3534.52, 0
underflow
62.9447, 8071.55, 0
underflow
62.9447, 16229.2, 0
underflow
*** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***

##### Error Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data Bessel Kn: Random Data

underflow
0, 1007.46, 0
underflow
0, 1185.4, 0
underflow
0, 3534.52, 0
underflow
0, 8071.55, 0
underflow
0, 16229.2, 0
underflow
0, 32066.2, 0
underflow
0, 36367.9, 0
underflow
1, 1007.46, 0
underflow
1, 1185.4, 0
underflow
1, 3534.52, 0
underflow
1, 8071.55, 0
underflow
1, 16229.2, 0
underflow
1, 32066.2, 0
underflow
1, 36367.9, 0
underflow
4, 1007.46, 0
underflow
4, 1185.4, 0
underflow
4, 3534.52, 0
underflow
4, 8071.55, 0
underflow
4, 16229.2, 0
underflow
4, 32066.2, 0
underflow
4, 36367.9, 0
underflow
7, 1007.46, 0
underflow
7, 1185.4, 0
underflow
7, 3534.52, 0
underflow
7, 8071.55, 0
underflow
7, 16229.2, 0
underflow
7, 32066.2, 0
underflow
7, 36367.9, 0
underflow
10, 1007.46, 0
underflow
10, 1185.4, 0
underflow
10, 3534.52, 0
underflow
10, 8071.55, 0
underflow
10, 16229.2, 0
underflow
10, 32066.2, 0
underflow
10, 36367.9, 0
underflow
13, 1007.46, 0
underflow
13, 1185.4, 0
underflow
13, 3534.52, 0
underflow
13, 8071.55, 0
underflow
13, 16229.2, 0
underflow
13, 32066.2, 0
underflow
13, 36367.9, 0
underflow
16, 1007.46, 0
underflow
16, 1185.4, 0
underflow
16, 3534.52, 0
underflow
16, 8071.55, 0
underflow
16, 16229.2, 0
underflow
16, 32066.2, 0
underflow
16, 36367.9, 0
underflow
19, 1007.46, 0
underflow
19, 1185.4, 0
underflow
19, 3534.52, 0
underflow
19, 8071.55, 0
underflow
19, 16229.2, 0
underflow
19, 32066.2, 0
underflow
19, 36367.9, 0
underflow
22, 1007.46, 0
underflow
22, 1185.4, 0
underflow
22, 3534.52, 0
underflow
22, 8071.55, 0
underflow
22, 16229.2, 0
underflow
22, 32066.2, 0
underflow
22, 36367.9, 0
underflow
25, 1007.46, 0
underflow
25, 1185.4, 0
underflow
25, 3534.52, 0
underflow
25, 8071.55, 0
underflow
25, 16229.2, 0
underflow
25, 32066.2, 0
underflow
25, 36367.9, 0
underflow
28, 1007.46, 0
underflow
28, 1185.4, 0
underflow
28, 3534.52, 0
underflow
28, 8071.55, 0
underflow
28, 16229.2, 0
underflow
28, 32066.2, 0
underflow
28, 36367.9, 0
underflow
31, 1007.46, 0
underflow
31, 1185.4, 0
underflow
31, 3534.52, 0
underflow
31, 8071.55, 0
underflow
31, 16229.2, 0
underflow
31, 32066.2, 0
underflow
31, 36367.9, 0
underflow
34, 1007.46, 0
underflow
34, 1185.4, 0
underflow
34, 3534.52, 0
underflow
34, 8071.55, 0
underflow
34, 16229.2, 0
underflow
34, 32066.2, 0
underflow
34, 36367.9, 0
underflow
37, 1007.46, 0
underflow
37, 1185.4, 0
underflow
37, 3534.52, 0
underflow
37, 8071.55, 0
underflow
37, 16229.2, 0
underflow
37, 32066.2, 0
underflow
37, 36367.9, 0
underflow
40, 1007.46, 0
underflow
40, 1185.4, 0
underflow
40, 3534.52, 0
underflow
40, 8071.55, 0
underflow
40, 16229.2, 0
underflow
40, 32066.2, 0
underflow
40, 36367.9, 0
underflow
43, 1007.46, 0
underflow
43, 1185.4, 0
underflow
43, 3534.52, 0
underflow
43, 8071.55, 0
underflow
43, 16229.2, 0
underflow
43, 32066.2, 0
underflow
43, 36367.9, 0
underflow
46, 1007.46, 0
underflow
46, 1185.4, 0
underflow
46, 3534.52, 0
underflow
46, 8071.55, 0
underflow
46, 16229.2, 0
underflow
46, 32066.2, 0
underflow
46, 36367.9, 0
underflow
49, 1007.46, 0
underflow
49, 1185.4, 0
underflow
49, 3534.52, 0
underflow
49, 8071.55, 0
underflow
49, 16229.2, 0
underflow
49, 32066.2, 0
underflow
49, 36367.9, 0
underflow
52, 1007.46, 0
underflow
52, 1185.4, 0
underflow
52, 3534.52, 0
underflow
52, 8071.55, 0
underflow
52, 16229.2, 0
underflow
52, 32066.2, 0
underflow
52, 36367.9, 0
underflow
55, 1007.46, 0
underflow
55, 1185.4, 0
underflow
55, 3534.52, 0
underflow
55, 8071.55, 0
underflow
55, 16229.2, 0
underflow
55, 32066.2, 0
underflow
55, 36367.9, 0
underflow
58, 1007.46, 0
underflow
58, 1185.4, 0
underflow
58, 3534.52, 0
underflow
58, 8071.55, 0
underflow
58, 16229.2, 0
underflow
58, 32066.2, 0
underflow
58, 36367.9, 0
underflow
61, 1007.46, 0
underflow
61, 1185.4, 0
underflow
61, 3534.52, 0
underflow
61, 8071.55, 0
underflow
61, 16229.2, 0
underflow
61, 32066.2, 0
underflow
61, 36367.9, 0
underflow
64, 1007.46, 0
underflow
64, 1185.4, 0
underflow
64, 3534.52, 0
underflow
64, 8071.55, 0
underflow
64, 16229.2, 0
underflow
64, 32066.2, 0
underflow
64, 36367.9, 0
underflow
67, 1007.46, 0
underflow
67, 1185.4, 0
underflow
67, 3534.52, 0
underflow
67, 8071.55, 0
underflow
67, 16229.2, 0
*** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***

##### Error Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data Bessel Kv: Mathworld Data (large values)

domain error
-1, 3.72917e-155, 2.68156e+154
domain error
-1.125, 3.72917e-155, 5.53984e+173

##### Error Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data Bessel Kv: Mathworld Data

domain error
-5.5, 10, 7.33045e-05
domain error
-5.5, 100, 5.41275e-45
domain error
-141.399, 50, 1.30185e+42

##### Error Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data Bessel Kn: Mathworld Data

domain error
-5, 100, 5.27326e-45
domain error
-10, 1, 1.80713e+08
domain error
-1000, 700, 6.51562e-31

##### Error Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library <cmath> and test data Bessel Kv: Random Data

Bad argument in __cyl_bessel_k.
-80.4919, 24.7501, 6.57902e+28
Bad argument in __cyl_bessel_k.
-80.4919, 63.7722, 2.39552e-09
Bad argument in __cyl_bessel_k.
-80.4919, 125.28, 3.06904e-45
Bad argument in __cyl_bessel_k.
-80.4919, 255.547, 2.30343e-107
Bad argument in __cyl_bessel_k.
-80.4919, 503.011, 1.20315e-217
Bad argument in __cyl_bessel_k.
-80.4919, 1007.46, 2.86537e-438
Bad argument in __cyl_bessel_k.
-80.4919, 1185.4, 8.63263e-516
Bad argument in __cyl_bessel_k.
-80.4919, 3534.52, 5.01367e-1537
Bad argument in __cyl_bessel_k.
-80.4919, 8071.55, 7.76555e-3508
Bad argument in __cyl_bessel_k.
-80.4919, 16229.2, 0
Bad argument in __cyl_bessel_k.
-80.4919, 32066.2, 0
Bad argument in __cyl_bessel_k.
-80.4919, 36367.9, 0
Bad argument in __cyl_bessel_k.
-74.6026, 24.7501, 1.19405e+24
Bad argument in __cyl_bessel_k.
-74.6026, 63.7722, 5.81897e-12
Bad argument in __cyl_bessel_k.
-74.6026, 125.28, 9.89214e-47
Bad argument in __cyl_bessel_k.
-74.6026, 255.547, 3.9726e-108
Bad argument in __cyl_bessel_k.
-74.6026, 503.011, 4.87462e-218
Bad argument in __cyl_bessel_k.
-74.6026, 1007.46, 1.82221e-438
Bad argument in __cyl_bessel_k.
-74.6026, 1185.4, 5.87506e-516
Bad argument in __cyl_bessel_k.
-74.6026, 3534.52, 4.40608e-1537
Bad argument in __cyl_bessel_k.
-74.6026, 8071.55, 7.3384e-3508
Bad argument in __cyl_bessel_k.
-74.6026, 16229.2, 0
Bad argument in __cyl_bessel_k.
-74.6026, 32066.2, 0
Bad argument in __cyl_bessel_k.
-74.6026, 36367.9, 0
Bad argument in __cyl_bessel_k.
-72.9046, 24.7501, 5.5618e+22
Bad argument in __cyl_bessel_k.
-72.9046, 63.7722, 1.09452e-12
Bad argument in __cyl_bessel_k.
-72.9046, 125.28, 3.8393e-47
Bad argument in __cyl_bessel_k.
-72.9046, 255.547, 2.45173e-108
Bad argument in __cyl_bessel_k.
-72.9046, 503.011, 3.80454e-218
Bad argument in __cyl_bessel_k.
-72.9046, 1007.46, 1.60949e-438
Bad argument in __cyl_bessel_k.
-72.9046, 1185.4, 5.28662e-516
Bad argument in __cyl_bessel_k.
-72.9046, 3534.52, 4.25273e-1537
Bad argument in __cyl_bessel_k.
-72.9046, 8071.55, 7.22542e-3508
Bad argument in __cyl_bessel_k.
-72.9046, 16229.2, 0
Bad argument in __cyl_bessel_k.
-72.9046, 32066.2, 0
Bad argument in __cyl_bessel_k.
-72.9046, 36367.9, 0
Bad argument in __cyl_bessel_k.
-62.3236, 24.7501, 6.74518e+14
Bad argument in __cyl_bessel_k.
-62.3236, 63.7722, 6.54531e-17
Bad argument in __cyl_bessel_k.
-62.3236, 125.28, 1.65653e-49
Bad argument in __cyl_bessel_k.
-62.3236, 255.547, 1.54767e-109
Bad argument in __cyl_bessel_k.
-62.3236, 503.011, 9.22721e-219
Bad argument in __cyl_bessel_k.
-62.3236, 1007.46, 7.91894e-439
Bad argument in __cyl_bessel_k.
-62.3236, 1185.4, 2.89281e-516
Bad argument in __cyl_bessel_k.
-62.3236, 3534.52, 3.4736e-1537
Bad argument in __cyl_bessel_k.
-62.3236, 8071.55, 6.6126e-3508
Bad argument in __cyl_bessel_k.
-62.3236, 16229.2, 0
Bad argument in __cyl_bessel_k.
-62.3236, 32066.2, 0
Bad argument in __cyl_bessel_k.
-62.3236, 36367.9, 0
Bad argument in __cyl_bessel_k.
-55.7932, 24.7501, 2.00028e+10
Bad argument in __cyl_bessel_k.
-55.7932, 63.7722, 3.01107e-19
Bad argument in __cyl_bessel_k.
-55.7932, 125.28, 8.54693e-51
Bad argument in __cyl_bessel_k.
-55.7932, 255.547, 3.47666e-110
Bad argument in __cyl_bessel_k.
-55.7932, 503.011, 4.29705e-219
Bad argument in __cyl_bessel_k.
-55.7932, 1007.46, 5.40242e-439
Bad argument in __cyl_bessel_k.
-55.7932, 1185.4, 2.08996e-516
Bad argument in __cyl_bessel_k.
-55.7932, 3534.52, 3.11458e-1537
Bad argument in __cyl_bessel_k.
-55.7932, 8071.55, 6.30409e-3508
Bad argument in __cyl_bessel_k.
-55.7932, 16229.2, 0
Bad argument in __cyl_bessel_k.
-55.7932, 32066.2, 0
Bad argument in __cyl_bessel_k.
-55.7932, 36367.9, 0
Bad argument in __cyl_bessel_k.
-44.3004, 9.50706, 5.6936e+22
Bad argument in __cyl_bessel_k.
-44.3004, 24.7501, 1242.73
Bad argument in __cyl_bessel_k.
-44.3004, 63.7722, 7.99341e-23
Bad argument in __cyl_bessel_k.
-44.3004, 125.28, 9.88149e-53
Bad argument in __cyl_bessel_k.
-44.3004, 255.547, 3.73007e-111
Bad argument in __cyl_bessel_k.
-44.3004, 503.011, 1.37367e-219
Bad argument in __cyl_bessel_k.
-44.3004, 1007.46, 3.05398e-439
Bad argument in __cyl_bessel_k.
*** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***

##### Error Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library <cmath> and test data Bessel Kv: Mathworld Data (large values)

Bad argument in __cyl_bessel_k.
-1, 3.72917e-155, 2.68156e+154
Bad argument in __cyl_bessel_k.
-1.125, 3.72917e-155, 5.53984e+173

##### Error Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library <cmath> and test data Bessel Kv: Mathworld Data

Bad argument in __cyl_bessel_k.
-5.5, 10, 7.33045e-05
Bad argument in __cyl_bessel_k.
-5.5, 100, 5.41275e-45
Bad argument in __cyl_bessel_k.
-141.399, 50, 1.30185e+42

##### Error Output For cyl_bessel_k (integer orders) with compiler GNU C++ version 7.1.0 and library <cmath> and test data Bessel Kn: Mathworld Data (Integer Version)

Bad argument in __cyl_bessel_k.
-5, 100, 5.27326e-45
Bad argument in __cyl_bessel_k.
-10, 1, 1.80713e+08
Bad argument in __cyl_bessel_k.
-1000, 700, 6.51562e-31

##### Error Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library <cmath> and test data Bessel Kn: Mathworld Data

Bad argument in __cyl_bessel_k.
-5, 100, 5.27326e-45
Bad argument in __cyl_bessel_k.
-10, 1, 1.80713e+08
Bad argument in __cyl_bessel_k.
-1000, 700, 6.51562e-31

##### Error Output For cyl_neumann with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data Yv: Mathworld Data (large values)

domain error
-0.5, 1.2459e-206, 8.90598e-104

##### Error Output For cyl_neumann with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data Yv: Mathworld Data

domain error
-5.5, 3.125, -0.0274994
domain error
-5.5, 10000, -0.00759344
domain error
-10.0003, 0.000976562, -1.50382e+38
domain error
-10.0003, 100, 0.0583042
domain error
-141.75, 100, -3.8101e+09
domain error
-8.5, 12.5664, 0.0436808

##### Error Output For cyl_neumann with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data Yn: Mathworld Data

domain error
-5, 1e+06, 0.000331052
domain error
-10, 1e+06, 0.000725952
domain error
-1000, 700, -1.88753e+77
domain error
-25, 8, 3.45114e+08

##### Error Output For cyl_neumann with compiler GNU C++ version 7.1.0 and library <cmath> and test data Yv: Random Data

CAUTION: Gross error found at entry 394.
Found: -3.29903 Expected 0.0192842 Error: 1.18973e+4932
125.28, 1007.46, 0.0192842
CAUTION: Gross error found at entry 395.
Found: 1.13543 Expected 0.0230358 Error: 48.2897
125.28, 1185.4, 0.0230358
CAUTION: Gross error found at entry 396.
Found: 0.00119445 Expected 0.00460223 Error: 2.85302
125.28, 3534.52, 0.00460223
CAUTION: Gross error found at entry 403.
Found: 1068 Expected -0.00270959 Error: 1.18973e+4932
255.547, 1007.46, -0.00270959
CAUTION: Gross error found at entry 404.
Found: -395.006 Expected 0.00738845 Error: 1.18973e+4932
255.547, 1185.4, 0.00738845
CAUTION: Gross error found at entry 405.
Found: 1.08701 Expected -0.000407036 Error: 1.18973e+4932
255.547, 3534.52, -0.000407036
CAUTION: Gross error found at entry 406.
Found: 0.0232211 Expected 0.00886946 Error: 1.61809
255.547, 8071.55, 0.00886946
CAUTION: Gross error found at entry 411.
Found: 65895.7 Expected -0.0158467 Error: 1.18973e+4932
503.011, 1007.46, -0.0158467
CAUTION: Gross error found at entry 412.
Found: -123316 Expected 0.00594357 Error: 1.18973e+4932
503.011, 1185.4, 0.00594357
CAUTION: Gross error found at entry 413.
Found: -706.209 Expected 0.010151 Error: 1.18973e+4932
503.011, 3534.52, 0.010151
CAUTION: Gross error found at entry 414.
Found: -21.2081 Expected 0.00888375 Error: 1.18973e+4932
503.011, 8071.55, 0.00888375
CAUTION: Gross error found at entry 415.
Found: 0.0272835 Expected 0.00552287 Error: 3.94008
503.011, 16229.2, 0.00552287
CAUTION: Gross error found at entry 416.
Found: 0.0103324 Expected 0.00445559 Error: 1.31898
503.011, 32066.2, 0.00445559
CAUTION: Gross error found at entry 417.
Found: 0.00540788 Expected -0.00384344 Error: 1.18973e+4932
503.011, 36367.9, -0.00384344
CAUTION: Gross error found at entry 418.
Found: 5.43091e+07 Expected -0.0772843 Error: 1.18973e+4932
1007.46, 1007.46, -0.0772843
CAUTION: Gross error found at entry 419.
Found: -2.84383e+07 Expected 0.0304312 Error: 1.18973e+4932
1007.46, 1185.4, 0.0304312
CAUTION: Gross error found at entry 420.
Found: -61440.2 Expected -0.00474217 Error: 1.29562e+07
1007.46, 3534.52, -0.00474217
CAUTION: Gross error found at entry 421.
Found: -4126.89 Expected -0.0074205 Error: 556146
1007.46, 8071.55, -0.0074205
CAUTION: Gross error found at entry 422.
Found: -69.2831 Expected -0.00179572 Error: 38581.4
1007.46, 16229.2, -0.00179572
CAUTION: Gross error found at entry 423.
Found: 2.32048 Expected 0.000750053 Error: 3092.76
1007.46, 32066.2, 0.000750053
CAUTION: Gross error found at entry 424.
Found: 3.90724 Expected 0.00305125 Error: 1279.54
1007.46, 36367.9, 0.00305125
CAUTION: Gross error found at entry 425.
Found: -1.83374e+08 Expected -7.25176e+28 Error: 3.95463e+20
1185.4, 1007.46, -7.25176e+28
CAUTION: Gross error found at entry 426.
Found: 1.09822e+08 Expected -0.0732059 Error: 1.18973e+4932
1185.4, 1185.4, -0.0732059
CAUTION: Gross error found at entry 427.
Found: 315632 Expected 0.000479585 Error: 6.58136e+08
1185.4, 3534.52, 0.000479585
CAUTION: Gross error found at entry 428.
Found: 16815.6 Expected 0.00174909 Error: 9.61391e+06
1185.4, 8071.55, 0.00174909
CAUTION: Gross error found at entry 429.
Found: 133.356 Expected 0.00416288 Error: 32033.6
1185.4, 16229.2, 0.00416288
CAUTION: Gross error found at entry 430.
Found: -1.38401 Expected -0.000320056 Error: 4323.27
1185.4, 32066.2, -0.000320056
CAUTION: Gross error found at entry 431.
Found: -17.7085 Expected -0.00417656 Error: 4238.96
1185.4, 36367.9, -0.00417656

##### Error Output For cyl_neumann with compiler GNU C++ version 7.1.0 and library <cmath> and test data Yv: Mathworld Data (large values)

Bad argument in __cyl_neumann_n.
-0.5, 1.2459e-206, 8.90598e-104

##### Error Output For cyl_neumann with compiler GNU C++ version 7.1.0 and library <cmath> and test data Yv: Mathworld Data

Bad argument in __cyl_neumann_n.
-5.5, 3.125, -0.0274994
Bad argument in __cyl_neumann_n.
-5.5, 10000, -0.00759344
Bad argument in __cyl_neumann_n.
-10.0003, 0.000976562, -1.50382e+38
Bad argument in __cyl_neumann_n.
-10.0003, 100, 0.0583042
Bad argument in __cyl_neumann_n.
-141.75, 100, -3.8101e+09
Bad argument in __cyl_neumann_n.
-8.5, 12.5664, 0.0436808

##### Error Output For cyl_neumann (integer orders) with compiler GNU C++ version 7.1.0 and library <cmath> and test data Yn: Mathworld Data (Integer Version)

Bad argument in __cyl_neumann_n.
-5, 1e+06, 0.000331052
Bad argument in __cyl_neumann_n.
-10, 1e+06, 0.000725952
CAUTION: Gross error found at entry 7.
Found: 0.0540745 Expected 0.00217255 Error: 23.8899
1000, 100000, 0.00217255
Bad argument in __cyl_neumann_n.
-1000, 700, -1.88753e+77
Bad argument in __cyl_neumann_n.
-25, 8, 3.45114e+08

##### Error Output For cyl_neumann with compiler GNU C++ version 7.1.0 and library <cmath> and test data Yn: Mathworld Data

Bad argument in __cyl_neumann_n.
-5, 1e+06, 0.000331052
Bad argument in __cyl_neumann_n.
-10, 1e+06, 0.000725952
CAUTION: Gross error found at entry 7.
Found: 0.0540745 Expected 0.00217255 Error: 23.8899
1000, 100000, 0.00217255
Bad argument in __cyl_neumann_n.
-1000, 700, -1.88753e+77
Bad argument in __cyl_neumann_n.
-25, 8, 3.45114e+08

##### Error Output For beta with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data Beta Function: Small Values

CAUTION: Found non-finite result, when a finite value was expected at entry 22
Found: inf Expected 5.69832e+154 Error: 1.79769e+308
2.98334e-154, 1.86459e-155, 5.69832e+154
CAUTION: Gross error found at entry 22.
Found: inf Expected 5.69832e+154 Error: 1.79769e+308
2.98334e-154, 1.86459e-155, 5.69832e+154

##### Error Output For ellint_rj with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data RJ: Random data

domain error
1.77787e-31, 1.40657e+18, 10.046, -4.8298e-10, -2.51795e-10
domain error
3.37448e-31, 4.65772e+22, 0.469831, -4.33756e-09, -2.95865e-11
domain error
5.25297e-31, 5.85483e+25, 2.02482e-15, -1.87347e-28, 3.36445e+07
domain error
6.22216e-31, 3.43401e+23, 0.673005, -2.7626e-13, -7.58898e-12
domain error
6.26875e-31, 2.62568e-13, 1.06394e+24, -1.36451e+14, -6.70372e-25
domain error
6.84599e-31, 3.57666e-29, 1.82191e+11, -3.63292e+08, -8.35235e-13
domain error
8.90482e-31, 1.97093e-28, 1.14939e-31, -1.26424e-12, -6.39454e+26
domain error
1.07374e-30, 1.70005e-12, 1.88773e-25, -1.16558e-29, 4.31668e+32
domain error
1.17141e-30, 24.2523, 3.67522e+21, -4.79065e-22, 2.2702e-05
domain error
1.64143e-30, 2.01978e-22, 2.58942e+12, -8.52649e-12, -2.82629e+06
domain error
1.85141e-30, 0.0386712, 2.37846e-13, -1.57357e+15, -1.38574e-13
domain error
2.70034e-30, 4.43896e-24, 7.54576e+16, -1.1436e-14, -1.10082e+07
domain error
4.01162e-30, 2.73343e+23, 1.32333e+13, -1.86032e-07, -4.16626e-25
domain error
4.13665e-30, 1.08034e-30, 3.13547e-16, -5.58099e-08, -5.14643e+16
domain error
4.3728e-30, 7.79812e+12, 8.58894e+21, -4.58312e-24, 5.28901e-09
domain error
5.6397e-30, 1.64768e+23, 9.64423e-15, -1.82207e+20, -1.62886e-30
domain error
9.89841e-30, 9.69731e+10, 1.03263e+21, -0.00343967, -9.62714e-22
domain error
1.3797e-29, 6.03357e+08, 5.62497e-15, -5.87235e+16, -5.80287e-20
domain error
1.96963e-29, 3.22384e-25, 2.92187e+23, -3.80643e+27, -8.2513e-38
domain error
2.00927e-29, 5.6976e-05, 1.16219e+25, -1.64129e-22, 0.00318397
domain error
7.29506e-29, 5904.94, 9.93922e+10, -19.528, -1.60795e-09
domain error
1.19698e-28, 1.66816e-22, 28472, -1.21137e-19, -5.84699e+17
domain error
1.64095e-28, 2.13421e-21, 7.8914e-15, -1.77584e-07, -1.70156e+15
domain error
2.03475e-28, 4.40987e+15, 28739.1, -9624.5, -1.29418e-12
domain error
2.73113e-28, 1.08457e+19, 4.00674e+08, -5.70043e-11, 1.092e-17
domain error
5.52633e-28, 1.45707e-17, 1.29411e-27, -1.67255e-15, -5.84881e+24
domain error
5.61278e-28, 9.22881e-12, 8.64222e-13, -5.6282e+23, -4.57782e-18
domain error
6.08465e-28, 1.32249e+26, 1.25536e-30, -1.89097e-14, -223.246
domain error
9.50943e-28, 2.49682e-18, 0.000904584, -3.1419e-12, -2.44954e+14
domain error
1.20779e-27, 35383.2, 1.35533e-15, -4.67834e-24, 3.20581e+15
domain error
2.29822e-27, 3.35258e-16, 2.60689e+08, -9.99161e-20, -5.4924e+11
domain error
3.0926e-27, 3.11839e-13, 3.37883e-23, -1.94349e+26, -3.55191e-19
domain error
3.12803e-27, 1.15118e+16, 1.52495e+10, -4.2399e+13, -3.07515e-21
domain error
4.49747e-27, 716.685, 1.69018e-23, -1.32558e-14, -9.2291e+13
domain error
4.84575e-27, 3.44028e-27, 3.42665e+09, -812.399, -2.12767e-06
domain error
5.81424e-27, 3.70845e-15, 3.69338e+11, -4.15794e+06, -2.95944e-11
domain error
6.08654e-27, 1.23742e+08, 1.09124e-26, -2.19946e+16, -4.90896e-19
domain error
7.71967e-27, 9.46115e-26, 1.24324e+25, -522800, -5.83203e-17
domain error
9.20037e-27, 207550, 2.45782e-17, -6.06901e+29, -2.88945e-31
domain error
1.75502e-26, 5.81507e+16, 8.83063e+21, -1.11214e-21, 1.57697e-11
domain error
2.29965e-26, 2.9716e-21, 1.81059e-25, -5.23972e-08, -6.23302e+18
domain error
2.32628e-26, 0.0655133, 1.62901e-21, -7.15441e-17, -9.88586e+17
domain error
3.49194e-26, 2.53343e+14, 756.217, -1.3359e+10, -1.275e-16
domain error
1.009e-25, 0.0694304, 1.20267e-14, -1.55746e-22, 2.10701e+17
domain error
3.54771e-25, 1.67999e-27, 2.3917e+24, -9.98754e+25, -1.11704e-36
domain error
6.31714e-25, 3.4594e-28, 6.37951e-24, -1.25529e-24, -9.56292e+35
domain error
6.74086e-25, 2.47169e+12, 1.32962e+23, -6.78845e+06, -3.32861e-24
domain error
1.8099e-24, 4.5215e-06, 8.66937e-11, -3.70795e-08, -1.41893e+11
domain error
2.29798e-24, 9.30454e-30, 6.56584e-17, -9890.38, -373149
domain error
2.88161e-24, 8.82377e-05, 1.57747e+21, -4.25068e-24, 2260.61
domain error
3.25991e-24, 1.92923e+29, 3.09752e-05, -1.00986e+11, -1.25485e-24
domain error
6.36705e-24, 2.8074e+22, 1.75569e-13, -1.53152e+24, -4.89823e-34
domain error
7.90772e-24, 2.11611e-30, 1.42682e-07, -0.00296297, -5.38814e+07
domain error
1.05302e-23, 4.83473e+26, 4.43149e-30, -1.56818e+13, -3.6836e-25
*** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***

