scalar sasfit_r0(scalar epsilon, scalar s0)
{
scalar r0, ae;
if (epsilon < 1.)
{
ae = acos(epsilon);
r0 = sqrt(s0/(1.+epsilon*gsl_atanh(sin(ae))/sin(ae)) / (2.*M_PI));
}
else if (epsilon > 1.)
{
ae = acos(1./epsilon);
r0 = sqrt(s0/(1.+epsilon*ae/tan(ae)) / (2.*M_PI));
} else
{
r0 = sqrt(s0 / 4./M_PI);
}
return r0;
}
scalar sasfit_thinEll_P_core(scalar alpha, sasfit_param * param)
{
scalar S, ae;
SASFIT_ASSERT_PTR(param);
if (EPSILON < 1.)
{
ae = acos(EPSILON);
S = 2.*M_PI*R*R*(1.+EPSILON*gsl_atanh(sin(ae))/sin(ae));
}
else if (EPSILON > 1.)
{
ae = acos(1./EPSILON);
S = 2.*M_PI*R*R*(1.+EPSILON*ae/tan(ae));
} else
{
S = 4.*M_PI*R*R;
}
return pow(S * thinF1(Q, R, EPSILON, alpha),2.0)*sin(alpha);
}
int
main (void)
{
double y, y_expected;
int e, e_expected;
gsl_ieee_env_setup ();
/* Test for expm1 */
y = gsl_expm1 (0.0);
y_expected = 0.0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_expm1(0.0)");
y = gsl_expm1 (1e-10);
y_expected = 1.000000000050000000002e-10;
gsl_test_rel (y, y_expected, 1e-15, "gsl_expm1(1e-10)");
y = gsl_expm1 (-1e-10);
y_expected = -9.999999999500000000017e-11;
gsl_test_rel (y, y_expected, 1e-15, "gsl_expm1(-1e-10)");
y = gsl_expm1 (0.1);
y_expected = 0.1051709180756476248117078264902;
gsl_test_rel (y, y_expected, 1e-15, "gsl_expm1(0.1)");
y = gsl_expm1 (-0.1);
y_expected = -0.09516258196404042683575094055356;
gsl_test_rel (y, y_expected, 1e-15, "gsl_expm1(-0.1)");
y = gsl_expm1 (10.0);
y_expected = 22025.465794806716516957900645284;
gsl_test_rel (y, y_expected, 1e-15, "gsl_expm1(10.0)");
y = gsl_expm1 (-10.0);
y_expected = -0.99995460007023751514846440848444;
gsl_test_rel (y, y_expected, 1e-15, "gsl_expm1(-10.0)");
/* Test for log1p */
y = gsl_log1p (0.0);
y_expected = 0.0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_log1p(0.0)");
y = gsl_log1p (1e-10);
y_expected = 9.9999999995000000000333333333308e-11;
gsl_test_rel (y, y_expected, 1e-15, "gsl_log1p(1e-10)");
y = gsl_log1p (0.1);
y_expected = 0.095310179804324860043952123280765;
gsl_test_rel (y, y_expected, 1e-15, "gsl_log1p(0.1)");
y = gsl_log1p (10.0);
y_expected = 2.3978952727983705440619435779651;
gsl_test_rel (y, y_expected, 1e-15, "gsl_log1p(10.0)");
/* Test for gsl_hypot */
y = gsl_hypot (0.0, 0.0);
y_expected = 0.0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(0.0, 0.0)");
y = gsl_hypot (1e-10, 1e-10);
y_expected = 1.414213562373095048801688e-10;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(1e-10, 1e-10)");
y = gsl_hypot (1e-38, 1e-38);
y_expected = 1.414213562373095048801688e-38;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(1e-38, 1e-38)");
y = gsl_hypot (1e-10, -1.0);
y_expected = 1.000000000000000000005;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(1e-10, -1)");
y = gsl_hypot (-1.0, 1e-10);
y_expected = 1.000000000000000000005;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(-1, 1e-10)");
y = gsl_hypot (1e307, 1e301);
y_expected = 1.000000000000499999999999e307;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(1e307, 1e301)");
