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Retro68/gcc/libstdc++-v3/testsuite/tr1/5_numerical_facilities/special_functions/08_cyl_bessel_i/check_value.cc
Wolfgang Thaller 65c83606fb Update gcc to 7.2.0, binutils to 2.29, newlib to 2.5.0
2017-10-07 02:16:47 +02:00

1128 lines
47 KiB
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// 2007-02-04 Edward Smith-Rowland <3dw4rd@verizon.net>
//
// Copyright (C) 2007-2017 Free Software Foundation, Inc.
//
// This file is part of the GNU ISO C++ Library. This library is free
// software; you can redistribute it and/or modify it under the
// terms of the GNU General Public License as published by the
// Free Software Foundation; either version 3, or (at your option)
// any later version.
//
// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License along
// with this library; see the file COPYING3. If not see
// <http://www.gnu.org/licenses/>.
// cyl_bessel_i
// Compare against values generated by the GNU Scientific Library.
// The GSL can be found on the web: http://www.gnu.org/software/gsl/
#include <tr1/cmath>
#if defined(__TEST_DEBUG)
#include <iostream>
#define VERIFY(A) \
if (!(A)) \
{ \
std::cout << "line " << __LINE__ \
<< " max_abs_frac = " << max_abs_frac \
<< std::endl; \
}
#else
#include <testsuite_hooks.h>
#endif
#include "../testcase.h"
// Test data for nu=0.0000000000000000.
testcase_cyl_bessel_i<double> data001[] = {
{ 1.0000000000000000, 0.0000000000000000, 0.0000000000000000 },
{ 1.0156861412236078, 0.0000000000000000, 0.25000000000000000 },
{ 1.0634833707413236, 0.0000000000000000, 0.50000000000000000 },
{ 1.1456467780440014, 0.0000000000000000, 0.75000000000000000 },
{ 1.2660658777520082, 0.0000000000000000, 1.0000000000000000 },
{ 1.4304687177218294, 0.0000000000000000, 1.2500000000000000 },
{ 1.6467231897728904, 0.0000000000000000, 1.5000000000000000 },
{ 1.9252521538585023, 0.0000000000000000, 1.7500000000000000 },
{ 2.2795853023360668, 0.0000000000000000, 2.0000000000000000 },
{ 2.7270783071907951, 0.0000000000000000, 2.2500000000000000 },
{ 3.2898391440501231, 0.0000000000000000, 2.5000000000000000 },
{ 3.9959131072376550, 0.0000000000000000, 2.7500000000000000 },
{ 4.8807925858650245, 0.0000000000000000, 3.0000000000000000 },
{ 5.9893359979395138, 0.0000000000000000, 3.2500000000000000 },
{ 7.3782034322254750, 0.0000000000000000, 3.5000000000000000 },
{ 9.1189458608445655, 0.0000000000000000, 3.7500000000000000 },
{ 11.301921952136325, 0.0000000000000000, 4.0000000000000000 },
{ 14.041263683000595, 0.0000000000000000, 4.2500000000000000 },
{ 17.481171855609272, 0.0000000000000000, 4.5000000000000000 },
{ 21.803898740902120, 0.0000000000000000, 4.7500000000000000 },
{ 27.239871823604439, 0.0000000000000000, 5.0000000000000000 },
};
// Test function for nu=0.0000000000000000.
template<typename Tp>
void
test001()
{
const Tp eps = std::numeric_limits<Tp>::epsilon();
Tp max_abs_diff = -Tp(1);
Tp max_abs_frac = -Tp(1);
unsigned int num_datum = sizeof(data001)
/ sizeof(testcase_cyl_bessel_i<double>);
for (unsigned int i = 0; i < num_datum; ++i)
{
const Tp f = std::tr1::cyl_bessel_i(Tp(data001[i].nu), Tp(data001[i].x));
const Tp f0 = data001[i].f0;
const Tp diff = f - f0;
if (std::abs(diff) > max_abs_diff)
max_abs_diff = std::abs(diff);
if (std::abs(f0) > Tp(10) * eps
&& std::abs(f) > Tp(10) * eps)
{
const Tp frac = diff / f0;
if (std::abs(frac) > max_abs_frac)
max_abs_frac = std::abs(frac);
}
}
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
}
// Test data for nu=0.33333333333333331.
testcase_cyl_bessel_i<double> data002[] = {
{ 0.0000000000000000, 0.33333333333333331, 0.0000000000000000 },
{ 0.56650686557808660, 0.33333333333333331, 0.25000000000000000 },
{ 0.73897315642511863, 0.33333333333333331, 0.50000000000000000 },
{ 0.89532320365836804, 0.33333333333333331, 0.75000000000000000 },
{ 1.0646313978895285, 0.33333333333333331, 1.0000000000000000 },
{ 1.2623776732605250, 0.33333333333333331, 1.2500000000000000 },
{ 1.5014290000224382, 0.33333333333333331, 1.5000000000000000 },
{ 1.7951195525946044, 0.33333333333333331, 1.7500000000000000 },
{ 2.1587825813728614, 0.33333333333333331, 2.0000000000000000 },
{ 2.6109134564811405, 0.33333333333333331, 2.2500000000000000 },
{ 3.1743242297241938, 0.33333333333333331, 2.5000000000000000 },
{ 3.8774551722182107, 0.33333333333333331, 2.7500000000000000 },
{ 4.7559569371646946, 0.33333333333333331, 3.0000000000000000 },
{ 5.8546499652731825, 0.33333333333333331, 3.2500000000000000 },
{ 7.2299798619171147, 0.33333333333333331, 3.5000000000000000 },
{ 8.9531114355506318, 0.33333333333333331, 3.7500000000000000 },
{ 11.113838389991479, 0.33333333333333331, 4.0000000000000000 },
{ 13.825531136529117, 0.33333333333333331, 4.2500000000000000 },
{ 17.231403968478318, 0.33333333333333331, 4.5000000000000000 },
{ 21.512458099556554, 0.33333333333333331, 4.7500000000000000 },
{ 26.897553069268362, 0.33333333333333331, 5.0000000000000000 },
};
// Test function for nu=0.33333333333333331.
template<typename Tp>
void
test002()
{
const Tp eps = std::numeric_limits<Tp>::epsilon();
Tp max_abs_diff = -Tp(1);
Tp max_abs_frac = -Tp(1);
unsigned int num_datum = sizeof(data002)
/ sizeof(testcase_cyl_bessel_i<double>);
for (unsigned int i = 0; i < num_datum; ++i)
{
const Tp f = std::tr1::cyl_bessel_i(Tp(data002[i].nu), Tp(data002[i].x));
const Tp f0 = data002[i].f0;
const Tp diff = f - f0;
if (std::abs(diff) > max_abs_diff)
max_abs_diff = std::abs(diff);
if (std::abs(f0) > Tp(10) * eps
&& std::abs(f) > Tp(10) * eps)
{
const Tp frac = diff / f0;
if (std::abs(frac) > max_abs_frac)
max_abs_frac = std::abs(frac);
}
}
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
}
// Test data for nu=0.50000000000000000.
