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[lmi-commits] [lmi] master dcb1fc5 3/5: Show number of evaluations for a
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From: |
Greg Chicares |
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Subject: |
[lmi-commits] [lmi] master dcb1fc5 3/5: Show number of evaluations for all TOMS 748 tests |
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Date: |
Mon, 27 Sep 2021 17:46:55 -0400 (EDT) |
branch: master
commit dcb1fc572280b993ee1c7f63e3b9e0b76adca1f5
Author: Gregory W. Chicares <gchicares@sbcglobal.net>
Commit: Gregory W. Chicares <gchicares@sbcglobal.net>
Show number of evaluations for all TOMS 748 tests
---
zero.hpp | 7 +-
zero_test.cpp | 841 +++++++++++++++++++++++++++++++++++++++++++++++-----------
2 files changed, 688 insertions(+), 160 deletions(-)
diff --git a/zero.hpp b/zero.hpp
index 7590812..c511f10 100644
--- a/zero.hpp
+++ b/zero.hpp
@@ -1195,9 +1195,10 @@ inline int tole_(double* b, double* tol, int* neps,
double* eps)
if (*neps == 1000) {
*tol = 0.;
} else {
-// *tol = 1.;
-// Changed by GWC: same tolerance as decimal_root()
- *tol = 0.5;
+ *tol = 1.;
+// GWC modification: change this from 1 to 1/2 iff the same
+// tolerance as decimal_root() is wanted.
+// *tol = 0.5;
i1 = *neps;
for (i0 = 1; i0 <= i1; ++i0) {
*tol /= 10.;
diff --git a/zero_test.cpp b/zero_test.cpp
index 75f6836..1819e7e 100644
--- a/zero_test.cpp
+++ b/zero_test.cpp
@@ -150,6 +150,8 @@ int max_n_eval_brent(double a, double b, double tol, double
zeta)
/// -0.222222222222222431931 x^2, on another path
/// so this comparison is not made for x87.
+//#define TEST_ALEFELD
+
template<typename F>
int test_a_function
(F f
@@ -184,6 +186,17 @@ int test_a_function
INVOKE_LMI_TEST_EQUAL(os0.str(),os1.str(),file,line);
#endif // !defined LMI_X87
+#if defined TEST_ALEFELD
+ // This temporary modification returns TOMS 748 measurements.
+ int dec = 1000; // Alefeld's magic value indicating zero tolerance
+ if(0.0 != tol)
+ {
+ dec = static_cast<int>(-std::log10(tol));
+ }
+//std::cout << "dec: " << dec << std::endl;
+ r = toms748_root(f, bound0, bound1, bias_none, dec);
+#endif // defined TEST_ALEFELD
+
return r.n_eval;
}
@@ -1449,16 +1462,38 @@ void test_alefeld_examples(int alefeld_count, double
tol)
double n {0.0};
int n_eval {};
+ int total_evals {};
+
+ // Ordinals:
+ int e {}; // Problem number in Table I.
+ int f {}; // Problem number in FORTRAN.
+ int g {}; // Serial number of test.
+
+ auto show_details = [&]()
+ {
+ std::cout
+ << std::setw(4) << e
+ << std::setw(4) << f
+ << std::setw(4) << g
+ << std::setw(4) << n_eval
+ << std::endl
+ ;
+ };
// Table I #1 = FORTRAN #1
+ e = 1; f = 1;
auto f01n01 = [](double x) {return std::sin(x) - x / 2.0;};
// Alefeld: 1.8954942670340;
double r01n01 = 1.89549426703398093963;
bound0 = pi_alefeld / 2.0e0;
bound1 = pi_alefeld;
- n_eval += test_a_function(f01n01, r01n01, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f01n01, r01n01, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
// Table I #2 = FORTRAN #2-11
+ e = 2; f = 2;
auto f02 = [](double x)
{
double sum = 0.0;
@@ -1472,77 +1507,128 @@ void test_alefeld_examples(int alefeld_count, double
tol)
double r02n02 = 3.0229153472730572183;
bound0 = 1.0e0 * 1.0e0 + 1.0e-9;
bound1 = 2.0e0 * 2.0e0 - 1.0e-9;
- n_eval += test_a_function(f02, r02n02, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f02, r02n02, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
// Test the same function with different intervals.
