-// 2007-02-04 Edward Smith-Rowland <3dw4rd@verizon.net>
+// { dg-do run { target c++11 } }
+// { dg-options "-D__STDCPP_WANT_MATH_SPEC_FUNCS__" }
//
-// Copyright (C) 2007-2017 Free Software Foundation, Inc.
+// Copyright (C) 2016-2017 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
// <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 <limits>
#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; \
- }
+# include <iostream>
+# define VERIFY(A) \
+ if (!(A)) \
+ { \
+ std::cout << "line " << __LINE__ \
+ << " max_abs_frac = " << max_abs_frac \
+ << std::endl; \
+ }
#else
-#include <testsuite_hooks.h>
+# include <testsuite_hooks.h>
#endif
-#include "../testcase.h"
-
+#include <specfun_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 },
+// max(|f - f_GSL|): 5.2402526762307389e-14 at index 12
+// max(|f - f_GSL| / |f_GSL|): 1.0747725055352992e-14
+// mean(f - f_GSL): -1.9624513654326576e-14
+// variance(f - f_GSL): 4.0630093099383162e-30
+// stddev(f - f_GSL): 2.0156907773610308e-15
+const testcase_cyl_bessel_i<double>
+data007[21] =
+{
+ { 1.0000000000000000, 0.0000000000000000, 0.0000000000000000, 0.0 },
+ { 1.0156861412236078, 0.0000000000000000, 0.25000000000000000, 0.0 },
+ { 1.0634833707413236, 0.0000000000000000, 0.50000000000000000, 0.0 },
+ { 1.1456467780440014, 0.0000000000000000, 0.75000000000000000, 0.0 },
+ { 1.2660658777520082, 0.0000000000000000, 1.0000000000000000, 0.0 },
+ { 1.4304687177218294, 0.0000000000000000, 1.2500000000000000, 0.0 },
+ { 1.6467231897728904, 0.0000000000000000, 1.5000000000000000, 0.0 },
+ { 1.9252521538585021, 0.0000000000000000, 1.7500000000000000, 0.0 },
+ { 2.2795853023360668, 0.0000000000000000, 2.0000000000000000, 0.0 },
+ { 2.7270783071907951, 0.0000000000000000, 2.2500000000000000, 0.0 },
+ { 3.2898391440501231, 0.0000000000000000, 2.5000000000000000, 0.0 },
+ { 3.9959131072376550, 0.0000000000000000, 2.7500000000000000, 0.0 },
+ { 4.8807925858650245, 0.0000000000000000, 3.0000000000000000, 0.0 },
+ { 5.9893359979395138, 0.0000000000000000, 3.2500000000000000, 0.0 },
+ { 7.3782034322254750, 0.0000000000000000, 3.5000000000000000, 0.0 },
+ { 9.1189458608445655, 0.0000000000000000, 3.7500000000000000, 0.0 },
+ { 11.301921952136325, 0.0000000000000000, 4.0000000000000000, 0.0 },
+ { 14.041263683000595, 0.0000000000000000, 4.2500000000000000, 0.0 },
+ { 17.481171855609272, 0.0000000000000000, 4.5000000000000000, 0.0 },
+ { 21.803898740902120, 0.0000000000000000, 4.7500000000000000, 0.0 },
+ { 27.239871823604439, 0.0000000000000000, 5.0000000000000000, 0.0 },
};
-
-// 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));
- }
+const double toler007 = 1.0000000000000008e-12;
// 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 },
+// max(|f - f_GSL|): 6.2172489379008766e-15 at index 14
+// max(|f - f_GSL| / |f_GSL|): 9.1624880778907085e-16
+// mean(f - f_GSL): 1.1525172350870673e-15
+// variance(f - f_GSL): 6.9735538801568761e-32
+// stddev(f - f_GSL): 2.6407487347638500e-16
+const testcase_cyl_bessel_i<double>
+data008[21] =
+{
+ { 0.0000000000000000, 0.33333333333333331, 0.0000000000000000, 0.0 },
+ { 0.56650686557808660, 0.33333333333333331, 0.25000000000000000, 0.0 },
+ { 0.73897315642511863, 0.33333333333333331, 0.50000000000000000, 0.0 },
+ { 0.89532320365836815, 0.33333333333333331, 0.75000000000000000, 0.0 },
+ { 1.0646313978895283, 0.33333333333333331, 1.0000000000000000, 0.0 },
+ { 1.2623776732605250, 0.33333333333333331, 1.2500000000000000, 0.0 },
+ { 1.5014290000224382, 0.33333333333333331, 1.5000000000000000, 0.0 },
+ { 1.7951195525946040, 0.33333333333333331, 1.7500000000000000, 0.0 },
+ { 2.1587825813728614, 0.33333333333333331, 2.0000000000000000, 0.0 },
+ { 2.6109134564811405, 0.33333333333333331, 2.2500000000000000, 0.0 },
+ { 3.1743242297241938, 0.33333333333333331, 2.5000000000000000, 0.0 },
+ { 3.8774551722182093, 0.33333333333333331, 2.7500000000000000, 0.0 },
+ { 4.7559569371646946, 0.33333333333333331, 3.0000000000000000, 0.0 },
+ { 5.8546499652731825, 0.33333333333333331, 3.2500000000000000, 0.0 },
+ { 7.2299798619171129, 0.33333333333333331, 3.5000000000000000, 0.0 },
+ { 8.9531114355506318, 0.33333333333333331, 3.7500000000000000, 0.0 },
+ { 11.113838389991479, 0.33333333333333331, 4.0000000000000000, 0.0 },
+ { 13.825531136529117, 0.33333333333333331, 4.2500000000000000, 0.0 },
+ { 17.231403968478318, 0.33333333333333331, 4.5000000000000000, 0.0 },
+ { 21.512458099556554, 0.33333333333333331, 4.7500000000000000, 0.0 },
+ { 26.897553069268362, 0.33333333333333331, 5.0000000000000000, 0.0 },
};
-
-// 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));
- }
+const double toler008 = 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 },
+// max(|f - f_GSL|): 1.4210854715202004e-14 at index 19
+// max(|f - f_GSL| / |f_GSL|): 9.6042704318763827e-16
+// mean(f - f_GSL): 1.9296733523246769e-16
+// variance(f - f_GSL): 1.9549106045027772e-33
+// stddev(f - f_GSL): 4.4214371017835108e-17
+const testcase_cyl_bessel_i<double>
+data009[21] =
+{
+ { 0.0000000000000000, 0.50000000000000000, 0.0000000000000000, 0.0 },
+ { 0.40311093489975897, 0.50000000000000000, 0.25000000000000000, 0.0 },
+ { 0.58799308679041573, 0.50000000000000000, 0.50000000000000000, 0.0 },