testcase_cyl_bessel_i<double> data003[] = {
{ 0.0000000000000000, 0.50000000000000000, 0.0000000000000000 },
{ 0.40311093489975897, 0.50000000000000000, 0.25000000000000000 },
{ 0.58799308679041573, 0.50000000000000000, 0.50000000000000000 },
{ 0.75761498638991298, 0.50000000000000000, 0.75000000000000000 },
{ 0.93767488824548695, 0.50000000000000000, 1.0000000000000000 },
{ 1.1432089853159872, 0.50000000000000000, 1.2500000000000000 },
{ 1.3871617204034761, 0.50000000000000000, 1.5000000000000000 },
{ 1.6830217804556815, 0.50000000000000000, 1.7500000000000000 },
{ 2.0462368630890526, 0.50000000000000000, 2.0000000000000000 },
{ 2.4953405089360041, 0.50000000000000000, 2.2500000000000000 },
{ 3.0530935381967175, 0.50000000000000000, 2.5000000000000000 },
{ 3.7477882494879449, 0.50000000000000000, 2.7500000000000000 },
{ 4.6148229034075969, 0.50000000000000000, 3.0000000000000000 },
{ 5.6986505325335495, 0.50000000000000000, 3.2500000000000000 },
{ 7.0552194086911877, 0.50000000000000000, 3.5000000000000000 },
{ 8.7550467841188944, 0.50000000000000000, 3.7500000000000000 },
{ 10.887101798588422, 0.50000000000000000, 4.0000000000000000 },
{ 13.563718712579764, 0.50000000000000000, 4.2500000000000000 },
{ 16.926820080158183, 0.50000000000000000, 4.5000000000000000 },
{ 21.155804306570005, 0.50000000000000000, 4.7500000000000000 },
{ 26.477547497559065, 0.50000000000000000, 5.0000000000000000 },
};
// Test function for nu=0.50000000000000000.
template<typename Tp>
void
test003()
{
const Tp eps = std::numeric_limits<Tp>::epsilon();
Tp max_abs_diff = -Tp(1);
Tp max_abs_frac = -Tp(1);
unsigned int num_datum = sizeof(data003)
/ sizeof(testcase_cyl_bessel_i<double>);
for (unsigned int i = 0; i < num_datum; ++i)
{
const Tp f = std::tr1::cyl_bessel_i(Tp(data003[i].nu), Tp(data003[i].x));
const Tp f0 = data003[i].f0;
const Tp diff = f - f0;
if (std::abs(diff) > max_abs_diff)
max_abs_diff = std::abs(diff);
if (std::abs(f0) > Tp(10) * eps
&& std::abs(f) > Tp(10) * eps)
{
const Tp frac = diff / f0;
if (std::abs(frac) > max_abs_frac)
max_abs_frac = std::abs(frac);
}
}
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
}
// Test data for nu=0.66666666666666663.
testcase_cyl_bessel_i<double> data004[] = {
{ 0.0000000000000000, 0.66666666666666663, 0.0000000000000000 },
{ 0.27953690613200438, 0.66666666666666663, 0.25000000000000000 },
{ 0.45628323113556879, 0.66666666666666663, 0.50000000000000000 },
{ 0.62594569838182612, 0.66666666666666663, 0.75000000000000000 },
{ 0.80752128860612948, 0.66666666666666663, 1.0000000000000000 },
{ 1.0139484513577168, 0.66666666666666663, 1.2500000000000000 },
{ 1.2572918396962991, 0.66666666666666663, 1.5000000000000000 },
{ 1.5505806938325577, 0.66666666666666663, 1.7500000000000000 },
{ 1.9089492968236206, 0.66666666666666663, 2.0000000000000000 },
{ 2.3506463490300331, 0.66666666666666663, 2.2500000000000000 },
{ 2.8981161894224892, 0.66666666666666663, 2.5000000000000000 },
{ 3.5792654911068720, 0.66666666666666663, 2.7500000000000000 },
{ 4.4290087213549505, 0.66666666666666663, 3.0000000000000000 },
{ 5.4911895720097688, 0.66666666666666663, 3.2500000000000000 },
{ 6.8209918044137305, 0.66666666666666663, 3.5000000000000000 },
{ 8.4879784249619767, 0.66666666666666663, 3.7500000000000000 },
{ 10.579932774013002, 0.66666666666666663, 4.0000000000000000 },
{ 13.207720355482458, 0.66666666666666663, 4.2500000000000000 },
{ 16.511448404200543, 0.66666666666666663, 4.5000000000000000 },
{ 20.668274532832392, 0.66666666666666663, 4.7500000000000000 },
{ 25.902310583215122, 0.66666666666666663, 5.0000000000000000 },
};
// Test function for nu=0.66666666666666663.
template<typename Tp>
void
test004()
{
const Tp eps = std::numeric_limits<Tp>::epsilon();
Tp max_abs_diff = -Tp(1);
Tp max_abs_frac = -Tp(1);
unsigned int num_datum = sizeof(data004)
/ sizeof(testcase_cyl_bessel_i<double>);
for (unsigned int i = 0; i < num_datum; ++i)
{
const Tp f = std::tr1::cyl_bessel_i(Tp(data004[i].nu), Tp(data004[i].x));
const Tp f0 = data004[i].f0;
const Tp diff = f - f0;
if (std::abs(diff) > max_abs_diff)
max_abs_diff = std::abs(diff);
if (std::abs(f0) > Tp(10) * eps
&& std::abs(f) > Tp(10) * eps)
{
const Tp frac = diff / f0;
if (std::abs(frac) > max_abs_frac)
max_abs_frac = std::abs(frac);
}
}
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
}
// Test data for nu=1.0000000000000000.
testcase_cyl_bessel_i<double> data005[] = {
{ 0.0000000000000000, 1.0000000000000000, 0.0000000000000000 },
{ 0.12597910894546793, 1.0000000000000000, 0.25000000000000000 },
{ 0.25789430539089631, 1.0000000000000000, 0.50000000000000000 },
{ 0.40199246158092228, 1.0000000000000000, 0.75000000000000000 },
{ 0.56515910399248503, 1.0000000000000000, 1.0000000000000000 },
{ 0.75528141834074725, 1.0000000000000000, 1.2500000000000000 },
{ 0.98166642857790720, 1.0000000000000000, 1.5000000000000000 },
{ 1.2555375122401731, 1.0000000000000000, 1.7500000000000000 },
{ 1.5906368546373291, 1.0000000000000000, 2.0000000000000000 },
{ 2.0039674569295931, 1.0000000000000000, 2.2500000000000000 },
{ 2.5167162452886984, 1.0000000000000000, 2.5000000000000000 },
{ 3.1554101386190028, 1.0000000000000000, 2.7500000000000000 },
{ 3.9533702174026097, 1.0000000000000000, 3.0000000000000000 },
{ 4.9525461659085490, 1.0000000000000000, 3.2500000000000000 },
{ 6.2058349222583642, 1.0000000000000000, 3.5000000000000000 },
{ 7.7800152298244161, 1.0000000000000000, 3.7500000000000000 },
{ 9.7594651537044488, 1.0000000000000000, 4.0000000000000000 },
{ 12.250874667409304, 1.0000000000000000, 4.2500000000000000 },
{ 15.389222753735924, 1.0000000000000000, 4.5000000000000000 },
{ 19.345361447520226, 1.0000000000000000, 4.7500000000000000 },
{ 24.335642142450524, 1.0000000000000000, 5.0000000000000000 },
};
// Test function for nu=1.0000000000000000.