##### Error Output For ellint_1 with compiler GNU C++ version 7.1.0 and library <cmath> and test data Elliptic Integral F: Mathworld Data

CAUTION: Gross error found at entry 9.
Found: -7.02862e+09 Expected 1.04181e+20 Error: 1.18973e+4932
1e+20, 0.390625, 1.04181e+20
CAUTION: Gross error found at entry 10.
Found: -9.3866e+09 Expected 1.39133e+50 Error: 1.18973e+4932
1e+50, 0.875, 1.39133e+50

##### Error Output For ellint_2 (complete) with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data Elliptic Integral E: Mathworld Data

domain error
-1, 1

##### Error Output For ellint_2 with compiler GNU C++ version 7.1.0 and library <cmath> and test data Elliptic Integral E: Mathworld Data

CAUTION: Gross error found at entry 7.
Found: -6.3027e+09 Expected 9.34215e+09 Error: 1.18973e+4932
1e+10, -0.5, 9.34215e+09
CAUTION: Gross error found at entry 8.
Found: -6.48129e+09 Expected 7.08861e+19 Error: 1.18973e+4932
7.3787e+19, 0.390625, 7.08861e+19
CAUTION: Gross error found at entry 9.
Found: -5.13973e+09 Expected 7.1259e+49 Error: 1.18973e+4932
9.35361e+49, 0.878906, 7.1259e+49

##### Error Output For ellint_3 (complete) with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data Complete Elliptic Integral PI: Mathworld Data

domain error
-4.14952e+180, 0.5, 7.71119e-91

##### Error Output For ellint_3 with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data Elliptic Integral PI: Mathworld Data

domain error
1.125, 10, 0.25, 0.662468
domain error
1.125, 3, 0.25, -0.142697
domain error
1.00391, 21.5, 0.125, -0.535406
domain error
1, 2, 0.5, -2.87535
domain error
1, -2, 0.5, 2.87535
domain error
1, 2, 6.22302e-61, -2.18504
domain error
1, -2, 6.22302e-61, 2.18504
domain error
20, 3.14257, 0.5, 0.000975941
domain error
20, -3.14257, 0.5, -0.000975941
domain error
1.01562, 1.6958, 0.5, -27.1647
domain error
1.01562, -1.6958, 0.5, 27.1647

##### Error Output For ellint_3 (complete) with compiler GNU C++ version 7.1.0 and library <cmath> and test data Complete Elliptic Integral PI: Random Data

Argument too small in __ellint_rj
-87.1743, 0.126987, 0.167413
Argument too small in __ellint_rj
-87.1743, 0.135477, 0.167431
Argument too small in __ellint_rj
-87.1743, 0.221034, 0.167683
Argument too small in __ellint_rj
-87.1743, 0.308167, 0.168078
Argument too small in __ellint_rj
-87.1743, 0.632359, 0.17122
Argument too small in __ellint_rj
-87.1743, 0.814724, 0.175341
Argument too small in __ellint_rj
-87.1743, 0.835009, 0.176056
Argument too small in __ellint_rj
-87.1743, 0.905792, 0.179501
Argument too small in __ellint_rj
-87.1743, 0.913376, 0.180014
Argument too small in __ellint_rj
-87.1743, 0.968868, 0.186162
Argument too small in __ellint_rj
-86.3168, 0.126987, 0.168233
Argument too small in __ellint_rj
-86.3168, 0.135477, 0.168252
Argument too small in __ellint_rj
-86.3168, 0.221034, 0.168506
Argument too small in __ellint_rj
-86.3168, 0.308167, 0.168905
Argument too small in __ellint_rj
-86.3168, 0.632359, 0.172077
Argument too small in __ellint_rj
-86.3168, 0.814724, 0.176237
Argument too small in __ellint_rj
-86.3168, 0.835009, 0.176958
Argument too small in __ellint_rj
-86.3168, 0.905792, 0.180437
Argument too small in __ellint_rj
-86.3168, 0.913376, 0.180955
Argument too small in __ellint_rj
-86.3168, 0.968868, 0.187163
Argument too small in __ellint_rj
-77.6756, 0.126987, 0.177238
Argument too small in __ellint_rj
-77.6756, 0.135477, 0.177258
Argument too small in __ellint_rj
-77.6756, 0.221034, 0.17754
Argument too small in __ellint_rj
-77.6756, 0.308167, 0.17798
Argument too small in __ellint_rj
-77.6756, 0.632359, 0.181485
Argument too small in __ellint_rj
-77.6756, 0.814724, 0.186089
Argument too small in __ellint_rj
-77.6756, 0.835009, 0.186888
Argument too small in __ellint_rj
-77.6756, 0.905792, 0.190742
Argument too small in __ellint_rj
-77.6756, 0.913376, 0.191315
Argument too small in __ellint_rj
-77.6756, 0.968868, 0.1982
Argument too small in __ellint_rj
-68.8751, 0.126987, 0.188077
Argument too small in __ellint_rj
-68.8751, 0.135477, 0.188099
Argument too small in __ellint_rj
-68.8751, 0.221034, 0.188414
Argument too small in __ellint_rj
-68.8751, 0.308167, 0.188907
Argument too small in __ellint_rj
-68.8751, 0.632359, 0.192834
Argument too small in __ellint_rj
-68.8751, 0.814724, 0.198
Argument too small in __ellint_rj
-68.8751, 0.835009, 0.198896
Argument too small in __ellint_rj
-68.8751, 0.905792, 0.203226
Argument too small in __ellint_rj
-68.8751, 0.913376, 0.203871
Argument too small in __ellint_rj
-68.8751, 0.968868, 0.211615
Argument too small in __ellint_rj
-36.1317, 0.126987, 0.258074
Argument too small in __ellint_rj
-36.1317, 0.135477, 0.258115
Argument too small in __ellint_rj
-36.1317, 0.221034, 0.258686
Argument too small in __ellint_rj
-36.1317, 0.308167, 0.259579
Argument too small in __ellint_rj
-36.1317, 0.632359, 0.266738
Argument too small in __ellint_rj
-36.1317, 0.814724, 0.276242
Argument too small in __ellint_rj
-36.1317, 0.835009, 0.2779
Argument too small in __ellint_rj
-36.1317, 0.905792, 0.285938
Argument too small in __ellint_rj
-36.1317, 0.913376, 0.287139
Argument too small in __ellint_rj
-36.1317, 0.968868, 0.301608
Argument too small in __ellint_rj
-17.7129, 0.126987, 0.363673
Argument too small in __ellint_rj
-17.7129, 0.135477, 0.36375
Argument too small in __ellint_rj
-17.7129, 0.221034, 0.364822
Argument too small in __ellint_rj
-17.7129, 0.308167, 0.366503
Argument too small in __ellint_rj
-17.7129, 0.632359, 0.380066
Argument too small in __ellint_rj
-17.7129, 0.814724, 0.398311
Argument too small in __ellint_rj
-17.7129, 0.835009, 0.401518
Argument too small in __ellint_rj
-17.7129, 0.905792, 0.417145
Argument too small in __ellint_rj
-17.7129, 0.913376, 0.41949
Argument too small in __ellint_rj
-17.7129, 0.968868, 0.447893
Argument too small in __ellint_rj
-15.6641, 0.126987, 0.385409
Argument too small in __ellint_rj
-15.6641, 0.135477, 0.385495
Argument too small in __ellint_rj
-15.6641, 0.221034, 0.386686
Argument too small in __ellint_rj
-15.6641, 0.308167, 0.388553
Argument too small in __ellint_rj
-15.6641, 0.632359, 0.403643
Argument too small in __ellint_rj
*** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***

##### Error Output For ellint_3 (complete) with compiler GNU C++ version 7.1.0 and library <cmath> and test data Complete Elliptic Integral PI: Mathworld Data

CAUTION: Gross error found at entry 3.
Found: 1.28255 Expected 2.22144 Error: 0.732051
0.5, 0, 2.22144
Argument too small in __ellint_rj
-4, 0.3, 0.712709
Argument too small in __ellint_rj
-100000, -0.5, 0.00496945
Argument too small in __ellint_rj
-1e+10, -0.75, 1.5708e-05
CAUTION: Gross error found at entry 8.
Found: 1.45615 Expected 101.045 Error: 68.3919
0.999023, -0.875, 101.045
Argument too small in __ellint_rj
-4.14952e+180, 0.5, 7.71119e-91

##### Error Output For ellint_3 with compiler GNU C++ version 7.1.0 and library <cmath> and test data Elliptic Integral PI: Large Random Data

Argument too small in __ellint_rj
-88.2952, -8.04919, 0.814724, -0.874724
Argument too small in __ellint_rj
-88.2952, -7.46026, 0.135477, -0.827189
Argument too small in __ellint_rj
-88.2952, -7.29046, 0.905792, -0.877476
Argument too small in __ellint_rj
-88.2952, -6.23236, 0.835009, -0.652152
Argument too small in __ellint_rj
-88.2952, -5.57932, 0.126987, -0.512276
Argument too small in __ellint_rj
-88.2952, -4.43004, 0.968868, -0.543324
Argument too small in __ellint_rj
-88.2952, -3.83666, 0.913376, -0.513389
Argument too small in __ellint_rj
-88.2952, 0.93763, 0.221034, 0.158243
Argument too small in __ellint_rj
-88.2952, 0.944412, 0.632359, 0.160101
Argument too small in __ellint_rj
-88.2952, 2.64719, 0.308167, 0.188127
Argument too small in __ellint_rj
-88.2952, 6.29447, 0.0975404, 0.676465
Argument too small in __ellint_rj
-88.2952, 6.70017, 0.547221, 0.817785
Argument too small in __ellint_rj
-88.2952, 8.11584, 0.278498, 0.837452
Argument too small in __ellint_rj
-88.2952, 8.26752, 0.188382, 0.837571
Argument too small in __ellint_rj
-88.2952, 9.15014, 0.546881, 0.885365
Argument too small in __ellint_rj
-88.2952, 9.29777, 0.992881, 1.06701
Argument too small in __ellint_rj
-88.2952, 9.3539, 0.957507, 1.03573
Argument too small in __ellint_rj
-88.2952, 9.37736, 0.996461, 1.13933
Argument too small in __ellint_rj
-88.2952, 9.85763, 0.964889, 1.24906
Argument too small in __ellint_rj
-88.2952, 9.92923, 0.967695, 1.25621
Argument too small in __ellint_rj
-86.8166, -8.04919, 0.157613, -0.841405
Argument too small in __ellint_rj
-86.8166, -7.46026, 0.725839, -0.859877
Argument too small in __ellint_rj
-86.8166, -7.29046, 0.970593, -0.914439
Argument too small in __ellint_rj
-86.8166, -6.23236, 0.98111, -0.710627
Argument too small in __ellint_rj
-86.8166, -5.57932, 0.957167, -0.58106
Argument too small in __ellint_rj
-86.8166, -4.43004, 0.109862, -0.499839
Argument too small in __ellint_rj
-86.8166, -3.83666, 0.485376, -0.494286
Argument too small in __ellint_rj
-86.8166, 0.93763, 0.798106, 0.162644
Argument too small in __ellint_rj
-86.8166, 0.944412, 0.80028, 0.16282
Argument too small in __ellint_rj
-86.8166, 2.64719, 0.297029, 0.18978
Argument too small in __ellint_rj
-86.8166, 6.29447, 0.141886, 0.682392
Argument too small in __ellint_rj
-86.8166, 6.70017, 0.00478348, 0.812885
Argument too small in __ellint_rj
-86.8166, 8.11584, 0.421761, 0.849249
Argument too small in __ellint_rj
-86.8166, 8.26752, 0.112465, 0.843648
Argument too small in __ellint_rj
-86.8166, 9.15014, 0.915736, 0.953733
Argument too small in __ellint_rj
-86.8166, 9.29777, 0.639763, 0.936743
Argument too small in __ellint_rj
-86.8166, 9.3539, 0.792207, 0.987359
Argument too small in __ellint_rj
-86.8166, 9.37736, 0.878431, 1.02525
Argument too small in __ellint_rj
-86.8166, 9.85763, 0.959492, 1.25508
Argument too small in __ellint_rj
-86.8166, 9.92923, 0.503663, 1.16735
Argument too small in __ellint_rj
-84.7616, -8.04919, 0.655741, -0.873305
Argument too small in __ellint_rj
-84.7616, -7.46026, 0.797929, -0.879044
Argument too small in __ellint_rj
-84.7616, -7.29046, 0.0357117, -0.840785
Argument too small in __ellint_rj
-84.7616, -6.23236, 0.361294, -0.635502
Argument too small in __ellint_rj
-84.7616, -5.57932, 0.849129, -0.558231
Argument too small in __ellint_rj
-84.7616, -4.43004, 0.211924, -0.506533
Argument too small in __ellint_rj
-84.7616, -3.83666, 0.933993, -0.527681
Argument too small in __ellint_rj
-84.7616, 0.93763, 0.68136, 0.163458
Argument too small in __ellint_rj
-84.7616, 0.944412, 0.678735, 0.163582
Argument too small in __ellint_rj
-84.7616, 2.64719, 0.398739, 0.193458
Argument too small in __ellint_rj
-84.7616, 6.29447, 0.75774, 0.716086
Argument too small in __ellint_rj
-84.7616, 6.70017, 0.740647, 0.847849
Argument too small in __ellint_rj
-84.7616, 8.11584, 0.743132, 0.883827
Argument too small in __ellint_rj
-84.7616, 8.26752, 0.474759, 0.864181
Argument too small in __ellint_rj
-84.7616, 9.15014, 0.392227, 0.895646
Argument too small in __ellint_rj
-84.7616, 9.29777, 0.422088, 0.933423
Argument too small in __ellint_rj
*** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***

##### Error Output For ellint_3 with compiler GNU C++ version 7.1.0 and library <cmath> and test data Elliptic Integral PI: Random Data

CAUTION: Gross error found at entry 150.
Found: 1.09748 Expected 1.76311 Error: 0.606506
0.546881, 1.27977, 0.349984, 1.76311
CAUTION: Gross error found at entry 151.
Found: 1.39529 Expected 2.4686 Error: 0.769232
0.546881, 1.31163, 0.907365, 2.4686
CAUTION: Gross error found at entry 152.
Found: 1.17627 Expected 2.03097 Error: 0.726615
0.546881, 1.42281, 0.196595, 2.03097
CAUTION: Gross error found at entry 153.
Found: 1.47192 Expected 2.76894 Error: 0.881179
0.546881, 1.43473, 0.848468, 2.76894
CAUTION: Gross error found at entry 154.
Found: 1.23674 Expected 2.22733 Error: 0.800966
0.546881, 1.50405, 0.251084, 2.22733
CAUTION: Gross error found at entry 155.
Found: 1.87704 Expected 3.98415 Error: 1.12257
0.546881, 1.51564, 0.955018, 3.98415
CAUTION: Gross error found at entry 156.
Found: 1.35817 Expected 2.53989 Error: 0.870091
0.546881, 1.52005, 0.616045, 2.53989
CAUTION: Gross error found at entry 157.
Found: 1.48427 Expected 2.87082 Error: 0.934166
0.546881, 1.52189, 0.778898, 2.87082
CAUTION: Gross error found at entry 158.
Found: 1.32687 Expected 2.48679 Error: 0.874176
0.546881, 1.55961, 0.473289, 2.48679
CAUTION: Gross error found at entry 159.
Found: 2.37485 Expected 5.58805 Error: 1.35301
0.546881, 1.56524, 0.98746, 5.58805
CAUTION: Gross error found at entry 170.
Found: 1.08889 Expected 1.74565 Error: 0.603142
0.547221, 1.27977, 0.285839, 1.74565
CAUTION: Gross error found at entry 171.
Found: 1.21346 Expected 2.03956 Error: 0.680778
0.547221, 1.31163, 0.67982, 2.03956
CAUTION: Gross error found at entry 172.
Found: 1.36407 Expected 2.48392 Error: 0.820965
0.547221, 1.42281, 0.7572, 2.48392
CAUTION: Gross error found at entry 173.
Found: 1.21442 Expected 2.12881 Error: 0.752947
0.547221, 1.43473, 0.39232, 2.12881
CAUTION: Gross error found at entry 174.
Found: 1.4409 Expected 2.74399 Error: 0.904352
0.547221, 1.50405, 0.753729, 2.74399
CAUTION: Gross error found at entry 175.
Found: 1.32796 Expected 2.46156 Error: 0.853642
0.547221, 1.51564, 0.561557, 2.46156
CAUTION: Gross error found at entry 176.
Found: 1.27163 Expected 2.32413 Error: 0.82767
0.547221, 1.52005, 0.380446, 2.32413
CAUTION: Gross error found at entry 177.
Found: 1.24298 Expected 2.25511 Error: 0.814274
0.547221, 1.52189, 0.208068, 2.25511
CAUTION: Gross error found at entry 178.
Found: 1.36528 Expected 2.58635 Error: 0.894379
0.547221, 1.55961, 0.567822, 2.58635
CAUTION: Gross error found at entry 179.
Found: 1.35151 Expected 2.55463 Error: 0.890206
0.547221, 1.56524, 0.527371, 2.55463
CAUTION: Gross error found at entry 189.
Found: 1.01047 Expected 1.52344 Error: 0.507658
0.632359, 0.993308, 0.964966, 1.52344
CAUTION: Gross error found at entry 190.
Found: 1.05231 Expected 1.84135 Error: 0.749817
0.632359, 1.27977, 0.129906, 1.84135
CAUTION: Gross error found at entry 191.
Found: 1.07393 Expected 1.92224 Error: 0.789918
0.632359, 1.31163, 0.154438, 1.92224
CAUTION: Gross error found at entry 192.
Found: 1.22616 Expected 2.43657 Error: 0.987156
0.632359, 1.42281, 0.568824, 2.43657
CAUTION: Gross error found at entry 193.
Found: 1.18462 Expected 2.33142 Error: 0.968083
0.632359, 1.43473, 0.394908, 2.33142
CAUTION: Gross error found at entry 194.
Found: 1.25094 Expected 2.59169 Error: 1.0718
0.632359, 1.50405, 0.469391, 2.59169
CAUTION: Gross error found at entry 195.
Found: 1.23693 Expected 2.56158 Error: 1.07091
0.632359, 1.51564, 0.387296, 2.56158
CAUTION: Gross error found at entry 196.
Found: 1.19839 Expected 2.45293 Error: 1.04685
0.632359, 1.52005, 0.0119021, 2.45293
CAUTION: Gross error found at entry 197.
Found: 1.39415 Expected 3.05228 Error: 1.18935
0.632359, 1.52189, 0.726955, 3.05228
CAUTION: Gross error found at entry 198.
Found: 1.25489 Expected 2.6569 Error: 1.11723
0.632359, 1.55961, 0.337123, 2.6569
CAUTION: Gross error found at entry 199.
Found: 1.27021 Expected 2.70857 Error: 1.13237
0.632359, 1.56524, 0.38857, 2.70857
CAUTION: Gross error found at entry 209.
Found: 0.83304 Expected 1.35947 Error: 0.631944
0.814724, 0.993308, 0.119547, 1.35947
CAUTION: Gross error found at entry 210.
Found: 1.07764 Expected 2.50291 Error: 1.32258
*** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***

##### Error Output For ellint_3 with compiler GNU C++ version 7.1.0 and library <cmath> and test data Elliptic Integral PI: Mathworld Data

CAUTION: Gross error found at entry 0.
Found: -0.809353 Expected -1.55741 Error: 0.924263
1, -1, 0, -1.55741
CAUTION: Gross error found at entry 11.
Found: 1.07555 Expected 13.2822 Error: 11.3492
0.999023, 1.5, 0, 13.2822
CAUTION: Gross error found at entry 13.
Found: -5.86896e+09 Expected 1.53659e+10 Error: 1.18973e+4932
0.5, 1e+10, 0.5, 1.53659e+10
Argument too small in __ellint_rj
-100000, 10, 0.75, 0.0347926
Argument too small in __ellint_rj
-1e+10, 10, 0.875, 0.000109956
Argument too small in __ellint_rj
-1e+10, 1e+20, 0.875, 1.00001e+15
Argument too small in __ellint_rj
-1e+10, 1.57031, 0.875, 1.57081e-05
CAUTION: Gross error found at entry 18.
Found: -6.25413e+09 Expected 6.43274e+21 Error: 1.18973e+4932
0.999023, 1e+20, 0.875, 6.43274e+21
CAUTION: Gross error found at entry 19.
Found: 0.102424 Expected 0.196321 Error: 0.916748
50, 0.125, 0.25, 0.196321
CAUTION: Gross error found at entry 20.
Found: 0.798807 Expected 1.773 Error: 1.21956
1.125, 1, 0.25, 1.773
CAUTION: Gross error found at entry 21.
Found: 7.07138 Expected 0.662468 Error: 9.6743
1.125, 10, 0.25, 0.662468
CAUTION: Gross error found at entry 22.
Found: 2.04288 Expected -0.142697 Error: 1.18973e+4932
1.125, 3, 0.25, -0.142697
CAUTION: Gross error found at entry 23.
Found: 1.07762 Expected 22.2699 Error: 19.6659
1.00391, 1.5, 0.125, 22.2699
CAUTION: Gross error found at entry 24.
Found: 15.1275 Expected -0.535406 Error: 1.18973e+4932
1.00391, 21.5, 0.125, -0.535406
CAUTION: Gross error found at entry 41.
Found: 1.57454 Expected 3.0338 Error: 0.926787
0.5, 2, 0, 3.0338
CAUTION: Gross error found at entry 42.
Found: 3.0338 Expected 1.57454 Error: 0.926787
-0.5, 2, 0, 1.57454
CAUTION: Gross error found at entry 43.
Found: -1.57454 Expected -3.0338 Error: 0.926787
0.5, -2, 0, -3.0338
CAUTION: Gross error found at entry 44.
Found: -3.0338 Expected -1.57454 Error: 0.926787
-0.5, -2, 0, -1.57454
CAUTION: Found non-finite result, when a finite value was expected at entry 51
Found: inf Expected -2.87535 Error: 1.18973e+4932
1, 2, 0.5, -2.87535
CAUTION: Gross error found at entry 51.
Found: inf Expected -2.87535 Error: 1.18973e+4932
1, 2, 0.5, -2.87535
CAUTION: Found non-finite result, when a finite value was expected at entry 52
Found: -inf Expected 2.87535 Error: 1.18973e+4932
1, -2, 0.5, 2.87535
CAUTION: Gross error found at entry 52.
Found: -inf Expected 2.87535 Error: 1.18973e+4932
1, -2, 0.5, 2.87535
CAUTION: Found non-finite result, when a finite value was expected at entry 53
Found: inf Expected -2.18504 Error: 1.18973e+4932
1, 2, 6.22302e-61, -2.18504
CAUTION: Gross error found at entry 53.
Found: inf Expected -2.18504 Error: 1.18973e+4932
1, 2, 6.22302e-61, -2.18504
CAUTION: Found non-finite result, when a finite value was expected at entry 54
Found: -inf Expected 2.18504 Error: 1.18973e+4932
1, -2, 6.22302e-61, 2.18504
CAUTION: Gross error found at entry 54.
Found: -inf Expected 2.18504 Error: 1.18973e+4932
1, -2, 6.22302e-61, 2.18504
CAUTION: Gross error found at entry 57.
Found: 0.703907 Expected 0.000975941 Error: 720.259
20, 3.14257, 0.5, 0.000975941
CAUTION: Gross error found at entry 58.
Found: -0.703907 Expected -0.000975941 Error: 720.259
20, -3.14257, 0.5, -0.000975941
CAUTION: Gross error found at entry 59.
Found: 1.24445 Expected -27.1647 Error: 1.18973e+4932
1.01562, 1.6958, 0.5, -27.1647
CAUTION: Gross error found at entry 60.
Found: -1.24445 Expected 27.1647 Error: 1.18973e+4932
1.01562, -1.6958, 0.5, 27.1647

##### Error Output For expint (Ei) with compiler GNU C++ version 7.1.0 and library <cmath> and test data Exponential Integral Ei