+ f = 3;
// Alefeld: 6.6837535608081
double r02n03 = 6.68375356080807847547;
bound0 = 2.0e0 * 2.0e0 + 1.0e-9;
bound1 = 3.0e0 * 3.0e0 - 1.0e-9;
- n_eval += test_a_function(f02, r02n03, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f02, r02n03, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
+ f = 4;
// Alefeld: 11.238701655002
double r02n04 = 11.2387016550022114103;
bound0 = 3.0e0 * 3.0e0 + 1.0e-9;
bound1 = 4.0e0 * 4.0e0 - 1.0e-9;
- n_eval += test_a_function(f02, r02n04, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f02, r02n04, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
+ f = 5;
// Alefeld: 19.676000080623
double r02n05 = 19.6760000806234103266;
bound0 = 4.0e0 * 4.0e0 + 1.0e-9;
bound1 = 5.0e0 * 5.0e0 - 1.0e-9;
- n_eval += test_a_function(f02, r02n05, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f02, r02n05, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
+ f = 6;
// Alefeld: 29.828227326505
double r02n06 = 29.8282273265047557231;
bound0 = 5.0e0 * 5.0e0 + 1.0e-9;
bound1 = 6.0e0 * 6.0e0 - 1.0e-9;
- n_eval += test_a_function(f02, r02n06, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f02, r02n06, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
+ f = 7;
// Alefeld: 41.906116195289
double r02n07 = 41.9061161952894138949;
bound0 = 6.0e0 * 6.0e0 + 1.0e-9;
bound1 = 7.0e0 * 7.0e0 - 1.0e-9;
- n_eval += test_a_function(f02, r02n07, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f02, r02n07, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
+ f = 8;
// Alefeld: 55.953595800143
double r02n08 = 55.95359580014309131;
bound0 = 7.0e0 * 7.0e0 + 1.0e-9;
bound1 = 8.0e0 * 8.0e0 - 1.0e-9;
- n_eval += test_a_function(f02, r02n08, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f02, r02n08, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
+ f = 9;
// Alefeld: 71.985665586588
double r02n09 = 71.9856655865877996803;
bound0 = 8.0e0 * 8.0e0 + 1.0e-9;
bound1 = 9.0e0 * 9.0e0 - 1.0e-9;
- n_eval += test_a_function(f02, r02n09, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f02, r02n09, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
+ f = 10;
// Alefeld: 90.008868539167
double r02n10 = 90.0088685391666700752;
bound0 = 9.0e0 * 9.0e0 + 1.0e-9;
bound1 = 10.0e0 * 10.0e0 - 1.0e-9;
- n_eval += test_a_function(f02, r02n10, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f02, r02n10, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
+ f = 11;
// Alefeld: 110.02653274833
double r02n11 = 110.026532748330197364;
bound0 = 10.0e0 * 10.0e0 + 1.0e-9;
bound1 = 11.0e0 * 11.0e0 - 1.0e-9;
- n_eval += test_a_function(f02, r02n11, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f02, r02n11, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
// Table I #3 = FORTRAN #12-14
+ e = 3; f = 12;
auto f03n12 = [](double x) {return -40.0 * x * std::exp(-1.0 * x);};
// Alefeld: 0.0;
double r03 = 0.0;
bound0 = -9.0e0;
bound1 = 31.0e0;
- n_eval += test_a_function(f03n12, r03, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f03n12, r03, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
+ f = 13;
auto f03n13 = [](double x) {return -100.0 * x * std::exp(-2.0 * x);};
- n_eval += test_a_function(f03n13, r03, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f03n13, r03, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
+ f = 14;
auto f03n14 = [](double x) {return -200.0 * x * std::exp(-3.0 * x);};
- n_eval += test_a_function(f03n14, r03, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f03n14, r03, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
// Table I #4 = FORTRAN #15-17
//
@@ -1550,116 +1636,166 @@ void test_alefeld_examples(int alefeld_count, double
tol)
// there are really two variable parameters, 'n' and 'a'. The urge
// to treat 'a' as a variable is resisted to avoid confusion, as
// 'a' is both a parameter and a bound in the "[a,b]" column.
+ e = 4; f = 15;
auto f04n15 = [&n](double x) {return std::pow(x, n) - 0.2;};
n = 4.0;
// Alefeld: 0.66874030497642
double r04n15a = 0.668740304976422006433;
bound0 = 0.0e0;
bound1 = 5.0e0;
- n_eval += test_a_function(f04n15, r04n15a, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f04n15, r04n15a, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 6.0;
// Alefeld: 0.76472449133173
double r04n15b = 0.764724491331730038546;
bound0 = 0.0e0;
bound1 = 5.0e0;
- n_eval += test_a_function(f04n15, r04n15b, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f04n15, r04n15b, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 8.0;
// Alefeld: 0.81776543395794
double r04n15c = 0.817765433957942544652;
bound0 = 0.0e0;
bound1 = 5.0e0;
- n_eval += test_a_function(f04n15, r04n15c, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f04n15, r04n15c, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 10.0;
// Alefeld: 0.85133992252078
double r04n15d = 0.851339922520784608828;
bound0 = 0.0e0;
bound1 = 5.0e0;
- n_eval += test_a_function(f04n15, r04n15d, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f04n15, r04n15d, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 12.0;
// Alefeld: 0.87448527222117
double r04n15e = 0.874485272221167897477;
bound0 = 0.0e0;
bound1 = 5.0e0;
- n_eval += test_a_function(f04n15, r04n15e, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f04n15, r04n15e, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
+ f = 16;
auto f04n16 = [n](double x) {return std::pow(x, n) - 1.0;};
n = 4.0;
// Alefeld: 1.0000000000000
double r04n16a = 1.0;
bound0 = 0.0e0;
bound1 = 5.0e0;
- n_eval += test_a_function(f04n16, r04n16a, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f04n16, r04n16a, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 6.0;
// Alefeld: 1.0000000000000
double r04n16b = 1.0;
bound0 = 0.0e0;
bound1 = 5.0e0;
- n_eval += test_a_function(f04n16, r04n16b, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f04n16, r04n16b, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 8.0;
// Alefeld: 1.0000000000000
double r04n16c = 1.0;
bound0 = 0.0e0;
bound1 = 5.0e0;