template<typename Tp>
void
test005()
{
const Tp eps = std::numeric_limits<Tp>::epsilon();
Tp max_abs_diff = -Tp(1);
Tp max_abs_frac = -Tp(1);
unsigned int num_datum = sizeof(data005)
/ sizeof(testcase_cyl_bessel_i<double>);
for (unsigned int i = 0; i < num_datum; ++i)
{
const Tp f = std::tr1::cyl_bessel_i(Tp(data005[i].nu), Tp(data005[i].x));
const Tp f0 = data005[i].f0;
const Tp diff = f - f0;
if (std::abs(diff) > max_abs_diff)
max_abs_diff = std::abs(diff);
if (std::abs(f0) > Tp(10) * eps
&& std::abs(f) > Tp(10) * eps)
{
const Tp frac = diff / f0;
if (std::abs(frac) > max_abs_frac)
max_abs_frac = std::abs(frac);
}
}
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
}
// Test data for nu=2.0000000000000000.
testcase_cyl_bessel_i<double> data006[] = {
{ 0.0000000000000000, 2.0000000000000000, 0.0000000000000000 },
{ 0.0078532696598645167, 2.0000000000000000, 0.25000000000000000 },
{ 0.031906149177738249, 2.0000000000000000, 0.50000000000000000 },
{ 0.073666880494875436, 2.0000000000000000, 0.75000000000000000 },
{ 0.13574766976703831, 2.0000000000000000, 1.0000000000000000 },
{ 0.22201844837663415, 2.0000000000000000, 1.2500000000000000 },
{ 0.33783461833568068, 2.0000000000000000, 1.5000000000000000 },
{ 0.49035213986973319, 2.0000000000000000, 1.7500000000000000 },
{ 0.68894844769873831, 2.0000000000000000, 2.0000000000000000 },
{ 0.94577390103115722, 2.0000000000000000, 2.2500000000000000 },
{ 1.2764661478191643, 2.0000000000000000, 2.5000000000000000 },
{ 1.7010693700601991, 2.0000000000000000, 2.7500000000000000 },
{ 2.2452124409299512, 2.0000000000000000, 3.0000000000000000 },
{ 2.9416152804573357, 2.0000000000000000, 3.2500000000000000 },
{ 3.8320120480778415, 2.0000000000000000, 3.5000000000000000 },
{ 4.9696044049382113, 2.0000000000000000, 3.7500000000000000 },
{ 6.4221893752841046, 2.0000000000000000, 4.0000000000000000 },
{ 8.2761461924550552, 2.0000000000000000, 4.2500000000000000 },
{ 10.641517298393307, 2.0000000000000000, 4.5000000000000000 },
{ 13.658483394577813, 2.0000000000000000, 4.7500000000000000 },
{ 17.505614966624233, 2.0000000000000000, 5.0000000000000000 },
};
// Test function for nu=2.0000000000000000.
template<typename Tp>
void
test006()
{
const Tp eps = std::numeric_limits<Tp>::epsilon();
Tp max_abs_diff = -Tp(1);
Tp max_abs_frac = -Tp(1);
unsigned int num_datum = sizeof(data006)
/ sizeof(testcase_cyl_bessel_i<double>);
for (unsigned int i = 0; i < num_datum; ++i)
{
const Tp f = std::tr1::cyl_bessel_i(Tp(data006[i].nu), Tp(data006[i].x));
const Tp f0 = data006[i].f0;
const Tp diff = f - f0;
if (std::abs(diff) > max_abs_diff)
max_abs_diff = std::abs(diff);
if (std::abs(f0) > Tp(10) * eps
&& std::abs(f) > Tp(10) * eps)
{
const Tp frac = diff / f0;
if (std::abs(frac) > max_abs_frac)
max_abs_frac = std::abs(frac);
}
}
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
}
// Test data for nu=5.0000000000000000.
testcase_cyl_bessel_i<double> data007[] = {
{ 0.0000000000000000, 5.0000000000000000, 0.0000000000000000 },
{ 2.5497616449882785e-07, 5.0000000000000000, 0.25000000000000000 },
{ 8.2231713131092646e-06, 5.0000000000000000, 0.50000000000000000 },
{ 6.3261122739811725e-05, 5.0000000000000000, 0.75000000000000000 },
{ 0.00027146315595697195, 5.0000000000000000, 1.0000000000000000 },
{ 0.00084793613616686856, 5.0000000000000000, 1.2500000000000000 },
{ 0.0021705595690975554, 5.0000000000000000, 1.5000000000000000 },
{ 0.0048504513371845394, 5.0000000000000000, 1.7500000000000000 },
{ 0.0098256793231317023, 5.0000000000000000, 2.0000000000000000 },
{ 0.018486577941045829, 5.0000000000000000, 2.2500000000000000 },
{ 0.032843475172023219, 5.0000000000000000, 2.5000000000000000 },
{ 0.055750882754221943, 5.0000000000000000, 2.7500000000000000 },
{ 0.091206477661513338, 5.0000000000000000, 3.0000000000000000 },
{ 0.14474880546308083, 5.0000000000000000, 3.2500000000000000 },
{ 0.22398495470190780, 5.0000000000000000, 3.5000000000000000 },
{ 0.33928899170999866, 5.0000000000000000, 3.7500000000000000 },
{ 0.50472436311316626, 5.0000000000000000, 4.0000000000000000 },
{ 0.73925961816682961, 5.0000000000000000, 4.2500000000000000 },
{ 1.0683677743764699, 5.0000000000000000, 4.5000000000000000 },
{ 1.5261268693599621, 5.0000000000000000, 4.7500000000000000 },
{ 2.1579745473225476, 5.0000000000000000, 5.0000000000000000 },
};
// Test function for nu=5.0000000000000000.
template<typename Tp>
void
test007()
{
const Tp eps = std::numeric_limits<Tp>::epsilon();
Tp max_abs_diff = -Tp(1);
Tp max_abs_frac = -Tp(1);
unsigned int num_datum = sizeof(data007)
/ sizeof(testcase_cyl_bessel_i<double>);
for (unsigned int i = 0; i < num_datum; ++i)
{
const Tp f = std::tr1::cyl_bessel_i(Tp(data007[i].nu), Tp(data007[i].x));
const Tp f0 = data007[i].f0;
const Tp diff = f - f0;
if (std::abs(diff) > max_abs_diff)
max_abs_diff = std::abs(diff);
if (std::abs(f0) > Tp(10) * eps
&& std::abs(f) > Tp(10) * eps)
{
const Tp frac = diff / f0;
if (std::abs(frac) > max_abs_frac)
max_abs_frac = std::abs(frac);
}
}
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
}
// Test data for nu=10.000000000000000.
testcase_cyl_bessel_i<double> data008[] = {
{ 0.0000000000000000, 10.000000000000000, 0.0000000000000000 },
{ 2.5701232848571186e-16, 10.000000000000000, 0.25000000000000000 },
{ 2.6430419258812784e-13, 10.000000000000000, 0.50000000000000000 },
{ 1.5349659676120412e-11, 10.000000000000000, 0.75000000000000000 },
{ 2.7529480398368732e-10, 10.000000000000000, 1.0000000000000000 },
{ 2.5967897782035928e-09, 10.000000000000000, 1.2500000000000000 },
{ 1.6330924437799743e-08, 10.000000000000000, 1.5000000000000000 },
{ 7.7706676834614093e-08, 10.000000000000000, 1.7500000000000000 },
{ 3.0169638793506839e-07, 10.000000000000000, 2.0000000000000000 },
{ 1.0034459057774481e-06, 10.000000000000000, 2.2500000000000000 },
{ 2.9557436109680578e-06, 10.000000000000000, 2.5000000000000000 },
{ 7.8955603774082724e-06, 10.000000000000000, 2.7500000000000000 },
{ 1.9464393470612970e-05, 10.000000000000000, 3.0000000000000000 },
{ 4.4875369479742435e-05, 10.000000000000000, 3.2500000000000000 },
{ 9.7760848514528916e-05, 10.000000000000000, 3.5000000000000000 },
{ 0.00020289011210063493, 10.000000000000000, 3.7500000000000000 },
{ 0.00040378896132693047, 10.000000000000000, 4.0000000000000000 },
{ 0.00077478519551669892, 10.000000000000000, 4.2500000000000000 },
{ 0.0014397060684919682, 10.000000000000000, 4.5000000000000000 },
{ 0.0026004486016189452, 10.000000000000000, 4.7500000000000000 },
{ 0.0045800444191760525, 10.000000000000000, 5.0000000000000000 },
};
// Test function for nu=10.000000000000000.