+ { 0.75761498638991298, 0.50000000000000000, 0.75000000000000000, 0.0 },
+ { 0.93767488824548695, 0.50000000000000000, 1.0000000000000000, 0.0 },
+ { 1.1432089853159872, 0.50000000000000000, 1.2500000000000000, 0.0 },
+ { 1.3871617204034761, 0.50000000000000000, 1.5000000000000000, 0.0 },
+ { 1.6830217804556813, 0.50000000000000000, 1.7500000000000000, 0.0 },
+ { 2.0462368630890526, 0.50000000000000000, 2.0000000000000000, 0.0 },
+ { 2.4953405089360046, 0.50000000000000000, 2.2500000000000000, 0.0 },
+ { 3.0530935381967175, 0.50000000000000000, 2.5000000000000000, 0.0 },
+ { 3.7477882494879449, 0.50000000000000000, 2.7500000000000000, 0.0 },
+ { 4.6148229034075969, 0.50000000000000000, 3.0000000000000000, 0.0 },
+ { 5.6986505325335486, 0.50000000000000000, 3.2500000000000000, 0.0 },
+ { 7.0552194086911859, 0.50000000000000000, 3.5000000000000000, 0.0 },
+ { 8.7550467841188979, 0.50000000000000000, 3.7500000000000000, 0.0 },
+ { 10.887101798588422, 0.50000000000000000, 4.0000000000000000, 0.0 },
+ { 13.563718712579764, 0.50000000000000000, 4.2500000000000000, 0.0 },
+ { 16.926820080158183, 0.50000000000000000, 4.5000000000000000, 0.0 },
+ { 21.155804306570005, 0.50000000000000000, 4.7500000000000000, 0.0 },
+ { 26.477547497559065, 0.50000000000000000, 5.0000000000000000, 0.0 },
};
-
-// 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));
- }
+const double toler009 = 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 },
+// max(|f - f_GSL|): 1.9539925233402755e-14 at index 16
+// max(|f - f_GSL| / |f_GSL|): 2.2100364323953014e-15
+// mean(f - f_GSL): -5.2312651565075830e-15
+// variance(f - f_GSL): 1.4792059082391298e-31
+// stddev(f - f_GSL): 3.8460446022363414e-16
+const testcase_cyl_bessel_i<double>
+data010[21] =
+{
+ { 0.0000000000000000, 0.66666666666666663, 0.0000000000000000, 0.0 },
+ { 0.27953690613200444, 0.66666666666666663, 0.25000000000000000, 0.0 },
+ { 0.45628323113556890, 0.66666666666666663, 0.50000000000000000, 0.0 },
+ { 0.62594569838182623, 0.66666666666666663, 0.75000000000000000, 0.0 },
+ { 0.80752128860612971, 0.66666666666666663, 1.0000000000000000, 0.0 },
+ { 1.0139484513577173, 0.66666666666666663, 1.2500000000000000, 0.0 },
+ { 1.2572918396962993, 0.66666666666666663, 1.5000000000000000, 0.0 },
+ { 1.5505806938325581, 0.66666666666666663, 1.7500000000000000, 0.0 },
+ { 1.9089492968236210, 0.66666666666666663, 2.0000000000000000, 0.0 },
+ { 2.3506463490300340, 0.66666666666666663, 2.2500000000000000, 0.0 },
+ { 2.8981161894224896, 0.66666666666666663, 2.5000000000000000, 0.0 },
+ { 3.5792654911068724, 0.66666666666666663, 2.7500000000000000, 0.0 },
+ { 4.4290087213549514, 0.66666666666666663, 3.0000000000000000, 0.0 },
+ { 5.4911895720097705, 0.66666666666666663, 3.2500000000000000, 0.0 },
+ { 6.8209918044137305, 0.66666666666666663, 3.5000000000000000, 0.0 },
+ { 8.4879784249619785, 0.66666666666666663, 3.7500000000000000, 0.0 },
+ { 10.579932774013004, 0.66666666666666663, 4.0000000000000000, 0.0 },
+ { 13.207720355482458, 0.66666666666666663, 4.2500000000000000, 0.0 },
+ { 16.511448404200543, 0.66666666666666663, 4.5000000000000000, 0.0 },
+ { 20.668274532832392, 0.66666666666666663, 4.7500000000000000, 0.0 },
+ { 25.902310583215122, 0.66666666666666663, 5.0000000000000000, 0.0 },
};
-
-// 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));
- }
+const double toler010 = 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 },
+// max(|f - f_GSL|): 1.2967404927621828e-13 at index 17
+// max(|f - f_GSL| / |f_GSL|): 1.0977631741433893e-14
+// mean(f - f_GSL): -3.0188814411265717e-14
+// variance(f - f_GSL): 3.7247797767076778e-29
+// stddev(f - f_GSL): 6.1030973912495271e-15
+const testcase_cyl_bessel_i<double>
+data011[21] =
+{
+ { 0.0000000000000000, 1.0000000000000000, 0.0000000000000000, 0.0 },
+ { 0.12597910894546793, 1.0000000000000000, 0.25000000000000000, 0.0 },
+ { 0.25789430539089631, 1.0000000000000000, 0.50000000000000000, 0.0 },
+ { 0.40199246158092228, 1.0000000000000000, 0.75000000000000000, 0.0 },
+ { 0.56515910399248503, 1.0000000000000000, 1.0000000000000000, 0.0 },
+ { 0.75528141834074725, 1.0000000000000000, 1.2500000000000000, 0.0 },
+ { 0.98166642857790720, 1.0000000000000000, 1.5000000000000000, 0.0 },
+ { 1.2555375122401728, 1.0000000000000000, 1.7500000000000000, 0.0 },
+ { 1.5906368546373291, 1.0000000000000000, 2.0000000000000000, 0.0 },
+ { 2.0039674569295931, 1.0000000000000000, 2.2500000000000000, 0.0 },
+ { 2.5167162452886984, 1.0000000000000000, 2.5000000000000000, 0.0 },
+ { 3.1554101386190028, 1.0000000000000000, 2.7500000000000000, 0.0 },
+ { 3.9533702174026097, 1.0000000000000000, 3.0000000000000000, 0.0 },
+ { 4.9525461659085490, 1.0000000000000000, 3.2500000000000000, 0.0 },
+ { 6.2058349222583642, 1.0000000000000000, 3.5000000000000000, 0.0 },
+ { 7.7800152298244170, 1.0000000000000000, 3.7500000000000000, 0.0 },
+ { 9.7594651537044523, 1.0000000000000000, 4.0000000000000000, 0.0 },
+ { 12.250874667409304, 1.0000000000000000, 4.2500000000000000, 0.0 },
+ { 15.389222753735924, 1.0000000000000000, 4.5000000000000000, 0.0 },
+ { 19.345361447520226, 1.0000000000000000, 4.7500000000000000, 0.0 },
+ { 24.335642142450524, 1.0000000000000000, 5.0000000000000000, 0.0 },
};
-
-// 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));