- n_eval += test_a_function(f04n16, r04n16c, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f04n16, r04n16c, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 10.0;
// Alefeld: 1.0000000000000
double r04n16d = 1.0;
bound0 = 0.0e0;
bound1 = 5.0e0;
- n_eval += test_a_function(f04n16, r04n16d, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f04n16, r04n16d, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 12.0;
// Alefeld: 1.0000000000000
double r04n16e = 1.0;
bound0 = 0.0e0;
bound1 = 5.0e0;
- n_eval += test_a_function(f04n16, r04n16e, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f04n16, r04n16e, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
+ f = 17;
auto f04n17 = [n](double x) {return std::pow(x, n) - 1.0;};
n = 8.0;
// Alefeld: 1.0000000000000
double r04n17a = 1.0;
bound0 = -0.95e0;
bound1 = 4.05e0;
- n_eval += test_a_function(f04n17, r04n17a, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f04n17, r04n17a, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 10.0;
// Alefeld: 1.0000000000000
double r04n17b = 1.0;
bound0 = -0.95e0;
bound1 = 4.05e0;
- n_eval += test_a_function(f04n17, r04n17b, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f04n17, r04n17b, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 12.0;
// Alefeld: 1.0000000000000
double r04n17c = 1.0;
bound0 = -0.95e0;
bound1 = 4.05e0;
- n_eval += test_a_function(f04n17, r04n17c, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f04n17, r04n17c, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 14.0;
// Alefeld: 1.0000000000000
double r04n17d = 1.0;
bound0 = -0.95e0;
bound1 = 4.05e0;
- n_eval += test_a_function(f04n17, r04n17d, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f04n17, r04n17d, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
// Table I #5 = FORTRAN #18
+ e = 5; f = 18;
auto f05n18 = [](double x) {return std::sin(x) - 0.5;};
// Alefeld: 0.52359877559830;
double r05n18 = 0.523598775598298815659;
bound0 = 0.0e0;
bound1 = 1.5e0;
- n_eval += test_a_function(f05n18, r05n18, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f05n18, r05n18, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
// Table I #6 = FORTRAN #19
+ e = 6; f = 19;
auto f06n19 = [&n](double x)
{
return 2.0 * x * std::exp(-n) - 2.0 * std::exp(-n * x) + 1.0;
@@ -1669,54 +1805,85 @@ void test_alefeld_examples(int alefeld_count, double
tol)
double r06n19a = 0.422477709641236709448;
bound0 = 0.0e0;
bound1 = 1.0e0;
- n_eval += test_a_function(f06n19, r06n19a, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f06n19, r06n19a, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 2.0;
// Alefeld: 0.30669941048320
double r06n19b = 0.306699410483203704914;
- n_eval += test_a_function(f06n19, r06n19b, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f06n19, r06n19b, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 3.0;
// Alefeld: 0.22370545765466
double r06n19c = 0.223705457654662959177;
- n_eval += test_a_function(f06n19, r06n19c, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f06n19, r06n19c, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 4.0;
// Alefeld: 0.17171914751951
double r06n19d = 0.171719147519508369415;
- n_eval += test_a_function(f06n19, r06n19d, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f06n19, r06n19d, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 5.0;
// Alefeld: 0.13825715505682
double r06n19e = 0.13825715505682406592;
- n_eval += test_a_function(f06n19, r06n19e, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f06n19, r06n19e, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 20.0;
// Alefeld: 3.4657359020854e-02
double r06n19f = 0.0346573590208538451218;
- n_eval += test_a_function(f06n19, r06n19f, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f06n19, r06n19f, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 40.0;
// Alefeld: 1.7328679513999e-02
double r06n19g = 0.0173286795139986349312;
- n_eval += test_a_function(f06n19, r06n19g, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f06n19, r06n19g, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 60.0;
// Alefeld: 1.1552453009332e-02
double r06n19h = 0.0115524530093324209745;
- n_eval += test_a_function(f06n19, r06n19h, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f06n19, r06n19h, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 80.0;
// Alefeld: 8.6643397569993e-03
double r06n19i = 0.00866433975699931746561;
- n_eval += test_a_function(f06n19, r06n19i, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f06n19, r06n19i, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 100.0;
// Alefeld: 6.9314718055995e-03
double r06n19j = 0.00693147180559945241124;
- n_eval += test_a_function(f06n19, r06n19j, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f06n19, r06n19j, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
// Table I #7 = FORTRAN #20
+ e = 7; f = 20;
auto f07n20 = [&n](double x)
{
return
@@ -1729,23 +1896,33 @@ void test_alefeld_examples(int alefeld_count, double
tol)
double r07n20a = 0.0384025518406218985268;
bound0 = 0.0e0;
bound1 = 1.0e0;
- n_eval += test_a_function(f07n20, r07n20a, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f07n20, r07n20a, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 10.0;
// Alefeld: 9.9000099980005e-03
double r07n20b = 0.00990000999800050122956;
bound0 = 0.0e0;
bound1 = 1.0e0;
- n_eval += test_a_function(f07n20, r07n20b, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f07n20, r07n20b, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 20.0;
// Alefeld: 2.4937500390620e-03
double r07n20c = 0.00249375003906201174464;
bound0 = 0.0e0;
bound1 = 1.0e0;
- n_eval += test_a_function(f07n20, r07n20c, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f07n20, r07n20c, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
// Table I #8 = FORTRAN #21
+ e = 8; f = 21;
auto f08n21 = [&n](double x)
{
return std::pow(x, 2.0) - std::pow(1.0 - x, n);
@@ -1755,37 +1932,53 @@ void test_alefeld_examples(int alefeld_count, double
tol)
double r08n21a = 0.5;