template<typename Tp>
void
test008()
{
const Tp eps = std::numeric_limits<Tp>::epsilon();
Tp max_abs_diff = -Tp(1);
Tp max_abs_frac = -Tp(1);
unsigned int num_datum = sizeof(data008)
/ sizeof(testcase_cyl_bessel_i<double>);
for (unsigned int i = 0; i < num_datum; ++i)
{
const Tp f = std::tr1::cyl_bessel_i(Tp(data008[i].nu), Tp(data008[i].x));
const Tp f0 = data008[i].f0;
const Tp diff = f - f0;
if (std::abs(diff) > max_abs_diff)
max_abs_diff = std::abs(diff);
if (std::abs(f0) > Tp(10) * eps
&& std::abs(f) > Tp(10) * eps)
{
const Tp frac = diff / f0;
if (std::abs(frac) > max_abs_frac)
max_abs_frac = std::abs(frac);
}
}
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
}
// Test data for nu=20.000000000000000.
testcase_cyl_bessel_i<double> data009[] = {
{ 0.0000000000000000, 20.000000000000000, 0.0000000000000000 },
{ 3.5677858077910353e-37, 20.000000000000000, 0.25000000000000000 },
{ 3.7494538480790194e-31, 20.000000000000000, 0.50000000000000000 },
{ 1.2514356342425337e-27, 20.000000000000000, 0.75000000000000000 },
{ 3.9668359858190197e-25, 20.000000000000000, 1.0000000000000000 },
{ 3.4637832909868234e-23, 20.000000000000000, 1.2500000000000000 },
{ 1.3388331839683472e-21, 20.000000000000000, 1.5000000000000000 },
{ 2.9502376732679751e-20, 20.000000000000000, 1.7500000000000000 },
{ 4.3105605761095479e-19, 20.000000000000000, 2.0000000000000000 },
{ 4.6032451406433059e-18, 20.000000000000000, 2.2500000000000000 },
{ 3.8400317244170310e-17, 20.000000000000000, 2.5000000000000000 },
{ 2.6239115263043263e-16, 20.000000000000000, 2.7500000000000000 },
{ 1.5209660019426689e-15, 20.000000000000000, 3.0000000000000000 },
{ 7.6806450728249953e-15, 20.000000000000000, 3.2500000000000000 },
{ 3.4495528847222945e-14, 20.000000000000000, 3.5000000000000000 },
{ 1.4006589294850672e-13, 20.000000000000000, 3.7500000000000000 },
{ 5.2100734221993044e-13, 20.000000000000000, 4.0000000000000000 },
{ 1.7946903269488168e-12, 20.000000000000000, 4.2500000000000000 },
{ 5.7763830562279683e-12, 20.000000000000000, 4.5000000000000000 },
{ 1.7502433074548735e-11, 20.000000000000000, 4.7500000000000000 },
{ 5.0242393579718066e-11, 20.000000000000000, 5.0000000000000000 },
};
// Test function for nu=20.000000000000000.
template<typename Tp>
void
test009()
{
const Tp eps = std::numeric_limits<Tp>::epsilon();
Tp max_abs_diff = -Tp(1);
Tp max_abs_frac = -Tp(1);
unsigned int num_datum = sizeof(data009)
/ sizeof(testcase_cyl_bessel_i<double>);
for (unsigned int i = 0; i < num_datum; ++i)
{
const Tp f = std::tr1::cyl_bessel_i(Tp(data009[i].nu), Tp(data009[i].x));
const Tp f0 = data009[i].f0;
const Tp diff = f - f0;
if (std::abs(diff) > max_abs_diff)
max_abs_diff = std::abs(diff);
if (std::abs(f0) > Tp(10) * eps
&& std::abs(f) > Tp(10) * eps)
{
const Tp frac = diff / f0;
if (std::abs(frac) > max_abs_frac)
max_abs_frac = std::abs(frac);
}
}
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
}
// cyl_bessel_i
// Test data for nu=0.0000000000000000.
testcase_cyl_bessel_i<double> data010[] = {
{ 1.0000000000000000, 0.0000000000000000, 0.0000000000000000 },
{ 27.239871823604439, 0.0000000000000000, 5.0000000000000000 },
{ 2815.7166284662558, 0.0000000000000000, 10.000000000000000 },
{ 339649.37329791381, 0.0000000000000000, 15.000000000000000 },
{ 43558282.559553474, 0.0000000000000000, 20.000000000000000 },
{ 5774560606.4663124, 0.0000000000000000, 25.000000000000000 },
{ 781672297823.97925, 0.0000000000000000, 30.000000000000000 },
{ 107338818494514.42, 0.0000000000000000, 35.000000000000000 },
{ 14894774793419918., 0.0000000000000000, 40.000000000000000 },
{ 2.0834140751773164e+18, 0.0000000000000000, 45.000000000000000 },
{ 2.9325537838493457e+20, 0.0000000000000000, 50.000000000000000 },
{ 4.1487895607332160e+22, 0.0000000000000000, 55.000000000000000 },
{ 5.8940770556098216e+24, 0.0000000000000000, 60.000000000000000 },
{ 8.4030398456255596e+26, 0.0000000000000000, 65.000000000000000 },
{ 1.2015889579125424e+29, 0.0000000000000000, 70.000000000000000 },
{ 1.7226390780357976e+31, 0.0000000000000000, 75.000000000000000 },
{ 2.4751784043341661e+33, 0.0000000000000000, 80.000000000000000 },
{ 3.5634776304081403e+35, 0.0000000000000000, 85.000000000000000 },
{ 5.1392383455086475e+37, 0.0000000000000000, 90.000000000000000 },
{ 7.4233258618752072e+39, 0.0000000000000000, 95.000000000000000 },
{ 1.0737517071310986e+42, 0.0000000000000000, 100.00000000000000 },
};
// Test function for nu=0.0000000000000000.
template<typename Tp>
void
test010()
{
const Tp eps = std::numeric_limits<Tp>::epsilon();
Tp max_abs_diff = -Tp(1);
Tp max_abs_frac = -Tp(1);
unsigned int num_datum = sizeof(data010)
/ sizeof(testcase_cyl_bessel_i<double>);
for (unsigned int i = 0; i < num_datum; ++i)
{
const Tp f = std::tr1::cyl_bessel_i(Tp(data010[i].nu), Tp(data010[i].x));
const Tp f0 = data010[i].f0;
const Tp diff = f - f0;
if (std::abs(diff) > max_abs_diff)
max_abs_diff = std::abs(diff);
if (std::abs(f0) > Tp(10) * eps
&& std::abs(f) > Tp(10) * eps)
{
const Tp frac = diff / f0;
if (std::abs(frac) > max_abs_frac)
max_abs_frac = std::abs(frac);
}
}
VERIFY(max_abs_frac < Tp(2.5000000000000015e-12));
}
// Test data for nu=0.33333333333333331.