y = gsl_hypot (1e301, 1e307);
y_expected = 1.000000000000499999999999e307;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(1e301, 1e307)");
y = gsl_hypot (1e307, 1e307);
y_expected = 1.414213562373095048801688e307;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(1e307, 1e307)");
/* Test +-Inf, finite */
y = gsl_hypot (GSL_POSINF, 1.2);
y_expected = GSL_POSINF;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(GSL_POSINF, 1.2)");
y = gsl_hypot (GSL_NEGINF, 1.2);
y_expected = GSL_POSINF;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(GSL_NEGINF, 1.2)");
y = gsl_hypot (1.2, GSL_POSINF);
y_expected = GSL_POSINF;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(1.2, GSL_POSINF)");
y = gsl_hypot (1.2, GSL_NEGINF);
y_expected = GSL_POSINF;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(1.2, GSL_NEGINF)");
/* Test NaN, finite */
y = gsl_hypot (GSL_NAN, 1.2);
y_expected = GSL_NAN;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(GSL_NAN, 1.2)");
y = gsl_hypot (1.2, GSL_NAN);
y_expected = GSL_NAN;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(1.2, GSL_NAN)");
/* Test NaN, NaN */
y = gsl_hypot (GSL_NAN, GSL_NAN);
y_expected = GSL_NAN;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(GSL_NAN, GSL_NAN)");
/* Test +Inf, NaN */
y = gsl_hypot (GSL_POSINF, GSL_NAN);
y_expected = GSL_POSINF;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(GSL_POSINF, GSL_NAN)");
/* Test -Inf, NaN */
y = gsl_hypot (GSL_NEGINF, GSL_NAN);
y_expected = GSL_POSINF;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(GSL_NEGINF, GSL_NAN)");
/* Test NaN, +Inf */
y = gsl_hypot (GSL_NAN, GSL_POSINF);
y_expected = GSL_POSINF;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(GSL_NAN, GSL_POSINF)");
/* Test NaN, -Inf */
y = gsl_hypot (GSL_NAN, GSL_NEGINF);
y_expected = GSL_POSINF;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(GSL_NAN, GSL_NEGINF)");
/* Test for gsl_hypot3 */
y = gsl_hypot3 (0.0, 0.0, 0.0);
y_expected = 0.0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot3(0.0, 0.0, 0.0)");
y = gsl_hypot3 (1e-10, 1e-10, 1e-10);
y_expected = 1.732050807568877293527446e-10;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot3(1e-10, 1e-10, 1e-10)");
y = gsl_hypot3 (1e-38, 1e-38, 1e-38);
y_expected = 1.732050807568877293527446e-38;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot3(1e-38, 1e-38, 1e-38)");
y = gsl_hypot3 (1e-10, 1e-10, -1.0);
y_expected = 1.000000000000000000099;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot3(1e-10, 1e-10, -1)");
y = gsl_hypot3 (1e-10, -1.0, 1e-10);
y_expected = 1.000000000000000000099;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot3(1e-10, -1, 1e-10)");
y = gsl_hypot3 (-1.0, 1e-10, 1e-10);
y_expected = 1.000000000000000000099;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot3(-1, 1e-10, 1e-10)");
y = gsl_hypot3 (1e307, 1e301, 1e301);
y_expected = 1.0000000000009999999999995e307;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot3(1e307, 1e301, 1e301)");