bound0 = 0.0e0;
bound1 = 1.0e0;
- n_eval += test_a_function(f08n21, r08n21a, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f08n21, r08n21a, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 5.0;
// Alefeld: 0.34595481584824
double r08n21b = 0.345954815848241947762;
bound0 = 0.0e0;
bound1 = 1.0e0;
- n_eval += test_a_function(f08n21, r08n21b, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f08n21, r08n21b, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 10.0;
// Alefeld: 0.24512233375331
double r08n21c = 0.245122333753307247717;
bound0 = 0.0e0;
bound1 = 1.0e0;
- n_eval += test_a_function(f08n21, r08n21c, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f08n21, r08n21c, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 15.0;
// Alefeld: 0.19554762353657
double r08n21d = 0.19554762353656562901;
bound0 = 0.0e0;
bound1 = 1.0e0;
- n_eval += test_a_function(f08n21, r08n21d, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f08n21, r08n21d, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 20.0;
// Alefeld: 0.16492095727644
double r08n21e = 0.164920957276440960371;
bound0 = 0.0e0;
bound1 = 1.0e0;
- n_eval += test_a_function(f08n21, r08n21e, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f08n21, r08n21e, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
// Table I #9 = FORTRAN #22
+ e = 9; f = 22;
auto f09n22 = [&n](double x)
{
return (1.0 + std::pow(1.0 - n, 4.0)) * x - std::pow(1.0 - n * x, 4.0);
@@ -1795,39 +1988,61 @@ void test_alefeld_examples(int alefeld_count, double
tol)
double r09n22a = 0.27550804099948439374;
bound0 = 0.0e0;
bound1 = 1.0e0;
- n_eval += test_a_function(f09n22, r09n22a, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f09n22, r09n22a, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 2.0;
// Alefeld: 0.13775402049974
double r09n22b = 0.13775402049974219687;
- n_eval += test_a_function(f09n22, r09n22b, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f09n22, r09n22b, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 4.0;
// Alefeld: 1.0305283778156e-02
double r09n22c = 0.0103052837781564439468;
- n_eval += test_a_function(f09n22, r09n22c, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f09n22, r09n22c, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 5.0;
// Alefeld: 3.6171081789041e-03
double r09n22d = 0.00361710817890406339387;
- n_eval += test_a_function(f09n22, r09n22d, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f09n22, r09n22d, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 8.0;
// Alefeld: 4.1087291849640e-04
double r09n22e = 0.000410872918496395320848;
- n_eval += test_a_function(f09n22, r09n22e, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f09n22, r09n22e, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 15.0;
// Alefeld: 2.5989575892908e-05
double r09n22f = 2.59895758929076292133e-05;
- n_eval += test_a_function(f09n22, r09n22f, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f09n22, r09n22f, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 20.0;
// Alefeld: 7.6685951221853e-06
double r09n22g = 7.66859512218533888794e-06;
- n_eval += test_a_function(f09n22, r09n22g, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f09n22, r09n22g, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
// Table I #10 = FORTRAN #23
+ e = 10; f = 23;
auto f10n23 = [&n](double x)
{
return std::exp(-n * x) * (x - 1.0) + std::pow(x, n);
@@ -1837,29 +2052,45 @@ void test_alefeld_examples(int alefeld_count, double
tol)
double r10n23a = 0.401058137541547010674;
bound0 = 0.0e0;
bound1 = 1.0e0;
- n_eval += test_a_function(f10n23, r10n23a, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f10n23, r10n23a, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 5.0;
// Alefeld: 0.51615351875793
double r10n23b = 0.516153518757933582606;
- n_eval += test_a_function(f10n23, r10n23b, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f10n23, r10n23b, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 10.0;
// Alefeld: 0.53952222690842
double r10n23c = 0.539522226908415780677;
- n_eval += test_a_function(f10n23, r10n23c, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f10n23, r10n23c, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 15.0;
// Alefeld: 0.54818229434066
double r10n23d = 0.548182294340655240639;
- n_eval += test_a_function(f10n23, r10n23d, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f10n23, r10n23d, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 20.0;
// Alefeld: 0.55270466667849
double r10n23e = 0.552704666678487832598;
- n_eval += test_a_function(f10n23, r10n23e, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f10n23, r10n23e, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
// Table I #11 = FORTRAN #24
+ e = 11; f = 24;
auto f11n24 = [&n](double x)
{
return (n * x - 1.0) / ((n - 1.0) * x);
@@ -1869,28 +2100,41 @@ void test_alefeld_examples(int alefeld_count, double
tol)
double r11n24a = 0.5;
bound0 = 1.0e-2;
bound1 = 1.0e0;
- n_eval += test_a_function(f11n24, r11n24a, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f11n24, r11n24a, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 5.0;
// Alefeld: 0.20000000000000
double r11n24b = 0.2;
- n_eval += test_a_function(f11n24, r11n24b, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f11n24, r11n24b, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 15.0;
// Alefeld: 6.6666666666667e-02
double r11n24c = 0.066666666666666667;
- n_eval += test_a_function(f11n24, r11n24c, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f11n24, r11n24c, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 20.0;
// Alefeld: 5.0000000000000e-02
double r11n24d = 0.05;
- n_eval += test_a_function(f11n24, r11n24d, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f11n24, r11n24d, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
// Table I #12 = FORTRAN #25
//
// Presumably due to inaccuracy in std::pow(), the calculated
// zero differs from the theoretical one (equal to 'n') by at
// least one ulp for some values of 'n'.