Continued fraction failed in __expint_En_cont_frac.
-1.30539, -0.134326

##### Error Output For ibeta with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data Incomplete Beta Function: Large and Diverse Values

underflow
1.04761e-05, 39078.2, 0.913384, 95444.4, 0, 1, 0
underflow
1.2158e-05, 24110.5, 0.135563, 82239.7, 0, 1, 0
underflow
1.30342e-05, 26168.3, 0.127074, 76710.7, 0, 1, 0
underflow
1.51962e-05, 16177.5, 0.814742, 65795.4, 0, 1, 0
underflow
1.64873e-05, 470997, 0.127074, 60639.1, 0, 1, 0
underflow
1.66259e-05, 147819, 0.632396, 60134.5, 0, 1, 0
underflow
1.78638e-05, 439.387, 0.835025, 55972.4, 0, 1, 0
underflow
2.00434e-05, 482.007, 0.905801, 49885.1, 0, 1, 0
underflow
2.05189e-05, 236088, 0.835025, 48722.7, 0, 1, 0
underflow
2.14336e-05, 3719.28, 0.814742, 46647, 0, 1, 0
underflow
2.24486e-05, 445071, 0.221112, 44532.6, 0, 1, 0
underflow
2.34849e-05, 25542.8, 0.968871, 42569.8, 0, 1, 0
underflow
2.39993e-05, 462.946, 0.814742, 41661.1, 0, 1, 0
underflow
2.52178e-05, 1832.27, 0.913384, 39646.4, 0, 1, 0
underflow
2.87756e-05, 25491.8, 0.905801, 34740.9, 0, 1, 0
underflow
2.89316e-05, 494.984, 0.968871, 34557.6, 0, 1, 0
underflow
3.11413e-05, 348144, 0.308236, 32098.3, 0, 1, 0
underflow
3.12319e-05, 33713, 0.221112, 32007.5, 0, 1, 0
underflow
3.19889e-05, 3931.19, 0.308236, 31251.9, 0, 1, 0
underflow
3.27129e-05, 3109.49, 0.968871, 30560.4, 0, 1, 0
underflow
3.27529e-05, 25796.3, 0.835025, 30520.9, 0, 1, 0
underflow
3.34106e-05, 3378.01, 0.221112, 29922, 0, 1, 0
underflow
3.40793e-05, 288783, 0.814742, 29330.2, 0, 1, 0
underflow
3.46418e-05, 411.559, 0.913384, 28860.3, 0, 1, 0
underflow
3.61632e-05, 311937, 0.905801, 27639.2, 0, 1, 0
underflow
3.75686e-05, 386440, 0.913384, 26604.5, 0, 1, 0
underflow
3.99261e-05, 495352, 0.968871, 25032.6, 0, 1, 0
underflow
4.01492e-05, 3246.23, 0.905801, 24898.5, 0, 1, 0
underflow
4.0288e-05, 2569.28, 0.835025, 24812.9, 0, 1, 0
underflow
4.11667e-05, 24253.8, 0.308236, 24280.8, 0, 1, 0
underflow
4.17714e-05, 274447, 0.135563, 23926.7, 0, 1, 0
underflow
4.66877e-05, 3780.93, 0.632396, 21410.1, 0, 1, 0
underflow
4.73604e-05, 48598.7, 0.632396, 21103.3, 0, 1, 0
underflow
0.00013245, 251.768, 0.968871, 7543.9, 0, 1, 0
underflow
0.000168283, 195801, 0.905801, 5929.61, 0, 1, 0
underflow
0.000177906, 276489, 0.814742, 5607.86, 0, 1, 0
underflow
0.000183097, 316055, 0.127074, 5448.36, 0, 1, 0
underflow
0.000190369, 159132, 0.835025, 5240.42, 0, 1, 0
underflow
0.000191066, 419861, 0.913384, 5220.29, 0, 1, 0
underflow
0.000192195, 177798, 0.308236, 5190.39, 0, 1, 0
underflow
0.000220499, 107380, 0.135563, 4523.03, 0, 1, 0
underflow
0.00022254, 1432.25, 0.814742, 4485.74, 0, 1, 0
underflow
0.000240291, 49604.4, 0.632396, 4150.25, 0, 1, 0
underflow
0.000251444, 15605.8, 0.135563, 3966.81, 0, 1, 0
underflow
0.000274279, 289206, 0.968871, 3632.79, 0, 1, 0
underflow
0.000274343, 2954.47, 0.308236, 3636.51, 0, 1, 0
underflow
0.000278714, 4023.16, 0.632396, 3579.05, 0, 1, 0
underflow
0.000288369, 460073, 0.221112, 3454.19, 0, 1, 0
underflow
0.000294717, 4642.26, 0.221112, 3384.08, 0, 1, 0
underflow
0.000303403, 2574.36, 0.835025, 3287.52, 0, 1, 0
underflow
0.000304309, 4480.75, 0.905801, 3277.17, 0, 1, 0
underflow
0.00031313, 47957, 0.308236, 3182.22, 0, 1, 0
underflow
0.000320063, 25544.6, 0.905801, 3113.68, 0, 1, 0
underflow
0.000334818, 29065.5, 0.968871, 2975.86, 0, 1, 0
underflow
0.00034899, 41187.6, 0.913384, 2854.23, 0, 1, 0
underflow
0.000350247, 426.308, 0.905801, 2848.5, 0, 1, 0
underflow
0.000357727, 31752.2, 0.127074, 2784.5, 0, 1, 0
underflow
0.000412091, 367.714, 0.913384, 2420.17, 0, 1, 0
underflow
0.000417933, 4668.47, 0.968871, 2383.72, 0, 1, 0
underflow
0.000424632, 17994.9, 0.221112, 2344.63, 0, 1, 0
underflow
0.000427051, 2443.44, 0.913384, 2333.28, 0, 1, 0
underflow
0.000437724, 454399, 0.632396, 2270.98, 0, 1, 0
underflow
0.000450377, 10660.8, 0.835025, 2210.53, 0, 1, 0
underflow
0.000475601, 19603, 0.814742, 2092.17, 0, 1, 0
underflow
0.00116972, 4487.22, 0.221112, 845.964, 0, 1, 0
underflow
0.00124188, 211066, 0.632396, 792.493, 0, 1, 0
underflow
0.00128578, 4738.41, 0.308236, 768.75, 0, 1, 0
underflow
0.00133388, 46277.8, 0.913384, 738.46, 0, 1, 0
underflow
0.00138692, 2158.76, 0.814742, 712.816, 0, 1, 0
underflow
0.00153268, 13060.2, 0.968871, 642.474, 0, 1, 0
underflow
0.00159946, 1780.43, 0.968871, 617.202, 0, 1, 0
*** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***

##### Error Output For jacobi_dn with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data Jacobi Elliptic: Modulus near 1

|m| > 1.0
-4.0246, 1, -0.999361, 0.0357365, 0.0357231
|m| > 1.0
-4.0246, 1, -0.999361, 0.0357497, 0.0357097
|m| > 1.0
-4.0246, 1, -0.99936, 0.0357762, 0.0356829
|m| > 1.0
-4.0246, 1, -0.999359, 0.0357895, 0.0356695
|m| > 1.0
-4.0246, 1.00001, -0.999354, 0.0359354, 0.0355222
|m| > 1.0
-4.0246, 1.00003, -0.999347, 0.0361343, 0.0353212
|m| > 1.0
-4.0246, 1.00004, -0.999343, 0.036247, 0.0352073
|m| > 1.0
-4.0246, 1.0001, -0.999311, 0.0371157, 0.0343296
|m| > 1.0
-4.0246, 1.00016, -0.99928, 0.0379513, 0.0334851
|m| > 1.0
-4.0246, 1.00027, -0.999221, 0.0394571, 0.0319634
|m| > 1.0
-4.0246, 1.00076, -0.99893, 0.0462407, 0.0251046
|m| > 1.0
-4.0246, 1.00125, -0.998589, 0.0531109, 0.0181532
|m| > 1.0
-4.0246, 1.00232, -0.99768, 0.0680761, 0.0029944
|m| > 1.0
-4.0246, 1.00604, -0.992752, 0.120179, -0.049966
|m| > 1.0
-4.0246, 1.01557, -0.967356, 0.25342, -0.186698
|m| > 1.0
-4.0246, 1.03059, -0.890373, 0.455232, -0.397492
|m| > 1.0
-4.0246, 1.06239, -0.607191, 0.794556, -0.76412
|m| > 1.0
-3.73013, 1, -0.998849, 0.0479567, 0.0479467
|m| > 1.0
-3.73013, 1, -0.998849, 0.0479665, 0.0479367
|m| > 1.0
-3.73013, 1, -0.998848, 0.0479862, 0.0479167
|m| > 1.0
-3.73013, 1, -0.998848, 0.047996, 0.0479067
|m| > 1.0
-3.73013, 1.00001, -0.998842, 0.0481042, 0.0477966
|m| > 1.0
-3.73013, 1.00003, -0.998835, 0.0482517, 0.0476465
|m| > 1.0
-3.73013, 1.00004, -0.998831, 0.0483354, 0.0475615
|m| > 1.0
-3.73013, 1.0001, -0.9988, 0.0489797, 0.0469059
|m| > 1.0
-3.73013, 1.00016, -0.998769, 0.0495995, 0.0462752
|m| > 1.0
-3.73013, 1.00027, -0.998713, 0.0507164, 0.0451386
|m| > 1.0
-3.73013, 1.00076, -0.998445, 0.0557477, 0.0400164
|m| > 1.0
-3.73013, 1.00125, -0.998147, 0.0608429, 0.0348257
|m| > 1.0
-3.73013, 1.00232, -0.997409, 0.0719406, 0.0235071
|m| > 1.0
-3.73013, 1.00604, -0.993866, 0.110593, -0.016048
|m| > 1.0
-3.73013, 1.01557, -0.977708, 0.209971, -0.118704
|m| > 1.0
-3.73013, 1.03059, -0.931162, 0.364606, -0.281224
|m| > 1.0
-3.73013, 1.06239, -0.753495, 0.657453, -0.599326
|m| > 1.0
-3.64523, 1, -0.998637, 0.0521997, 0.0521906
|m| > 1.0
-3.64523, 1, -0.998636, 0.0522087, 0.0521814
|m| > 1.0
-3.64523, 1, -0.998635, 0.0522268, 0.052163
|m| > 1.0
-3.64523, 1, -0.998635, 0.0522358, 0.0521538
|m| > 1.0
-3.64523, 1.00001, -0.99863, 0.052335, 0.0520526
|m| > 1.0
-3.64523, 1.00003, -0.998622, 0.0524703, 0.0519145
|m| > 1.0
-3.64523, 1.00004, -0.998618, 0.052547, 0.0518363
|m| > 1.0
-3.64523, 1.0001, -0.998587, 0.0531379, 0.0512335
|m| > 1.0
-3.64523, 1.00016, -0.998557, 0.0537063, 0.0506536
|m| > 1.0
-3.64523, 1.00027, -0.998501, 0.0547305, 0.0496084
|m| > 1.0
-3.64523, 1.00076, -0.998238, 0.0593443, 0.0448986
|m| > 1.0
-3.64523, 1.00125, -0.997949, 0.0640165, 0.0401258
|m| > 1.0
-3.64523, 1.00232, -0.997244, 0.0741927, 0.0297191
|m| > 1.0
-3.64523, 1.00604, -0.993972, 0.109636, -0.00664888
|m| > 1.0
-3.64523, 1.01557, -0.979623, 0.200844, -0.101111
|m| > 1.0
-3.64523, 1.03059, -0.939163, 0.343472, -0.251382
|m| > 1.0
-3.64523, 1.06239, -0.784719, 0.619852, -0.552253
|m| > 1.0
-3.11618, 1, -0.996078, 0.0884811, 0.0884757
|m| > 1.0
-3.11618, 1, -0.996077, 0.0884863, 0.0884702
|m| > 1.0
-3.11618, 1, -0.996076, 0.0884967, 0.0884593
|m| > 1.0
-3.11618, 1, -0.996076, 0.0885019, 0.0884538
|m| > 1.0
-3.11618, 1.00001, -0.996071, 0.0885593, 0.0883936
|m| > 1.0
-3.11618, 1.00003, -0.996064, 0.0886376, 0.0883114
|m| > 1.0
-3.11618, 1.00004, -0.99606, 0.0886819, 0.0882648
|m| > 1.0
-3.11618, 1.0001, -0.99603, 0.0890236, 0.0879059
|m| > 1.0
-3.11618, 1.00016, -0.996, 0.0893523, 0.0875607
|m| > 1.0
-3.11618, 1.00027, -0.995947, 0.0899445, 0.0869386
|m| > 1.0
-3.11618, 1.00076, -0.995702, 0.092612, 0.0841353
|m| > 1.0
-3.11618, 1.00125, -0.995447, 0.0953126, 0.0812953
|m| > 1.0
-3.11618, 1.00232, -0.994867, 0.101193, 0.0751049
|m| > 1.0
-3.11618, 1.00604, -0.992571, 0.121667, 0.0534858
|m| > 1.0
-3.11618, 1.01557, -0.984666, 0.174451, -0.00273723
|m| > 1.0
-3.11618, 1.03059, -0.966077, 0.258253, -0.0934336
|m| > 1.0
-3.11618, 1.06239, -0.901067, 0.433681, -0.289151
|m| > 1.0
-2.78966, 1, -0.992478, 0.122424, 0.12242
|m| > 1.0
-2.78966, 1, -0.992477, 0.122428, 0.122416
*** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***

##### Error Output For jacobi_cn with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data Jacobi Elliptic: Modulus near 1

|m| > 1.0
-4.0246, 1, -0.999361, 0.0357365, 0.0357231
|m| > 1.0
-4.0246, 1, -0.999361, 0.0357497, 0.0357097
|m| > 1.0
-4.0246, 1, -0.99936, 0.0357762, 0.0356829
|m| > 1.0
-4.0246, 1, -0.999359, 0.0357895, 0.0356695
|m| > 1.0
-4.0246, 1.00001, -0.999354, 0.0359354, 0.0355222
|m| > 1.0
-4.0246, 1.00003, -0.999347, 0.0361343, 0.0353212
|m| > 1.0
-4.0246, 1.00004, -0.999343, 0.036247, 0.0352073
|m| > 1.0
-4.0246, 1.0001, -0.999311, 0.0371157, 0.0343296
|m| > 1.0
-4.0246, 1.00016, -0.99928, 0.0379513, 0.0334851
|m| > 1.0
-4.0246, 1.00027, -0.999221, 0.0394571, 0.0319634
|m| > 1.0
-4.0246, 1.00076, -0.99893, 0.0462407, 0.0251046
|m| > 1.0
-4.0246, 1.00125, -0.998589, 0.0531109, 0.0181532
|m| > 1.0
-4.0246, 1.00232, -0.99768, 0.0680761, 0.0029944
|m| > 1.0
-4.0246, 1.00604, -0.992752, 0.120179, -0.049966
|m| > 1.0
-4.0246, 1.01557, -0.967356, 0.25342, -0.186698
|m| > 1.0
-4.0246, 1.03059, -0.890373, 0.455232, -0.397492
|m| > 1.0
-4.0246, 1.06239, -0.607191, 0.794556, -0.76412
|m| > 1.0
-3.73013, 1, -0.998849, 0.0479567, 0.0479467
|m| > 1.0
-3.73013, 1, -0.998849, 0.0479665, 0.0479367
|m| > 1.0
-3.73013, 1, -0.998848, 0.0479862, 0.0479167
|m| > 1.0
-3.73013, 1, -0.998848, 0.047996, 0.0479067
|m| > 1.0
-3.73013, 1.00001, -0.998842, 0.0481042, 0.0477966
|m| > 1.0
-3.73013, 1.00003, -0.998835, 0.0482517, 0.0476465
|m| > 1.0
-3.73013, 1.00004, -0.998831, 0.0483354, 0.0475615
|m| > 1.0
-3.73013, 1.0001, -0.9988, 0.0489797, 0.0469059
|m| > 1.0
-3.73013, 1.00016, -0.998769, 0.0495995, 0.0462752
|m| > 1.0
-3.73013, 1.00027, -0.998713, 0.0507164, 0.0451386
|m| > 1.0
-3.73013, 1.00076, -0.998445, 0.0557477, 0.0400164
|m| > 1.0
-3.73013, 1.00125, -0.998147, 0.0608429, 0.0348257
|m| > 1.0
-3.73013, 1.00232, -0.997409, 0.0719406, 0.0235071
|m| > 1.0
-3.73013, 1.00604, -0.993866, 0.110593, -0.016048
|m| > 1.0
-3.73013, 1.01557, -0.977708, 0.209971, -0.118704
|m| > 1.0
-3.73013, 1.03059, -0.931162, 0.364606, -0.281224
|m| > 1.0
-3.73013, 1.06239, -0.753495, 0.657453, -0.599326
|m| > 1.0
-3.64523, 1, -0.998637, 0.0521997, 0.0521906
|m| > 1.0
-3.64523, 1, -0.998636, 0.0522087, 0.0521814
|m| > 1.0
-3.64523, 1, -0.998635, 0.0522268, 0.052163
|m| > 1.0
-3.64523, 1, -0.998635, 0.0522358, 0.0521538
|m| > 1.0
-3.64523, 1.00001, -0.99863, 0.052335, 0.0520526
|m| > 1.0
-3.64523, 1.00003, -0.998622, 0.0524703, 0.0519145
|m| > 1.0
-3.64523, 1.00004, -0.998618, 0.052547, 0.0518363
|m| > 1.0
-3.64523, 1.0001, -0.998587, 0.0531379, 0.0512335
|m| > 1.0
-3.64523, 1.00016, -0.998557, 0.0537063, 0.0506536
|m| > 1.0
-3.64523, 1.00027, -0.998501, 0.0547305, 0.0496084
|m| > 1.0
-3.64523, 1.00076, -0.998238, 0.0593443, 0.0448986
|m| > 1.0
-3.64523, 1.00125, -0.997949, 0.0640165, 0.0401258
|m| > 1.0
-3.64523, 1.00232, -0.997244, 0.0741927, 0.0297191
|m| > 1.0
-3.64523, 1.00604, -0.993972, 0.109636, -0.00664888
|m| > 1.0
-3.64523, 1.01557, -0.979623, 0.200844, -0.101111
|m| > 1.0
-3.64523, 1.03059, -0.939163, 0.343472, -0.251382
|m| > 1.0
-3.64523, 1.06239, -0.784719, 0.619852, -0.552253
|m| > 1.0
-3.11618, 1, -0.996078, 0.0884811, 0.0884757
|m| > 1.0
-3.11618, 1, -0.996077, 0.0884863, 0.0884702
|m| > 1.0
-3.11618, 1, -0.996076, 0.0884967, 0.0884593
|m| > 1.0
-3.11618, 1, -0.996076, 0.0885019, 0.0884538
|m| > 1.0
-3.11618, 1.00001, -0.996071, 0.0885593, 0.0883936
|m| > 1.0
-3.11618, 1.00003, -0.996064, 0.0886376, 0.0883114
|m| > 1.0
-3.11618, 1.00004, -0.99606, 0.0886819, 0.0882648
|m| > 1.0
-3.11618, 1.0001, -0.99603, 0.0890236, 0.0879059
|m| > 1.0
-3.11618, 1.00016, -0.996, 0.0893523, 0.0875607
|m| > 1.0
-3.11618, 1.00027, -0.995947, 0.0899445, 0.0869386
|m| > 1.0
-3.11618, 1.00076, -0.995702, 0.092612, 0.0841353
|m| > 1.0
-3.11618, 1.00125, -0.995447, 0.0953126, 0.0812953
|m| > 1.0
-3.11618, 1.00232, -0.994867, 0.101193, 0.0751049
|m| > 1.0
-3.11618, 1.00604, -0.992571, 0.121667, 0.0534858
|m| > 1.0
-3.11618, 1.01557, -0.984666, 0.174451, -0.00273723
|m| > 1.0
-3.11618, 1.03059, -0.966077, 0.258253, -0.0934336
|m| > 1.0
-3.11618, 1.06239, -0.901067, 0.433681, -0.289151
|m| > 1.0
-2.78966, 1, -0.992478, 0.122424, 0.12242
|m| > 1.0
-2.78966, 1, -0.992477, 0.122428, 0.122416
*** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***

##### Error Output For jacobi_sn with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data Jacobi Elliptic: Modulus near 1

|m| > 1.0
-4.0246, 1, -0.999361, 0.0357365, 0.0357231
|m| > 1.0
-4.0246, 1, -0.999361, 0.0357497, 0.0357097
|m| > 1.0
-4.0246, 1, -0.99936, 0.0357762, 0.0356829
|m| > 1.0
-4.0246, 1, -0.999359, 0.0357895, 0.0356695
|m| > 1.0
-4.0246, 1.00001, -0.999354, 0.0359354, 0.0355222
|m| > 1.0
-4.0246, 1.00003, -0.999347, 0.0361343, 0.0353212
|m| > 1.0
-4.0246, 1.00004, -0.999343, 0.036247, 0.0352073
|m| > 1.0
-4.0246, 1.0001, -0.999311, 0.0371157, 0.0343296
|m| > 1.0
-4.0246, 1.00016, -0.99928, 0.0379513, 0.0334851
|m| > 1.0
-4.0246, 1.00027, -0.999221, 0.0394571, 0.0319634
|m| > 1.0
-4.0246, 1.00076, -0.99893, 0.0462407, 0.0251046
|m| > 1.0
-4.0246, 1.00125, -0.998589, 0.0531109, 0.0181532
|m| > 1.0
-4.0246, 1.00232, -0.99768, 0.0680761, 0.0029944
|m| > 1.0
-4.0246, 1.00604, -0.992752, 0.120179, -0.049966
|m| > 1.0
-4.0246, 1.01557, -0.967356, 0.25342, -0.186698
|m| > 1.0
-4.0246, 1.03059, -0.890373, 0.455232, -0.397492
|m| > 1.0
-4.0246, 1.06239, -0.607191, 0.794556, -0.76412
|m| > 1.0
-3.73013, 1, -0.998849, 0.0479567, 0.0479467
|m| > 1.0
-3.73013, 1, -0.998849, 0.0479665, 0.0479367
|m| > 1.0
-3.73013, 1, -0.998848, 0.0479862, 0.0479167
|m| > 1.0
-3.73013, 1, -0.998848, 0.047996, 0.0479067
|m| > 1.0
-3.73013, 1.00001, -0.998842, 0.0481042, 0.0477966
|m| > 1.0
-3.73013, 1.00003, -0.998835, 0.0482517, 0.0476465
|m| > 1.0
-3.73013, 1.00004, -0.998831, 0.0483354, 0.0475615
|m| > 1.0
-3.73013, 1.0001, -0.9988, 0.0489797, 0.0469059
|m| > 1.0
-3.73013, 1.00016, -0.998769, 0.0495995, 0.0462752
|m| > 1.0
-3.73013, 1.00027, -0.998713, 0.0507164, 0.0451386
|m| > 1.0
-3.73013, 1.00076, -0.998445, 0.0557477, 0.0400164
|m| > 1.0
-3.73013, 1.00125, -0.998147, 0.0608429, 0.0348257
|m| > 1.0
-3.73013, 1.00232, -0.997409, 0.0719406, 0.0235071
|m| > 1.0
-3.73013, 1.00604, -0.993866, 0.110593, -0.016048
|m| > 1.0
-3.73013, 1.01557, -0.977708, 0.209971, -0.118704
|m| > 1.0
-3.73013, 1.03059, -0.931162, 0.364606, -0.281224
|m| > 1.0
-3.73013, 1.06239, -0.753495, 0.657453, -0.599326
|m| > 1.0
-3.64523, 1, -0.998637, 0.0521997, 0.0521906
|m| > 1.0
-3.64523, 1, -0.998636, 0.0522087, 0.0521814
|m| > 1.0
-3.64523, 1, -0.998635, 0.0522268, 0.052163
|m| > 1.0
-3.64523, 1, -0.998635, 0.0522358, 0.0521538
|m| > 1.0
-3.64523, 1.00001, -0.99863, 0.052335, 0.0520526
|m| > 1.0
-3.64523, 1.00003, -0.998622, 0.0524703, 0.0519145
|m| > 1.0
-3.64523, 1.00004, -0.998618, 0.052547, 0.0518363
|m| > 1.0
-3.64523, 1.0001, -0.998587, 0.0531379, 0.0512335
|m| > 1.0
-3.64523, 1.00016, -0.998557, 0.0537063, 0.0506536
|m| > 1.0
-3.64523, 1.00027, -0.998501, 0.0547305, 0.0496084
|m| > 1.0
-3.64523, 1.00076, -0.998238, 0.0593443, 0.0448986
|m| > 1.0
-3.64523, 1.00125, -0.997949, 0.0640165, 0.0401258
|m| > 1.0
-3.64523, 1.00232, -0.997244, 0.0741927, 0.0297191
|m| > 1.0
-3.64523, 1.00604, -0.993972, 0.109636, -0.00664888
|m| > 1.0
-3.64523, 1.01557, -0.979623, 0.200844, -0.101111
|m| > 1.0
-3.64523, 1.03059, -0.939163, 0.343472, -0.251382
|m| > 1.0
-3.64523, 1.06239, -0.784719, 0.619852, -0.552253
|m| > 1.0
-3.11618, 1, -0.996078, 0.0884811, 0.0884757
|m| > 1.0
-3.11618, 1, -0.996077, 0.0884863, 0.0884702
|m| > 1.0
-3.11618, 1, -0.996076, 0.0884967, 0.0884593
|m| > 1.0
-3.11618, 1, -0.996076, 0.0885019, 0.0884538
|m| > 1.0
-3.11618, 1.00001, -0.996071, 0.0885593, 0.0883936
|m| > 1.0
-3.11618, 1.00003, -0.996064, 0.0886376, 0.0883114
|m| > 1.0
-3.11618, 1.00004, -0.99606, 0.0886819, 0.0882648
|m| > 1.0
-3.11618, 1.0001, -0.99603, 0.0890236, 0.0879059
|m| > 1.0
-3.11618, 1.00016, -0.996, 0.0893523, 0.0875607
|m| > 1.0
-3.11618, 1.00027, -0.995947, 0.0899445, 0.0869386
|m| > 1.0
-3.11618, 1.00076, -0.995702, 0.092612, 0.0841353
|m| > 1.0
-3.11618, 1.00125, -0.995447, 0.0953126, 0.0812953
|m| > 1.0
-3.11618, 1.00232, -0.994867, 0.101193, 0.0751049
|m| > 1.0
-3.11618, 1.00604, -0.992571, 0.121667, 0.0534858
|m| > 1.0
-3.11618, 1.01557, -0.984666, 0.174451, -0.00273723
|m| > 1.0
-3.11618, 1.03059, -0.966077, 0.258253, -0.0934336
|m| > 1.0
-3.11618, 1.06239, -0.901067, 0.433681, -0.289151
|m| > 1.0
-2.78966, 1, -0.992478, 0.122424, 0.12242
|m| > 1.0
-2.78966, 1, -0.992477, 0.122428, 0.122416
*** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***