y = gsl_hypot3 (1e307, 1e307, 1e307);
y_expected = 1.732050807568877293527446e307;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot3(1e307, 1e307, 1e307)");
y = gsl_hypot3 (1e307, 1e-307, 1e-307);
y_expected = 1.0e307;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot3(1e307, 1e-307, 1e-307)");
/* Test for acosh */
y = gsl_acosh (1.0);
y_expected = 0.0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_acosh(1.0)");
y = gsl_acosh (1.1);
y_expected = 4.435682543851151891329110663525e-1;
gsl_test_rel (y, y_expected, 1e-15, "gsl_acosh(1.1)");
y = gsl_acosh (10.0);
y_expected = 2.9932228461263808979126677137742e0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_acosh(10.0)");
y = gsl_acosh (1e10);
y_expected = 2.3718998110500402149594646668302e1;
gsl_test_rel (y, y_expected, 1e-15, "gsl_acosh(1e10)");
/* Test for asinh */
y = gsl_asinh (0.0);
y_expected = 0.0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(0.0)");
y = gsl_asinh (1e-10);
y_expected = 9.9999999999999999999833333333346e-11;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(1e-10)");
y = gsl_asinh (-1e-10);
y_expected = -9.9999999999999999999833333333346e-11;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(1e-10)");
y = gsl_asinh (0.1);
y_expected = 9.983407889920756332730312470477e-2;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(0.1)");
y = gsl_asinh (-0.1);
y_expected = -9.983407889920756332730312470477e-2;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(-0.1)");
y = gsl_asinh (1.0);
y_expected = 8.8137358701954302523260932497979e-1;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(1.0)");
y = gsl_asinh (-1.0);
y_expected = -8.8137358701954302523260932497979e-1;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(-1.0)");
y = gsl_asinh (10.0);
y_expected = 2.9982229502979697388465955375965e0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(10)");
y = gsl_asinh (-10.0);
y_expected = -2.9982229502979697388465955375965e0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(-10)");
y = gsl_asinh (1e10);
y_expected = 2.3718998110500402149599646668302e1;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(1e10)");
y = gsl_asinh (-1e10);
y_expected = -2.3718998110500402149599646668302e1;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(-1e10)");
/* Test for atanh */
y = gsl_atanh (0.0);
y_expected = 0.0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_atanh(0.0)");
y = gsl_atanh (1e-20);
y_expected = 1e-20;
gsl_test_rel (y, y_expected, 1e-15, "gsl_atanh(1e-20)");
y = gsl_atanh (-1e-20);
y_expected = -1e-20;
gsl_test_rel (y, y_expected, 1e-15, "gsl_atanh(-1e-20)");
y = gsl_atanh (0.1);
y_expected = 1.0033534773107558063572655206004e-1;
gsl_test_rel (y, y_expected, 1e-15, "gsl_atanh(0.1)");
y = gsl_atanh (-0.1);
y_expected = -1.0033534773107558063572655206004e-1;
gsl_test_rel (y, y_expected, 1e-15, "gsl_atanh(-0.1)");
y = gsl_atanh (0.9);
y_expected = 1.4722194895832202300045137159439e0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_atanh(0.9)");