+ e = 12; f = 25;
auto f12n25 = [&n](double x)
{
return std::pow(x, 1.0 / n) - std::pow(n, 1.0 / n);
@@ -1900,97 +2144,154 @@ void test_alefeld_examples(int alefeld_count, double
tol)
double r12n25a = 2.0;
bound0 = 1.0e0;
bound1 = 100.0e0;
- n_eval += test_a_function(f12n25, r12n25a, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f12n25, r12n25a, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 3.0;
// Alefeld: 3.0000000000000
double r12n25b = 3.0;
- n_eval += test_a_function(f12n25, r12n25b, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f12n25, r12n25b, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 4.0;
// Alefeld: 4.0000000000000
double r12n25c = 4.0;
- n_eval += test_a_function(f12n25, r12n25c, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f12n25, r12n25c, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 5.0;
// Alefeld: 5.0000000000000
double r12n25d = 5.0;
- n_eval += test_a_function(f12n25, r12n25d, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f12n25, r12n25d, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 6.0;
// Alefeld: 6.0000000000000
double r12n25e = 6.0;
- n_eval += test_a_function(f12n25, r12n25e, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f12n25, r12n25e, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 7.0;
// Alefeld: 7.0000000000000
double r12n25f = 7.0;
- n_eval += test_a_function(f12n25, r12n25f, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f12n25, r12n25f, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 9.0;
// Alefeld: 9.0000000000000
double r12n25g = 9.0;
- n_eval += test_a_function(f12n25, r12n25g, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f12n25, r12n25g, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 11.0;
// Alefeld: 11.000000000000
double r12n25h = 11.0;
- n_eval += test_a_function(f12n25, r12n25h, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f12n25, r12n25h, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 13.0;
// Alefeld: 13.000000000000
double r12n25i = 13.0;
- n_eval += test_a_function(f12n25, r12n25i, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f12n25, r12n25i, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 15.0;
// Alefeld: 15.000000000000
double r12n25j = 15.0;
- n_eval += test_a_function(f12n25, r12n25j, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f12n25, r12n25j, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 17.0;
// Alefeld: 17.000000000000
double r12n25k = 16.9999999999999715783;
- n_eval += test_a_function(f12n25, r12n25k, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f12n25, r12n25k, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 19.0;
// Alefeld: 19.000000000000
double r12n25l = 19.0;
- n_eval += test_a_function(f12n25, r12n25l, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f12n25, r12n25l, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 21.0;
// Alefeld: 21.000000000000
double r12n25m = 21.0000000000000355271;
- n_eval += test_a_function(f12n25, r12n25m, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f12n25, r12n25m, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 23.0;
// Alefeld: 23.000000000000
double r12n25n = 23.0000000000000568434;
- n_eval += test_a_function(f12n25, r12n25n, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f12n25, r12n25n, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 25.0;
// Alefeld: 25.000000000000
double r12n25o = 25.000000000000024869;
- n_eval += test_a_function(f12n25, r12n25o, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f12n25, r12n25o, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 27.0;
// Alefeld: 27.000000000000
double r12n25p = 26.9999999999999573674;
- n_eval += test_a_function(f12n25, r12n25p, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f12n25, r12n25p, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 29.0;
// Alefeld: 29.000000000000
double r12n25q = 28.9999999999999076294;
- n_eval += test_a_function(f12n25, r12n25q, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f12n25, r12n25q, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 31.0;
// Alefeld: 31.000000000000
double r12n25r = 31.0000000000000568434;
- n_eval += test_a_function(f12n25, r12n25r, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f12n25, r12n25r, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 33.0;
// Alefeld: 33.000000000000
double r12n25s = 33.0000000000000852651;
- n_eval += test_a_function(f12n25, r12n25s, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f12n25, r12n25s, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
// Table I #13 = FORTRAN #26
//
@@ -2016,6 +2317,7 @@ void test_alefeld_examples(int alefeld_count, double tol)
// records the number of evaluations, without which Alefeld's
// totals in Table I could not be (approximately) reproduced,
// and ignores the meaningless false root.