##### Error Output For jacobi_dn with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data Jacobi Elliptic: Random Small Values

|m| > 1.0
1.65048e-12, 1.65574, 1.65048e-12, 1, 1
|m| > 1.0
2.06542e-12, 1.65574, 2.06542e-12, 1, 1
|m| > 1.0
6.93323e-12, 1.65574, 6.93323e-12, 1, 1
|m| > 1.0
1.33514e-11, 1.65574, 1.33514e-11, 1, 1
|m| > 1.0
1.63998e-11, 1.65574, 1.63998e-11, 1, 1
|m| > 1.0
5.73016e-11, 1.65574, 5.73016e-11, 1, 1
|m| > 1.0
1.11373e-10, 1.65574, 1.11373e-10, 1, 1
|m| > 1.0
1.42147e-10, 1.65574, 1.42147e-10, 1, 1
|m| > 1.0
3.80063e-10, 1.65574, 3.80063e-10, 1, 1
|m| > 1.0
6.09163e-10, 1.65574, 6.09163e-10, 1, 1
|m| > 1.0
1.02216e-09, 1.65574, 1.02216e-09, 1, 1
|m| > 1.0
2.88192e-09, 1.65574, 2.88192e-09, 1, 1
|m| > 1.0
4.76278e-09, 1.65574, 4.76278e-09, 1, 1
|m| > 1.0
8.85413e-09, 1.65574, 8.85413e-09, 1, 1
|m| > 1.0
2.30503e-08, 1.65574, 2.30503e-08, 1, 1
|m| > 1.0
5.93925e-08, 1.65574, 5.93925e-08, 1, 1
|m| > 1.0
1.16676e-07, 1.65574, 1.16676e-07, 1, 1
|m| > 1.0
2.37997e-07, 1.65574, 2.37997e-07, 1, 1
|m| > 1.0
4.68466e-07, 1.65574, 4.68466e-07, 1, 1
|m| > 1.0
9.3827e-07, 1.65574, 9.3827e-07, 1, 1
|m| > 1.0
1.10399e-06, 1.65574, 1.10399e-06, 1, 1
|m| > 1.0
3.29178e-06, 1.65574, 3.29178e-06, 1, 1
|m| > 1.0
7.51721e-06, 1.65574, 7.51721e-06, 1, 1
|m| > 1.0
1.51147e-05, 1.65574, 1.51147e-05, 1, 1
|m| > 1.0
2.9864e-05, 1.65574, 2.9864e-05, 1, 1
|m| > 1.0
3.38703e-05, 1.65574, 3.38703e-05, 1, 1
|m| > 1.0
9.06601e-05, 1.65574, 9.06601e-05, 1, 1
|m| > 1.0
0.000219495, 1.65574, 0.000219495, 1, 1
|m| > 1.0
0.000439522, 1.65574, 0.000439521, 1, 1
|m| > 1.0
0.000633315, 1.65574, 0.000633315, 1, 0.999999
|m| > 1.0
0.00111512, 1.65574, 0.00111512, 0.999999, 0.999998
|m| > 1.0
0.00196247, 1.65574, 0.00196246, 0.999998, 0.999995
|m| > 1.0
0.00555375, 1.65574, 0.00555365, 0.999985, 0.999958
|m| > 1.0
0.00869113, 1.65574, 0.00869072, 0.999962, 0.999896
|m| > 1.0
0.0299334, 1.65574, 0.0299166, 0.999552, 0.998772
|m| > 1.0
0.0512426, 1.65574, 0.0511588, 0.998691, 0.996406
|m| > 1.0
0.112013, 1.65574, 0.111143, 0.993804, 0.982922
|m| > 1.0
0.234804, 1.65574, 0.227, 0.973895, 0.926679
|m| > 1.0
0.489873, 1.65574, 0.425971, 0.904737, 0.708912
|m| > 1.0
0.751831, 1.65574, 0.553446, 0.832885, 0.400346
|m| > 1.0
1.65574, 1.65574, 0.408154, 0.912913, -0.737088

##### Error Output For jacobi_cn with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data Jacobi Elliptic: Random Small Values

|m| > 1.0
1.65048e-12, 1.65574, 1.65048e-12, 1, 1
|m| > 1.0
2.06542e-12, 1.65574, 2.06542e-12, 1, 1
|m| > 1.0
6.93323e-12, 1.65574, 6.93323e-12, 1, 1
|m| > 1.0
1.33514e-11, 1.65574, 1.33514e-11, 1, 1
|m| > 1.0
1.63998e-11, 1.65574, 1.63998e-11, 1, 1
|m| > 1.0
5.73016e-11, 1.65574, 5.73016e-11, 1, 1
|m| > 1.0
1.11373e-10, 1.65574, 1.11373e-10, 1, 1
|m| > 1.0
1.42147e-10, 1.65574, 1.42147e-10, 1, 1
|m| > 1.0
3.80063e-10, 1.65574, 3.80063e-10, 1, 1
|m| > 1.0
6.09163e-10, 1.65574, 6.09163e-10, 1, 1
|m| > 1.0
1.02216e-09, 1.65574, 1.02216e-09, 1, 1
|m| > 1.0
2.88192e-09, 1.65574, 2.88192e-09, 1, 1
|m| > 1.0
4.76278e-09, 1.65574, 4.76278e-09, 1, 1
|m| > 1.0
8.85413e-09, 1.65574, 8.85413e-09, 1, 1
|m| > 1.0
2.30503e-08, 1.65574, 2.30503e-08, 1, 1
|m| > 1.0
5.93925e-08, 1.65574, 5.93925e-08, 1, 1
|m| > 1.0
1.16676e-07, 1.65574, 1.16676e-07, 1, 1
|m| > 1.0
2.37997e-07, 1.65574, 2.37997e-07, 1, 1
|m| > 1.0
4.68466e-07, 1.65574, 4.68466e-07, 1, 1
|m| > 1.0
9.3827e-07, 1.65574, 9.3827e-07, 1, 1
|m| > 1.0
1.10399e-06, 1.65574, 1.10399e-06, 1, 1
|m| > 1.0
3.29178e-06, 1.65574, 3.29178e-06, 1, 1
|m| > 1.0
7.51721e-06, 1.65574, 7.51721e-06, 1, 1
|m| > 1.0
1.51147e-05, 1.65574, 1.51147e-05, 1, 1
|m| > 1.0
2.9864e-05, 1.65574, 2.9864e-05, 1, 1
|m| > 1.0
3.38703e-05, 1.65574, 3.38703e-05, 1, 1
|m| > 1.0
9.06601e-05, 1.65574, 9.06601e-05, 1, 1
|m| > 1.0
0.000219495, 1.65574, 0.000219495, 1, 1
|m| > 1.0
0.000439522, 1.65574, 0.000439521, 1, 1
|m| > 1.0
0.000633315, 1.65574, 0.000633315, 1, 0.999999
|m| > 1.0
0.00111512, 1.65574, 0.00111512, 0.999999, 0.999998
|m| > 1.0
0.00196247, 1.65574, 0.00196246, 0.999998, 0.999995
|m| > 1.0
0.00555375, 1.65574, 0.00555365, 0.999985, 0.999958
|m| > 1.0
0.00869113, 1.65574, 0.00869072, 0.999962, 0.999896
|m| > 1.0
0.0299334, 1.65574, 0.0299166, 0.999552, 0.998772
|m| > 1.0
0.0512426, 1.65574, 0.0511588, 0.998691, 0.996406
|m| > 1.0
0.112013, 1.65574, 0.111143, 0.993804, 0.982922
|m| > 1.0
0.234804, 1.65574, 0.227, 0.973895, 0.926679
|m| > 1.0
0.489873, 1.65574, 0.425971, 0.904737, 0.708912
|m| > 1.0
0.751831, 1.65574, 0.553446, 0.832885, 0.400346
|m| > 1.0
1.65574, 1.65574, 0.408154, 0.912913, -0.737088

##### Error Output For jacobi_sn with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data Jacobi Elliptic: Random Small Values

|m| > 1.0
1.65048e-12, 1.65574, 1.65048e-12, 1, 1
|m| > 1.0
2.06542e-12, 1.65574, 2.06542e-12, 1, 1
|m| > 1.0
6.93323e-12, 1.65574, 6.93323e-12, 1, 1
|m| > 1.0
1.33514e-11, 1.65574, 1.33514e-11, 1, 1
|m| > 1.0
1.63998e-11, 1.65574, 1.63998e-11, 1, 1
|m| > 1.0
5.73016e-11, 1.65574, 5.73016e-11, 1, 1
|m| > 1.0
1.11373e-10, 1.65574, 1.11373e-10, 1, 1
|m| > 1.0
1.42147e-10, 1.65574, 1.42147e-10, 1, 1
|m| > 1.0
3.80063e-10, 1.65574, 3.80063e-10, 1, 1
|m| > 1.0
6.09163e-10, 1.65574, 6.09163e-10, 1, 1
|m| > 1.0
1.02216e-09, 1.65574, 1.02216e-09, 1, 1
|m| > 1.0
2.88192e-09, 1.65574, 2.88192e-09, 1, 1
|m| > 1.0
4.76278e-09, 1.65574, 4.76278e-09, 1, 1
|m| > 1.0
8.85413e-09, 1.65574, 8.85413e-09, 1, 1
|m| > 1.0
2.30503e-08, 1.65574, 2.30503e-08, 1, 1
|m| > 1.0
5.93925e-08, 1.65574, 5.93925e-08, 1, 1
|m| > 1.0
1.16676e-07, 1.65574, 1.16676e-07, 1, 1
|m| > 1.0
2.37997e-07, 1.65574, 2.37997e-07, 1, 1
|m| > 1.0
4.68466e-07, 1.65574, 4.68466e-07, 1, 1
|m| > 1.0
9.3827e-07, 1.65574, 9.3827e-07, 1, 1
|m| > 1.0
1.10399e-06, 1.65574, 1.10399e-06, 1, 1
|m| > 1.0
3.29178e-06, 1.65574, 3.29178e-06, 1, 1
|m| > 1.0
7.51721e-06, 1.65574, 7.51721e-06, 1, 1
|m| > 1.0
1.51147e-05, 1.65574, 1.51147e-05, 1, 1
|m| > 1.0
2.9864e-05, 1.65574, 2.9864e-05, 1, 1
|m| > 1.0
3.38703e-05, 1.65574, 3.38703e-05, 1, 1
|m| > 1.0
9.06601e-05, 1.65574, 9.06601e-05, 1, 1
|m| > 1.0
0.000219495, 1.65574, 0.000219495, 1, 1
|m| > 1.0
0.000439522, 1.65574, 0.000439521, 1, 1
|m| > 1.0
0.000633315, 1.65574, 0.000633315, 1, 0.999999
|m| > 1.0
0.00111512, 1.65574, 0.00111512, 0.999999, 0.999998
|m| > 1.0
0.00196247, 1.65574, 0.00196246, 0.999998, 0.999995
|m| > 1.0
0.00555375, 1.65574, 0.00555365, 0.999985, 0.999958
|m| > 1.0
0.00869113, 1.65574, 0.00869072, 0.999962, 0.999896
|m| > 1.0
0.0299334, 1.65574, 0.0299166, 0.999552, 0.998772
|m| > 1.0
0.0512426, 1.65574, 0.0511588, 0.998691, 0.996406
|m| > 1.0
0.112013, 1.65574, 0.111143, 0.993804, 0.982922
|m| > 1.0
0.234804, 1.65574, 0.227, 0.973895, 0.926679
|m| > 1.0
0.489873, 1.65574, 0.425971, 0.904737, 0.708912
|m| > 1.0
0.751831, 1.65574, 0.553446, 0.832885, 0.400346
|m| > 1.0
1.65574, 1.65574, 0.408154, 0.912913, -0.737088

##### Error Output For jacobi_dn with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data Jacobi Elliptic: Mathworld Data

|m| > 1.0
2.98023e-08, 1.5, 2.98023e-08, 1, 1
|m| > 1.0
-2.98023e-08, 1.5, -2.98023e-08, 1, 1
|m| > 1.0
0.25, 1.5, 0.24183, 0.970319, 0.931888
|m| > 1.0
-0.25, 1.5, -0.24183, 0.970319, 0.931888
|m| > 1.0
1.25, 1.5, 0.665876, 0.746063, -0.0486921
|m| > 1.0
-1.25, 1.5, -0.665876, 0.746063, -0.0486921
|m| > 1.0
25, 1.5, 0.618665, 0.785655, 0.372585
|m| > 1.0
-25, 1.5, -0.618665, 0.785655, 0.372585

##### Error Output For jacobi_cn with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data Jacobi Elliptic: Mathworld Data

|m| > 1.0
2.98023e-08, 1.5, 2.98023e-08, 1, 1
|m| > 1.0
-2.98023e-08, 1.5, -2.98023e-08, 1, 1
|m| > 1.0
0.25, 1.5, 0.24183, 0.970319, 0.931888
|m| > 1.0
-0.25, 1.5, -0.24183, 0.970319, 0.931888
|m| > 1.0
1.25, 1.5, 0.665876, 0.746063, -0.0486921
|m| > 1.0
-1.25, 1.5, -0.665876, 0.746063, -0.0486921
|m| > 1.0
25, 1.5, 0.618665, 0.785655, 0.372585
|m| > 1.0
-25, 1.5, -0.618665, 0.785655, 0.372585

##### Error Output For jacobi_sn with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data Jacobi Elliptic: Mathworld Data

|m| > 1.0
2.98023e-08, 1.5, 2.98023e-08, 1, 1
|m| > 1.0
-2.98023e-08, 1.5, -2.98023e-08, 1, 1
|m| > 1.0
0.25, 1.5, 0.24183, 0.970319, 0.931888
|m| > 1.0
-0.25, 1.5, -0.24183, 0.970319, 0.931888
|m| > 1.0
1.25, 1.5, 0.665876, 0.746063, -0.0486921
|m| > 1.0
-1.25, 1.5, -0.665876, 0.746063, -0.0486921
|m| > 1.0
25, 1.5, 0.618665, 0.785655, 0.372585
|m| > 1.0
-25, 1.5, -0.618665, 0.785655, 0.372585

##### Error Output For polygamma with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data Mathematica Data - Large orders and other bug cases

underflow
168, 150, -6.52661e-66
underflow
169, 202, 9.2734e-88
domain error
20, -9.5, -0.00103076
domain error
21, -9.5, 4.28582e+26
domain error
22, -9.5, -0.00419144
domain error
23, -9.5, 8.6745e+29
domain error
24, -9.5, -0.0204825
domain error
25, -9.5, 2.08188e+33
domain error
26, -9.5, -0.118403
domain error
27, -9.5, 5.84592e+36
domain error
28, -9.5, -0.798969
domain error
29, -9.5, 1.89875e+40
domain error
30, -9.5, -6.22245
underflow
10, 1.32923e+36, -0
underflow
15, 1.32923e+36, 0

##### Error Output For polygamma with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data Mathematica Data - large negative arguments

domain error
124, -1.5, 7.63705e+240
domain error
124, -2.5, 7.63705e+240
domain error
124, -3.5, 7.63705e+240
domain error
124, -4.5, 7.63705e+240
domain error
124, -5.5, 7.63705e+240
domain error
124, -6.5, 7.63705e+240
domain error
124, -7.5, 7.63705e+240
domain error
124, -8.5, 7.63705e+240
domain error
124, -9.5, 7.63705e+240
domain error
124, -10.5, 7.63705e+240
domain error
124, -11.5, 7.63705e+240
domain error
124, -12.5, 7.63705e+240
domain error
124, -13.5, 7.63705e+240
domain error
124, -14.5, 7.63705e+240
domain error
124, -15.5, 7.63705e+240
domain error
124, -16.5, 7.63705e+240
domain error
124, -17.5, 7.63705e+240
domain error
124, -18.5, 7.63705e+240
domain error
124, -19.5, 7.63705e+240
domain error
124, -20.5, 7.63705e+240
domain error
124, -1.5, -7.63705e+240
domain error
124, -2.5, -7.63705e+240
domain error
124, -3.5, -7.63705e+240
domain error
124, -4.5, -7.63705e+240
domain error
124, -5.5, -7.63705e+240
domain error
124, -6.5, -7.63705e+240
domain error
124, -7.5, -7.63705e+240
domain error
124, -8.5, -7.63705e+240
domain error
124, -9.5, -7.63705e+240
domain error
124, -10.5, -7.63705e+240
domain error
124, -11.5, -7.63705e+240
domain error
124, -12.5, -7.63705e+240
domain error
124, -13.5, -7.63705e+240
domain error
124, -14.5, -7.63705e+240
domain error
124, -15.5, -7.63705e+240
domain error
124, -16.5, -7.63705e+240
domain error
124, -17.5, -7.63705e+240
domain error
124, -18.5, -7.63705e+240
domain error
124, -19.5, -7.63705e+240
domain error
124, -20.5, -7.63705e+240
domain error
2, -0.5, -0.828797
domain error
3, -0.5, 193.409
domain error
4, -0.5, -3.47425
domain error
5, -0.5, 15371.1
domain error
6, -0.5, -43.4579
domain error
7, -0.5, 2.58068e+06
domain error
8, -0.5, -1059.96
domain error
9, -0.5, 7.43185e+08
domain error
10, -0.5, -42108.9
domain error
11, -0.5, 3.26999e+11
domain error
12, -0.5, -2.46448e+06
domain error
13, -0.5, 2.04047e+14
domain error
14, -0.5, -1.9918e+08
domain error
15, -0.5, 1.71399e+17
domain error
16, -0.5, -2.12394e+10
domain error
17, -0.5, 1.86483e+20
domain error
18, -0.5, -2.88824e+12
domain error
19, -0.5, 2.55108e+23
domain error
20, -0.5, -4.87773e+14
domain error
21, -0.5, 4.28582e+26
domain error
2, -0.5, -0.828843
domain error
3, -0.5, 193.409
domain error
4, -0.5, -3.47791
domain error
5, -0.5, 15371.1
domain error
6, -0.5, -44.0732
domain error
7, -0.5, 2.58068e+06
domain error
8, -0.5, -1237.15
domain error
9, -0.5, 7.43185e+08
domain error
10, -0.5, -120071
domain error
11, -0.5, 3.26999e+11
domain error
12, -0.5, -5.11131e+07
domain error
13, -0.5, 2.04047e+14
domain error
14, -0.5, -4.1064e+10
domain error
15, -0.5, 1.71399e+17
domain error
16, -0.5, -4.44822e+13
domain error
17, -0.5, 1.86483e+20
domain error
18, -0.5, -6.08254e+16
domain error
19, -0.5, 2.55108e+23
domain error
20, -0.5, -1.02182e+20
domain error
21, -0.5, 4.28582e+26
domain error
2, -0.5, -0.828751
domain error
3, -0.5, 193.409
domain error
4, -0.5, -3.47059
domain error
5, -0.5, 15371.1
domain error
6, -0.5, -42.8426
domain error
7, -0.5, 2.58068e+06
domain error
8, -0.5, -882.773
domain error
9, -0.5, 7.43185e+08
domain error
10, -0.5, 35853.7
domain error
11, -0.5, 3.26999e+11
domain error
12, -0.5, 4.61841e+07
domain error
13, -0.5, 2.04047e+14
domain error
14, -0.5, 4.06656e+10
domain error
15, -0.5, 1.71399e+17
domain error
16, -0.5, 4.44397e+13
domain error
17, -0.5, 1.86483e+20
domain error
18, -0.5, 6.08197e+16
domain error
19, -0.5, 2.55108e+23
domain error
20, -0.5, 1.02181e+20
domain error
21, -0.5, 4.28582e+26

##### Error Output For polygamma with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data Mathematica Data - negative arguments

domain error
2, -12.75, -124.031
domain error
2, -12.25, 124.019
domain error
2, -11.75, -124.032
domain error
2, -11.25, 124.018
domain error
2, -10.75, -124.033
domain error
2, -10.25, 124.016
domain error
2, -9.75, -124.035
domain error
2, -9.25, 124.015
domain error
2, -8.75, -124.037
domain error
2, -8.25, 124.012
domain error
2, -7.75, -124.04
domain error
2, -7.25, 124.009
domain error
2, -6.75, -124.044
domain error
2, -6.25, 124.003
domain error
2, -5.75, -124.051
domain error
2, -5.25, 123.995
domain error
2, -4.75, -124.061
domain error
2, -4.25, 123.981
domain error
2, -3.75, -124.08
domain error
2, -3.25, 123.955
domain error
2, -2.75, -124.118
domain error
2, -2.25, 123.897
domain error
2, -1.75, -124.214
domain error
2, -1.25, 123.721
domain error
2, -0.75, -124.587
domain error
2, -0.25, 122.697
domain error
3, -12.75, 1558.54
domain error
3, -12.25, 1558.54
domain error
3, -11.75, 1558.54
domain error
3, -11.25, 1558.54
domain error
3, -10.75, 1558.54
domain error
3, -10.25, 1558.54
domain error
3, -9.75, 1558.54
domain error
3, -9.25, 1558.54
domain error
3, -8.75, 1558.54
domain error
3, -8.25, 1558.54
domain error
3, -7.75, 1558.54
domain error
3, -7.25, 1558.54
domain error
3, -6.75, 1558.54
domain error
3, -6.25, 1558.54
domain error
3, -5.75, 1558.54
domain error
3, -5.25, 1558.54
domain error
3, -4.75, 1558.53
domain error
3, -4.25, 1558.53
domain error
3, -3.75, 1558.52
domain error
3, -3.25, 1558.51
domain error
3, -2.75, 1558.49
domain error
3, -2.25, 1558.46
domain error
3, -1.75, 1558.38
domain error
3, -1.25, 1558.22
domain error
3, -0.75, 1557.75
domain error
3, -0.25, 1555.76
domain error
4, -12.75, -24481.6
domain error
4, -12.25, 24481.6
domain error
4, -11.75, -24481.6
domain error
4, -11.25, 24481.6
domain error
4, -10.75, -24481.6
domain error
4, -10.25, 24481.6
domain error
4, -9.75, -24481.6
domain error
4, -9.25, 24481.6
domain error
4, -8.75, -24481.6
domain error
4, -8.25, 24481.6
domain error
4, -7.75, -24481.6
domain error
4, -7.25, 24481.6
domain error
4, -6.75, -24481.6
domain error
4, -6.25, 24481.6
domain error
4, -5.75, -24481.6
domain error
4, -5.25, 24481.6
domain error
4, -4.75, -24481.6
domain error
4, -4.25, 24481.6
domain error
4, -3.75, -24481.6
domain error
4, -3.25, 24481.5
domain error
4, -2.75, -24481.6
domain error
4, -2.25, 24481.5
domain error
4, -1.75, -24481.8
domain error
4, -1.25, 24481.1
domain error
4, -0.75, -24483.2
domain error
4, -0.25, 24473.2
domain error
5, -12.75, 492231
domain error
5, -12.25, 492231
domain error
5, -11.75, 492231
domain error
5, -11.25, 492231
domain error
5, -10.75, 492231
domain error
5, -10.25, 492231
domain error
5, -9.75, 492231
domain error
5, -9.25, 492231
domain error
5, -8.75, 492231
domain error
5, -8.25, 492231
domain error
5, -7.75, 492231
domain error
5, -7.25, 492231
domain error
5, -6.75, 492231
domain error
5, -6.25, 492231
domain error
5, -5.75, 492231
domain error
5, -5.25, 492231
domain error
5, -4.75, 492231
domain error
5, -4.25, 492231
domain error
5, -3.75, 492231
domain error
5, -3.25, 492231
domain error
5, -2.75, 492231
domain error
5, -2.25, 492231
domain error
5, -1.75, 492231
domain error
5, -1.25, 492230
domain error
5, -0.75, 492227
domain error
5, -0.25, 492199
domain error
6, -12.75, -1.17912e+07
domain error
6, -12.25, 1.17912e+07
domain error
6, -11.75, -1.17912e+07
domain error
6, -11.25, 1.17912e+07
domain error
6, -10.75, -1.17912e+07
domain error
6, -10.25, 1.17912e+07
domain error
6, -9.75, -1.17912e+07
domain error
6, -9.25, 1.17912e+07
domain error
6, -8.75, -1.17912e+07
domain error
6, -8.25, 1.17912e+07
domain error
6, -7.75, -1.17912e+07
domain error
6, -7.25, 1.17912e+07
domain error
6, -6.75, -1.17912e+07
domain error
6, -6.25, 1.17912e+07
domain error
6, -5.75, -1.17912e+07
domain error
6, -5.25, 1.17912e+07
domain error
6, -4.75, -1.17912e+07
domain error
6, -4.25, 1.17912e+07
domain error
6, -3.75, -1.17912e+07
domain error
6, -3.25, 1.17912e+07
domain error
6, -2.75, -1.17912e+07
domain error
6, -2.25, 1.17912e+07
domain error
6, -1.75, -1.17912e+07
domain error
6, -1.25, 1.17912e+07
*** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***

##### Error Output For polygamma with compiler GNU C++ version 7.1.0 and library GSL 2.1 and test data Mathematica Data - large arguments

underflow
30, 8.58993e+09, -8.44974e-268
underflow
30, 1.71799e+10, -7.86943e-277
underflow
30, 3.43597e+10, -7.32898e-286
underflow
30, 6.87195e+10, -6.82564e-295
underflow
30, 1.37439e+11, -6.35687e-304
underflow
30, 2.74878e+11, -5.9203e-313
underflow
30, 5.49756e+11, -5.53354e-322
underflow
30, 1.09951e+12, -0
underflow
30, 2.19902e+12, -0
underflow
30, 4.39805e+12, -0
underflow
30, 8.79609e+12, -0
underflow
30, 1.75922e+13, -0
underflow
30, 3.51844e+13, -0
underflow
30, 7.03687e+13, -0
underflow
30, 1.40737e+14, -0
underflow
30, 2.81475e+14, -0
underflow
30, 5.6295e+14, -0
underflow
30, 1.1259e+15, -0
underflow
30, 2.2518e+15, -0
underflow
30, 4.5036e+15, -0
underflow
30, 9.0072e+15, -0
underflow
30, 1.80144e+16, -0
underflow
30, 3.60288e+16, -0
underflow
30, 7.20576e+16, -0
underflow
30, 1.44115e+17, -0
underflow
30, 2.8823e+17, -0
underflow
30, 5.76461e+17, -0
underflow
30, 1.15292e+18, -0
underflow
30, 2.30584e+18, -0
underflow
30, 4.61169e+18, -0
underflow
30, 9.22337e+18, -0
underflow
30, 1.84467e+19, -0
underflow
30, 3.68935e+19, -0
underflow
30, 7.3787e+19, -0
underflow
30, 1.47574e+20, -0
underflow
30, 2.95148e+20, -0
underflow
30, 5.90296e+20, -0
underflow
30, 1.18059e+21, -0
underflow
30, 2.36118e+21, -0
underflow
30, 4.72237e+21, -0
underflow
30, 9.44473e+21, -0
underflow
30, 1.88895e+22, -0
underflow
30, 3.77789e+22, -0
underflow
30, 7.55579e+22, -0
underflow
30, 1.51116e+23, -0
underflow
30, 3.02231e+23, -0
underflow
30, 6.04463e+23, -0
underflow
30, 1.20893e+24, -0
underflow
30, 2.41785e+24, -0
underflow
30, 4.8357e+24, -0
underflow
30, 9.67141e+24, -0
underflow
30, 1.93428e+25, -0
underflow
30, 3.86856e+25, -0
underflow
30, 7.73713e+25, -0
underflow
30, 1.54743e+26, -0
underflow
30, 3.09485e+26, -0
underflow
30, 6.1897e+26, -0
underflow
30, 1.23794e+27, -0
underflow
30, 2.47588e+27, -0
underflow
30, 4.95176e+27, -0
underflow
30, 9.90352e+27, -0
underflow
30, 1.9807e+28, -0
underflow
30, 3.96141e+28, -0
underflow
30, 7.92282e+28, -0
underflow
30, 1.58456e+29, -0
underflow
30, 3.16913e+29, -0
underflow
30, 6.33825e+29, -0
underflow
30, 1.26765e+30, -0