y = gsl_atanh (-0.9);
y_expected = -1.4722194895832202300045137159439e0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_atanh(0.9)");
/* Test for pow_int */
y = gsl_pow_2 (-3.14);
y_expected = pow (-3.14, 2.0);
gsl_test_rel (y, y_expected, 1e-15, "gsl_pow_2(-3.14)");
y = gsl_pow_3 (-3.14);
y_expected = pow (-3.14, 3.0);
gsl_test_rel (y, y_expected, 1e-15, "gsl_pow_3(-3.14)");
y = gsl_pow_4 (-3.14);
y_expected = pow (-3.14, 4.0);
gsl_test_rel (y, y_expected, 1e-15, "gsl_pow_4(-3.14)");
y = gsl_pow_5 (-3.14);
y_expected = pow (-3.14, 5.0);
gsl_test_rel (y, y_expected, 1e-15, "gsl_pow_5(-3.14)");
y = gsl_pow_6 (-3.14);
y_expected = pow (-3.14, 6.0);
gsl_test_rel (y, y_expected, 1e-15, "gsl_pow_6(-3.14)");
y = gsl_pow_7 (-3.14);
y_expected = pow (-3.14, 7.0);
gsl_test_rel (y, y_expected, 1e-15, "gsl_pow_7(-3.14)");
y = gsl_pow_8 (-3.14);
y_expected = pow (-3.14, 8.0);
gsl_test_rel (y, y_expected, 1e-15, "gsl_pow_8(-3.14)");
y = gsl_pow_9 (-3.14);
y_expected = pow (-3.14, 9.0);
gsl_test_rel (y, y_expected, 1e-15, "gsl_pow_9(-3.14)");
{
int n;
for (n = -9; n < 10; n++)
{
y = gsl_pow_int (-3.14, n);
y_expected = pow (-3.14, n);
gsl_test_rel (y, y_expected, 1e-15, "gsl_pow_int(-3.14,%d)", n);
}
}
{
unsigned int n;
for (n = 0; n < 10; n++)
{
y = gsl_pow_uint (-3.14, n);
y_expected = pow (-3.14, n);
gsl_test_rel (y, y_expected, 1e-15, "gsl_pow_uint(-3.14,%d)", n);
}
}
/* Test case for n at INT_MAX, INT_MIN */
{
double u = 1.0000001;
int n = INT_MAX;
y = gsl_pow_int (u, n);
y_expected = pow (u, n);
gsl_test_rel (y, y_expected, 1e-6, "gsl_pow_int(%.7f,%d)", u, n);
n = INT_MIN;
y = gsl_pow_int (u, n);
y_expected = pow (u, n);
gsl_test_rel (y, y_expected, 1e-6, "gsl_pow_int(%.7f,%d)", u, n);
}
/* Test for ldexp */
y = gsl_ldexp (M_PI, -2);
y_expected = M_PI_4;
gsl_test_rel (y, y_expected, 1e-15, "gsl_ldexp(pi,-2)");
y = gsl_ldexp (1.0, 2);
y_expected = 4.000000;
gsl_test_rel (y, y_expected, 1e-15, "gsl_ldexp(1.0,2)");
y = gsl_ldexp (0.0, 2);
y_expected = 0.0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_ldexp(0.0,2)");
y = gsl_ldexp (9.999999999999998890e-01, 1024);
y_expected = GSL_DBL_MAX;
gsl_test_rel (y, y_expected, 1e-15, "gsl_ldexp DBL_MAX");
y = gsl_ldexp (1e308, -2000);
y_expected = 8.7098098162172166755761e-295;
gsl_test_rel (y, y_expected, 1e-15, "gsl_ldexp(1e308,-2000)");
y = gsl_ldexp (GSL_DBL_MIN, 2000);
y_expected = 2.554675596204441378334779940e294;
gsl_test_rel (y, y_expected, 1e-15, "gsl_ldexp(DBL_MIN,2000)");
/* Test subnormals */
{
int i = 0;
volatile double x = GSL_DBL_MIN;
y_expected = 2.554675596204441378334779940e294;
x /= 2;
while (x > 0)
{
i++ ;
y = gsl_ldexp (x, 2000 + i);
gsl_test_rel (y, y_expected, 1e-15, "gsl_ldexp(DBL_MIN/2**%d,%d)",i,2000+i);
x /= 2;
}
}
/* Test for frexp */
y = gsl_frexp (0.0, &e);
y_expected = 0;
e_expected = 0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_frexp(0) fraction");
gsl_test_int (e, e_expected, "gsl_frexp(0) exponent");
y = gsl_frexp (M_PI, &e);