+ e = 13; f = 26;
auto f13n26 = [](double x)
{
return
@@ -2045,12 +2347,16 @@ void test_alefeld_examples(int alefeld_count, double
tol)
bound0 = -1.0e0;
bound1 = 4.0e0;
#if 0
- n_eval += test_a_function(f13n26, r13n26, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f13n26, r13n26, bound0, bound1, tol, __LINE__);
#endif // 0
root_type r = lmi_root(f13n26, bound0, bound1, tol);
- n_eval += r.n_eval;
+ n_eval = r.n_eval;
+ total_evals += n_eval;
+ ++g;
+ show_details();
// Table I #14 = FORTRAN #27
+ e = 14; f = 27;
auto f14n27 = [&n](double x)
{
return
@@ -2064,204 +2370,325 @@ void test_alefeld_examples(int alefeld_count, double
tol)
double r14n27a = 0.623806518961612321839;
bound0 = -10000;
bound1 = pi_alefeld / 2.0e0;
- n_eval += test_a_function(f14n27, r14n27a, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f14n27, r14n27a, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 2.0;
// Alefeld: 0.62380651896161
double r14n27b = 0.623806518961612321839;
- n_eval += test_a_function(f14n27, r14n27b, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f14n27, r14n27b, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 3.0;
// Alefeld: 0.62380651896161
double r14n27c = 0.623806518961612321839;
- n_eval += test_a_function(f14n27, r14n27c, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f14n27, r14n27c, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 4.0;
// Alefeld: 0.62380651896161
double r14n27d = 0.623806518961612321839;
- n_eval += test_a_function(f14n27, r14n27d, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f14n27, r14n27d, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 5.0;
// Alefeld: 0.62380651896161
double r14n27e = 0.623806518961612321839;
- n_eval += test_a_function(f14n27, r14n27e, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f14n27, r14n27e, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 6.0;
// Alefeld: 0.62380651896161
double r14n27f = 0.623806518961612321839;
- n_eval += test_a_function(f14n27, r14n27f, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f14n27, r14n27f, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 7.0;
// Alefeld: 0.62380651896161
double r14n27g = 0.623806518961612321839;
- n_eval += test_a_function(f14n27, r14n27g, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f14n27, r14n27g, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 8.0;
// Alefeld: 0.62380651896161
double r14n27h = 0.623806518961612321839;
- n_eval += test_a_function(f14n27, r14n27h, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f14n27, r14n27h, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 9.0;
// Alefeld: 0.62380651896161
double r14n27i = 0.623806518961612321839;
- n_eval += test_a_function(f14n27, r14n27i, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f14n27, r14n27i, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 10.0;
// Alefeld: 0.62380651896161
double r14n27j = 0.623806518961612321839;
- n_eval += test_a_function(f14n27, r14n27j, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f14n27, r14n27j, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 11.0;
// Alefeld: 0.62380651896161
double r14n27k = 0.623806518961612321839;
- n_eval += test_a_function(f14n27, r14n27k, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f14n27, r14n27k, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 12.0;
// Alefeld: 0.62380651896161
double r14n27l = 0.623806518961612321839;
- n_eval += test_a_function(f14n27, r14n27l, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f14n27, r14n27l, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 13.0;
// Alefeld: 0.62380651896161
double r14n27m = 0.623806518961612321839;
- n_eval += test_a_function(f14n27, r14n27m, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f14n27, r14n27m, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 14.0;
// Alefeld: 0.62380651896161
double r14n27n = 0.623806518961612321839;
- n_eval += test_a_function(f14n27, r14n27n, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f14n27, r14n27n, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 15.0;
// Alefeld: 0.62380651896161
double r14n27o = 0.623806518961612321839;
- n_eval += test_a_function(f14n27, r14n27o, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f14n27, r14n27o, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 16.0;
// Alefeld: 0.62380651896161
double r14n27p = 0.623806518961612321839;
- n_eval += test_a_function(f14n27, r14n27p, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f14n27, r14n27p, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 17.0;
// Alefeld: 0.62380651896161
double r14n27q = 0.623806518961612321839;
- n_eval += test_a_function(f14n27, r14n27q, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f14n27, r14n27q, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 18.0;
// Alefeld: 0.62380651896161
double r14n27r = 0.623806518961612321839;
- n_eval += test_a_function(f14n27, r14n27r, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f14n27, r14n27r, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 19.0;
// Alefeld: 0.62380651896161
double r14n27s = 0.623806518961612321839;
- n_eval += test_a_function(f14n27, r14n27s, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f14n27, r14n27s, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 20.0;
// Alefeld: 0.62380651896161
double r14n27t = 0.623806518961612321839;
- n_eval += test_a_function(f14n27, r14n27t, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f14n27, r14n27t, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 21.0;
// Alefeld: 0.62380651896161
double r14n27u = 0.623806518961612321839;
- n_eval += test_a_function(f14n27, r14n27u, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f14n27, r14n27u, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 22.0;
// Alefeld: 0.62380651896161
double r14n27v = 0.623806518961612321839;
- n_eval += test_a_function(f14n27, r14n27v, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f14n27, r14n27v, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 23.0;
// Alefeld: 0.62380651896161
double r14n27w = 0.623806518961612321839;
- n_eval += test_a_function(f14n27, r14n27w, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f14n27, r14n27w, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 24.0;
// Alefeld: 0.62380651896161
double r14n27x = 0.623806518961612321839;