- }
+const double toler011 = 1.0000000000000008e-12;
// 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 },
+// max(|f - f_GSL|): 1.8474111129762605e-13 at index 20
+// max(|f - f_GSL| / |f_GSL|): 1.0796880796865132e-14
+// mean(f - f_GSL): -3.8692841919903068e-14
+// variance(f - f_GSL): 1.1198300918819667e-27
+// stddev(f - f_GSL): 3.3463862477035829e-14
+const testcase_cyl_bessel_i<double>
+data012[21] =
+{
+ { 0.0000000000000000, 2.0000000000000000, 0.0000000000000000, 0.0 },
+ { 0.0078532696598645167, 2.0000000000000000, 0.25000000000000000, 0.0 },
+ { 0.031906149177738249, 2.0000000000000000, 0.50000000000000000, 0.0 },
+ { 0.073666880494875436, 2.0000000000000000, 0.75000000000000000, 0.0 },
+ { 0.13574766976703831, 2.0000000000000000, 1.0000000000000000, 0.0 },
+ { 0.22201844837663415, 2.0000000000000000, 1.2500000000000000, 0.0 },
+ { 0.33783461833568068, 2.0000000000000000, 1.5000000000000000, 0.0 },
+ { 0.49035213986973314, 2.0000000000000000, 1.7500000000000000, 0.0 },
+ { 0.68894844769873831, 2.0000000000000000, 2.0000000000000000, 0.0 },
+ { 0.94577390103115722, 2.0000000000000000, 2.2500000000000000, 0.0 },
+ { 1.2764661478191643, 2.0000000000000000, 2.5000000000000000, 0.0 },
+ { 1.7010693700601991, 2.0000000000000000, 2.7500000000000000, 0.0 },
+ { 2.2452124409299512, 2.0000000000000000, 3.0000000000000000, 0.0 },
+ { 2.9416152804573357, 2.0000000000000000, 3.2500000000000000, 0.0 },
+ { 3.8320120480778415, 2.0000000000000000, 3.5000000000000000, 0.0 },
+ { 4.9696044049382113, 2.0000000000000000, 3.7500000000000000, 0.0 },
+ { 6.4221893752841055, 2.0000000000000000, 4.0000000000000000, 0.0 },
+ { 8.2761461924550552, 2.0000000000000000, 4.2500000000000000, 0.0 },
+ { 10.641517298393307, 2.0000000000000000, 4.5000000000000000, 0.0 },
+ { 13.658483394577813, 2.0000000000000000, 4.7500000000000000, 0.0 },
+ { 17.505614966624233, 2.0000000000000000, 5.0000000000000000, 0.0 },
};
-
-// 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));
- }
+const double toler012 = 1.0000000000000008e-12;
// 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 },
+// max(|f - f_GSL|): 2.2204460492503131e-14 at index 20
+// max(|f - f_GSL| / |f_GSL|): 1.1379865680381910e-14
+// mean(f - f_GSL): -3.4502652328999478e-15
+// variance(f - f_GSL): 1.8465291591354433e-29
+// stddev(f - f_GSL): 4.2971259687556788e-15
+const testcase_cyl_bessel_i<double>
+data013[21] =
+{
+ { 0.0000000000000000, 5.0000000000000000, 0.0000000000000000, 0.0 },
+ { 2.5497616449882785e-07, 5.0000000000000000, 0.25000000000000000, 0.0 },
+ { 8.2231713131092646e-06, 5.0000000000000000, 0.50000000000000000, 0.0 },
+ { 6.3261122739811725e-05, 5.0000000000000000, 0.75000000000000000, 0.0 },
+ { 0.00027146315595697195, 5.0000000000000000, 1.0000000000000000, 0.0 },
+ { 0.00084793613616686856, 5.0000000000000000, 1.2500000000000000, 0.0 },
+ { 0.0021705595690975554, 5.0000000000000000, 1.5000000000000000, 0.0 },
+ { 0.0048504513371845385, 5.0000000000000000, 1.7500000000000000, 0.0 },
+ { 0.0098256793231317023, 5.0000000000000000, 2.0000000000000000, 0.0 },
+ { 0.018486577941045829, 5.0000000000000000, 2.2500000000000000, 0.0 },
+ { 0.032843475172023219, 5.0000000000000000, 2.5000000000000000, 0.0 },
+ { 0.055750882754221943, 5.0000000000000000, 2.7500000000000000, 0.0 },
+ { 0.091206477661513338, 5.0000000000000000, 3.0000000000000000, 0.0 },
+ { 0.14474880546308083, 5.0000000000000000, 3.2500000000000000, 0.0 },
+ { 0.22398495470190780, 5.0000000000000000, 3.5000000000000000, 0.0 },
+ { 0.33928899170999877, 5.0000000000000000, 3.7500000000000000, 0.0 },
+ { 0.50472436311316637, 5.0000000000000000, 4.0000000000000000, 0.0 },
+ { 0.73925961816682961, 5.0000000000000000, 4.2500000000000000, 0.0 },
+ { 1.0683677743764701, 5.0000000000000000, 4.5000000000000000, 0.0 },
+ { 1.5261268693599621, 5.0000000000000000, 4.7500000000000000, 0.0 },
+ { 2.1579745473225476, 5.0000000000000000, 5.0000000000000000, 0.0 },
};
-
-// 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));
- }
+const double toler013 = 1.0000000000000008e-12;
// 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 },
+// max(|f - f_GSL|): 5.0306980803327406e-17 at index 20
+// max(|f - f_GSL| / |f_GSL|): 1.2741587624782699e-14
+// mean(f - f_GSL): -5.4602116438803446e-18
+// variance(f - f_GSL): 1.0558971696213844e-34
+// stddev(f - f_GSL): 1.0275685717368863e-17
+const testcase_cyl_bessel_i<double>
+data014[21] =
+{
+ { 0.0000000000000000, 10.000000000000000, 0.0000000000000000, 0.0 },
+ { 2.5701232848571186e-16, 10.000000000000000, 0.25000000000000000, 0.0 },
+ { 2.6430419258812784e-13, 10.000000000000000, 0.50000000000000000, 0.0 },
+ { 1.5349659676120412e-11, 10.000000000000000, 0.75000000000000000, 0.0 },
+ { 2.7529480398368732e-10, 10.000000000000000, 1.0000000000000000, 0.0 },
+ { 2.5967897782035928e-09, 10.000000000000000, 1.2500000000000000, 0.0 },
+ { 1.6330924437799743e-08, 10.000000000000000, 1.5000000000000000, 0.0 },
+ { 7.7706676834614079e-08, 10.000000000000000, 1.7500000000000000, 0.0 },
+ { 3.0169638793506839e-07, 10.000000000000000, 2.0000000000000000, 0.0 },
+ { 1.0034459057774481e-06, 10.000000000000000, 2.2500000000000000, 0.0 },
+ { 2.9557436109680578e-06, 10.000000000000000, 2.5000000000000000, 0.0 },