testcase_cyl_bessel_i<double> data011[] = {
{ 0.0000000000000000, 0.33333333333333331, 0.0000000000000000 },
{ 26.897553069268362, 0.33333333333333331, 5.0000000000000000 },
{ 2799.2396097056790, 0.33333333333333331, 10.000000000000000 },
{ 338348.63146593666, 0.33333333333333331, 15.000000000000000 },
{ 43434263.927938424, 0.33333333333333331, 20.000000000000000 },
{ 5761474759.6213636, 0.33333333333333331, 25.000000000000000 },
{ 780201111830.30237, 0.33333333333333331, 30.000000000000000 },
{ 107166066959051.91, 0.33333333333333331, 35.000000000000000 },
{ 14873836574083764., 0.33333333333333331, 40.000000000000000 },
{ 2.0808143020217085e+18, 0.33333333333333331, 45.000000000000000 },
{ 2.9292639365644226e+20, 0.33333333333333331, 50.000000000000000 },
{ 4.1445621624120489e+22, 0.33333333333333331, 55.000000000000000 },
{ 5.8885758374365916e+24, 0.33333333333333331, 60.000000000000000 },
{ 8.3958047021083955e+26, 0.33333333333333331, 65.000000000000000 },
{ 1.2006287819446431e+29, 0.33333333333333331, 70.000000000000000 },
{ 1.7213548977150022e+31, 0.33333333333333331, 75.000000000000000 },
{ 2.4734492458444449e+33, 0.33333333333333331, 80.000000000000000 },
{ 3.5611354547857122e+35, 0.33333333333333331, 85.000000000000000 },
{ 5.1360491295551848e+37, 0.33333333333333331, 90.000000000000000 },
{ 7.4189629097600431e+39, 0.33333333333333331, 95.000000000000000 },
{ 1.0731523308358370e+42, 0.33333333333333331, 100.00000000000000 },
};
// Test function for nu=0.33333333333333331.
template<typename Tp>
void
test011()
{
const Tp eps = std::numeric_limits<Tp>::epsilon();
Tp max_abs_diff = -Tp(1);
Tp max_abs_frac = -Tp(1);
unsigned int num_datum = sizeof(data011)
/ sizeof(testcase_cyl_bessel_i<double>);
for (unsigned int i = 0; i < num_datum; ++i)
{
const Tp f = std::tr1::cyl_bessel_i(Tp(data011[i].nu), Tp(data011[i].x));
const Tp f0 = data011[i].f0;
const Tp diff = f - f0;
if (std::abs(diff) > max_abs_diff)
max_abs_diff = std::abs(diff);
if (std::abs(f0) > Tp(10) * eps
&& std::abs(f) > Tp(10) * eps)
{
const Tp frac = diff / f0;
if (std::abs(frac) > max_abs_frac)
max_abs_frac = std::abs(frac);
}
}
VERIFY(max_abs_frac < Tp(1.0000000000000008e-12));
}
// Test data for nu=0.50000000000000000.
testcase_cyl_bessel_i<double> data012[] = {
{ 0.0000000000000000, 0.50000000000000000, 0.0000000000000000 },
{ 26.477547497559065, 0.50000000000000000, 5.0000000000000000 },
{ 2778.7846038745711, 0.50000000000000000, 10.000000000000000 },
{ 336729.88718706399, 0.50000000000000000, 15.000000000000000 },
{ 43279746.272428922, 0.50000000000000000, 20.000000000000000 },
{ 5745159748.3464680, 0.50000000000000000, 25.000000000000000 },
{ 778366068840.44580, 0.50000000000000000, 30.000000000000000 },
{ 106950522408567.66, 0.50000000000000000, 35.000000000000000 },
{ 14847705549021962., 0.50000000000000000, 40.000000000000000 },
{ 2.0775691824625661e+18, 0.50000000000000000, 45.000000000000000 },
{ 2.9251568529912984e+20, 0.50000000000000000, 50.000000000000000 },
{ 4.1392840094781220e+22, 0.50000000000000000, 55.000000000000000 },
{ 5.8817065760751945e+24, 0.50000000000000000, 60.000000000000000 },
{ 8.3867695787277258e+26, 0.50000000000000000, 65.000000000000000 },
{ 1.1994296461653203e+29, 0.50000000000000000, 70.000000000000000 },
{ 1.7197510246063334e+31, 0.50000000000000000, 75.000000000000000 },
{ 2.4712895036230794e+33, 0.50000000000000000, 80.000000000000000 },
{ 3.5582099086757769e+35, 0.50000000000000000, 85.000000000000000 },
{ 5.1320654031231128e+37, 0.50000000000000000, 90.000000000000000 },
{ 7.4135128383495239e+39, 0.50000000000000000, 95.000000000000000 },
{ 1.0724035825423179e+42, 0.50000000000000000, 100.00000000000000 },
};
// Test function for nu=0.50000000000000000.
template<typename Tp>
void
test012()
{
const Tp eps = std::numeric_limits<Tp>::epsilon();
Tp max_abs_diff = -Tp(1);
Tp max_abs_frac = -Tp(1);
unsigned int num_datum = sizeof(data012)
/ sizeof(testcase_cyl_bessel_i<double>);
for (unsigned int i = 0; i < num_datum; ++i)
{
const Tp f = std::tr1::cyl_bessel_i(Tp(data012[i].nu), Tp(data012[i].x));
const Tp f0 = data012[i].f0;
const Tp diff = f - f0;
if (std::abs(diff) > max_abs_diff)
max_abs_diff = std::abs(diff);
if (std::abs(f0) > Tp(10) * eps
&& std::abs(f) > Tp(10) * eps)
{
const Tp frac = diff / f0;
if (std::abs(frac) > max_abs_frac)
max_abs_frac = std::abs(frac);
}
}
VERIFY(max_abs_frac < Tp(1.0000000000000008e-12));
}
// Test data for nu=0.66666666666666663.
testcase_cyl_bessel_i<double> data013[] = {
{ 0.0000000000000000, 0.66666666666666663, 0.0000000000000000 },
{ 25.902310583215122, 0.66666666666666663, 5.0000000000000000 },
{ 2750.4090423459315, 0.66666666666666663, 10.000000000000000 },
{ 334476.98138574377, 0.66666666666666663, 15.000000000000000 },
{ 43064361.686912313, 0.66666666666666663, 20.000000000000000 },
{ 5722397441.9603882, 0.66666666666666663, 25.000000000000000 },
{ 775804343498.02661, 0.66666666666666663, 30.000000000000000 },
{ 106649495512800.88, 0.66666666666666663, 35.000000000000000 },
{ 14811199896983756., 0.66666666666666663, 40.000000000000000 },
{ 2.0730345814356961e+18, 0.66666666666666663, 45.000000000000000 },
{ 2.9194166755257467e+20, 0.66666666666666663, 50.000000000000000 },
{ 4.1319059569935374e+22, 0.66666666666666663, 55.000000000000000 },
{ 5.8721031476386222e+24, 0.66666666666666663, 60.000000000000000 },
{ 8.3741368248217844e+26, 0.66666666666666663, 65.000000000000000 },
{ 1.1977528777008688e+29, 0.66666666666666663, 70.000000000000000 },
{ 1.7175081240014333e+31, 0.66666666666666663, 75.000000000000000 },
{ 2.4682690458513916e+33, 0.66666666666666663, 80.000000000000000 },
{ 3.5541181975850724e+35, 0.66666666666666663, 85.000000000000000 },
{ 5.1264933963228892e+37, 0.66666666666666663, 90.000000000000000 },
{ 7.4058894880134064e+39, 0.66666666666666663, 95.000000000000000 },
{ 1.0713562154788124e+42, 0.66666666666666663, 100.00000000000000 },
};
// Test function for nu=0.66666666666666663.