## Tables

Table 97. Error rates for beta

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Beta Function: Small Values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = +INFε (Mean = +INFε) And other failures.) (Rmath 3.2.3: Max = 1.14ε (Mean = 0.574ε)) | Max = 2.86ε (Mean = 1.22ε) (<cmath>: Max = 364ε (Mean = 76.2ε)) | Max = 2.86ε (Mean = 1.22ε) | Max = 2.23ε (Mean = 1.14ε)
Beta Function: Medium Values | Max = 0.978ε (Mean = 0.0595ε) (GSL 2.1: Max = 1.18e+03ε (Mean = 238ε)) (Rmath 3.2.3: Max = 1.09e+03ε (Mean = 265ε)) | Max = 61.4ε (Mean = 19.4ε) (<cmath>: Max = 1.07e+03ε (Mean = 264ε)) | Max = 107ε (Mean = 24.5ε) | Max = 96.5ε (Mean = 22.4ε)
Beta Function: Divergent Values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 12.1ε (Mean = 1.99ε)) (Rmath 3.2.3: Max = 176ε (Mean = 28ε)) | Max = 8.99ε (Mean = 2.44ε) (<cmath>: Max = 128ε (Mean = 23.8ε)) | Max = 18.8ε (Mean = 2.71ε) | Max = 11.4ε (Mean = 2.19ε)

Table 98. Error rates for beta (incomplete)

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Incomplete Beta Function: Small Values | Max = 0ε (Mean = 0ε) | Max = 11.1ε (Mean = 2.32ε) | Max = 18.7ε (Mean = 3.19ε) | Max = 9.94ε (Mean = 2.17ε)
Incomplete Beta Function: Medium Values | Max = 0.568ε (Mean = 0.0254ε) | Max = 69.2ε (Mean = 13.4ε) | Max = 174ε (Mean = 25ε) | Max = 90ε (Mean = 12.7ε)
Incomplete Beta Function: Large and Diverse Values | Max = 0.999ε (Mean = 0.0325ε) | Max = 6.84e+04ε (Mean = 2.76e+03ε) | Max = 6.86e+04ε (Mean = 2.79e+03ε) | Max = 633ε (Mean = 29.7ε)
Incomplete Beta Function: Small Integer Values | Max = 0.786ε (Mean = 0.0323ε) | Max = 11.6ε (Mean = 3.6ε) | Max = 51.8ε (Mean = 11ε) | Max = 26ε (Mean = 6.28ε)

Table 99. Error rates for betac

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Incomplete Beta Function: Small Values | Max = 0.676ε (Mean = 0.0302ε) | Max = 9.92ε (Mean = 2.3ε) | Max = 11.2ε (Mean = 2.94ε) | Max = 8.94ε (Mean = 2.06ε)
Incomplete Beta Function: Medium Values | Max = 0.949ε (Mean = 0.098ε) | Max = 63.5ε (Mean = 13.5ε) | Max = 97.6ε (Mean = 24.3ε) | Max = 90.6ε (Mean = 14.8ε)
Incomplete Beta Function: Large and Diverse Values | Max = 1.12ε (Mean = 0.0458ε) | Max = 1.05e+05ε (Mean = 5.45e+03ε) | Max = 1.04e+05ε (Mean = 5.46e+03ε) | Max = 3.72e+03ε (Mean = 113ε)
Incomplete Beta Function: Small Integer Values | Max = 0.586ε (Mean = 0.0314ε) | Max = 11.1ε (Mean = 3.65ε) | Max = 103ε (Mean = 17.4ε) | Max = 26.2ε (Mean = 6.36ε)

Table 100. Error rates for binomial_coefficient

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Binomials: small arguments | Max = 1ε (Mean = 0.369ε) | Max = 1.5ε (Mean = 0.339ε) | Max = 1.5ε (Mean = 0.339ε) | Max = 1ε (Mean = 0.369ε)
Binomials: large arguments | Max = 0.939ε (Mean = 0.314ε) | Max = 26.6ε (Mean = 6.13ε) | Max = 53.2ε (Mean = 10.8ε) | Max = 37.2ε (Mean = 7.4ε)

Table 101. Error rates for boost::math::powm1

| GNU C++ version 7.1.0 linux long double | GNU C++ version 7.1.0 linux double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
powm1 | (<math.h>: Max = 2.04ε (Mean = 0.493ε)) Max = 2.04ε (Mean = 0.493ε) (<cmath>: Max = 2.04ε (Mean = 0.493ε)) | (Rmath 3.2.3: Max = 1.06ε (Mean = 0.425ε)) (GSL 2.1: Max = 1.06ε (Mean = 0.425ε)) Max = 1.06ε (Mean = 0.425ε) | Max = 1.88ε (Mean = 0.49ε) (<math.h>: Max = 1.88ε (Mean = 0.49ε)) | (<math.h>: Max = 1.84ε (Mean = 0.486ε)) Max = 1.84ε (Mean = 0.486ε)

Table 102. Error rates for cbrt

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
cbrt Function | Max = 0ε (Mean = 0ε) | Max = 1.34ε (Mean = 0.471ε) (<cmath>: Max = 1.34ε (Mean = 0.471ε)) (<math.h>: Max = 1.34ε (Mean = 0.471ε)) | Max = 1.34ε (Mean = 0.471ε) (<math.h>: Max = 1.34ε (Mean = 0.471ε)) | Max = 1.7ε (Mean = 0.565ε) (<math.h>: Max = 1.7ε (Mean = 0.565ε))

Table 103. Error rates for cos_pi

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
sin_pi and cos_pi | Max = 0ε (Mean = 0ε) | Max = 0.991ε (Mean = 0.302ε) | Max = 0.991ε (Mean = 0.302ε) | Max = 0.996ε (Mean = 0.284ε)
sin_pi and cos_pi near integers and half integers | Max = 0ε (Mean = 0ε) | Max = 0.976ε (Mean = 0.28ε) | Max = 0.976ε (Mean = 0.28ε) | Max = 0.996ε (Mean = 0.298ε)

Table 104. Error rates for cyl_bessel_i

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Bessel I0: Mathworld Data | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 270ε (Mean = 91.6ε) And other failures.) (Rmath 3.2.3: Max = 1.52ε (Mean = 0.622ε) And other failures.) | Max = 1.95ε (Mean = 0.738ε) (<cmath>: Max = 8.49ε (Mean = 3.46ε) And other failures.) | Max = 1.95ε (Mean = 0.661ε) | Max = 0.762ε (Mean = 0.329ε)
Bessel I1: Mathworld Data | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 128ε (Mean = 41ε) And other failures.) (Rmath 3.2.3: Max = 1.53ε (Mean = 0.483ε) And other failures.) | Max = 0.64ε (Mean = 0.202ε) (<cmath>: Max = 5ε (Mean = 2.15ε) And other failures.) | Max = 0.64ε (Mean = 0.202ε) | Max = 0.767ε (Mean = 0.398ε)
Bessel In: Mathworld Data | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 2.31ε (Mean = 0.838ε) And other failures.) (Rmath 3.2.3: Max = 1.73ε (Mean = 0.601ε) And other failures.) | Max = 1.8ε (Mean = 1.33ε) (<cmath>: Max = 430ε (Mean = 163ε) And other failures.) | Max = 463ε (Mean = 140ε) | Max = 3.46ε (Mean = 1.32ε)
Bessel Iv: Mathworld Data | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 5.95ε (Mean = 2.08ε) And other failures.) (Rmath 3.2.3: Max = 3.53ε (Mean = 1.39ε)) | Max = 4.12ε (Mean = 1.85ε) (<cmath>: Max = 616ε (Mean = 221ε) And other failures.) | Max = 4.12ε (Mean = 1.95ε) | Max = 2.97ε (Mean = 1.24ε)
Bessel In: Random Data | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 261ε (Mean = 53.2ε) And other failures.) (Rmath 3.2.3: Max = 7.37ε (Mean = 2.4ε)) | Max = 4.62ε (Mean = 1.06ε) (<cmath>: Max = 645ε (Mean = 132ε)) | Max = 176ε (Mean = 39.1ε) | Max = 9.67ε (Mean = 1.88ε)
Bessel Iv: Random Data | Max = 0.661ε (Mean = 0.0441ε) (GSL 2.1: Max = 6.18e+03ε (Mean = 1.55e+03ε) And other failures.) (Rmath 3.2.3: Max = 4.28e+08ε (Mean = 2.85e+07ε)) | Max = 8.35ε (Mean = 1.62ε) (<cmath>: Max = 1.05e+03ε (Mean = 224ε) And other failures.) | Max = 283ε (Mean = 88.4ε) | Max = 7.46ε (Mean = 1.71ε)
Bessel Iv: Mathworld Data (large values) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 37ε (Mean = 18ε) And other failures.) (Rmath 3.2.3: Max = 3.77e+168ε (Mean = 2.39e+168ε) And other failures.) | Max = 14.7ε (Mean = 6.66ε) (<cmath>: Max = 118ε (Mean = 57.2ε) And other failures.) | Max = 14.7ε (Mean = 6.59ε) | Max = 3.67ε (Mean = 1.64ε)

Table 105. Error rates for cyl_bessel_i (integer orders)

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Bessel I0: Mathworld Data (Integer Version) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 0.79ε (Mean = 0.482ε)) (Rmath 3.2.3: Max = 1.52ε (Mean = 0.622ε) And other failures.) | Max = 1.95ε (Mean = 0.738ε) (<cmath>: Max = 8.49ε (Mean = 3.46ε) And other failures.) | Max = 1.95ε (Mean = 0.661ε) | Max = 0.762ε (Mean = 0.329ε)
Bessel I1: Mathworld Data (Integer Version) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 0.82ε (Mean = 0.456ε)) (Rmath 3.2.3: Max = 1.53ε (Mean = 0.483ε) And other failures.) | Max = 0.64ε (Mean = 0.202ε) (<cmath>: Max = 5ε (Mean = 2.15ε) And other failures.) | Max = 0.64ε (Mean = 0.202ε) | Max = 0.767ε (Mean = 0.398ε)
Bessel In: Mathworld Data (Integer Version) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 5.15ε (Mean = 2.13ε) And other failures.) (Rmath 3.2.3: Max = 1.73ε (Mean = 0.601ε) And other failures.) | Max = 1.8ε (Mean = 1.33ε) (<cmath>: Max = 430ε (Mean = 163ε) And other failures.) | Max = 463ε (Mean = 140ε) | Max = 3.46ε (Mean = 1.32ε)

Table 106. Error rates for cyl_bessel_i_prime

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Bessel I'0: Mathworld Data | Max = 0ε (Mean = 0ε) | Max = 0.82ε (Mean = 0.259ε) | Max = 0.82ε (Mean = 0.259ε) | Max = 0.82ε (Mean = 0.354ε)
Bessel I'1: Mathworld Data | Max = 0ε (Mean = 0ε) | Max = 1.97ε (Mean = 0.757ε) | Max = 1.97ε (Mean = 0.757ε) | Max = 1.36ε (Mean = 0.782ε)
Bessel I'n: Mathworld Data | Max = 0ε (Mean = 0ε) | Max = 2.31ε (Mean = 1.41ε) | Max = 701ε (Mean = 212ε) | Max = 3.61ε (Mean = 1.22ε)
Bessel I'v: Mathworld Data | Max = 1.62ε (Mean = 0.512ε) | Max = 2.89e+03ε (Mean = 914ε) | Max = 2.89e+03ε (Mean = 914ε) | Max = 3.76e+03ε (Mean = 1.19e+03ε)
Bessel I'n: Random Data | Max = 0ε (Mean = 0ε) | Max = 3.95ε (Mean = 1.06ε) | Max = 195ε (Mean = 37.1ε) | Max = 9.85ε (Mean = 1.82ε)
Bessel I'v: Random Data | Max = 0ε (Mean = 0ε) | Max = 14.1ε (Mean = 2.93ε) | Max = 336ε (Mean = 68.5ε) | Max = 14ε (Mean = 2.5ε)
Bessel I'v: Mathworld Data (large values) | Max = 0ε (Mean = 0ε) | Max = 42.6ε (Mean = 20.2ε) | Max = 42.6ε (Mean = 20.2ε) | Max = 59.5ε (Mean = 26.6ε)

Table 107. Error rates for cyl_bessel_i_prime (integer orders)

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Bessel I'0: Mathworld Data (Integer Version) | Max = 0ε (Mean = 0ε) | Max = 0.82ε (Mean = 0.259ε) | Max = 0.82ε (Mean = 0.259ε) | Max = 0.82ε (Mean = 0.354ε)
Bessel I'1: Mathworld Data (Integer Version) | Max = 0ε (Mean = 0ε) | Max = 1.97ε (Mean = 0.757ε) | Max = 1.97ε (Mean = 0.757ε) | Max = 1.36ε (Mean = 0.782ε)
Bessel I'n: Mathworld Data (Integer Version) | Max = 0ε (Mean = 0ε) | Max = 2.31ε (Mean = 1.41ε) | Max = 701ε (Mean = 212ε) | Max = 3.61ε (Mean = 1.22ε)

Table 108. Error rates for cyl_bessel_j

| GNU C++ version 7.1.0 linux long double | GNU C++ version 7.1.0 linux double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Bessel J0: Mathworld Data | Max = 6.55ε (Mean = 2.86ε) (<cmath>: Max = 5.04ε (Mean = 1.78ε) And other failures.) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 0.629ε (Mean = 0.223ε) And other failures.) (Rmath 3.2.3: Max = 0.629ε (Mean = 0.223ε) And other failures.) | Max = 6.55ε (Mean = 2.86ε) | Max = 2.52ε (Mean = 1.2ε)
Bessel J0: Mathworld Data (Tricky cases) | Max = 1.64e+08ε (Mean = 6.69e+07ε) (<cmath>: Max = 4.79e+08ε (Mean = 1.96e+08ε)) | Max = 8e+04ε (Mean = 3.27e+04ε) (GSL 2.1: Max = 6.5e+07ε (Mean = 2.66e+07ε)) (Rmath 3.2.3: Max = 1.04e+07ε (Mean = 4.29e+06ε)) | Max = 1.64e+08ε (Mean = 6.69e+07ε) | Max = 1e+07ε (Mean = 4.09e+06ε)
Bessel J1: Mathworld Data | Max = 3.59ε (Mean = 1.33ε) (<cmath>: Max = 6.1ε (Mean = 2.95ε) And other failures.) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 6.62ε (Mean = 2.35ε) And other failures.) (Rmath 3.2.3: Max = 0.946ε (Mean = 0.39ε) And other failures.) | Max = 1.44ε (Mean = 0.637ε) | Max = 1.73ε (Mean = 0.976ε)
Bessel J1: Mathworld Data (tricky cases) | Max = 2.18e+05ε (Mean = 9.76e+04ε) (<cmath>: Max = 2.15e+06ε (Mean = 1.58e+06ε)) | Max = 106ε (Mean = 47.5ε) (GSL 2.1: Max = 8.75e+05ε (Mean = 5.32e+05ε)) (Rmath 3.2.3: Max = 2.93e+06ε (Mean = 1.7e+06ε)) | Max = 2.18e+05ε (Mean = 9.76e+04ε) | Max = 3.23e+04ε (Mean = 1.45e+04ε)
Bessel JN: Mathworld Data | Max = 6.85ε (Mean = 3.35ε) (<cmath>: Max = 2.13e+19ε (Mean = 5.16e+18ε) And other failures.) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 6.9e+05ε (Mean = 2.15e+05ε) And other failures.) (Rmath 3.2.3: Max = +INFε (Mean = +INFε) And other failures.) | Max = 463ε (Mean = 112ε) | Max = 14.7ε (Mean = 5.4ε)
Bessel J: Mathworld Data | Max = 14.7ε (Mean = 4.11ε) (<cmath>: Max = 3.49e+05ε (Mean = 8.09e+04ε) And other failures.) | Max = 10ε (Mean = 2.24ε) (GSL 2.1: Max = 2.39e+05ε (Mean = 5.37e+04ε) And other failures.) (Rmath 3.2.3: Max = +INFε (Mean = +INFε) And other failures.) | Max = 14.7ε (Mean = 4.22ε) | Max = 14.9ε (Mean = 3.89ε)
Bessel J: Mathworld Data (large values) | Max = 607ε (Mean = 305ε) (<cmath>: Max = 34.9ε (Mean = 17.4ε) And other failures.) | Max = 0.536ε (Mean = 0.268ε) (GSL 2.1: Max = 4.91e+03ε (Mean = 2.46e+03ε) And other failures.) (Rmath 3.2.3: Max = 5.9ε (Mean = 3.76ε)) | Max = 607ε (Mean = 305ε) | Max = 9.31ε (Mean = 5.52ε)
Bessel JN: Random Data | Max = 50.8ε (Mean = 3.69ε) (<cmath>: Max = 1.12e+03ε (Mean = 88.7ε)) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 75.7ε (Mean = 5.36ε)) (Rmath 3.2.3: Max = 3.93ε (Mean = 1.22ε)) | Max = 99.6ε (Mean = 22ε) | Max = 17.5ε (Mean = 1.46ε)
Bessel J: Random Data | Max = 11.4ε (Mean = 1.68ε) (<cmath>: Max = 501ε (Mean = 52.3ε)) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 15.5ε (Mean = 3.33ε) And other failures.) (Rmath 3.2.3: Max = 6.74ε (Mean = 1.3ε)) | Max = 260ε (Mean = 34ε) | Max = 9.24ε (Mean = 1.17ε)
Bessel J: Random Data (Tricky large values) | Max = 785ε (Mean = 94.2ε) (<cmath>: Max = 5.01e+17ε (Mean = 6.23e+16ε)) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 2.48e+05ε (Mean = 5.11e+04ε)) (Rmath 3.2.3: Max = 71.6ε (Mean = 11.7ε)) | Max = 785ε (Mean = 97.4ε) | Max = 59.2ε (Mean = 8.67ε)

Table 109. Error rates for cyl_bessel_j (integer orders)

| GNU C++ version 7.1.0 linux long double | GNU C++ version 7.1.0 linux double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Bessel J0: Mathworld Data (Integer Version) | Max = 6.55ε (Mean = 2.86ε) (<cmath>: Max = 5.04ε (Mean = 1.78ε) And other failures.) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 1.12ε (Mean = 0.488ε)) (Rmath 3.2.3: Max = 0.629ε (Mean = 0.223ε) And other failures.) | Max = 6.55ε (Mean = 2.86ε) | Max = 2.52ε (Mean = 1.2ε) (<math.h>: Max = 1.89ε (Mean = 0.988ε))
Bessel J0: Mathworld Data (Tricky cases) (Integer Version) | Max = 1.64e+08ε (Mean = 6.69e+07ε) (<cmath>: Max = 4.79e+08ε (Mean = 1.96e+08ε)) | Max = 8e+04ε (Mean = 3.27e+04ε) (GSL 2.1: Max = 1e+07ε (Mean = 4.11e+06ε)) (Rmath 3.2.3: Max = 1.04e+07ε (Mean = 4.29e+06ε)) | Max = 1.64e+08ε (Mean = 6.69e+07ε) | Max = 1e+07ε (Mean = 4.09e+06ε) (<math.h>: Max = 2.54e+08ε (Mean = 1.04e+08ε))
Bessel J1: Mathworld Data (Integer Version) | Max = 3.59ε (Mean = 1.33ε) (<cmath>: Max = 6.1ε (Mean = 2.95ε) And other failures.) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 1.89ε (Mean = 0.721ε)) (Rmath 3.2.3: Max = 0.946ε (Mean = 0.39ε) And other failures.) | Max = 1.44ε (Mean = 0.637ε) | Max = 1.73ε (Mean = 0.976ε) (<math.h>: Max = 11.4ε (Mean = 4.15ε))
Bessel J1: Mathworld Data (tricky cases) (Integer Version) | Max = 2.18e+05ε (Mean = 9.76e+04ε) (<cmath>: Max = 2.15e+06ε (Mean = 1.58e+06ε)) | Max = 106ε (Mean = 47.5ε) (GSL 2.1: Max = 1.26e+06ε (Mean = 6.28e+05ε)) (Rmath 3.2.3: Max = 2.93e+06ε (Mean = 1.7e+06ε)) | Max = 2.18e+05ε (Mean = 9.76e+04ε) | Max = 3.23e+04ε (Mean = 1.45e+04ε) (<math.h>: Max = 1.44e+07ε (Mean = 6.5e+06ε))
Bessel JN: Mathworld Data (Integer Version) | Max = 6.85ε (Mean = 3.35ε) (<cmath>: Max = 2.13e+19ε (Mean = 5.16e+18ε) And other failures.) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 6.9e+05ε (Mean = 2.53e+05ε) And other failures.) (Rmath 3.2.3: Max = +INFε (Mean = +INFε) And other failures.) | Max = 463ε (Mean = 112ε) | Max = 14.7ε (Mean = 5.4ε) (<math.h>: Max = +INFε (Mean = +INFε) And other failures.)

Table 110. Error rates for cyl_bessel_j_prime

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Bessel J0': Mathworld Data | Max = 0ε (Mean = 0ε) | Max = 18.9ε (Mean = 6.82ε) | Max = 18.9ε (Mean = 6.72ε) | Max = 6.62ε (Mean = 2.55ε)
Bessel J0': Mathworld Data (Tricky cases) | Max = 0ε (Mean = 0ε) | Max = 7.44ε (Mean = 3.34ε) | Max = 7.44ε (Mean = 3.31ε) | Max = 3.67ε (Mean = 1.74ε)
Bessel J1': Mathworld Data | Max = 0ε (Mean = 0ε) | Max = 7.9ε (Mean = 3.37ε) | Max = 7.9ε (Mean = 3.37ε) | Max = 0.999ε (Mean = 0.627ε)
Bessel J1': Mathworld Data (tricky cases) | Max = 287ε (Mean = 129ε) | Max = 5.88e+05ε (Mean = 2.63e+05ε) | Max = 5.88e+05ε (Mean = 2.63e+05ε) | Max = 288ε (Mean = 129ε)
Bessel JN': Mathworld Data | Max = 0.527ε (Mean = 0.128ε) | Max = 1.29e+03ε (Mean = 312ε) | Max = 1.29e+03ε (Mean = 355ε) | Max = 14ε (Mean = 6.13ε)
Bessel J': Mathworld Data | Max = 21.5ε (Mean = 4.7ε) | Max = 42.5ε (Mean = 9.31ε) | Max = 42.5ε (Mean = 9.32ε) | Max = 23.7ε (Mean = 8ε)
Bessel J': Mathworld Data (large values) | Max = 0ε (Mean = 0ε) | Max = 989ε (Mean = 495ε) | Max = 989ε (Mean = 495ε) | Max = 2.9ε (Mean = 1.61ε)
Bessel JN': Random Data | Max = 0.593ε (Mean = 0.0396ε) | Max = 11.3ε (Mean = 1.85ε) | Max = 79.4ε (Mean = 16.2ε) | Max = 6.34ε (Mean = 0.999ε)
Bessel J': Random Data | Max = 0.885ε (Mean = 0.033ε) | Max = 139ε (Mean = 6.47ε) | Max = 279ε (Mean = 27.2ε) | Max = 176ε (Mean = 9.75ε)
Bessel J': Random Data (Tricky large values) | Max = 0ε (Mean = 0ε) | Max = 474ε (Mean = 62.2ε) | Max = 474ε (Mean = 64.5ε) | Max = 379ε (Mean = 45.4ε)

Table 111. Error rates for cyl_bessel_j_prime (integer orders)

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Bessel J0': Mathworld Data (Integer Version) | Max = 0ε (Mean = 0ε) | Max = 18.9ε (Mean = 6.82ε) | Max = 18.9ε (Mean = 6.72ε) | Max = 6.62ε (Mean = 2.55ε)
Bessel J0': Mathworld Data (Tricky cases) (Integer Version) | Max = 0ε (Mean = 0ε) | Max = 7.44ε (Mean = 3.34ε) | Max = 7.44ε (Mean = 3.31ε) | Max = 3.67ε (Mean = 1.74ε)
Bessel J1': Mathworld Data (Integer Version) | Max = 0ε (Mean = 0ε) | Max = 7.9ε (Mean = 3.37ε) | Max = 7.9ε (Mean = 3.37ε) | Max = 0.999ε (Mean = 0.627ε)
Bessel J1': Mathworld Data (tricky cases) (Integer Version) | Max = 287ε (Mean = 129ε) | Max = 5.88e+05ε (Mean = 2.63e+05ε) | Max = 5.88e+05ε (Mean = 2.63e+05ε) | Max = 288ε (Mean = 129ε)
Bessel JN': Mathworld Data (Integer Version) | Max = 0.527ε (Mean = 0.128ε) | Max = 1.29e+03ε (Mean = 312ε) | Max = 1.29e+03ε (Mean = 355ε) | Max = 14ε (Mean = 6.13ε)