+ { 7.8955603774082724e-06, 10.000000000000000, 2.7500000000000000, 0.0 },
+ { 1.9464393470612970e-05, 10.000000000000000, 3.0000000000000000, 0.0 },
+ { 4.4875369479742435e-05, 10.000000000000000, 3.2500000000000000, 0.0 },
+ { 9.7760848514528916e-05, 10.000000000000000, 3.5000000000000000, 0.0 },
+ { 0.00020289011210063496, 10.000000000000000, 3.7500000000000000, 0.0 },
+ { 0.00040378896132693058, 10.000000000000000, 4.0000000000000000, 0.0 },
+ { 0.00077478519551669892, 10.000000000000000, 4.2500000000000000, 0.0 },
+ { 0.0014397060684919682, 10.000000000000000, 4.5000000000000000, 0.0 },
+ { 0.0026004486016189452, 10.000000000000000, 4.7500000000000000, 0.0 },
+ { 0.0045800444191760525, 10.000000000000000, 5.0000000000000000, 0.0 },
};
-
-// 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));
- }
+const double toler014 = 1.0000000000000008e-12;
// 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 },
+// max(|f - f_GSL|): 6.9147129330604657e-25 at index 20
+// max(|f - f_GSL| / |f_GSL|): 1.6061319023473306e-14
+// mean(f - f_GSL): -5.1436249496041580e-26
+// variance(f - f_GSL): 2.1506355008505938e-50
+// stddev(f - f_GSL): 1.4665045178418625e-25
+const testcase_cyl_bessel_i<double>
+data015[21] =
+{
+ { 0.0000000000000000, 20.000000000000000, 0.0000000000000000, 0.0 },
+ { 3.5677858077910353e-37, 20.000000000000000, 0.25000000000000000, 0.0 },
+ { 3.7494538480790194e-31, 20.000000000000000, 0.50000000000000000, 0.0 },
+ { 1.2514356342425337e-27, 20.000000000000000, 0.75000000000000000, 0.0 },
+ { 3.9668359858190197e-25, 20.000000000000000, 1.0000000000000000, 0.0 },
+ { 3.4637832909868234e-23, 20.000000000000000, 1.2500000000000000, 0.0 },
+ { 1.3388331839683472e-21, 20.000000000000000, 1.5000000000000000, 0.0 },
+ { 2.9502376732679751e-20, 20.000000000000000, 1.7500000000000000, 0.0 },
+ { 4.3105605761095479e-19, 20.000000000000000, 2.0000000000000000, 0.0 },
+ { 4.6032451406433059e-18, 20.000000000000000, 2.2500000000000000, 0.0 },
+ { 3.8400317244170310e-17, 20.000000000000000, 2.5000000000000000, 0.0 },
+ { 2.6239115263043263e-16, 20.000000000000000, 2.7500000000000000, 0.0 },
+ { 1.5209660019426689e-15, 20.000000000000000, 3.0000000000000000, 0.0 },
+ { 7.6806450728249953e-15, 20.000000000000000, 3.2500000000000000, 0.0 },
+ { 3.4495528847222945e-14, 20.000000000000000, 3.5000000000000000, 0.0 },
+ { 1.4006589294850677e-13, 20.000000000000000, 3.7500000000000000, 0.0 },
+ { 5.2100734221993054e-13, 20.000000000000000, 4.0000000000000000, 0.0 },
+ { 1.7946903269488168e-12, 20.000000000000000, 4.2500000000000000, 0.0 },
+ { 5.7763830562279699e-12, 20.000000000000000, 4.5000000000000000, 0.0 },
+ { 1.7502433074548735e-11, 20.000000000000000, 4.7500000000000000, 0.0 },
+ { 5.0242393579718066e-11, 20.000000000000000, 5.0000000000000000, 0.0 },
};
-
-// 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));
- }
+const double toler015 = 1.0000000000000008e-12;
// 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 },
+// max(|f - f_GSL|): 2.5841998320082313e+28 at index 20
+// max(|f - f_GSL| / |f_GSL|): 2.4067014886642843e-14
+// mean(f - f_GSL): -1.2242902567974868e+27
+// variance(f - f_GSL): inf
+// stddev(f - f_GSL): inf
+const testcase_cyl_bessel_i<double>
+data016[21] =
+{
+ { 1.0000000000000000, 0.0000000000000000, 0.0000000000000000, 0.0 },
+ { 27.239871823604439, 0.0000000000000000, 5.0000000000000000, 0.0 },
+ { 2815.7166284662558, 0.0000000000000000, 10.000000000000000, 0.0 },
+ { 339649.37329791381, 0.0000000000000000, 15.000000000000000, 0.0 },
+ { 43558282.559553474, 0.0000000000000000, 20.000000000000000, 0.0 },
+ { 5774560606.4663124, 0.0000000000000000, 25.000000000000000, 0.0 },
+ { 781672297823.97925, 0.0000000000000000, 30.000000000000000, 0.0 },
+ { 107338818494514.42, 0.0000000000000000, 35.000000000000000, 0.0 },
+ { 14894774793419916., 0.0000000000000000, 40.000000000000000, 0.0 },
+ { 2.0834140751773164e+18, 0.0000000000000000, 45.000000000000000, 0.0 },
+ { 2.9325537838493457e+20, 0.0000000000000000, 50.000000000000000, 0.0 },
+ { 4.1487895607332160e+22, 0.0000000000000000, 55.000000000000000, 0.0 },
+ { 5.8940770556098216e+24, 0.0000000000000000, 60.000000000000000, 0.0 },
+ { 8.4030398456255582e+26, 0.0000000000000000, 65.000000000000000, 0.0 },
+ { 1.2015889579125424e+29, 0.0000000000000000, 70.000000000000000, 0.0 },
+ { 1.7226390780357976e+31, 0.0000000000000000, 75.000000000000000, 0.0 },
+ { 2.4751784043341661e+33, 0.0000000000000000, 80.000000000000000, 0.0 },
+ { 3.5634776304081403e+35, 0.0000000000000000, 85.000000000000000, 0.0 },
+ { 5.1392383455086475e+37, 0.0000000000000000, 90.000000000000000, 0.0 },
+ { 7.4233258618752072e+39, 0.0000000000000000, 95.000000000000000, 0.0 },
+ { 1.0737517071310986e+42, 0.0000000000000000, 100.00000000000000, 0.0 },
};
-
-// 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));
- }
+const double toler016 = 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 },
+// max(|f - f_GSL|): 1.0986717848657750e+28 at index 20
+// max(|f - f_GSL| / |f_GSL|): 1.2017640663876795e-14
+// mean(f - f_GSL): -5.2068252642007974e+26
+// variance(f - f_GSL): inf
+// stddev(f - f_GSL): inf
+const testcase_cyl_bessel_i<double>
+data017[21] =
+{