template<typename Tp>
void
test013()
{
const Tp eps = std::numeric_limits<Tp>::epsilon();
Tp max_abs_diff = -Tp(1);
Tp max_abs_frac = -Tp(1);
unsigned int num_datum = sizeof(data013)
/ sizeof(testcase_cyl_bessel_i<double>);
for (unsigned int i = 0; i < num_datum; ++i)
{
const Tp f = std::tr1::cyl_bessel_i(Tp(data013[i].nu), Tp(data013[i].x));
const Tp f0 = data013[i].f0;
const Tp diff = f - f0;
if (std::abs(diff) > max_abs_diff)
max_abs_diff = std::abs(diff);
if (std::abs(f0) > Tp(10) * eps
&& std::abs(f) > Tp(10) * eps)
{
const Tp frac = diff / f0;
if (std::abs(frac) > max_abs_frac)
max_abs_frac = std::abs(frac);
}
}
VERIFY(max_abs_frac < Tp(5.0000000000000039e-13));
}
// Test data for nu=1.0000000000000000.
testcase_cyl_bessel_i<double> data014[] = {
{ 0.0000000000000000, 1.0000000000000000, 0.0000000000000000 },
{ 24.335642142450524, 1.0000000000000000, 5.0000000000000000 },
{ 2670.9883037012560, 1.0000000000000000, 10.000000000000000 },
{ 328124.92197020649, 1.0000000000000000, 15.000000000000000 },
{ 42454973.385127783, 1.0000000000000000, 20.000000000000000 },
{ 5657865129.8787022, 1.0000000000000000, 25.000000000000000 },
{ 768532038938.95667, 1.0000000000000000, 30.000000000000000 },
{ 105794126051896.17, 1.0000000000000000, 35.000000000000000 },
{ 14707396163259354., 1.0000000000000000, 40.000000000000000 },
{ 2.0601334620815780e+18, 1.0000000000000000, 45.000000000000000 },
{ 2.9030785901035638e+20, 1.0000000000000000, 50.000000000000000 },
{ 4.1108986452992812e+22, 1.0000000000000000, 55.000000000000000 },
{ 5.8447515883904527e+24, 1.0000000000000000, 60.000000000000000 },
{ 8.3381485471501302e+26, 1.0000000000000000, 65.000000000000000 },
{ 1.1929750788892366e+29, 1.0000000000000000, 70.000000000000000 },
{ 1.7111160152965382e+31, 1.0000000000000000, 75.000000000000000 },
{ 2.4596595795675343e+33, 1.0000000000000000, 80.000000000000000 },
{ 3.5424536064404024e+35, 1.0000000000000000, 85.000000000000000 },
{ 5.1106068152566129e+37, 1.0000000000000000, 90.000000000000000 },
{ 7.3841518091360182e+39, 1.0000000000000000, 95.000000000000000 },
{ 1.0683693903381569e+42, 1.0000000000000000, 100.00000000000000 },
};
// Test function for nu=1.0000000000000000.
template<typename Tp>
void
test014()
{
const Tp eps = std::numeric_limits<Tp>::epsilon();
Tp max_abs_diff = -Tp(1);
Tp max_abs_frac = -Tp(1);
unsigned int num_datum = sizeof(data014)
/ sizeof(testcase_cyl_bessel_i<double>);
for (unsigned int i = 0; i < num_datum; ++i)
{
const Tp f = std::tr1::cyl_bessel_i(Tp(data014[i].nu), Tp(data014[i].x));
const Tp f0 = data014[i].f0;
const Tp diff = f - f0;
if (std::abs(diff) > max_abs_diff)
max_abs_diff = std::abs(diff);
if (std::abs(f0) > Tp(10) * eps
&& std::abs(f) > Tp(10) * eps)
{
const Tp frac = diff / f0;
if (std::abs(frac) > max_abs_frac)
max_abs_frac = std::abs(frac);
}
}
VERIFY(max_abs_frac < Tp(5.0000000000000039e-13));
}
// Test data for nu=2.0000000000000000.
testcase_cyl_bessel_i<double> data015[] = {
{ 0.0000000000000000, 2.0000000000000000, 0.0000000000000000 },
{ 17.505614966624233, 2.0000000000000000, 5.0000000000000000 },
{ 2281.5189677260046, 2.0000000000000000, 10.000000000000000 },
{ 295899.38370188628, 2.0000000000000000, 15.000000000000000 },
{ 39312785.221040756, 2.0000000000000000, 20.000000000000000 },
{ 5321931396.0760155, 2.0000000000000000, 25.000000000000000 },
{ 730436828561.38013, 2.0000000000000000, 30.000000000000000 },
{ 101293439862977.19, 2.0000000000000000, 35.000000000000000 },
{ 14159404985256922., 2.0000000000000000, 40.000000000000000 },
{ 1.9918525879736883e+18, 2.0000000000000000, 45.000000000000000 },
{ 2.8164306402451938e+20, 2.0000000000000000, 50.000000000000000 },
{ 3.9993023372677540e+22, 2.0000000000000000, 55.000000000000000 },
{ 5.6992520026634433e+24, 2.0000000000000000, 60.000000000000000 },
{ 8.1464814287900378e+26, 2.0000000000000000, 65.000000000000000 },
{ 1.1675039556585663e+29, 2.0000000000000000, 70.000000000000000 },
{ 1.6770093176278926e+31, 2.0000000000000000, 75.000000000000000 },
{ 2.4136869148449879e+33, 2.0000000000000000, 80.000000000000000 },
{ 3.4801257808448186e+35, 2.0000000000000000, 85.000000000000000 },
{ 5.0256693051696307e+37, 2.0000000000000000, 90.000000000000000 },
{ 7.2678700343145818e+39, 2.0000000000000000, 95.000000000000000 },
{ 1.0523843193243042e+42, 2.0000000000000000, 100.00000000000000 },
};
// Test function for nu=2.0000000000000000.
template<typename Tp>
void
test015()
{
const Tp eps = std::numeric_limits<Tp>::epsilon();
Tp max_abs_diff = -Tp(1);
Tp max_abs_frac = -Tp(1);
unsigned int num_datum = sizeof(data015)
/ sizeof(testcase_cyl_bessel_i<double>);
for (unsigned int i = 0; i < num_datum; ++i)
{
const Tp f = std::tr1::cyl_bessel_i(Tp(data015[i].nu), Tp(data015[i].x));
const Tp f0 = data015[i].f0;
const Tp diff = f - f0;
if (std::abs(diff) > max_abs_diff)
max_abs_diff = std::abs(diff);
if (std::abs(f0) > Tp(10) * eps
&& std::abs(f) > Tp(10) * eps)
{
const Tp frac = diff / f0;
if (std::abs(frac) > max_abs_frac)
max_abs_frac = std::abs(frac);
}
}
VERIFY(max_abs_frac < Tp(5.0000000000000039e-13));
}
// Test data for nu=5.0000000000000000.