Table 112. Error rates for cyl_bessel_k

| GNU C++ version 7.1.0 linux long double | GNU C++ version 7.1.0 linux double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Bessel K0: Mathworld Data | Max = 0.833ε (Mean = 0.436ε) (<cmath>: Max = 9.33ε (Mean = 3.25ε)) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 6.04ε (Mean = 2.16ε)) (Rmath 3.2.3: Max = 0.833ε (Mean = 0.601ε)) | Max = 0.833ε (Mean = 0.436ε) | Max = 0.833ε (Mean = 0.552ε)
Bessel K1: Mathworld Data | Max = 0.786ε (Mean = 0.329ε) (<cmath>: Max = 8.94ε (Mean = 3.19ε)) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 6.26ε (Mean = 2.21ε)) (Rmath 3.2.3: Max = 0.894ε (Mean = 0.516ε)) | Max = 0.786ε (Mean = 0.329ε) | Max = 0.786ε (Mean = 0.39ε)
Bessel Kn: Mathworld Data | Max = 2.6ε (Mean = 1.21ε) (<cmath>: Max = 12.9ε (Mean = 4.91ε) And other failures.) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 3.36ε (Mean = 1.43ε) And other failures.) (Rmath 3.2.3: Max = 8.48ε (Mean = 2.98ε)) | Max = 2.6ε (Mean = 1.21ε) | Max = 3.63ε (Mean = 1.46ε)
Bessel Kv: Mathworld Data | Max = 3.58ε (Mean = 2.39ε) (<cmath>: Max = 13ε (Mean = 4.81ε) And other failures.) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 5.47ε (Mean = 2.04ε) And other failures.) (Rmath 3.2.3: Max = 3.15ε (Mean = 1.35ε)) | Max = 5.21ε (Mean = 2.53ε) | Max = 4.78ε (Mean = 2.19ε)
Bessel Kv: Mathworld Data (large values) | Max = 42.3ε (Mean = 21ε) (<cmath>: Max = 42.3ε (Mean = 19.8ε) And other failures.) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 308ε (Mean = 142ε) And other failures.) (Rmath 3.2.3: Max = 84.6ε (Mean = 37.8ε)) | Max = 42.3ε (Mean = 21ε) | Max = 59.8ε (Mean = 26.9ε)
Bessel Kn: Random Data | Max = 4.55ε (Mean = 1.12ε) (<cmath>: Max = 13.9ε (Mean = 2.91ε)) | Max = 0.764ε (Mean = 0.0348ε) (GSL 2.1: Max = 8.71ε (Mean = 1.76ε) And other failures.) (Rmath 3.2.3: Max = 7.47ε (Mean = 1.34ε)) | Max = 4.55ε (Mean = 1.12ε) | Max = 9.34ε (Mean = 1.7ε)
Bessel Kv: Random Data | Max = 7.88ε (Mean = 1.48ε) (<cmath>: Max = 13.6ε (Mean = 2.68ε) And other failures.) | Max = 0.507ε (Mean = 0.0313ε) (GSL 2.1: Max = 9.71ε (Mean = 1.47ε) And other failures.) (Rmath 3.2.3: Max = 7.37ε (Mean = 1.49ε)) | Max = 7.88ε (Mean = 1.47ε) | Max = 8.33ε (Mean = 1.62ε)

Table 113. Error rates for cyl_bessel_k (integer orders)

| GNU C++ version 7.1.0 linux long double | GNU C++ version 7.1.0 linux double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Bessel K0: Mathworld Data (Integer Version) | Max = 0.833ε (Mean = 0.436ε) (<cmath>: Max = 9.33ε (Mean = 3.25ε)) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 1.2ε (Mean = 0.733ε)) (Rmath 3.2.3: Max = 0.833ε (Mean = 0.601ε)) | Max = 0.833ε (Mean = 0.436ε) | Max = 0.833ε (Mean = 0.552ε)
Bessel K1: Mathworld Data (Integer Version) | Max = 0.786ε (Mean = 0.329ε) (<cmath>: Max = 8.94ε (Mean = 3.19ε)) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 0.626ε (Mean = 0.333ε)) (Rmath 3.2.3: Max = 0.894ε (Mean = 0.516ε)) | Max = 0.786ε (Mean = 0.329ε) | Max = 0.786ε (Mean = 0.39ε)
Bessel Kn: Mathworld Data (Integer Version) | Max = 2.6ε (Mean = 1.21ε) (<cmath>: Max = 12.9ε (Mean = 4.91ε) And other failures.) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 168ε (Mean = 59.5ε)) (Rmath 3.2.3: Max = 8.48ε (Mean = 2.98ε)) | Max = 2.6ε (Mean = 1.21ε) | Max = 3.63ε (Mean = 1.46ε)

Table 114. Error rates for cyl_bessel_k_prime

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Bessel K'0: Mathworld Data | Max = 0ε (Mean = 0ε) | Max = 0.786ε (Mean = 0.329ε) | Max = 0.786ε (Mean = 0.329ε) | Max = 0.786ε (Mean = 0.39ε)
Bessel K'1: Mathworld Data | Max = 0ε (Mean = 0ε) | Max = 0.736ε (Mean = 0.389ε) | Max = 0.736ε (Mean = 0.389ε) | Max = 0.761ε (Mean = 0.444ε)
Bessel K'n: Mathworld Data | Max = 0ε (Mean = 0ε) | Max = 2.16ε (Mean = 1.08ε) | Max = 2.16ε (Mean = 1.08ε) | Max = 4.17ε (Mean = 1.75ε)
Bessel K'v: Mathworld Data | Max = 0ε (Mean = 0ε) | Max = 3.94ε (Mean = 2.44ε) | Max = 3.94ε (Mean = 2.34ε) | Max = 3.94ε (Mean = 1.47ε)
Bessel K'v: Mathworld Data (large values) | Max = 0ε (Mean = 0ε) | Max = 59.2ε (Mean = 42.9ε) | Max = 58.7ε (Mean = 42.6ε) | Max = 18.6ε (Mean = 11.8ε)
Bessel K'n: Random Data | Max = 0ε (Mean = 0ε) | Max = 4.45ε (Mean = 1.19ε) | Max = 4.45ε (Mean = 1.19ε) | Max = 9.67ε (Mean = 1.73ε)
Bessel K'v: Random Data | Max = 0ε (Mean = 0ε) | Max = 7.95ε (Mean = 1.53ε) | Max = 7.95ε (Mean = 1.52ε) | Max = 8.32ε (Mean = 1.65ε)

Table 115. Error rates for cyl_bessel_k_prime (integer orders)

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Bessel K'0: Mathworld Data (Integer Version) | Max = 0ε (Mean = 0ε) | Max = 0.786ε (Mean = 0.329ε) | Max = 0.786ε (Mean = 0.329ε) | Max = 0.786ε (Mean = 0.39ε)
Bessel K'1: Mathworld Data (Integer Version) | Max = 0ε (Mean = 0ε) | Max = 0.736ε (Mean = 0.389ε) | Max = 0.736ε (Mean = 0.389ε) | Max = 0.761ε (Mean = 0.444ε)
Bessel K'n: Mathworld Data (Integer Version) | Max = 0ε (Mean = 0ε) | Max = 2.16ε (Mean = 1.08ε) | Max = 2.16ε (Mean = 1.08ε) | Max = 4.17ε (Mean = 1.75ε)

Table 116. Error rates for cyl_neumann

| GNU C++ version 7.1.0 linux long double | GNU C++ version 7.1.0 linux double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Y0: Mathworld Data | Max = 5.53ε (Mean = 2.4ε) (<cmath>: Max = 2.05e+05ε (Mean = 6.87e+04ε)) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 60.9ε (Mean = 20.4ε)) (Rmath 3.2.3: Max = 167ε (Mean = 56.5ε)) | Max = 5.53ε (Mean = 2.4ε) | Max = 4.61ε (Mean = 2.29ε)
Y1: Mathworld Data | Max = 6.33ε (Mean = 2.25ε) (<cmath>: Max = 9.71e+03ε (Mean = 4.08e+03ε)) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 23.4ε (Mean = 8.1ε)) (Rmath 3.2.3: Max = 193ε (Mean = 64.4ε)) | Max = 6.33ε (Mean = 2.29ε) | Max = 4.75ε (Mean = 1.72ε)
Yn: Mathworld Data | Max = 55.2ε (Mean = 17.8ε) (<cmath>: Max = 2.2e+20ε (Mean = 6.97e+19ε) And other failures.) | Max = 0.993ε (Mean = 0.314ε) (GSL 2.1: Max = 2.41e+05ε (Mean = 7.62e+04ε) And other failures.) (Rmath 3.2.3: Max = 1.24e+04ε (Mean = 4e+03ε)) | Max = 55.2ε (Mean = 17.8ε) | Max = 35ε (Mean = 11.9ε)
Yv: Mathworld Data | Max = 10.7ε (Mean = 4.93ε) (<cmath>: Max = 3.49e+15ε (Mean = 1.05e+15ε) And other failures.) | Max = 10ε (Mean = 3.02ε) (GSL 2.1: Max = 1.07e+05ε (Mean = 3.22e+04ε) And other failures.) (Rmath 3.2.3: Max = 243ε (Mean = 73.9ε)) | Max = 10.7ε (Mean = 5.1ε) | Max = 7.89ε (Mean = 3.27ε)
Yv: Mathworld Data (large values) | Max = 1.7ε (Mean = 1.33ε) (<cmath>: Max = 43.2ε (Mean = 16.3ε) And other failures.) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 60.8ε (Mean = 23ε) And other failures.) (Rmath 3.2.3: Max = 0.682ε (Mean = 0.335ε)) | Max = 1.7ε (Mean = 1.33ε) | Max = 0.682ε (Mean = 0.423ε)
Y0 and Y1: Random Data | Max = 10.8ε (Mean = 3.04ε) (<cmath>: Max = 2.59e+03ε (Mean = 500ε)) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 34.4ε (Mean = 8.9ε)) (Rmath 3.2.3: Max = 83ε (Mean = 14.2ε)) | Max = 10.8ε (Mean = 3.04ε) | Max = 4.17ε (Mean = 1.24ε)
Yn: Random Data | Max = 338ε (Mean = 27.5ε) (<cmath>: Max = 4.01e+03ε (Mean = 348ε)) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 500ε (Mean = 47.8ε)) (Rmath 3.2.3: Max = 691ε (Mean = 67.9ε)) | Max = 338ε (Mean = 27.5ε) | Max = 117ε (Mean = 10.2ε)
Yv: Random Data | Max = 2.08e+03ε (Mean = 149ε) (<cmath>: Max = +INFε (Mean = +INFε) And other failures.) | Max = 1.53ε (Mean = 0.102ε) (GSL 2.1: Max = 1.41e+06ε (Mean = 7.67e+04ε)) (Rmath 3.2.3: Max = 1.79e+05ε (Mean = 9.64e+03ε)) | Max = 2.08e+03ε (Mean = 149ε) | Max = 1.23e+03ε (Mean = 69.9ε)

Table 117. Error rates for cyl_neumann (integer orders)

| GNU C++ version 7.1.0 linux long double | GNU C++ version 7.1.0 linux double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Y0: Mathworld Data (Integer Version) | Max = 5.53ε (Mean = 2.4ε) (<cmath>: Max = 2.05e+05ε (Mean = 6.87e+04ε)) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 6.46ε (Mean = 2.38ε)) (Rmath 3.2.3: Max = 167ε (Mean = 56.5ε)) | Max = 5.53ε (Mean = 2.4ε) | Max = 4.61ε (Mean = 2.29ε) (<math.h>: Max = 5.37e+03ε (Mean = 1.81e+03ε))
Y1: Mathworld Data (Integer Version) | Max = 6.33ε (Mean = 2.25ε) (<cmath>: Max = 9.71e+03ε (Mean = 4.08e+03ε)) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 1.51ε (Mean = 0.839ε)) (Rmath 3.2.3: Max = 193ε (Mean = 64.4ε)) | Max = 6.33ε (Mean = 2.29ε) | Max = 4.75ε (Mean = 1.72ε) (<math.h>: Max = 1.86e+04ε (Mean = 6.2e+03ε))
Yn: Mathworld Data (Integer Version) | Max = 55.2ε (Mean = 17.8ε) (<cmath>: Max = 2.2e+20ε (Mean = 6.97e+19ε) And other failures.) | Max = 0.993ε (Mean = 0.314ε) (GSL 2.1: Max = 2.41e+05ε (Mean = 7.62e+04ε)) (Rmath 3.2.3: Max = 1.24e+04ε (Mean = 4e+03ε)) | Max = 55.2ε (Mean = 17.8ε) | Max = 35ε (Mean = 11.9ε) (<math.h>: Max = 2.49e+05ε (Mean = 8.14e+04ε))

Table 118. Error rates for cyl_neumann_prime

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Y'0: Mathworld Data | Max = 0ε (Mean = 0ε) | Max = 6.33ε (Mean = 3.12ε) | Max = 6.33ε (Mean = 3.14ε) | Max = 4.75ε (Mean = 1.75ε)
Y'1: Mathworld Data | Max = 0.58ε (Mean = 0.193ε) | Max = 37.1ε (Mean = 12.8ε) | Max = 34ε (Mean = 11.8ε) | Max = 3.08ε (Mean = 1.2ε)
Y'n: Mathworld Data | Max = 2.05ε (Mean = 0.677ε) | Max = 56ε (Mean = 18.2ε) | Max = 56ε (Mean = 21.3ε) | Max = 563ε (Mean = 178ε)
Y'v: Mathworld Data | Max = 21.5ε (Mean = 6.49ε) | Max = 42.5ε (Mean = 13.4ε) | Max = 42.5ε (Mean = 13.6ε) | Max = 23.7ε (Mean = 10.1ε)
Y'v: Mathworld Data (large values) | Max = 0ε (Mean = 0ε) | Max = 1.57ε (Mean = 1.24ε) | Max = 1.57ε (Mean = 1.24ε) | Max = 0.627ε (Mean = 0.237ε)
Y'0 and Y'1: Random Data | Max = 0ε (Mean = 0ε) | Max = 23.8ε (Mean = 3.69ε) | Max = 23.8ε (Mean = 3.69ε) | Max = 5.95ε (Mean = 1.36ε)
Y'n: Random Data | Max = 1.53ε (Mean = 0.0885ε) | Max = 2.35e+03ε (Mean = 136ε) | Max = 2.35e+03ε (Mean = 136ε) | Max = 621ε (Mean = 36ε)
Y'v: Random Data | Max = 56.8ε (Mean = 2.59ε) | Max = 1.16e+05ε (Mean = 5.28e+03ε) | Max = 1.16e+05ε (Mean = 5.28e+03ε) | Max = 3.23e+04ε (Mean = 1.13e+03ε)

Table 119. Error rates for cyl_neumann_prime (integer orders)

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Y'0: Mathworld Data (Integer Version) | Max = 0ε (Mean = 0ε) | Max = 6.33ε (Mean = 3.12ε) | Max = 6.33ε (Mean = 3.14ε) | Max = 4.75ε (Mean = 1.75ε)
Y'1: Mathworld Data (Integer Version) | Max = 0.58ε (Mean = 0.193ε) | Max = 37.1ε (Mean = 12.8ε) | Max = 34ε (Mean = 11.8ε) | Max = 3.08ε (Mean = 1.2ε)
Y'n: Mathworld Data (Integer Version) | Max = 2.05ε (Mean = 0.677ε) | Max = 56ε (Mean = 18.2ε) | Max = 56ε (Mean = 21.3ε) | Max = 563ε (Mean = 178ε)

Table 120. Error rates for digamma

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Digamma Function: Large Values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 1.84ε (Mean = 0.71ε)) (Rmath 3.2.3: Max = 1.18ε (Mean = 0.331ε)) | Max = 1.39ε (Mean = 0.413ε) | Max = 1.39ε (Mean = 0.413ε) | Max = 0.98ε (Mean = 0.369ε)
Digamma Function: Near the Positive Root | Max = 0.891ε (Mean = 0.0995ε) (GSL 2.1: Max = 135ε (Mean = 11.9ε)) (Rmath 3.2.3: Max = 2.02e+03ε (Mean = 256ε)) | Max = 1.37ε (Mean = 0.477ε) | Max = 1.31ε (Mean = 0.471ε) | Max = 0.997ε (Mean = 0.527ε)
Digamma Function: Near Zero | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 0.953ε (Mean = 0.348ε)) (Rmath 3.2.3: Max = 1.17ε (Mean = 0.564ε)) | Max = 0.984ε (Mean = 0.361ε) | Max = 0.984ε (Mean = 0.361ε) | Max = 0.953ε (Mean = 0.337ε)
Digamma Function: Negative Values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 4.56e+04ε (Mean = 3.91e+03ε)) (Rmath 3.2.3: Max = 4.6e+04ε (Mean = 3.94e+03ε)) | Max = 180ε (Mean = 13ε) | Max = 180ε (Mean = 13ε) | Max = 214ε (Mean = 16.1ε)
Digamma Function: Values near 0 | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 0.866ε (Mean = 0.387ε)) (Rmath 3.2.3: Max = 3.58e+05ε (Mean = 1.6e+05ε)) | Max = 1ε (Mean = 0.592ε) | Max = 1ε (Mean = 0.592ε) | Max = 0ε (Mean = 0ε)
Digamma Function: Integer arguments | Max = 0.992ε (Mean = 0.215ε) (GSL 2.1: Max = 1.18ε (Mean = 0.607ε)) (Rmath 3.2.3: Max = 4.33ε (Mean = 0.982ε)) | Max = 0.888ε (Mean = 0.403ε) | Max = 0.888ε (Mean = 0.403ε) | Max = 0.992ε (Mean = 0.452ε)
Digamma Function: Half integer arguments | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 1.09ε (Mean = 0.531ε)) (Rmath 3.2.3: Max = 46.2ε (Mean = 7.24ε)) | Max = 0.906ε (Mean = 0.409ε) | Max = 0.906ε (Mean = 0.409ε) | Max = 0.78ε (Mean = 0.314ε)

Table 121. Error rates for ellint_1

| GNU C++ version 7.1.0 linux long double | GNU C++ version 7.1.0 linux double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Elliptic Integral F: Mathworld Data | Max = 0.94ε (Mean = 0.509ε) (<cmath>: Max = +INFε (Mean = +INFε) And other failures.) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 0.919ε (Mean = 0.544ε)) | Max = 0.94ε (Mean = 0.509ε) | Max = 0.919ε (Mean = 0.542ε)
Elliptic Integral F: Random Data | Max = 1.57ε (Mean = 0.56ε) (<cmath>: Max = 2.56ε (Mean = 0.816ε)) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 2.99ε (Mean = 0.797ε)) | Max = 1.57ε (Mean = 0.561ε) | Max = 2.26ε (Mean = 0.631ε)

Table 122. Error rates for ellint_1 (complete)

| GNU C++ version 7.1.0 linux long double | GNU C++ version 7.1.0 linux double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Elliptic Integral K: Mathworld Data | Max = 0.887ε (Mean = 0.296ε) (<cmath>: Max = 1.19ε (Mean = 0.765ε)) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 0.623ε (Mean = 0.393ε)) | Max = 0.887ε (Mean = 0.296ε) | Max = 0.915ε (Mean = 0.547ε)
Elliptic Integral K: Random Data | Max = 1.27ε (Mean = 0.473ε) (<cmath>: Max = 2.19ε (Mean = 0.694ε)) | Max = 0.851ε (Mean = 0.0851ε) (GSL 2.1: Max = 2.32ε (Mean = 0.688ε)) | Max = 1.27ε (Mean = 0.473ε) | Max = 0.958ε (Mean = 0.408ε)

Table 123. Error rates for ellint_2

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Elliptic Integral E: Mathworld Data | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 0.63ε (Mean = 0.325ε)) | Max = 0.656ε (Mean = 0.317ε) (<cmath>: Max = +INFε (Mean = +INFε) And other failures.) | Max = 0.656ε (Mean = 0.317ε) | Max = 1.31ε (Mean = 0.727ε)
Elliptic Integral E: Random Data | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 4.4ε (Mean = 1.16ε)) | Max = 2.05ε (Mean = 0.632ε) (<cmath>: Max = 3.08e+04ε (Mean = 3.84e+03ε)) | Max = 2.05ε (Mean = 0.632ε) | Max = 2.23ε (Mean = 0.639ε)
Elliptic Integral E: Small Angles | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 0.5ε (Mean = 0.118ε)) | Max = 1ε (Mean = 0.283ε) (<cmath>: Max = 2ε (Mean = 0.333ε)) | Max = 1ε (Mean = 0.283ε) | Max = 1ε (Mean = 0.421ε)

Table 124. Error rates for ellint_2 (complete)

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Elliptic Integral E: Mathworld Data | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 3.09ε (Mean = 1.04ε) And other failures.) | Max = 0.836ε (Mean = 0.469ε) (<cmath>: Max = 170ε (Mean = 55.1ε)) | Max = 0.836ε (Mean = 0.469ε) | Max = 1.3ε (Mean = 0.615ε)
Elliptic Integral E: Random Data | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 4.34ε (Mean = 1.18ε)) | Max = 1.97ε (Mean = 0.629ε) (<cmath>: Max = 2.49e+04ε (Mean = 3.39e+03ε)) | Max = 1.97ε (Mean = 0.629ε) | Max = 1.71ε (Mean = 0.553ε)

Table 125. Error rates for ellint_3

| GNU C++ version 7.1.0 linux long double | GNU C++ version 7.1.0 linux double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Elliptic Integral PI: Mathworld Data | Max = 475ε (Mean = 86.3ε) (<cmath>: Max = +INFε (Mean = +INFε) And other failures.) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 1.48e+05ε (Mean = 2.54e+04ε) And other failures.) | Max = 475ε (Mean = 86.3ε) | Max = 565ε (Mean = 102ε)
Elliptic Integral PI: Random Data | Max = 4.54ε (Mean = 0.895ε) (<cmath>: Max = 3.37e+20ε (Mean = 3.47e+19ε) And other failures.) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 633ε (Mean = 50.1ε)) | Max = 4.49ε (Mean = 0.885ε) | Max = 8.33ε (Mean = 0.971ε)
Elliptic Integral PI: Large Random Data | Max = 3.7ε (Mean = 0.893ε) (<cmath>: Max = 2.52e+18ε (Mean = 4.83e+17ε) And other failures.) | Max = 0.557ε (Mean = 0.0389ε) (GSL 2.1: Max = 40.1ε (Mean = 7.77ε)) | Max = 3.7ε (Mean = 0.892ε) | Max = 2.86ε (Mean = 0.944ε)

Table 126. Error rates for ellint_3 (complete)

| GNU C++ version 7.1.0 linux long double | GNU C++ version 7.1.0 linux double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Complete Elliptic Integral PI: Mathworld Data | Max = 1.4ε (Mean = 0.575ε) (<cmath>: Max = 6.31e+20ε (Mean = 1.53e+20ε) And other failures.) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 6.33e+04ε (Mean = 1.54e+04ε) And other failures.) | Max = 1.4ε (Mean = 0.575ε) | Max = 0.971ε (Mean = 0.464ε)
Complete Elliptic Integral PI: Random Data | Max = 2.45ε (Mean = 0.696ε) (<cmath>: Max = 8.78e+20ε (Mean = 1.02e+20ε) And other failures.) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 24ε (Mean = 2.99ε)) | Max = 2.4ε (Mean = 0.677ε) | Max = 2.46ε (Mean = 0.657ε)

Table 127. Error rates for ellint_d

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Elliptic Integral E: Mathworld Data | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 0.862ε (Mean = 0.568ε)) | Max = 1.3ε (Mean = 0.813ε) | Max = 1.3ε (Mean = 0.813ε) | Max = 0.862ε (Mean = 0.457ε)
Elliptic Integral D: Random Data | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 3.01ε (Mean = 0.928ε)) | Max = 2.51ε (Mean = 0.883ε) | Max = 2.51ε (Mean = 0.883ε) | Max = 2.87ε (Mean = 0.805ε)

Table 128. Error rates for ellint_d (complete)

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Elliptic Integral E: Mathworld Data | Max = 0.637ε (Mean = 0.368ε) | Max = 1.27ε (Mean = 0.735ε) | Max = 1.27ε (Mean = 0.735ε) | Max = 0.637ε (Mean = 0.368ε)
Elliptic Integral D: Random Data | Max = 0ε (Mean = 0ε) | Max = 1.27ε (Mean = 0.334ε) | Max = 1.27ε (Mean = 0.334ε) | Max = 1.27ε (Mean = 0.355ε)

Table 129. Error rates for ellint_rc

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | ---
RC: Random data | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 2.4ε (Mean = 0.624ε)) | Max = 0.995ε (Mean = 0.433ε) | Max = 0.962ε (Mean = 0.407ε)

Table 130. Error rates for ellint_rd

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | ---
RD: Random data | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 2.59ε (Mean = 0.878ε)) | Max = 2.73ε (Mean = 0.831ε) | Max = 2.16ε (Mean = 0.803ε)
RD: y = z | Max = 0.896ε (Mean = 0.022ε) (GSL 2.1: Max = 2.88ε (Mean = 0.839ε)) | Max = 2.65ε (Mean = 0.82ε) | Max = 16.5ε (Mean = 0.843ε)
RD: x = y | Max = 0.824ε (Mean = 0.0272ε) (GSL 2.1: Max = 3.74ε (Mean = 0.84ε)) | Max = 2.85ε (Mean = 0.865ε) | Max = 3.51ε (Mean = 0.816ε)
RD: x = 0, y = z | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 2ε (Mean = 0.656ε)) | Max = 1.19ε (Mean = 0.522ε) | Max = 1.16ε (Mean = 0.497ε)
RD: x = y = z | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 1.03ε (Mean = 0.418ε)) | Max = 0.998ε (Mean = 0.387ε) | Max = 1.03ε (Mean = 0.418ε)
RD: x = 0 | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 2.85ε (Mean = 0.781ε)) | Max = 2.79ε (Mean = 0.883ε) | Max = 2.64ε (Mean = 0.894ε)

Table 131. Error rates for ellint_rf

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | ---
RF: Random data | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 2.73ε (Mean = 0.804ε)) | Max = 2.54ε (Mean = 0.674ε) | Max = 2.02ε (Mean = 0.677ε)
RF: x = y = z | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 0.999ε (Mean = 0.34ε)) | Max = 0.991ε (Mean = 0.345ε) | Max = 0.999ε (Mean = 0.34ε)
RF: x = y or y = z or x = z | Max = 0.536ε (Mean = 0.00658ε) (GSL 2.1: Max = 2.89ε (Mean = 0.749ε)) | Max = 1.95ε (Mean = 0.418ε) | Max = 1.21ε (Mean = 0.394ε)
RF: x = 0, y = z | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 1.29ε (Mean = 0.527ε)) | Max = 0.894ε (Mean = 0.338ε) | Max = 0.999ε (Mean = 0.407ε)
RF: z = 0 | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 2.54ε (Mean = 0.781ε)) | Max = 1.7ε (Mean = 0.539ε) | Max = 1.89ε (Mean = 0.587ε)

Table 132. Error rates for ellint_rg

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | ---
RG: Random Data | Max = 0.983ε (Mean = 0.0172ε) (GSL 2.1: Max = 0.983ε (Mean = 0.0172ε)) | Max = 3.95ε (Mean = 0.951ε) | Max = 3.65ε (Mean = 0.929ε)
RG: two values 0 | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 0ε (Mean = 0ε)) | Max = 0ε (Mean = 0ε) | Max = 0ε (Mean = 0ε)
RG: All values the same or zero | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 0ε (Mean = 0ε)) | Max = 0.992ε (Mean = 0.288ε) | Max = 1.06ε (Mean = 0.348ε)
RG: two values the same | Max = 0.594ε (Mean = 0.0103ε) (GSL 2.1: Max = 0.594ε (Mean = 0.0103ε)) | Max = 1.51ε (Mean = 0.404ε) | Max = 1.96ε (Mean = 0.374ε)
RG: one value zero | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 0ε (Mean = 0ε)) | Max = 2.14ε (Mean = 0.722ε) | Max = 1.96ε (Mean = 0.674ε)