- n_eval += test_a_function(f14n27, r14n27x, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f14n27, r14n27x, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 25.0;
// Alefeld: 0.62380651896161
double r14n27y = 0.623806518961612321839;
- n_eval += test_a_function(f14n27, r14n27y, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f14n27, r14n27y, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 26.0;
// Alefeld: 0.62380651896161
double r14n27z = 0.623806518961612321839;
- n_eval += test_a_function(f14n27, r14n27z, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f14n27, r14n27z, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 27.0;
// Alefeld: 0.62380651896161
double r14n27A = 0.623806518961612321839;
- n_eval += test_a_function(f14n27, r14n27A, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f14n27, r14n27A, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 28.0;
// Alefeld: 0.62380651896161
double r14n27B = 0.623806518961612321839;
- n_eval += test_a_function(f14n27, r14n27B, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f14n27, r14n27B, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 29.0;
// Alefeld: 0.62380651896161
double r14n27C = 0.623806518961612321839;
- n_eval += test_a_function(f14n27, r14n27C, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f14n27, r14n27C, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 30.0;
// Alefeld: 0.62380651896161
double r14n27D = 0.623806518961612321839;
- n_eval += test_a_function(f14n27, r14n27D, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f14n27, r14n27D, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 31.0;
// Alefeld: 0.62380651896161
double r14n27E = 0.623806518961612321839;
- n_eval += test_a_function(f14n27, r14n27E, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f14n27, r14n27E, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 32.0;
// Alefeld: 0.62380651896161
double r14n27F = 0.623806518961612321839;
- n_eval += test_a_function(f14n27, r14n27F, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f14n27, r14n27F, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 33.0;
// Alefeld: 0.62380651896161
double r14n27G = 0.623806518961612321839;
- n_eval += test_a_function(f14n27, r14n27G, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f14n27, r14n27G, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 34.0;
// Alefeld: 0.62380651896161
double r14n27H = 0.623806518961612321839;
- n_eval += test_a_function(f14n27, r14n27H, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f14n27, r14n27H, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 35.0;
// Alefeld: 0.62380651896161
double r14n27I = 0.623806518961612321839;
- n_eval += test_a_function(f14n27, r14n27I, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f14n27, r14n27I, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 36.0;
// Alefeld: 0.62380651896161
double r14n27J = 0.623806518961612321839;
- n_eval += test_a_function(f14n27, r14n27J, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f14n27, r14n27J, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 37.0;
// Alefeld: 0.62380651896161
double r14n27K = 0.623806518961612321839;
- n_eval += test_a_function(f14n27, r14n27K, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f14n27, r14n27K, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 38.0;
// Alefeld: 0.62380651896161
double r14n27L = 0.623806518961612321839;
- n_eval += test_a_function(f14n27, r14n27L, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f14n27, r14n27L, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 39.0;
// Alefeld: 0.62380651896161
double r14n27M = 0.623806518961612321839;
- n_eval += test_a_function(f14n27, r14n27M, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f14n27, r14n27M, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 40.0;
// Alefeld: 0.62380651896161
double r14n27N = 0.623806518961612321839;
- n_eval += test_a_function(f14n27, r14n27N, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f14n27, r14n27N, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
// Table I #15 = FORTRAN #28
+ e = 15; f = 28;
auto f15n28 = [&n](double x)
{
double const k = 0.002 / (1.0 + n);
@@ -2277,160 +2704,253 @@ void test_alefeld_examples(int alefeld_count, double
tol)
double r15n28a = 5.90513055942197166237e-05;
bound0 = -10000;
bound1 = 1.0e-4;
- n_eval += test_a_function(f15n28, r15n28a, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f15n28, r15n28a, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 21.0;
// Alefeld: 5.6367155339937e-05
double r15n28b = 5.63671553399369966875e-05;
- n_eval += test_a_function(f15n28, r15n28b, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f15n28, r15n28b, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 22.0;
// Alefeld: 5.3916409455592e-05
double r15n28c = 5.39164094555919128212e-05;
- n_eval += test_a_function(f15n28, r15n28c, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f15n28, r15n28c, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 23.0;
// Alefeld: 5.1669892394942e-05
double r15n28d = 5.16698923949422605161e-05;
- n_eval += test_a_function(f15n28, r15n28d, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f15n28, r15n28d, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 24.0;
// Alefeld: 4.9603096699145e-05
double r15n28e = 4.9603096699144567656e-05;
- n_eval += test_a_function(f15n28, r15n28e, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f15n28, r15n28e, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 25.0;
// Alefeld: 4.7695285287639e-05
double r15n28f = 4.76952852876390018884e-05;
- n_eval += test_a_function(f15n28, r15n28f, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f15n28, r15n28f, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 26.0;
// Alefeld: 4.5928793239949e-05
double r15n28g = 4.59287932399486594501e-05;
- n_eval += test_a_function(f15n28, r15n28g, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f15n28, r15n28g, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 27.0;
// Alefeld: 4.4288479195665e-05
double r15n28h = 4.42884791956647908559e-05;
- n_eval += test_a_function(f15n28, r15n28h, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f15n28, r15n28h, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 28.0;
// Alefeld: 4.2761290257883e-05
double r15n28i = 4.27612902578832391001e-05;
- n_eval += test_a_function(f15n28, r15n28i, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f15n28, r15n28i, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 29.0;