testcase_cyl_bessel_i<double> data016[] = {
{ 0.0000000000000000, 5.0000000000000000, 0.0000000000000000 },
{ 2.1579745473225476, 5.0000000000000000, 5.0000000000000000 },
{ 777.18828640326012, 5.0000000000000000, 10.000000000000000 },
{ 144572.01120063409, 5.0000000000000000, 15.000000000000000 },
{ 23018392.213413671, 5.0000000000000000, 20.000000000000000 },
{ 3472466208.7419176, 5.0000000000000000, 25.000000000000000 },
{ 512151465476.93494, 5.0000000000000000, 30.000000000000000 },
{ 74756743552251.547, 5.0000000000000000, 35.000000000000000 },
{ 10858318337624280., 5.0000000000000000, 40.000000000000000 },
{ 1.5736087399245911e+18, 5.0000000000000000, 45.000000000000000 },
{ 2.2785483079112825e+20, 5.0000000000000000, 50.000000000000000 },
{ 3.2989391052963687e+22, 5.0000000000000000, 55.000000000000000 },
{ 4.7777652072561732e+24, 5.0000000000000000, 60.000000000000000 },
{ 6.9232165147172657e+26, 5.0000000000000000, 65.000000000000000 },
{ 1.0038643002095155e+29, 5.0000000000000000, 70.000000000000000 },
{ 1.4566328222327073e+31, 5.0000000000000000, 75.000000000000000 },
{ 2.1151488565944835e+33, 5.0000000000000000, 80.000000000000000 },
{ 3.0735883450768239e+35, 5.0000000000000000, 85.000000000000000 },
{ 4.4694790189230327e+37, 5.0000000000000000, 90.000000000000000 },
{ 6.5037505570430995e+39, 5.0000000000000000, 95.000000000000000 },
{ 9.4700938730355882e+41, 5.0000000000000000, 100.00000000000000 },
};
// Test function for nu=5.0000000000000000.
template<typename Tp>
void
test016()
{
const Tp eps = std::numeric_limits<Tp>::epsilon();
Tp max_abs_diff = -Tp(1);
Tp max_abs_frac = -Tp(1);
unsigned int num_datum = sizeof(data016)
/ sizeof(testcase_cyl_bessel_i<double>);
for (unsigned int i = 0; i < num_datum; ++i)
{
const Tp f = std::tr1::cyl_bessel_i(Tp(data016[i].nu), Tp(data016[i].x));
const Tp f0 = data016[i].f0;
const Tp diff = f - f0;
if (std::abs(diff) > max_abs_diff)
max_abs_diff = std::abs(diff);
if (std::abs(f0) > Tp(10) * eps
&& std::abs(f) > Tp(10) * eps)
{
const Tp frac = diff / f0;
if (std::abs(frac) > max_abs_frac)
max_abs_frac = std::abs(frac);
}
}
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
}
// Test data for nu=10.000000000000000.
testcase_cyl_bessel_i<double> data017[] = {
{ 0.0000000000000000, 10.000000000000000, 0.0000000000000000 },
{ 0.0045800444191760525, 10.000000000000000, 5.0000000000000000 },
{ 21.891706163723381, 10.000000000000000, 10.000000000000000 },
{ 12267.475049806462, 10.000000000000000, 15.000000000000000 },
{ 3540200.2090195213, 10.000000000000000, 20.000000000000000 },
{ 771298871.17072666, 10.000000000000000, 25.000000000000000 },
{ 145831809975.96710, 10.000000000000000, 30.000000000000000 },
{ 25449470018534.777, 10.000000000000000, 35.000000000000000 },
{ 4228469210516757.5, 10.000000000000000, 40.000000000000000 },
{ 6.8049404557505165e+17, 10.000000000000000, 45.000000000000000 },
{ 1.0715971594776370e+20, 10.000000000000000, 50.000000000000000 },
{ 1.6618215752886714e+22, 10.000000000000000, 55.000000000000000 },
{ 2.5486246072566784e+24, 10.000000000000000, 60.000000000000000 },
{ 3.8764628702155481e+26, 10.000000000000000, 65.000000000000000 },
{ 5.8592538145409686e+28, 10.000000000000000, 70.000000000000000 },
{ 8.8135370711317444e+30, 10.000000000000000, 75.000000000000000 },
{ 1.3207418268325279e+33, 10.000000000000000, 80.000000000000000 },
{ 1.9732791360862190e+35, 10.000000000000000, 85.000000000000000 },
{ 2.9411893748384672e+37, 10.000000000000000, 90.000000000000000 },
{ 4.3754494922439984e+39, 10.000000000000000, 95.000000000000000 },
{ 6.4989755247201446e+41, 10.000000000000000, 100.00000000000000 },
};
// Test function for nu=10.000000000000000.
template<typename Tp>
void
test017()
{
const Tp eps = std::numeric_limits<Tp>::epsilon();
Tp max_abs_diff = -Tp(1);
Tp max_abs_frac = -Tp(1);
unsigned int num_datum = sizeof(data017)
/ sizeof(testcase_cyl_bessel_i<double>);
for (unsigned int i = 0; i < num_datum; ++i)
{
const Tp f = std::tr1::cyl_bessel_i(Tp(data017[i].nu), Tp(data017[i].x));
const Tp f0 = data017[i].f0;
const Tp diff = f - f0;
if (std::abs(diff) > max_abs_diff)
max_abs_diff = std::abs(diff);
if (std::abs(f0) > Tp(10) * eps
&& std::abs(f) > Tp(10) * eps)
{
const Tp frac = diff / f0;
if (std::abs(frac) > max_abs_frac)
max_abs_frac = std::abs(frac);
}
}
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
}
// Test data for nu=20.000000000000000.
testcase_cyl_bessel_i<double> data018[] = {
{ 0.0000000000000000, 20.000000000000000, 0.0000000000000000 },
{ 5.0242393579718066e-11, 20.000000000000000, 5.0000000000000000 },
{ 0.00012507997356449481, 20.000000000000000, 10.000000000000000 },
{ 1.6470152535015836, 20.000000000000000, 15.000000000000000 },
{ 3188.7503288536154, 20.000000000000000, 20.000000000000000 },
{ 2449840.5422952301, 20.000000000000000, 25.000000000000000 },
{ 1126985104.4483771, 20.000000000000000, 30.000000000000000 },
{ 379617876611.88580, 20.000000000000000, 35.000000000000000 },
{ 104459633129479.89, 20.000000000000000, 40.000000000000000 },
{ 25039579987216524., 20.000000000000000, 45.000000000000000 },
{ 5.4420084027529984e+18, 20.000000000000000, 50.000000000000000 },
{ 1.1007498584335495e+21, 20.000000000000000, 55.000000000000000 },
{ 2.1091734863057236e+23, 20.000000000000000, 60.000000000000000 },
{ 3.8763618091286899e+25, 20.000000000000000, 65.000000000000000 },
{ 6.8946130527930870e+27, 20.000000000000000, 70.000000000000000 },
{ 1.1946319948836447e+30, 20.000000000000000, 75.000000000000000 },
{ 2.0265314377577587e+32, 20.000000000000000, 80.000000000000000 },
{ 3.3784665214179985e+34, 20.000000000000000, 85.000000000000000 },
{ 5.5516089411796646e+36, 20.000000000000000, 90.000000000000000 },
{ 9.0129310795305151e+38, 20.000000000000000, 95.000000000000000 },
{ 1.4483461256427176e+41, 20.000000000000000, 100.00000000000000 },
};
// Test function for nu=20.000000000000000.