Table 133. Error rates for ellint_rj

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | ---
RJ: Random data | Max = 0.52ε (Mean = 0.0184ε) (GSL 2.1: Max = 3.57ε (Mean = 0.704ε) And other failures.) | Max = 186ε (Mean = 6.67ε) | Max = 215ε (Mean = 7.66ε)
RJ: 4 Equal Values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 1.03ε (Mean = 0.418ε)) | Max = 0.998ε (Mean = 0.387ε) | Max = 1.03ε (Mean = 0.418ε)
RJ: 3 Equal Values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 3.96ε (Mean = 1.06ε)) | Max = 20.8ε (Mean = 0.986ε) | Max = 39.9ε (Mean = 1.17ε)
RJ: 2 Equal Values | Max = 0.6ε (Mean = 0.0228ε) (GSL 2.1: Max = 2.57ε (Mean = 0.754ε)) | Max = 220ε (Mean = 6.64ε) | Max = 214ε (Mean = 5.28ε)
RJ: Equal z and p | Max = 0.742ε (Mean = 0.0166ε) (GSL 2.1: Max = 2.62ε (Mean = 0.699ε)) | Max = 17.2ε (Mean = 1.16ε) | Max = 16.1ε (Mean = 1.14ε)

Table 134. Error rates for erf

| GNU C++ version 7.1.0 linux long double | GNU C++ version 7.1.0 linux double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Erf Function: Small Values | Max = 0.925ε (Mean = 0.193ε) (<cmath>: Max = 0.944ε (Mean = 0.191ε)) (<math.h>: Max = 0.944ε (Mean = 0.191ε)) | Max = 0.841ε (Mean = 0.0687ε) (GSL 2.1: Max = 2.06ε (Mean = 0.319ε)) | Max = 0.925ε (Mean = 0.193ε) (<math.h>: Max = 0.944ε (Mean = 0.194ε)) | Max = 0.996ε (Mean = 0.182ε) (<math.h>: Max = 1.57ε (Mean = 0.317ε))
Erf Function: Medium Values | Max = 1.5ε (Mean = 0.193ε) (<cmath>: Max = 0.921ε (Mean = 0.0723ε)) (<math.h>: Max = 0.921ε (Mean = 0.0723ε)) | Max = 1ε (Mean = 0.119ε) (GSL 2.1: Max = 2.31ε (Mean = 0.368ε)) | Max = 1.5ε (Mean = 0.197ε) (<math.h>: Max = 0.921ε (Mean = 0.071ε)) | Max = 1ε (Mean = 0.171ε) (<math.h>: Max = 1.19ε (Mean = 0.244ε))
Erf Function: Large Values | Max = 0ε (Mean = 0ε) (<cmath>: Max = 0ε (Mean = 0ε)) (<math.h>: Max = 0ε (Mean = 0ε)) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 0ε (Mean = 0ε)) | Max = 0ε (Mean = 0ε) (<math.h>: Max = 0ε (Mean = 0ε)) | Max = 0ε (Mean = 0ε) (<math.h>: Max = 0ε (Mean = 0ε))

Table 135. Error rates for erf_inv

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Inverse Erf Function | Max = 0ε (Mean = 0ε) | Max = 0.996ε (Mean = 0.389ε) | Max = 1.08ε (Mean = 0.395ε) | Max = 1.09ε (Mean = 0.502ε)

Table 136. Error rates for erfc

| GNU C++ version 7.1.0 linux long double | GNU C++ version 7.1.0 linux double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Erf Function: Small Values | Max = 0ε (Mean = 0ε) (<cmath>: Max = 0ε (Mean = 0ε)) (<math.h>: Max = 0ε (Mean = 0ε)) | Max = 0.658ε (Mean = 0.0537ε) (GSL 2.1: Max = 1.01ε (Mean = 0.485ε)) | Max = 0ε (Mean = 0ε) (<math.h>: Max = 0ε (Mean = 0ε)) | Max = 0ε (Mean = 0ε) (<math.h>: Max = 0ε (Mean = 0ε))
Erf Function: Medium Values | Max = 1.76ε (Mean = 0.365ε) (<cmath>: Max = 1.35ε (Mean = 0.307ε)) (<math.h>: Max = 1.35ε (Mean = 0.307ε)) | Max = 0.983ε (Mean = 0.213ε) (GSL 2.1: Max = 2.64ε (Mean = 0.662ε)) | Max = 1.76ε (Mean = 0.38ε) (<math.h>: Max = 2.81ε (Mean = 0.739ε)) | Max = 1.65ε (Mean = 0.373ε) (<math.h>: Max = 2.36ε (Mean = 0.539ε))
Erf Function: Large Values | Max = 1.57ε (Mean = 0.542ε) (<cmath>: Max = 1.26ε (Mean = 0.441ε)) (<math.h>: Max = 1.26ε (Mean = 0.441ε)) | Max = 0.868ε (Mean = 0.147ε) (GSL 2.1: Max = 3.9ε (Mean = 0.472ε)) | Max = 1.57ε (Mean = 0.564ε) (<math.h>: Max = 4.91ε (Mean = 1.54ε)) | Max = 1.14ε (Mean = 0.248ε) (<math.h>: Max = 1.84ε (Mean = 0.331ε))

Table 137. Error rates for erfc_inv

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Inverse Erfc Function | Max = 0ε (Mean = 0ε) | Max = 0.996ε (Mean = 0.397ε) | Max = 1.08ε (Mean = 0.403ε) | Max = 1ε (Mean = 0.491ε)
Inverse Erfc Function: extreme values |  | Max = 1.62ε (Mean = 0.383ε) | Max = 1.62ε (Mean = 0.383ε) |

Table 138. Error rates for expint (Ei)

| GNU C++ version 7.1.0 linux long double | GNU C++ version 7.1.0 linux double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Exponential Integral Ei | Max = 5.05ε (Mean = 0.821ε) (<cmath>: Max = 14.1ε (Mean = 2.43ε) And other failures.) | Max = 0.994ε (Mean = 0.142ε) (GSL 2.1: Max = 8.96ε (Mean = 0.703ε)) | Max = 5.05ε (Mean = 0.835ε) | Max = 1.43ε (Mean = 0.54ε)
Exponential Integral Ei: double exponent range | Max = 1.72ε (Mean = 0.593ε) (<cmath>: Max = 3.11ε (Mean = 1.13ε)) | Max = 0.998ε (Mean = 0.156ε) (GSL 2.1: Max = 1.5ε (Mean = 0.612ε)) | Max = 1.72ε (Mean = 0.607ε) | Max = 1.7ε (Mean = 0.66ε)
Exponential Integral Ei: long exponent range | Max = 1.98ε (Mean = 0.595ε) (<cmath>: Max = 1.93ε (Mean = 0.855ε)) |  | Max = 1.98ε (Mean = 0.575ε) |

Table 139. Error rates for expint (En)

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Exponential Integral En | Max = 0.589ε (Mean = 0.0331ε) (GSL 2.1: Max = 58.5ε (Mean = 17.1ε)) | Max = 9.97ε (Mean = 2.13ε) | Max = 9.97ε (Mean = 2.13ε) | Max = 7.16ε (Mean = 1.85ε)
Exponential Integral En: small z values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 115ε (Mean = 23.6ε)) | Max = 1.99ε (Mean = 0.559ε) | Max = 1.99ε (Mean = 0.559ε) | Max = 2.62ε (Mean = 0.531ε)
Exponential Integral E1 | Max = 0.556ε (Mean = 0.0625ε) (GSL 2.1: Max = 0.988ε (Mean = 0.469ε)) | Max = 0.965ε (Mean = 0.414ε) | Max = 0.965ε (Mean = 0.408ε) | Max = 0.988ε (Mean = 0.486ε)

Table 140. Error rates for expm1

| GNU C++ version 7.1.0 linux long double | GNU C++ version 7.1.0 linux double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Random test data | Max = 0.992ε (Mean = 0.402ε) (<cmath>: Max = 0.992ε (Mean = 0.402ε)) (<math.h>: Max = 0.992ε (Mean = 0.402ε)) | Max = 0.793ε (Mean = 0.126ε) (Rmath 3.2.3: Max = 0.793ε (Mean = 0.126ε)) | Max = 1.31ε (Mean = 0.428ε) (<math.h>: Max = 0.996ε (Mean = 0.426ε)) | Max = 1.31ε (Mean = 0.496ε) (<math.h>: Max = 1.31ε (Mean = 0.496ε))

Table 141. Error rates for gamma_p

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
tgamma(a, z) medium values | Max = 0.955ε (Mean = 0.05ε) (GSL 2.1: Max = 342ε (Mean = 45.8ε)) (Rmath 3.2.3: Max = 389ε (Mean = 44ε)) | Max = 41.6ε (Mean = 8.09ε) | Max = 239ε (Mean = 30.2ε) | Max = 35.1ε (Mean = 6.98ε)
tgamma(a, z) small values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 4.82ε (Mean = 0.758ε)) (Rmath 3.2.3: Max = 1.01ε (Mean = 0.306ε)) | Max = 2ε (Mean = 0.464ε) | Max = 2ε (Mean = 0.461ε) | Max = 1.54ε (Mean = 0.439ε)
tgamma(a, z) large values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 1.02e+03ε (Mean = 105ε)) (Rmath 3.2.3: Max = 1.11e+03ε (Mean = 67.5ε)) | Max = 3.08e+04ε (Mean = 1.86e+03ε) | Max = 3.02e+04ε (Mean = 1.91e+03ε) | Max = 243ε (Mean = 20.2ε)
tgamma(a, z) integer and half integer values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 128ε (Mean = 22.6ε)) (Rmath 3.2.3: Max = 66.2ε (Mean = 12.2ε)) | Max = 11.8ε (Mean = 2.66ε) | Max = 71.6ε (Mean = 9.47ε) | Max = 13ε (Mean = 2.97ε)

Table 142. Error rates for gamma_p_inv

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
incomplete gamma inverse(a, z) medium values | Max = 0.993ε (Mean = 0.15ε) (Rmath 3.2.3: Max = 4.88ε (Mean = 0.868ε)) | Max = 1.8ε (Mean = 0.406ε) | Max = 1.89ε (Mean = 0.466ε) | Max = 1.71ε (Mean = 0.34ε)
incomplete gamma inverse(a, z) large values | Max = 0ε (Mean = 0ε) (Rmath 3.2.3: Max = 0.816ε (Mean = 0.0874ε)) | Max = 0.509ε (Mean = 0.0447ε) | Max = 0.509ε (Mean = 0.0447ε) | Max = 0.924ε (Mean = 0.108ε)
incomplete gamma inverse(a, z) small values | Max = 441ε (Mean = 53.9ε) (Rmath 3.2.3: Max = 547ε (Mean = 61.6ε)) | Max = 9.17e+03ε (Mean = 1.45e+03ε) | Max = 1.09e+04ε (Mean = 1.3e+03ε) | Max = 1.1e+03ε (Mean = 131ε)

Table 143. Error rates for gamma_p_inva

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Incomplete gamma inverses. | Max = 0ε (Mean = 0ε) | Max = 7.87ε (Mean = 1.15ε) | Max = 4.08ε (Mean = 1.12ε) | Max = 4.92ε (Mean = 1.03ε)

Table 144. Error rates for gamma_q

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
tgamma(a, z) medium values | Max = 0.927ε (Mean = 0.035ε) (GSL 2.1: Max = 201ε (Mean = 13.5ε)) (Rmath 3.2.3: Max = 131ε (Mean = 12.7ε)) | Max = 32.3ε (Mean = 6.61ε) | Max = 199ε (Mean = 26.6ε) | Max = 23.7ε (Mean = 4ε)
tgamma(a, z) small values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 1.38e+10ε (Mean = 1.05e+09ε)) (Rmath 3.2.3: Max = 65.6ε (Mean = 11ε)) | Max = 2.45ε (Mean = 0.885ε) | Max = 2.45ε (Mean = 0.819ε) | Max = 2.26ε (Mean = 0.74ε)
tgamma(a, z) large values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 2.71e+04ε (Mean = 2.16e+03ε)) (Rmath 3.2.3: Max = 1.02e+03ε (Mean = 62.7ε)) | Max = 6.82e+03ε (Mean = 414ε) | Max = 1.15e+04ε (Mean = 733ε) | Max = 469ε (Mean = 31.5ε)
tgamma(a, z) integer and half integer values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 118ε (Mean = 12.5ε)) (Rmath 3.2.3: Max = 138ε (Mean = 16.9ε)) | Max = 11.1ε (Mean = 2.07ε) | Max = 54.7ε (Mean = 6.16ε) | Max = 8.72ε (Mean = 1.48ε)

Table 145. Error rates for gamma_q_inv

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
incomplete gamma inverse(a, z) medium values | Max = 0.912ε (Mean = 0.154ε) (Rmath 3.2.3: Max = 4.66ε (Mean = 0.792ε)) | Max = 6.2ε (Mean = 0.627ε) | Max = 6.2ε (Mean = 0.683ε) | Max = 2.88ε (Mean = 0.469ε)
incomplete gamma inverse(a, z) large values | Max = 0.894ε (Mean = 0.0915ε) (Rmath 3.2.3: Max = 0.894ε (Mean = 0.106ε)) | Max = 0ε (Mean = 0ε) | Max = 0ε (Mean = 0ε) | Max = 0.814ε (Mean = 0.0856ε)
incomplete gamma inverse(a, z) small values | Max = 292ε (Mean = 36.4ε) (Rmath 3.2.3: Max = 415ε (Mean = 48.7ε)) | Max = 8.28e+03ε (Mean = 1.09e+03ε) | Max = 8.98e+03ε (Mean = 877ε) | Max = 451ε (Mean = 64.7ε)

Table 146. Error rates for gamma_q_inva

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Incomplete gamma inverses. | Max = 0ε (Mean = 0ε) | Max = 8.42ε (Mean = 1.3ε) | Max = 7.86ε (Mean = 1.24ε) | Max = 5.05ε (Mean = 1.08ε)

Table 147. Error rates for hermite

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Hermite Polynomials | Max = 0ε (Mean = 0ε) | Max = 6.24ε (Mean = 2.07ε) | Max = 6.24ε (Mean = 2.07ε) | Max = 4.46ε (Mean = 1.41ε)

Table 148. Error rates for heuman_lambda

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Elliptic Integral Jacobi Zeta: Mathworld Data | Max = 0ε (Mean = 0ε) | Max = 1.89ε (Mean = 0.887ε) | Max = 1.89ε (Mean = 0.887ε) | Max = 1.08ε (Mean = 0.734ε)
Elliptic Integral Heuman Lambda: Random Data | Max = 0ε (Mean = 0ε) | Max = 3.82ε (Mean = 0.609ε) | Max = 3.82ε (Mean = 0.608ε) | Max = 2.12ε (Mean = 0.588ε)

Table 149. Error rates for ibeta

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Incomplete Beta Function: Small Values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 682ε (Mean = 32.6ε)) (Rmath 3.2.3: Max = 22.9ε (Mean = 3.35ε)) | Max = 8.97ε (Mean = 2.09ε) | Max = 21.3ε (Mean = 2.75ε) | Max = 8.4ε (Mean = 1.93ε)
Incomplete Beta Function: Medium Values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 690ε (Mean = 151ε)) (Rmath 3.2.3: Max = 232ε (Mean = 27.9ε)) | Max = 50ε (Mean = 12.1ε) | Max = 124ε (Mean = 18.4ε) | Max = 106ε (Mean = 16.3ε)
Incomplete Beta Function: Large and Diverse Values | Max = 1.26ε (Mean = 0.063ε) (GSL 2.1: Max = 3.9e+05ε (Mean = 1.82e+04ε) And other failures.) (Rmath 3.2.3: Max = 574ε (Mean = 49.4ε)) | Max = 1.96e+04ε (Mean = 997ε) | Max = 4.98e+04ε (Mean = 2.07e+03ε) | Max = 1.32e+03ε (Mean = 68.5ε)
Incomplete Beta Function: Small Integer Values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 254ε (Mean = 50.9ε)) (Rmath 3.2.3: Max = 62.2ε (Mean = 8.95ε)) | Max = 4.45ε (Mean = 0.814ε) | Max = 44.5ε (Mean = 10.1ε) | Max = 3.85ε (Mean = 0.791ε)

Table 150. Error rates for ibeta_inv

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Inverse incomplete beta | Max = 11ε (Mean = 0.345ε) (Rmath 3.2.3: Max = 1.14e+121ε (Mean = 3.28e+119ε) And other failures.) | Max = 3.8e+04ε (Mean = 2.66e+03ε) | Max = 4.07e+04ε (Mean = 2.86e+03ε) | Max = 8.59e+03ε (Mean = 277ε)

Table 151. Error rates for ibeta_inva

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Inverse incomplete beta | Max = 0.602ε (Mean = 0.0239ε) | Max = 377ε (Mean = 24.4ε) | Max = 438ε (Mean = 31.3ε) | Max = 242ε (Mean = 22.9ε)

Table 152. Error rates for ibeta_invb

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Inverse incomplete beta | Max = 0.765ε (Mean = 0.0422ε) | Max = 407ε (Mean = 27.2ε) | Max = 407ε (Mean = 24.4ε) | Max = 409ε (Mean = 19.3ε)

Table 153. Error rates for ibetac

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Incomplete Beta Function: Small Values | Max = 0ε (Mean = 0ε) (Rmath 3.2.3: Max = 22.4ε (Mean = 3.67ε)) | Max = 10.6ε (Mean = 2.22ε) | Max = 13.8ε (Mean = 2.68ε) | Max = 6.94ε (Mean = 1.71ε)
Incomplete Beta Function: Medium Values | Max = 0ε (Mean = 0ε) (Rmath 3.2.3: Max = 204ε (Mean = 25.8ε)) | Max = 73.9ε (Mean = 11.2ε) | Max = 132ε (Mean = 19.8ε) | Max = 56.7ε (Mean = 14.3ε)
Incomplete Beta Function: Large and Diverse Values | Max = 0.981ε (Mean = 0.0573ε) (Rmath 3.2.3: Max = 889ε (Mean = 68.4ε)) | Max = 3.45e+04ε (Mean = 1.32e+03ε) | Max = 6.31e+04ε (Mean = 2.04e+03ε) | Max = 1.88e+03ε (Mean = 82.7ε)
Incomplete Beta Function: Small Integer Values | Max = 0ε (Mean = 0ε) (Rmath 3.2.3: Max = 84.6ε (Mean = 18ε)) | Max = 5.34ε (Mean = 1.11ε) | Max = 107ε (Mean = 17.1ε) | Max = 6.37ε (Mean = 1.03ε)

Table 154. Error rates for ibetac_inv

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Inverse incomplete beta | Max = 0.977ε (Mean = 0.0976ε) (Rmath 3.2.3: Max = 3.01e+132ε (Mean = 8.65e+130ε) And other failures.) | Max = 4.88e+04ε (Mean = 3.16e+03ε) | Max = 5.05e+04ε (Mean = 3.33e+03ε) | Max = 2.93e+03ε (Mean = 198ε)

Table 155. Error rates for ibetac_inva

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Inverse incomplete beta | Max = 0.683ε (Mean = 0.0314ε) | Max = 382ε (Mean = 22.2ε) | Max = 315ε (Mean = 23.7ε) | Max = 408ε (Mean = 26.7ε)

Table 156. Error rates for ibetac_invb

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Inverse incomplete beta | Max = 0.724ε (Mean = 0.0303ε) | Max = 317ε (Mean = 19.8ε) | Max = 369ε (Mean = 22.6ε) | Max = 271ε (Mean = 16.4ε)

Table 157. Error rates for jacobi_cn

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Jacobi Elliptic: Mathworld Data | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 17.3ε (Mean = 4.29ε) And other failures.) | Max = 71.6ε (Mean = 19.3ε) | Max = 71.6ε (Mean = 19.4ε) | Max = 45.8ε (Mean = 11.4ε)
Jacobi Elliptic: Random Data | Max = 0.816ε (Mean = 0.0563ε) (GSL 2.1: Max = 2.43ε (Mean = 0.803ε)) | Max = 1.68ε (Mean = 0.443ε) | Max = 1.68ε (Mean = 0.454ε) | Max = 1.83ε (Mean = 0.455ε)
Jacobi Elliptic: Random Small Values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 55.2ε (Mean = 1.64ε) And other failures.) | Max = 10.4ε (Mean = 0.594ε) | Max = 10.4ε (Mean = 0.602ε) | Max = 26.2ε (Mean = 1.17ε)
Jacobi Elliptic: Modulus near 1 | Max = 0.919ε (Mean = 0.127ε) (GSL 2.1: Max = 0ε (Mean = 0ε) And other failures.) | Max = 675ε (Mean = 87.1ε) | Max = 675ε (Mean = 86.8ε) | Max = 513ε (Mean = 126ε)
Jacobi Elliptic: Large Phi | Max = 14.2ε (Mean = 0.927ε) (GSL 2.1: Max = 5.92e+03ε (Mean = 477ε)) | Max = 2.97e+04ε (Mean = 1.9e+03ε) | Max = 2.97e+04ε (Mean = 1.9e+03ε) | Max = 3.27e+04ε (Mean = 1.93e+03ε)

Table 158. Error rates for jacobi_dn

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Jacobi Elliptic: Mathworld Data | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 2.82ε (Mean = 1.18ε) And other failures.) | Max = 49ε (Mean = 14ε) | Max = 49ε (Mean = 14ε) | Max = 34.3ε (Mean = 8.71ε)
Jacobi Elliptic: Random Data | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 3ε (Mean = 0.61ε)) | Max = 1.53ε (Mean = 0.473ε) | Max = 1.53ε (Mean = 0.481ε) | Max = 1.52ε (Mean = 0.466ε)
Jacobi Elliptic: Random Small Values | Max = 0.5ε (Mean = 0.0122ε) (GSL 2.1: Max = 1.5ε (Mean = 0.391ε) And other failures.) | Max = 22.4ε (Mean = 0.777ε) | Max = 22.4ε (Mean = 0.763ε) | Max = 16.1ε (Mean = 0.685ε)
Jacobi Elliptic: Modulus near 1 | Max = 2.28ε (Mean = 0.194ε) (GSL 2.1: Max = 0ε (Mean = 0ε) And other failures.) | Max = 3.75e+03ε (Mean = 293ε) | Max = 3.75e+03ε (Mean = 293ε) | Max = 6.24e+03ε (Mean = 482ε)
Jacobi Elliptic: Large Phi | Max = 14.1ε (Mean = 0.897ε) (GSL 2.1: Max = 121ε (Mean = 22ε)) | Max = 2.82e+04ε (Mean = 1.79e+03ε) | Max = 2.82e+04ε (Mean = 1.79e+03ε) | Max = 1.67e+04ε (Mean = 1e+03ε)

Table 159. Error rates for jacobi_sn

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Jacobi Elliptic: Mathworld Data | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 588ε (Mean = 146ε) And other failures.) | Max = 341ε (Mean = 80.7ε) | Max = 341ε (Mean = 80.7ε) | Max = 481ε (Mean = 113ε)
Jacobi Elliptic: Random Data | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 4.02ε (Mean = 1.07ε)) | Max = 2.01ε (Mean = 0.584ε) | Max = 2.01ε (Mean = 0.593ε) | Max = 1.92ε (Mean = 0.567ε)
Jacobi Elliptic: Random Small Values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 11.7ε (Mean = 1.65ε) And other failures.) | Max = 1.99ε (Mean = 0.347ε) | Max = 1.99ε (Mean = 0.347ε) | Max = 2.11ε (Mean = 0.385ε)
Jacobi Elliptic: Modulus near 1 | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 0ε (Mean = 0ε) And other failures.) | Max = 109ε (Mean = 7.35ε) | Max = 109ε (Mean = 7.38ε) | Max = 23.2ε (Mean = 1.85ε)
Jacobi Elliptic: Large Phi | Max = 12ε (Mean = 0.771ε) (GSL 2.1: Max = 4.54e+04ε (Mean = 2.63e+03ε)) | Max = 2.45e+04ε (Mean = 1.51e+03ε) | Max = 2.45e+04ε (Mean = 1.51e+03ε) | Max = 4.36e+04ε (Mean = 2.54e+03ε)

Table 160. Error rates for jacobi_zeta

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Elliptic Integral Jacobi Zeta: Mathworld Data | Max = 0ε (Mean = 0ε) | Max = 1.66ε (Mean = 0.48ε) | Max = 1.66ε (Mean = 0.48ε) | Max = 1.52ε (Mean = 0.357ε)
Elliptic Integral Jacobi Zeta: Random Data | Max = 0ε (Mean = 0ε) | Max = 2.99ε (Mean = 0.824ε) | Max = 3.96ε (Mean = 1.06ε) | Max = 3.89ε (Mean = 0.824ε)
Elliptic Integral Jacobi Zeta: Large Phi Values | Max = 0ε (Mean = 0ε) | Max = 2.92ε (Mean = 0.951ε) | Max = 3.05ε (Mean = 1.13ε) | Max = 2.52ε (Mean = 0.977ε)

Table 161. Error rates for laguerre(n, m, x)

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Associated Laguerre Polynomials | Max = 0.84ε (Mean = 0.0358ε) (GSL 2.1: Max = 434ε (Mean = 10.7ε)) | Max = 167ε (Mean = 6.38ε) (<cmath>: Max = 206ε (Mean = 6.86ε)) | Max = 167ε (Mean = 6.38ε) | Max = 434ε (Mean = 11.1ε)

Table 162. Error rates for laguerre(n, x)

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Laguerre Polynomials | Max = 6.82ε (Mean = 0.408ε) (GSL 2.1: Max = 3.1e+03ε (Mean = 185ε)) | Max = 1.39e+04ε (Mean = 828ε) (<cmath>: Max = 4.2e+03ε (Mean = 251ε)) | Max = 1.39e+04ε (Mean = 828ε) | Max = 3.1e+03ε (Mean = 185ε)