+ { 0.0000000000000000, 0.33333333333333331, 0.0000000000000000, 0.0 },
+ { 26.897553069268362, 0.33333333333333331, 5.0000000000000000, 0.0 },
+ { 2799.2396097056790, 0.33333333333333331, 10.000000000000000, 0.0 },
+ { 338348.63146593666, 0.33333333333333331, 15.000000000000000, 0.0 },
+ { 43434263.927938424, 0.33333333333333331, 20.000000000000000, 0.0 },
+ { 5761474759.6213636, 0.33333333333333331, 25.000000000000000, 0.0 },
+ { 780201111830.30237, 0.33333333333333331, 30.000000000000000, 0.0 },
+ { 107166066959051.91, 0.33333333333333331, 35.000000000000000, 0.0 },
+ { 14873836574083762., 0.33333333333333331, 40.000000000000000, 0.0 },
+ { 2.0808143020217085e+18, 0.33333333333333331, 45.000000000000000, 0.0 },
+ { 2.9292639365644226e+20, 0.33333333333333331, 50.000000000000000, 0.0 },
+ { 4.1445621624120489e+22, 0.33333333333333331, 55.000000000000000, 0.0 },
+ { 5.8885758374365916e+24, 0.33333333333333331, 60.000000000000000, 0.0 },
+ { 8.3958047021083941e+26, 0.33333333333333331, 65.000000000000000, 0.0 },
+ { 1.2006287819446431e+29, 0.33333333333333331, 70.000000000000000, 0.0 },
+ { 1.7213548977150022e+31, 0.33333333333333331, 75.000000000000000, 0.0 },
+ { 2.4734492458444449e+33, 0.33333333333333331, 80.000000000000000, 0.0 },
+ { 3.5611354547857122e+35, 0.33333333333333331, 85.000000000000000, 0.0 },
+ { 5.1360491295551848e+37, 0.33333333333333331, 90.000000000000000, 0.0 },
+ { 7.4189629097600431e+39, 0.33333333333333331, 95.000000000000000, 0.0 },
+ { 1.0731523308358370e+42, 0.33333333333333331, 100.00000000000000, 0.0 },
};
-
-// 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));
- }
+const double toler017 = 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 },
+// max(|f - f_GSL|): 7.1181552258909366e+27 at index 20
+// max(|f - f_GSL| / |f_GSL|): 1.2230293310085236e-14
+// mean(f - f_GSL): -3.3462733503919608e+26
+// variance(f - f_GSL): inf
+// stddev(f - f_GSL): inf
+const testcase_cyl_bessel_i<double>
+data018[21] =
+{
+ { 0.0000000000000000, 0.50000000000000000, 0.0000000000000000, 0.0 },
+ { 26.477547497559065, 0.50000000000000000, 5.0000000000000000, 0.0 },
+ { 2778.7846038745711, 0.50000000000000000, 10.000000000000000, 0.0 },
+ { 336729.88718706399, 0.50000000000000000, 15.000000000000000, 0.0 },
+ { 43279746.272428922, 0.50000000000000000, 20.000000000000000, 0.0 },
+ { 5745159748.3464680, 0.50000000000000000, 25.000000000000000, 0.0 },
+ { 778366068840.44580, 0.50000000000000000, 30.000000000000000, 0.0 },
+ { 106950522408567.66, 0.50000000000000000, 35.000000000000000, 0.0 },
+ { 14847705549021960., 0.50000000000000000, 40.000000000000000, 0.0 },
+ { 2.0775691824625661e+18, 0.50000000000000000, 45.000000000000000, 0.0 },
+ { 2.9251568529912984e+20, 0.50000000000000000, 50.000000000000000, 0.0 },
+ { 4.1392840094781220e+22, 0.50000000000000000, 55.000000000000000, 0.0 },
+ { 5.8817065760751945e+24, 0.50000000000000000, 60.000000000000000, 0.0 },
+ { 8.3867695787277245e+26, 0.50000000000000000, 65.000000000000000, 0.0 },
+ { 1.1994296461653203e+29, 0.50000000000000000, 70.000000000000000, 0.0 },
+ { 1.7197510246063334e+31, 0.50000000000000000, 75.000000000000000, 0.0 },
+ { 2.4712895036230794e+33, 0.50000000000000000, 80.000000000000000, 0.0 },
+ { 3.5582099086757769e+35, 0.50000000000000000, 85.000000000000000, 0.0 },
+ { 5.1320654031231128e+37, 0.50000000000000000, 90.000000000000000, 0.0 },
+ { 7.4135128383495239e+39, 0.50000000000000000, 95.000000000000000, 0.0 },
+ { 1.0724035825423179e+42, 0.50000000000000000, 100.00000000000000, 0.0 },
};
-
-// 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));
- }
+const double toler018 = 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 },
+// max(|f - f_GSL|): 4.6422751473201760e+27 at index 20
+// max(|f - f_GSL| / |f_GSL|): 8.8432218147527708e-15
+// mean(f - f_GSL): -2.2367290021744526e+26
+// variance(f - f_GSL): inf
+// stddev(f - f_GSL): inf
+const testcase_cyl_bessel_i<double>
+data019[21] =
+{
+ { 0.0000000000000000, 0.66666666666666663, 0.0000000000000000, 0.0 },
+ { 25.902310583215122, 0.66666666666666663, 5.0000000000000000, 0.0 },
+ { 2750.4090423459315, 0.66666666666666663, 10.000000000000000, 0.0 },
+ { 334476.98138574377, 0.66666666666666663, 15.000000000000000, 0.0 },
+ { 43064361.686912313, 0.66666666666666663, 20.000000000000000, 0.0 },
+ { 5722397441.9603882, 0.66666666666666663, 25.000000000000000, 0.0 },
+ { 775804343498.02661, 0.66666666666666663, 30.000000000000000, 0.0 },
+ { 106649495512800.88, 0.66666666666666663, 35.000000000000000, 0.0 },
+ { 14811199896983754., 0.66666666666666663, 40.000000000000000, 0.0 },
+ { 2.0730345814356961e+18, 0.66666666666666663, 45.000000000000000, 0.0 },
+ { 2.9194166755257467e+20, 0.66666666666666663, 50.000000000000000, 0.0 },
+ { 4.1319059569935374e+22, 0.66666666666666663, 55.000000000000000, 0.0 },
+ { 5.8721031476386222e+24, 0.66666666666666663, 60.000000000000000, 0.0 },
+ { 8.3741368248217830e+26, 0.66666666666666663, 65.000000000000000, 0.0 },
+ { 1.1977528777008688e+29, 0.66666666666666663, 70.000000000000000, 0.0 },
+ { 1.7175081240014333e+31, 0.66666666666666663, 75.000000000000000, 0.0 },
+ { 2.4682690458513916e+33, 0.66666666666666663, 80.000000000000000, 0.0 },
+ { 3.5541181975850724e+35, 0.66666666666666663, 85.000000000000000, 0.0 },