template<typename Tp>
void
test018()
{
const Tp eps = std::numeric_limits<Tp>::epsilon();
Tp max_abs_diff = -Tp(1);
Tp max_abs_frac = -Tp(1);
unsigned int num_datum = sizeof(data018)
/ sizeof(testcase_cyl_bessel_i<double>);
for (unsigned int i = 0; i < num_datum; ++i)
{
const Tp f = std::tr1::cyl_bessel_i(Tp(data018[i].nu), Tp(data018[i].x));
const Tp f0 = data018[i].f0;
const Tp diff = f - f0;
if (std::abs(diff) > max_abs_diff)
max_abs_diff = std::abs(diff);
if (std::abs(f0) > Tp(10) * eps
&& std::abs(f) > Tp(10) * eps)
{
const Tp frac = diff / f0;
if (std::abs(frac) > max_abs_frac)
max_abs_frac = std::abs(frac);
}
}
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
}
// Test data for nu=50.000000000000000.
testcase_cyl_bessel_i<double> data019[] = {
{ 0.0000000000000000, 50.000000000000000, 0.0000000000000000 },
{ 2.9314696468108517e-45, 50.000000000000000, 5.0000000000000000 },
{ 4.7568945607268442e-30, 50.000000000000000, 10.000000000000000 },
{ 5.5468372730667069e-21, 50.000000000000000, 15.000000000000000 },
{ 2.2551205757604056e-14, 50.000000000000000, 20.000000000000000 },
{ 4.5344251866130257e-09, 50.000000000000000, 25.000000000000000 },
{ 0.00014590106916468940, 50.000000000000000, 30.000000000000000 },
{ 1.3965549457254882, 50.000000000000000, 35.000000000000000 },
{ 5726.8656631289896, 50.000000000000000, 40.000000000000000 },
{ 12672593.113027781, 50.000000000000000, 45.000000000000000 },
{ 17650802430.016712, 50.000000000000000, 50.000000000000000 },
{ 17220231607789.926, 50.000000000000000, 55.000000000000000 },
{ 12704607933652176., 50.000000000000000, 60.000000000000000 },
{ 7.4989491942193725e+18, 50.000000000000000, 65.000000000000000 },
{ 3.6944034898904922e+21, 50.000000000000000, 70.000000000000000 },
{ 1.5691634774370186e+24, 50.000000000000000, 75.000000000000000 },
{ 5.8927749458163587e+26, 50.000000000000000, 80.000000000000000 },
{ 1.9958849054749339e+29, 50.000000000000000, 85.000000000000000 },
{ 6.1946050361781500e+31, 50.000000000000000, 90.000000000000000 },
{ 1.7845429728697119e+34, 50.000000000000000, 95.000000000000000 },
{ 4.8219580855940819e+36, 50.000000000000000, 100.00000000000000 },
};
// Test function for nu=50.000000000000000.
template<typename Tp>
void
test019()
{
const Tp eps = std::numeric_limits<Tp>::epsilon();
Tp max_abs_diff = -Tp(1);
Tp max_abs_frac = -Tp(1);
unsigned int num_datum = sizeof(data019)
/ sizeof(testcase_cyl_bessel_i<double>);
for (unsigned int i = 0; i < num_datum; ++i)
{
const Tp f = std::tr1::cyl_bessel_i(Tp(data019[i].nu), Tp(data019[i].x));
const Tp f0 = data019[i].f0;
const Tp diff = f - f0;
if (std::abs(diff) > max_abs_diff)
max_abs_diff = std::abs(diff);
if (std::abs(f0) > Tp(10) * eps
&& std::abs(f) > Tp(10) * eps)
{
const Tp frac = diff / f0;
if (std::abs(frac) > max_abs_frac)
max_abs_frac = std::abs(frac);
}
}
VERIFY(max_abs_frac < Tp(5.0000000000000029e-12));
}
// Test data for nu=100.00000000000000.
testcase_cyl_bessel_i<double> data020[] = {
{ 0.0000000000000000, 100.00000000000000, 0.0000000000000000 },
{ 7.0935514885313123e-119, 100.00000000000000, 5.0000000000000000 },
{ 1.0823442017492018e-88, 100.00000000000000, 10.000000000000000 },
{ 5.9887888536468904e-71, 100.00000000000000, 15.000000000000000 },
{ 2.8703193216428771e-58, 100.00000000000000, 20.000000000000000 },
{ 2.4426896913122370e-48, 100.00000000000000, 25.000000000000000 },
{ 3.9476420053334271e-40, 100.00000000000000, 30.000000000000000 },
{ 4.2836596180818780e-33, 100.00000000000000, 35.000000000000000 },
{ 6.6249380222596129e-27, 100.00000000000000, 40.000000000000000 },
{ 2.3702587262788900e-21, 100.00000000000000, 45.000000000000000 },
{ 2.7278879470966917e-16, 100.00000000000000, 50.000000000000000 },
{ 1.2763258878228082e-11, 100.00000000000000, 55.000000000000000 },
{ 2.8832770906491972e-07, 100.00000000000000, 60.000000000000000 },
{ 0.0035805902717061227, 100.00000000000000, 65.000000000000000 },
{ 27.017219102595387, 100.00000000000000, 70.000000000000000 },
{ 134001.44891209516, 100.00000000000000, 75.000000000000000 },
{ 465194832.85060996, 100.00000000000000, 80.000000000000000 },
{ 1189280653119.4814, 100.00000000000000, 85.000000000000000 },
{ 2334119331258728.0, 100.00000000000000, 90.000000000000000 },
{ 3.6399223078502436e+18, 100.00000000000000, 95.000000000000000 },
{ 4.6415349416162005e+21, 100.00000000000000, 100.00000000000000 },
};
// Test function for nu=100.00000000000000.
template<typename Tp>
void
test020()
{
const Tp eps = std::numeric_limits<Tp>::epsilon();
Tp max_abs_diff = -Tp(1);
Tp max_abs_frac = -Tp(1);
unsigned int num_datum = sizeof(data020)
/ sizeof(testcase_cyl_bessel_i<double>);
for (unsigned int i = 0; i < num_datum; ++i)
{
const Tp f = std::tr1::cyl_bessel_i(Tp(data020[i].nu), Tp(data020[i].x));
const Tp f0 = data020[i].f0;
const Tp diff = f - f0;
if (std::abs(diff) > max_abs_diff)
max_abs_diff = std::abs(diff);
if (std::abs(f0) > Tp(10) * eps
&& std::abs(f) > Tp(10) * eps)
{
const Tp frac = diff / f0;
if (std::abs(frac) > max_abs_frac)
max_abs_frac = std::abs(frac);
}
}
VERIFY(max_abs_frac < Tp(2.5000000000000014e-11));
}
int
main()
{
test001<double>();
test002<double>();
test003<double>();
test004<double>();
test005<double>();
test006<double>();
test007<double>();
test008<double>();
test009<double>();
test010<double>();
test011<double>();
test012<double>();
test013<double>();
test014<double>();
test015<double>();
test016<double>();
test017<double>();
test018<double>();
test019<double>();
test020<double>();
return 0;
}
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