Table 163. Error rates for legendre_p

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Legendre Polynomials: Small Values | Max = 0.732ε (Mean = 0.0619ε) (GSL 2.1: Max = 211ε (Mean = 20.4ε)) | Max = 69.2ε (Mean = 9.58ε) (<cmath>: Max = 124ε (Mean = 13.2ε)) | Max = 69.2ε (Mean = 9.58ε) | Max = 211ε (Mean = 20.4ε)
Legendre Polynomials: Large Values | Max = 0.632ε (Mean = 0.0693ε) (GSL 2.1: Max = 300ε (Mean = 33.2ε)) | Max = 699ε (Mean = 59.6ε) (<cmath>: Max = 343ε (Mean = 32.1ε)) | Max = 699ε (Mean = 59.6ε) | Max = 300ε (Mean = 33.2ε)

Table 164. Error rates for legendre_p (associated)

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Associated Legendre Polynomials: Small Values | Max = 0.999ε (Mean = 0.05ε) (GSL 2.1: Max = 121ε (Mean = 6.75ε) And other failures.) | Max = 175ε (Mean = 9.88ε) (<cmath>: Max = 175ε (Mean = 9.36ε) And other failures.) | Max = 77.7ε (Mean = 5.59ε) | Max = 121ε (Mean = 7.14ε)

Table 165. Error rates for legendre_q

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Legendre Polynomials: Small Values | Max = 0.612ε (Mean = 0.0517ε) (GSL 2.1: Max = 46.4ε (Mean = 7.46ε)) | Max = 50.9ε (Mean = 9ε) | Max = 50.9ε (Mean = 8.98ε) | Max = 46.4ε (Mean = 7.32ε)
Legendre Polynomials: Large Values | Max = 2.49ε (Mean = 0.202ε) (GSL 2.1: Max = 4.6e+03ε (Mean = 366ε)) | Max = 5.98e+03ε (Mean = 478ε) | Max = 5.98e+03ε (Mean = 478ε) | Max = 4.6e+03ε (Mean = 366ε)

Table 166. Error rates for lgamma

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
factorials | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 33.6ε (Mean = 2.78ε)) (Rmath 3.2.3: Max = 1.55ε (Mean = 0.592ε)) | Max = 0.991ε (Mean = 0.308ε) (<cmath>: Max = 1.67ε (Mean = 0.487ε)) (<math.h>: Max = 1.67ε (Mean = 0.487ε)) | Max = 0.991ε (Mean = 0.383ε) (<math.h>: Max = 1.36ε (Mean = 0.476ε)) | Max = 0.914ε (Mean = 0.175ε) (<math.h>: Max = 0.958ε (Mean = 0.38ε))
near 0 | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 5.21ε (Mean = 1.57ε)) (Rmath 3.2.3: Max = 0ε (Mean = 0ε)) | Max = 1.42ε (Mean = 0.566ε) (<cmath>: Max = 0.964ε (Mean = 0.543ε)) (<math.h>: Max = 0.964ε (Mean = 0.543ε)) | Max = 1.42ε (Mean = 0.566ε) (<math.h>: Max = 0.964ε (Mean = 0.543ε)) | Max = 0.964ε (Mean = 0.462ε) (<math.h>: Max = 0.962ε (Mean = 0.372ε))
near 1 | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 442ε (Mean = 88.8ε)) (Rmath 3.2.3: Max = 7.99e+04ε (Mean = 1.68e+04ε)) | Max = 0.948ε (Mean = 0.36ε) (<cmath>: Max = 0.615ε (Mean = 0.096ε)) (<math.h>: Max = 0.615ε (Mean = 0.096ε)) | Max = 0.948ε (Mean = 0.36ε) (<math.h>: Max = 1.71ε (Mean = 0.581ε)) | Max = 0.867ε (Mean = 0.468ε) (<math.h>: Max = 0.906ε (Mean = 0.565ε))
near 2 | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 1.17e+03ε (Mean = 274ε)) (Rmath 3.2.3: Max = 2.63e+05ε (Mean = 5.84e+04ε)) | Max = 0.878ε (Mean = 0.242ε) (<cmath>: Max = 0.741ε (Mean = 0.263ε)) (<math.h>: Max = 0.741ε (Mean = 0.263ε)) | Max = 0.878ε (Mean = 0.242ε) (<math.h>: Max = 0.598ε (Mean = 0.235ε)) | Max = 0.591ε (Mean = 0.159ε) (<math.h>: Max = 0.741ε (Mean = 0.473ε))
near -10 | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 24.9ε (Mean = 4.6ε)) (Rmath 3.2.3: Max = 4.22ε (Mean = 1.26ε)) | Max = 3.81ε (Mean = 1.01ε) (<cmath>: Max = 0.997ε (Mean = 0.412ε)) (<math.h>: Max = 0.997ε (Mean = 0.412ε)) | Max = 3.81ε (Mean = 1.01ε) (<math.h>: Max = 3.04ε (Mean = 1.01ε)) | Max = 4.22ε (Mean = 1.33ε) (<math.h>: Max = 0.997ε (Mean = 0.444ε))
near -55 | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 7.02ε (Mean = 1.47ε)) (Rmath 3.2.3: Max = 250ε (Mean = 60.9ε)) | Max = 0.821ε (Mean = 0.513ε) (<cmath>: Max = 1.58ε (Mean = 0.672ε)) (<math.h>: Max = 1.58ε (Mean = 0.672ε)) | Max = 1.59ε (Mean = 0.587ε) (<math.h>: Max = 0.821ε (Mean = 0.674ε)) | Max = 0.821ε (Mean = 0.419ε) (<math.h>: Max = 249ε (Mean = 43.1ε))

Table 167. Error rates for log1p

| GNU C++ version 7.1.0 linux long double | GNU C++ version 7.1.0 linux double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Random test data | Max = 0.818ε (Mean = 0.227ε) (<cmath>: Max = 0.818ε (Mean = 0.227ε)) (<math.h>: Max = 0.818ε (Mean = 0.227ε)) | Max = 0.846ε (Mean = 0.153ε) (Rmath 3.2.3: Max = 0.846ε (Mean = 0.153ε)) | Max = 2.3ε (Mean = 0.66ε) (<math.h>: Max = 0.818ε (Mean = 0.249ε)) | Max = 0.509ε (Mean = 0.057ε) (<math.h>: Max = 0.509ε (Mean = 0.057ε))

Table 168. Error rates for non central beta CDF

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Non Central Beta, medium parameters | Max = 0.998ε (Mean = 0.0649ε) (Rmath 3.2.3: Max = 1.46e+26ε (Mean = 3.5e+24ε) And other failures.) | Max = 824ε (Mean = 27.4ε) | Max = 832ε (Mean = 38.1ε) | Max = 242ε (Mean = 31ε)
Non Central Beta, large parameters | Max = 1.18ε (Mean = 0.175ε) (Rmath 3.2.3: Max = 1.01e+36ε (Mean = 1.19e+35ε) And other failures.) | Max = 2.5e+04ε (Mean = 3.78e+03ε) | Max = 2.57e+04ε (Mean = 4.45e+03ε) | Max = 3.66e+03ε (Mean = 500ε)

Table 169. Error rates for non central beta CDF complement

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Non Central Beta, medium parameters | Max = 0.998ε (Mean = 0.0936ε) (Rmath 3.2.3: Max = 7.5e+97ε (Mean = 1.37e+96ε) And other failures.) | Max = 396ε (Mean = 50.7ε) | Max = 554ε (Mean = 57.2ε) | Max = 624ε (Mean = 62.7ε)
Non Central Beta, large parameters | Max = 0.986ε (Mean = 0.188ε) (Rmath 3.2.3: Max = +INFε (Mean = +INFε) And other failures.) | Max = 6.83e+03ε (Mean = 993ε) | Max = 3.56e+03ε (Mean = 707ε) | Max = 1.25e+04ε (Mean = 1.49e+03ε)

Table 170. Error rates for non central chi squared CDF

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Non Central Chi Squared, medium parameters | Max = 0.99ε (Mean = 0.0544ε) (Rmath 3.2.3: Max = 727ε (Mean = 121ε)) | Max = 46.5ε (Mean = 10.3ε) | Max = 115ε (Mean = 13.9ε) | Max = 48.9ε (Mean = 10ε)
Non Central Chi Squared, large parameters | Max = 1.07ε (Mean = 0.102ε) (Rmath 3.2.3: Max = 3.27e+08ε (Mean = 2.23e+07ε)) | Max = 3.07e+03ε (Mean = 336ε) | Max = 6.17e+03ε (Mean = 677ε) | Max = 9.79e+03ε (Mean = 723ε)

Table 171. Error rates for non central chi squared CDF complement

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Non Central Chi Squared, medium parameters | Max = 0.96ε (Mean = 0.0635ε) (Rmath 3.2.3: Max = +INFε (Mean = +INFε) And other failures.) | Max = 107ε (Mean = 17.2ε) | Max = 171ε (Mean = 22.8ε) | Max = 98.6ε (Mean = 15.8ε)
Non Central Chi Squared, large parameters | Max = 2.11ε (Mean = 0.278ε) (Rmath 3.2.3: Max = +INFε (Mean = +INFε) And other failures.) | Max = 5.02e+03ε (Mean = 630ε) | Max = 5.1e+03ε (Mean = 577ε) | Max = 5.43e+03ε (Mean = 705ε)

Table 172. Error rates for non central t CDF

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Non Central T | Max = 0.796ε (Mean = 0.0691ε) (Rmath 3.2.3: Max = 5.28e+15ε (Mean = 8.49e+14ε) And other failures.) | Max = 139ε (Mean = 31ε) | Max = 145ε (Mean = 30.9ε) | Max = 135ε (Mean = 32.1ε)
Non Central T (small non-centrality) | Max = 0ε (Mean = 0ε) (Rmath 3.2.3: Max = 2.09e+03ε (Mean = 244ε)) | Max = 3.86ε (Mean = 1.4ε) | Max = 9.15ε (Mean = 2.13ε) | Max = 6.17ε (Mean = 1.45ε)
Non Central T (large parameters) | Max = 257ε (Mean = 72.1ε) (Rmath 3.2.3: Max = 2.46ε (Mean = 0.657ε)) | Max = 5.26e+05ε (Mean = 1.48e+05ε) | Max = 5.24e+05ε (Mean = 1.47e+05ε) | Max = 286ε (Mean = 62.8ε)

Table 173. Error rates for non central t CDF complement

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Non Central T | Max = 0.707ε (Mean = 0.0497ε) (Rmath 3.2.3: Max = 6.19e+15ε (Mean = 6.72e+14ε) And other failures.) | Max = 201ε (Mean = 31.7ε) | Max = 340ε (Mean = 43.2ε) | Max = 154ε (Mean = 32.1ε)
Non Central T (small non-centrality) | Max = 0ε (Mean = 0ε) (Rmath 3.2.3: Max = 1.87e+03ε (Mean = 263ε)) | Max = 10.5ε (Mean = 2.13ε) | Max = 10.5ε (Mean = 2.39ε) | Max = 4.6ε (Mean = 1.63ε)
Non Central T (large parameters) | Max = 478ε (Mean = 96.3ε) (Rmath 3.2.3: Max = 2.24ε (Mean = 0.945ε)) | Max = 9.79e+05ε (Mean = 1.97e+05ε) | Max = 9.79e+05ε (Mean = 1.97e+05ε) | Max = 227ε (Mean = 50.4ε)

Table 174. Error rates for owens_t

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Owens T (medium small values) | Max = 0ε (Mean = 0ε) | Max = 3.34ε (Mean = 0.944ε) | Max = 3.34ε (Mean = 0.911ε) | Max = 4.37ε (Mean = 0.98ε)
Owens T (large and diverse values) | Max = 0ε (Mean = 0ε) | Max = 49ε (Mean = 2.16ε) | Max = 24.5ε (Mean = 1.39ε) | Max = 3.78ε (Mean = 0.621ε)

Table 175. Error rates for polygamma

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Mathematica Data | Max = 0.824ε (Mean = 0.0574ε) (GSL 2.1: Max = 62.9ε (Mean = 12.8ε)) (Rmath 3.2.3: Max = 108ε (Mean = 15.2ε)) | Max = 7.38ε (Mean = 1.84ε) | Max = 34.3ε (Mean = 7.65ε) | Max = 9.32ε (Mean = 1.95ε)
Mathematica Data - large arguments | Max = 0.998ε (Mean = 0.0592ε) (GSL 2.1: Max = 244ε (Mean = 32.8ε) And other failures.) (Rmath 3.2.3: Max = 1.71e+56ε (Mean = 1.01e+55ε) And other failures.) | Max = 2.23ε (Mean = 0.323ε) | Max = 11.1ε (Mean = 0.848ε) | Max = 150ε (Mean = 13.9ε)
Mathematica Data - negative arguments | Max = 0.516ε (Mean = 0.022ε) (GSL 2.1: Max = 36.6ε (Mean = 3.04ε) And other failures.) (Rmath 3.2.3: Max = 0ε (Mean = 0ε) And other failures.) | Max = 269ε (Mean = 87.7ε) | Max = 269ε (Mean = 88.4ε) | Max = 497ε (Mean = 129ε)
Mathematica Data - large negative arguments | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 1.79ε (Mean = 0.197ε) And other failures.) (Rmath 3.2.3: Max = 0ε (Mean = 0ε) And other failures.) | Max = 155ε (Mean = 96.4ε) | Max = 155ε (Mean = 96.4ε) | Max = 162ε (Mean = 101ε)
Mathematica Data - small arguments | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 15.2ε (Mean = 5.03ε)) (Rmath 3.2.3: Max = 106ε (Mean = 20ε)) | Max = 3.33ε (Mean = 0.75ε) | Max = 3.33ε (Mean = 0.75ε) | Max = 3ε (Mean = 0.496ε)
Mathematica Data - Large orders and other bug cases | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 151ε (Mean = 39.3ε) And other failures.) (Rmath 3.2.3: Max = +INFε (Mean = +INFε) And other failures.) | Max = 54.5ε (Mean = 13.3ε) | Max = 145ε (Mean = 55.9ε) | Max = 200ε (Mean = 57.2ε)

Table 176. Error rates for powm1

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
powm1 | Max = 1.06ε (Mean = 0.425ε) | Max = 2.04ε (Mean = 0.493ε) | Max = 1.88ε (Mean = 0.49ε) | Max = 1.84ε (Mean = 0.486ε)

Table 177. Error rates for sin_pi

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
sin_pi and cos_pi | Max = 0ε (Mean = 0ε) | Max = 0.996ε (Mean = 0.335ε) | Max = 0.996ε (Mean = 0.336ε) | Max = 0.99ε (Mean = 0.328ε)
sin_pi and cos_pi near integers and half integers | Max = 0ε (Mean = 0ε) | Max = 0.976ε (Mean = 0.293ε) | Max = 0.976ε (Mean = 0.293ε) | Max = 0.996ε (Mean = 0.343ε)

Table 178. Error rates for sph_bessel

| GNU C++ version 7.1.0 linux long double | GNU C++ version 7.1.0 linux double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Bessel j: Random Data | Max = 243ε (Mean = 13.3ε) (<cmath>: Max = 1.91e+06ε (Mean = 1.09e+05ε)) | Max = 0.978ε (Mean = 0.0445ε) (GSL 2.1: Max = 1.79e+03ε (Mean = 107ε)) | Max = 243ε (Mean = 33.7ε) | Max = 245ε (Mean = 16.3ε)

Table 179. Error rates for sph_bessel_prime

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Bessel j': Random Data | Max = 0.753ε (Mean = 0.0343ε) | Max = 167ε (Mean = 12ε) | Max = 167ε (Mean = 33.2ε) | Max = 307ε (Mean = 25.2ε)

Table 180. Error rates for sph_neumann

| GNU C++ version 7.1.0 linux long double | GNU C++ version 7.1.0 linux double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
y: Random Data | Max = 234ε (Mean = 19.5ε) (<cmath>: Max = 1.6e+06ε (Mean = 1.4e+05ε)) | Max = 0.995ε (Mean = 0.0665ε) (GSL 2.1: Max = 8.5e+04ε (Mean = 5.33e+03ε)) | Max = 234ε (Mean = 19.8ε) | Max = 281ε (Mean = 31.1ε)

Table 181. Error rates for sph_neumann_prime

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
y': Random Data | Max = 0.988ε (Mean = 0.0869ε) | Max = 158ε (Mean = 18.8ε) | Max = 158ε (Mean = 20.2ε) | Max = 296ε (Mean = 25.6ε)

Table 182. Error rates for spherical_harmonic_i

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Spherical Harmonics | Max = 1.36ε (Mean = 0.0765ε) | Max = 2.89e+03ε (Mean = 108ε) | Max = 1.03e+04ε (Mean = 327ε) | Max = 2.27e+04ε (Mean = 725ε)

Table 183. Error rates for spherical_harmonic_r

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Spherical Harmonics | Max = 1.58ε (Mean = 0.0707ε) | Max = 2.89e+03ε (Mean = 108ε) | Max = 1.03e+04ε (Mean = 327ε) | Max = 2.27e+04ε (Mean = 725ε)

Table 184. Error rates for sqrt1pm1

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
sqrt1pm1 | Max = 1.3ε (Mean = 0.404ε) | Max = 1.33ε (Mean = 0.404ε) | Max = 1.54ε (Mean = 0.563ε) | Max = 1.35ε (Mean = 0.497ε)

Table 185. Error rates for tgamma

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
factorials | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 3.95ε (Mean = 0.783ε)) (Rmath 3.2.3: Max = 314ε (Mean = 93.4ε)) | Max = 2.67ε (Mean = 0.617ε) (<cmath>: Max = 1.66ε (Mean = 0.584ε)) (<math.h>: Max = 1.66ε (Mean = 0.584ε)) | Max = 172ε (Mean = 41ε) (<math.h>: Max = 0ε (Mean = 0ε)) | Max = 1.85ε (Mean = 0.566ε) (<math.h>: Max = 3.17ε (Mean = 0.928ε))
near 0 | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 4.51ε (Mean = 1.92ε)) (Rmath 3.2.3: Max = 1ε (Mean = 0.335ε)) | Max = 2ε (Mean = 0.608ε) (<cmath>: Max = 1ε (Mean = 0.376ε)) (<math.h>: Max = 1ε (Mean = 0.376ε)) | Max = 2ε (Mean = 0.647ε) (<math.h>: Max = 0.5ε (Mean = 0.0791ε)) | Max = 1.5ε (Mean = 0.635ε) (<math.h>: Max = 1ε (Mean = 0.405ε))
near 1 | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 4.41ε (Mean = 1.81ε)) (Rmath 3.2.3: Max = 1ε (Mean = 0.32ε)) | Max = 2.51ε (Mean = 1.02ε) (<cmath>: Max = 0.918ε (Mean = 0.203ε)) (<math.h>: Max = 0.918ε (Mean = 0.203ε)) | Max = 3.01ε (Mean = 1.06ε) (<math.h>: Max = 1ε (Mean = 0.175ε)) | Max = 1.1ε (Mean = 0.59ε) (<math.h>: Max = 1ε (Mean = 0.4ε))
near 2 | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 7.95ε (Mean = 3.12ε)) (Rmath 3.2.3: Max = 1ε (Mean = 0.191ε)) | Max = 4.1ε (Mean = 1.55ε) (<cmath>: Max = 0.558ε (Mean = 0.298ε)) (<math.h>: Max = 0.558ε (Mean = 0.298ε)) | Max = 5.01ε (Mean = 1.89ε) (<math.h>: Max = 0ε (Mean = 0ε)) | Max = 2ε (Mean = 0.733ε) (<math.h>: Max = 0ε (Mean = 0ε))
near -10 | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 2.6ε (Mean = 1.05ε)) (Rmath 3.2.3: Max = 34.9ε (Mean = 9.2ε)) | Max = 1.75ε (Mean = 0.895ε) (<cmath>: Max = 2.26ε (Mean = 1.08ε)) (<math.h>: Max = 2.26ε (Mean = 1.08ε)) | Max = 1.75ε (Mean = 0.819ε) (<math.h>: Max = 0ε (Mean = 0ε)) | Max = 1.86ε (Mean = 0.881ε) (<math.h>: Max = 0.866ε (Mean = 0.445ε))
near -55 | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 1.8ε (Mean = 0.782ε)) (Rmath 3.2.3: Max = 3.89e+04ε (Mean = 9.52e+03ε)) | Max = 2.69ε (Mean = 1.09ε) (<cmath>: Max = 1.79ε (Mean = 0.75ε)) (<math.h>: Max = 1.79ε (Mean = 0.75ε)) | Max = 98.5ε (Mean = 53.4ε) (<math.h>: Max = 0ε (Mean = 0ε)) | Max = 2.7ε (Mean = 1.35ε) (<math.h>: Max = 3.87e+04ε (Mean = 6.71e+03ε))

Table 186. Error rates for tgamma1pm1

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
tgamma1pm1(dz) | Max = 0ε (Mean = 0ε) | Max = 1.12ε (Mean = 0.49ε) | Max = 6.61ε (Mean = 0.84ε) | Max = 3.31ε (Mean = 0.517ε)

Table 187. Error rates for tgamma_delta_ratio

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
tgamma + small delta ratios | Max = 0ε (Mean = 0ε) | Max = 5.83ε (Mean = 1.3ε) | Max = 15.4ε (Mean = 2.09ε) | Max = 7.56ε (Mean = 1.31ε)
tgamma + small delta ratios (negative delta) | Max = 0ε (Mean = 0ε) | Max = 7.94ε (Mean = 1.4ε) | Max = 18.3ε (Mean = 2.03ε) | Max = 7.43ε (Mean = 1.42ε)
tgamma + small integer ratios | Max = 0ε (Mean = 0ε) | Max = 1.96ε (Mean = 0.677ε) | Max = 1.96ε (Mean = 0.677ε) | Max = 2.74ε (Mean = 0.736ε)
tgamma + small integer ratios (negative delta) | Max = 0ε (Mean = 0ε) | Max = 1.62ε (Mean = 0.451ε) | Max = 1.62ε (Mean = 0.451ε) | Max = 2.15ε (Mean = 0.685ε)
integer tgamma ratios | Max = 0ε (Mean = 0ε) | Max = 0.997ε (Mean = 0.4ε) | Max = 0.997ε (Mean = 0.4ε) | Max = 0.968ε (Mean = 0.386ε)
integer tgamma ratios (negative delta) | Max = 0ε (Mean = 0ε) | Max = 0.853ε (Mean = 0.176ε) | Max = 0.853ε (Mean = 0.176ε) | Max = 0.974ε (Mean = 0.175ε)

Table 188. Error rates for tgamma (incomplete)

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
tgamma(a, z) medium values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 200ε (Mean = 13.3ε)) | Max = 8.47ε (Mean = 1.9ε) | Max = 412ε (Mean = 95.5ε) | Max = 8.14ε (Mean = 1.76ε)
tgamma(a, z) small values | Max = 0.753ε (Mean = 0.0474ε) (GSL 2.1: Max = 1.38e+10ε (Mean = 1.05e+09ε)) | Max = 2.31ε (Mean = 0.775ε) | Max = 2.13ε (Mean = 0.717ε) | Max = 2.53ε (Mean = 0.66ε)
tgamma(a, z) integer and half integer values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 117ε (Mean = 12.5ε)) | Max = 5.52ε (Mean = 1.48ε) | Max = 79.6ε (Mean = 20.9ε) | Max = 5.16ε (Mean = 1.33ε)

Table 189. Error rates for tgamma_lower

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
tgamma(a, z) medium values | Max = 0.833ε (Mean = 0.0315ε) (GSL 2.1: Max = 0.833ε (Mean = 0.0315ε)) | Max = 6.79ε (Mean = 1.46ε) | Max = 363ε (Mean = 63.8ε) | Max = 5.62ε (Mean = 1.49ε)
tgamma(a, z) small values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 0ε (Mean = 0ε)) | Max = 1.97ε (Mean = 0.555ε) | Max = 1.97ε (Mean = 0.558ε) | Max = 1.57ε (Mean = 0.525ε)
tgamma(a, z) integer and half integer values | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 0ε (Mean = 0ε)) | Max = 4.83ε (Mean = 1.15ε) | Max = 84.7ε (Mean = 17.5ε) | Max = 2.69ε (Mean = 0.849ε)

Table 190. Error rates for tgamma_ratio

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
tgamma ratios | Max = 0.694ε (Mean = 0.0347ε) | Max = 2.99ε (Mean = 1.15ε) | Max = 174ε (Mean = 61.2ε) | Max = 3.28ε (Mean = 1.12ε)

Table 191. Error rates for trigamma

| GNU C++ version 7.1.0 linux double | GNU C++ version 7.1.0 linux long double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Mathematica Data | Max = 0.998ε (Mean = 0.105ε) (GSL 2.1: Max = 1.34e+04ε (Mean = 1.49e+03ε)) (Rmath 3.2.3: Max = 1.34e+04ε (Mean = 1.51e+03ε)) | Max = 1.28ε (Mean = 0.449ε) | Max = 1.28ε (Mean = 0.449ε) | Max = 1ε (Mean = 0.382ε)

Table 192. Error rates for zeta

| GNU C++ version 7.1.0 linux long double | GNU C++ version 7.1.0 linux double | Sun compiler version 0x5150 Sun Solaris long double | Microsoft Visual C++ version 14.1 Win32 double
--- | --- | --- | --- | ---
Zeta: Random values greater than 1 | Max = 0.846ε (Mean = 0.0833ε) (<cmath>: Max = 5.45ε (Mean = 1ε)) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 8.69ε (Mean = 1.03ε)) | Max = 0.846ε (Mean = 0.0833ε) | Max = 0.836ε (Mean = 0.093ε)
Zeta: Random values less than 1 | Max = 7.03ε (Mean = 2.93ε) (<cmath>: Max = 538ε (Mean = 59.3ε)) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 137ε (Mean = 13.8ε)) | Max = 70.1ε (Mean = 17.1ε) | Max = 6.84ε (Mean = 3.12ε)
Zeta: Values close to and greater than 1 | Max = 0.995ε (Mean = 0.5ε) (<cmath>: Max = 1.9e+06ε (Mean = 5.11e+05ε)) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 7.73ε (Mean = 4.07ε)) | Max = 0.995ε (Mean = 0.5ε) | Max = 0.994ε (Mean = 0.421ε)
Zeta: Values close to and less than 1 | Max = 0.998ε (Mean = 0.508ε) (<cmath>: Max = 8.53e+06ε (Mean = 1.87e+06ε)) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 0.991ε (Mean = 0.28ε)) | Max = 0.998ε (Mean = 0.508ε) | Max = 0.991ε (Mean = 0.375ε)
Zeta: Integer arguments | Max = 9ε (Mean = 3.06ε) (<cmath>: Max = 70.3ε (Mean = 17.4ε)) | Max = 0ε (Mean = 0ε) (GSL 2.1: Max = 3.75ε (Mean = 1.1ε)) | Max = 28ε (Mean = 5.62ε) | Max = 9ε (Mean = 3ε)

Last revised: March 09, 2018 at 13:43:44 GMT |