+ { 5.1264933963228892e+37, 0.66666666666666663, 90.000000000000000, 0.0 },
+ { 7.4058894880134064e+39, 0.66666666666666663, 95.000000000000000, 0.0 },
+ { 1.0713562154788124e+42, 0.66666666666666663, 100.00000000000000, 0.0 },
};
-
-// 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));
- }
+const double toler019 = 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 },
+// max(|f - f_GSL|): 5.4159876718735387e+27 at index 20
+// max(|f - f_GSL| / |f_GSL|): 7.0819761463168391e-15
+// mean(f - f_GSL): 2.5933470782682662e+26
+// variance(f - f_GSL): inf
+// stddev(f - f_GSL): inf
+const testcase_cyl_bessel_i<double>
+data020[21] =
+{
+ { 0.0000000000000000, 1.0000000000000000, 0.0000000000000000, 0.0 },
+ { 24.335642142450524, 1.0000000000000000, 5.0000000000000000, 0.0 },
+ { 2670.9883037012560, 1.0000000000000000, 10.000000000000000, 0.0 },
+ { 328124.92197020649, 1.0000000000000000, 15.000000000000000, 0.0 },
+ { 42454973.385127783, 1.0000000000000000, 20.000000000000000, 0.0 },
+ { 5657865129.8787022, 1.0000000000000000, 25.000000000000000, 0.0 },
+ { 768532038938.95667, 1.0000000000000000, 30.000000000000000, 0.0 },
+ { 105794126051896.17, 1.0000000000000000, 35.000000000000000, 0.0 },
+ { 14707396163259352., 1.0000000000000000, 40.000000000000000, 0.0 },
+ { 2.0601334620815780e+18, 1.0000000000000000, 45.000000000000000, 0.0 },
+ { 2.9030785901035638e+20, 1.0000000000000000, 50.000000000000000, 0.0 },
+ { 4.1108986452992812e+22, 1.0000000000000000, 55.000000000000000, 0.0 },
+ { 5.8447515883904527e+24, 1.0000000000000000, 60.000000000000000, 0.0 },
+ { 8.3381485471501288e+26, 1.0000000000000000, 65.000000000000000, 0.0 },
+ { 1.1929750788892366e+29, 1.0000000000000000, 70.000000000000000, 0.0 },
+ { 1.7111160152965382e+31, 1.0000000000000000, 75.000000000000000, 0.0 },
+ { 2.4596595795675343e+33, 1.0000000000000000, 80.000000000000000, 0.0 },
+ { 3.5424536064404024e+35, 1.0000000000000000, 85.000000000000000, 0.0 },
+ { 5.1106068152566129e+37, 1.0000000000000000, 90.000000000000000, 0.0 },
+ { 7.3841518091360182e+39, 1.0000000000000000, 95.000000000000000, 0.0 },
+ { 1.0683693903381569e+42, 1.0000000000000000, 100.00000000000000, 0.0 },
};
-
-// 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));
- }
+const double toler020 = 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 },
+// max(|f - f_GSL|): 6.1897001964269014e+27 at index 20
+// max(|f - f_GSL| / |f_GSL|): 1.0553248866140883e-14
+// mean(f - f_GSL): 2.9514880793266611e+26
+// variance(f - f_GSL): inf
+// stddev(f - f_GSL): inf
+const testcase_cyl_bessel_i<double>
+data021[21] =
+{
+ { 0.0000000000000000, 2.0000000000000000, 0.0000000000000000, 0.0 },
+ { 17.505614966624233, 2.0000000000000000, 5.0000000000000000, 0.0 },
+ { 2281.5189677260046, 2.0000000000000000, 10.000000000000000, 0.0 },
+ { 295899.38370188628, 2.0000000000000000, 15.000000000000000, 0.0 },
+ { 39312785.221040756, 2.0000000000000000, 20.000000000000000, 0.0 },
+ { 5321931396.0760155, 2.0000000000000000, 25.000000000000000, 0.0 },
+ { 730436828561.38013, 2.0000000000000000, 30.000000000000000, 0.0 },
+ { 101293439862977.19, 2.0000000000000000, 35.000000000000000, 0.0 },
+ { 14159404985256920., 2.0000000000000000, 40.000000000000000, 0.0 },
+ { 1.9918525879736883e+18, 2.0000000000000000, 45.000000000000000, 0.0 },
+ { 2.8164306402451938e+20, 2.0000000000000000, 50.000000000000000, 0.0 },
+ { 3.9993023372677540e+22, 2.0000000000000000, 55.000000000000000, 0.0 },
+ { 5.6992520026634433e+24, 2.0000000000000000, 60.000000000000000, 0.0 },
+ { 8.1464814287900364e+26, 2.0000000000000000, 65.000000000000000, 0.0 },
+ { 1.1675039556585663e+29, 2.0000000000000000, 70.000000000000000, 0.0 },
+ { 1.6770093176278926e+31, 2.0000000000000000, 75.000000000000000, 0.0 },
+ { 2.4136869148449879e+33, 2.0000000000000000, 80.000000000000000, 0.0 },
+ { 3.4801257808448186e+35, 2.0000000000000000, 85.000000000000000, 0.0 },
+ { 5.0256693051696307e+37, 2.0000000000000000, 90.000000000000000, 0.0 },
+ { 7.2678700343145818e+39, 2.0000000000000000, 95.000000000000000, 0.0 },
+ { 1.0523843193243042e+42, 2.0000000000000000, 100.00000000000000, 0.0 },
};
-
-// 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));
- }
+const double toler021 = 1.0000000000000008e-12;
// 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 },
+// max(|f - f_GSL|): 1.0831975343747077e+27 at index 20
+// max(|f - f_GSL| / |f_GSL|): 1.0289491375166011e-14
+// mean(f - f_GSL): -5.2041812077613416e+25
+// variance(f - f_GSL): inf
+// stddev(f - f_GSL): inf
+const testcase_cyl_bessel_i<double>
+data022[21] =
+{
+ { 0.0000000000000000, 5.0000000000000000, 0.0000000000000000, 0.0 },
+ { 2.1579745473225476, 5.0000000000000000, 5.0000000000000000, 0.0 },
+ { 777.18828640326012, 5.0000000000000000, 10.000000000000000, 0.0 },
+ { 144572.01120063409, 5.0000000000000000, 15.000000000000000, 0.0 },
+ { 23018392.213413671, 5.0000000000000000, 20.000000000000000, 0.0 },
+ { 3472466208.7419176, 5.0000000000000000, 25.000000000000000, 0.0 },
+ { 512151465476.93494, 5.0000000000000000, 30.000000000000000, 0.0 },
+ { 74756743552251.547, 5.0000000000000000, 35.000000000000000, 0.0 },
+ { 10858318337624278., 5.0000000000000000, 40.000000000000000, 0.0 },