// Alefeld: 4.1335913915954e-05
double r15n28j = 4.13359139159538029919e-05;
- n_eval += test_a_function(f15n28, r15n28j, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f15n28, r15n28j, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 30.0;
// Alefeld: 4.0002497338020e-05
double r15n28k = 4.00024973380198143745e-05;
- n_eval += test_a_function(f15n28, r15n28k, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f15n28, r15n28k, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 31.0;
// Alefeld: 3.8752419296207e-05
double r15n28l = 3.8752419296206693693e-05;
- n_eval += test_a_function(f15n28, r15n28l, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f15n28, r15n28l, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 32.0;
// Alefeld: 3.7578103559958e-05
double r15n28m = 3.75781035599579977917e-05;
- n_eval += test_a_function(f15n28, r15n28m, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f15n28, r15n28m, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 33.0;
// Alefeld: 3.6472865219959e-05
double r15n28n = 3.64728652199592355424e-05;
- n_eval += test_a_function(f15n28, r15n28n, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f15n28, r15n28n, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 34.0;
// Alefeld: 3.5430783356532e-05
double r15n28o = 3.54307833565318272637e-05;
- n_eval += test_a_function(f15n28, r15n28o, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f15n28, r15n28o, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 35.0;
// Alefeld: 3.4446594929961e-05
double r15n28p = 3.44465949299614979757e-05;
- n_eval += test_a_function(f15n28, r15n28p, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f15n28, r15n28p, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 36.0;
// Alefeld: 3.3515605877800e-05
double r15n28q = 3.35156058778003841008e-05;
- n_eval += test_a_function(f15n28, r15n28q, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f15n28, r15n28q, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 37.0;
// Alefeld: 3.2633616249437e-05
double r15n28r = 3.26336162494372057554e-05;
- n_eval += test_a_function(f15n28, r15n28r, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f15n28, r15n28r, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 38.0;
// Alefeld: 3.1796856858426e-05
double r15n28s = 3.17968568584259944827e-05;
- n_eval += test_a_function(f15n28, r15n28s, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f15n28, r15n28s, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 39.0;
// Alefeld: 3.1001935436965e-05
double r15n28t = 3.10019354369653454676e-05;
- n_eval += test_a_function(f15n28, r15n28t, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f15n28, r15n28t, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 40.0;
// Alefeld: 3.0245790670210e-05
double r15n28u = 3.02457906702100933871e-05;
- n_eval += test_a_function(f15n28, r15n28u, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f15n28, r15n28u, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 100.0;
// Alefeld: 1.2277994232462e-05
double r15n28v = 1.22779942324615231084e-05;
- n_eval += test_a_function(f15n28, r15n28v, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f15n28, r15n28v, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 200.0;
// Alefeld: 6.1695393904409e-06
double r15n28w = 6.16953939044086532173e-06;
- n_eval += test_a_function(f15n28, r15n28w, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f15n28, r15n28w, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 300.0;
// Alefeld: 4.1198585298293e-06
double r15n28x = 4.11985852982928247635e-06;
- n_eval += test_a_function(f15n28, r15n28x, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f15n28, r15n28x, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 400.0;
// Alefeld: 3.0924623877272e-06
double r15n28y = 3.09246238772721767043e-06;
- n_eval += test_a_function(f15n28, r15n28y, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f15n28, r15n28y, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 500.0;
// Alefeld: 2.4752044261050e-06
double r15n28z = 2.4752044261050178947e-06;
- n_eval += test_a_function(f15n28, r15n28z, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f15n28, r15n28z, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 600.0;
// Alefeld: 2.0633567678513e-06
double r15n28A = 2.06335676785127107013e-06;
- n_eval += test_a_function(f15n28, r15n28A, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f15n28, r15n28A, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 700.0;
// Alefeld: 1.7690120078154e-06
double r15n28B = 1.76901200781542650599e-06;
- n_eval += test_a_function(f15n28, r15n28B, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f15n28, r15n28B, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 800.0;
// Alefeld: 1.5481615698859e-06
double r15n28C = 1.54816156988591015938e-06;
- n_eval += test_a_function(f15n28, r15n28C, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f15n28, r15n28C, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 900.0;
// Alefeld: 1.3763345366022e-06
double r15n28D = 1.37633453660223511171e-06;
- n_eval += test_a_function(f15n28, r15n28D, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f15n28, r15n28D, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
n = 1000.0;
// Alefeld: 1.2388385788997e-06
double r15n28E = 1.23883857889971445027e-06;
- n_eval += test_a_function(f15n28, r15n28E, bound0, bound1, tol, __LINE__);
+ n_eval = test_a_function(f15n28, r15n28E, bound0, bound1, tol, __LINE__);
+ total_evals += n_eval;
+ ++g;
+ show_details();
std::cout
- << " evaluations: " << n_eval
+ << " evaluations: " << total_evals
<< " (vs. " << alefeld_count << " Alefeld Table II)"
<< "; tol " << tol
<< std::endl
@@ -2451,11 +2971,18 @@ int test_main(int, char*[])
test_former_rounding_problem();
test_toms748();
- std::cout << "TOMS 748 tests: " << std::endl;
+ std::cout << "TOMS 748 tests:" << std::endl;
+#if defined TEST_ALEFELD
+ test_alefeld_examples(2650, 1.0e-7);
+ test_alefeld_examples(2786, 1.0e-10);
+ test_alefeld_examples(2859, 1.0e-15);
+ test_alefeld_examples(2884, 0.0);
+#else // !defined TEST_ALEFELD
test_alefeld_examples(2804, 1.0e-7);
test_alefeld_examples(2905, 1.0e-10);
test_alefeld_examples(2975, 1.0e-15);
test_alefeld_examples(3008, 0.0);
+#endif // !defined TEST_ALEFELD
return 0;
}