+ { 1.5736087399245911e+18, 5.0000000000000000, 45.000000000000000, 0.0 },
+ { 2.2785483079112825e+20, 5.0000000000000000, 50.000000000000000, 0.0 },
+ { 3.2989391052963687e+22, 5.0000000000000000, 55.000000000000000, 0.0 },
+ { 4.7777652072561732e+24, 5.0000000000000000, 60.000000000000000, 0.0 },
+ { 6.9232165147172657e+26, 5.0000000000000000, 65.000000000000000, 0.0 },
+ { 1.0038643002095155e+29, 5.0000000000000000, 70.000000000000000, 0.0 },
+ { 1.4566328222327073e+31, 5.0000000000000000, 75.000000000000000, 0.0 },
+ { 2.1151488565944835e+33, 5.0000000000000000, 80.000000000000000, 0.0 },
+ { 3.0735883450768239e+35, 5.0000000000000000, 85.000000000000000, 0.0 },
+ { 4.4694790189230327e+37, 5.0000000000000000, 90.000000000000000, 0.0 },
+ { 6.5037505570430995e+39, 5.0000000000000000, 95.000000000000000, 0.0 },
+ { 9.4700938730355882e+41, 5.0000000000000000, 100.00000000000000, 0.0 },
};
-
-// 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));
- }
+const double toler022 = 1.0000000000000008e-12;
// 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 },
+// max(|f - f_GSL|): 1.5474250491067253e+26 at index 20
+// max(|f - f_GSL| / |f_GSL|): 1.2009151331790140e-14
+// mean(f - f_GSL): 7.4845081675400805e+24
+// variance(f - f_GSL): inf
+// stddev(f - f_GSL): inf
+const testcase_cyl_bessel_i<double>
+data023[21] =
+{
+ { 0.0000000000000000, 10.000000000000000, 0.0000000000000000, 0.0 },
+ { 0.0045800444191760525, 10.000000000000000, 5.0000000000000000, 0.0 },
+ { 21.891706163723381, 10.000000000000000, 10.000000000000000, 0.0 },
+ { 12267.475049806462, 10.000000000000000, 15.000000000000000, 0.0 },
+ { 3540200.2090195213, 10.000000000000000, 20.000000000000000, 0.0 },
+ { 771298871.17072666, 10.000000000000000, 25.000000000000000, 0.0 },
+ { 145831809975.96710, 10.000000000000000, 30.000000000000000, 0.0 },
+ { 25449470018534.777, 10.000000000000000, 35.000000000000000, 0.0 },
+ { 4228469210516757.0, 10.000000000000000, 40.000000000000000, 0.0 },
+ { 6.8049404557505165e+17, 10.000000000000000, 45.000000000000000, 0.0 },
+ { 1.0715971594776370e+20, 10.000000000000000, 50.000000000000000, 0.0 },
+ { 1.6618215752886714e+22, 10.000000000000000, 55.000000000000000, 0.0 },
+ { 2.5486246072566784e+24, 10.000000000000000, 60.000000000000000, 0.0 },
+ { 3.8764628702155475e+26, 10.000000000000000, 65.000000000000000, 0.0 },
+ { 5.8592538145409686e+28, 10.000000000000000, 70.000000000000000, 0.0 },
+ { 8.8135370711317444e+30, 10.000000000000000, 75.000000000000000, 0.0 },
+ { 1.3207418268325279e+33, 10.000000000000000, 80.000000000000000, 0.0 },
+ { 1.9732791360862190e+35, 10.000000000000000, 85.000000000000000, 0.0 },
+ { 2.9411893748384672e+37, 10.000000000000000, 90.000000000000000, 0.0 },
+ { 4.3754494922439984e+39, 10.000000000000000, 95.000000000000000, 0.0 },
+ { 6.4989755247201446e+41, 10.000000000000000, 100.00000000000000, 0.0 },
};
-
-// 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));
- }
+const double toler023 = 1.0000000000000008e-12;
// 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 },
+// max(|f - f_GSL|): 1.9342813113834067e+25 at index 20
+// max(|f - f_GSL| / |f_GSL|): 1.5819230756119302e-14
+// mean(f - f_GSL): 1.0213821732843951e+24
+// variance(f - f_GSL): inf
+// stddev(f - f_GSL): inf
+const testcase_cyl_bessel_i<double>
+data024[21] =
+{
+ { 0.0000000000000000, 20.000000000000000, 0.0000000000000000, 0.0 },
+ { 5.0242393579718066e-11, 20.000000000000000, 5.0000000000000000, 0.0 },
+ { 0.00012507997356449481, 20.000000000000000, 10.000000000000000, 0.0 },
+ { 1.6470152535015836, 20.000000000000000, 15.000000000000000, 0.0 },
+ { 3188.7503288536154, 20.000000000000000, 20.000000000000000, 0.0 },
+ { 2449840.5422952301, 20.000000000000000, 25.000000000000000, 0.0 },
+ { 1126985104.4483771, 20.000000000000000, 30.000000000000000, 0.0 },
+ { 379617876611.88580, 20.000000000000000, 35.000000000000000, 0.0 },
+ { 104459633129479.88, 20.000000000000000, 40.000000000000000, 0.0 },
+ { 25039579987216524., 20.000000000000000, 45.000000000000000, 0.0 },
+ { 5.4420084027529984e+18, 20.000000000000000, 50.000000000000000, 0.0 },
+ { 1.1007498584335495e+21, 20.000000000000000, 55.000000000000000, 0.0 },
+ { 2.1091734863057236e+23, 20.000000000000000, 60.000000000000000, 0.0 },
+ { 3.8763618091286891e+25, 20.000000000000000, 65.000000000000000, 0.0 },
+ { 6.8946130527930870e+27, 20.000000000000000, 70.000000000000000, 0.0 },
+ { 1.1946319948836447e+30, 20.000000000000000, 75.000000000000000, 0.0 },
+ { 2.0265314377577587e+32, 20.000000000000000, 80.000000000000000, 0.0 },
+ { 3.3784665214179985e+34, 20.000000000000000, 85.000000000000000, 0.0 },
+ { 5.5516089411796646e+36, 20.000000000000000, 90.000000000000000, 0.0 },
+ { 9.0129310795305151e+38, 20.000000000000000, 95.000000000000000, 0.0 },
+ { 1.4483461256427176e+41, 20.000000000000000, 100.00000000000000, 0.0 },
};
-
-// 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));
- }
+const double toler024 = 1.0000000000000008e-12;
// 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 },
+// max(|f - f_GSL|): 4.4862481587261630e+22 at index 20
+// max(|f - f_GSL| / |f_GSL|): 6.0191728870880627e-14
+// mean(f - f_GSL): 2.1246678955085789e+21
+// variance(f - f_GSL): inf
+// stddev(f - f_GSL): inf
+const testcase_cyl_bessel_i<double>
+data025[21] =
+{
+ { 0.0000000000000000, 50.000000000000000, 0.0000000000000000, 0.0 },
+ { 2.9314696468108517e-45, 50.000000000000000, 5.0000000000000000, 0.0 },
+ { 4.7568945607268435e-30, 50.000000000000000, 10.000000000000000, 0.0 },
+ { 5.5468372730667069e-21, 50.000000000000000, 15.000000000000000, 0.0 },
+ { 2.2551205757604056e-14, 50.000000000000000, 20.000000000000000, 0.0 },
+ { 4.5344251866130257e-09, 50.000000000000000, 25.000000000000000, 0.0 },
+ { 0.00014590106916468940, 50.000000000000000, 30.000000000000000, 0.0 },
+ { 1.3965549457254882, 50.000000000000000, 35.000000000000000, 0.0 },
+ { 5726.8656631289887, 50.000000000000000, 40.000000000000000, 0.0 },
+ { 12672593.113027781, 50.000000000000000, 45.000000000000000, 0.0 },
+ { 17650802430.016712, 50.000000000000000, 50.000000000000000, 0.0 },
+ { 17220231607789.926, 50.000000000000000, 55.000000000000000, 0.0 },
+ { 12704607933652176., 50.000000000000000, 60.000000000000000, 0.0 },
+ { 7.4989491942193715e+18, 50.000000000000000, 65.000000000000000, 0.0 },
+ { 3.6944034898904922e+21, 50.000000000000000, 70.000000000000000, 0.0 },
+ { 1.5691634774370186e+24, 50.000000000000000, 75.000000000000000, 0.0 },
+ { 5.8927749458163587e+26, 50.000000000000000, 80.000000000000000, 0.0 },
+ { 1.9958849054749339e+29, 50.000000000000000, 85.000000000000000, 0.0 },
+ { 6.1946050361781500e+31, 50.000000000000000, 90.000000000000000, 0.0 },
+ { 1.7845429728697119e+34, 50.000000000000000, 95.000000000000000, 0.0 },
+ { 4.8219580855940819e+36, 50.000000000000000, 100.00000000000000, 0.0 },
};
-
-// 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));
- }
+const double toler025 = 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 },
+// max(|f - f_GSL|): 185597952.00000000 at index 20
+// max(|f - f_GSL| / |f_GSL|): 2.8278213985558577e-13
+// mean(f - f_GSL): 8855366.2060860656
+// variance(f - f_GSL): 4.2527168883984777e+19
+// stddev(f - f_GSL): 6521285830.5693655
+const testcase_cyl_bessel_i<double>
+data026[21] =
+{
+ { 0.0000000000000000, 100.00000000000000, 0.0000000000000000, 0.0 },
+ { 7.0935514885313123e-119, 100.00000000000000, 5.0000000000000000, 0.0 },
+ { 1.0823442017492015e-88, 100.00000000000000, 10.000000000000000, 0.0 },
+ { 5.9887888536468904e-71, 100.00000000000000, 15.000000000000000, 0.0 },
+ { 2.8703193216428771e-58, 100.00000000000000, 20.000000000000000, 0.0 },
+ { 2.4426896913122370e-48, 100.00000000000000, 25.000000000000000, 0.0 },
+ { 3.9476420053334271e-40, 100.00000000000000, 30.000000000000000, 0.0 },
+ { 4.2836596180818780e-33, 100.00000000000000, 35.000000000000000, 0.0 },
+ { 6.6249380222596129e-27, 100.00000000000000, 40.000000000000000, 0.0 },
+ { 2.3702587262788900e-21, 100.00000000000000, 45.000000000000000, 0.0 },
+ { 2.7278879470966917e-16, 100.00000000000000, 50.000000000000000, 0.0 },
+ { 1.2763258878228082e-11, 100.00000000000000, 55.000000000000000, 0.0 },
+ { 2.8832770906491972e-07, 100.00000000000000, 60.000000000000000, 0.0 },
+ { 0.0035805902717061223, 100.00000000000000, 65.000000000000000, 0.0 },
+ { 27.017219102595387, 100.00000000000000, 70.000000000000000, 0.0 },
+ { 134001.44891209516, 100.00000000000000, 75.000000000000000, 0.0 },
+ { 465194832.85060996, 100.00000000000000, 80.000000000000000, 0.0 },
+ { 1189280653119.4814, 100.00000000000000, 85.000000000000000, 0.0 },
+ { 2334119331258728.0, 100.00000000000000, 90.000000000000000, 0.0 },
+ { 3.6399223078502436e+18, 100.00000000000000, 95.000000000000000, 0.0 },
+ { 4.6415349416162005e+21, 100.00000000000000, 100.00000000000000, 0.0 },
};
+const double toler026 = 2.5000000000000014e-11;
-// Test function for nu=100.00000000000000.
-template<typename Tp>
+template<typename Ret, unsigned int Num>
void
- test020()
+ test(const testcase_cyl_bessel_i<Ret> (&data)[Num], Ret toler)
{
- 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>);
+ bool test __attribute__((unused)) = true;
+ const Ret eps = std::numeric_limits<Ret>::epsilon();
+ Ret max_abs_diff = -Ret(1);
+ Ret max_abs_frac = -Ret(1);
+ unsigned int num_datum = Num;
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;
+ const Ret f = std::tr1::cyl_bessel_i(data[i].nu, data[i].x);
+ const Ret f0 = data[i].f0;
+ const Ret 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)
+ if (std::abs(f0) > Ret(10) * eps
+ && std::abs(f) > Ret(10) * eps)
{
- const Tp frac = diff / f0;
+ const Ret frac = diff / f0;
if (std::abs(frac) > max_abs_frac)
max_abs_frac = std::abs(frac);
}
}
- VERIFY(max_abs_frac < Tp(2.5000000000000014e-11));
+ VERIFY(max_abs_frac < toler);
}
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>();
+ test(data007, toler007);
+ test(data008, toler008);
+ test(data009, toler009);
+ test(data010, toler010);
+ test(data011, toler011);
+ test(data012, toler012);
+ test(data013, toler013);
+ test(data014, toler014);
+ test(data015, toler015);
+ test(data016, toler016);
+ test(data017, toler017);
+ test(data018, toler018);
+ test(data019, toler019);
+ test(data020, toler020);
+ test(data021, toler021);
+ test(data022, toler022);
+ test(data023, toler023);
+ test(data024, toler024);
+ test(data025, toler025);
+ test(data026, toler026);
return 0;
}
projects / thirdparty / gcc.git / blobdiff