y_expected = M_PI_4;
e_expected = 2;
gsl_test_rel (y, y_expected, 1e-15, "gsl_frexp(pi) fraction");
gsl_test_int (e, e_expected, "gsl_frexp(pi) exponent");
y = gsl_frexp (2.0, &e);
y_expected = 0.5;
e_expected = 2;
gsl_test_rel (y, y_expected, 1e-15, "gsl_frexp(2.0) fraction");
gsl_test_int (e, e_expected, "gsl_frexp(2.0) exponent");
y = gsl_frexp (1.0 / 4.0, &e);
y_expected = 0.5;
e_expected = -1;
gsl_test_rel (y, y_expected, 1e-15, "gsl_frexp(0.25) fraction");
gsl_test_int (e, e_expected, "gsl_frexp(0.25) exponent");
y = gsl_frexp (1.0 / 4.0 - 4.0 * GSL_DBL_EPSILON, &e);
y_expected = 0.999999999999996447;
e_expected = -2;
gsl_test_rel (y, y_expected, 1e-15, "gsl_frexp(0.25-eps) fraction");
gsl_test_int (e, e_expected, "gsl_frexp(0.25-eps) exponent");
y = gsl_frexp (GSL_DBL_MAX, &e);
y_expected = 9.999999999999998890e-01;
e_expected = 1024;
gsl_test_rel (y, y_expected, 1e-15, "gsl_frexp(DBL_MAX) fraction");
gsl_test_int (e, e_expected, "gsl_frexp(DBL_MAX) exponent");
y = gsl_frexp (-GSL_DBL_MAX, &e);
y_expected = -9.999999999999998890e-01;
e_expected = 1024;
gsl_test_rel (y, y_expected, 1e-15, "gsl_frexp(-DBL_MAX) fraction");
gsl_test_int (e, e_expected, "gsl_frexp(-DBL_MAX) exponent");
y = gsl_frexp (GSL_DBL_MIN, &e);
y_expected = 0.5;
e_expected = -1021;
gsl_test_rel (y, y_expected, 1e-15, "gsl_frexp(DBL_MIN) fraction");
gsl_test_int (e, e_expected, "gsl_frexp(DBL_MIN) exponent");
y = gsl_frexp (-GSL_DBL_MIN, &e);
y_expected = -0.5;
e_expected = -1021;
gsl_test_rel (y, y_expected, 1e-15, "gsl_frexp(-DBL_MIN) fraction");
gsl_test_int (e, e_expected, "gsl_frexp(-DBL_MIN) exponent");
/* Test subnormals */
{
int i = 0;
volatile double x = GSL_DBL_MIN;
y_expected = 0.5;
e_expected = -1021;
x /= 2;
while (x > 0)
{
e_expected--;
i++ ;
y = gsl_frexp (x, &e);
gsl_test_rel (y, y_expected, 1e-15, "gsl_frexp(DBL_MIN/2**%d) fraction",i);
gsl_test_int (e, e_expected, "gsl_frexp(DBL_MIN/2**%d) exponent", i);
x /= 2;
}
}
/* Test for approximate floating point comparison */
{
double x, y;
int i;
x = M_PI;
y = 22.0 / 7.0;
/* test the basic function */
for (i = 0; i < 10; i++)
{
double tol = pow (10, -i);
int res = gsl_fcmp (x, y, tol);
gsl_test_int (res, -(i >= 4), "gsl_fcmp(%.5f,%.5f,%g)", x, y, tol);
}
for (i = 0; i < 10; i++)
{
double tol = pow (10, -i);
int res = gsl_fcmp (y, x, tol);
gsl_test_int (res, (i >= 4), "gsl_fcmp(%.5f,%.5f,%g)", y, x, tol);
}
}
#if HAVE_IEEE_COMPARISONS
/* Test for isinf, isnan, finite */
{
double zero, one, inf, nan;
int s;
zero = 0.0;
one = 1.0;
inf = exp (1.0e10);
nan = inf / inf;
s = gsl_isinf (zero);
gsl_test_int (s, 0, "gsl_isinf(0)");
s = gsl_isinf (one);
gsl_test_int (s, 0, "gsl_isinf(1)");
s = gsl_isinf (inf);
gsl_test_int (s, 1, "gsl_isinf(inf)");
s = gsl_isinf (-inf);
gsl_test_int (s, -1, "gsl_isinf(-inf)");
s = gsl_isinf (nan);
gsl_test_int (s, 0, "gsl_isinf(nan)");
s = gsl_isnan (zero);
gsl_test_int (s, 0, "gsl_isnan(0)");
s = gsl_isnan (one);
gsl_test_int (s, 0, "gsl_isnan(1)");
s = gsl_isnan (inf);
gsl_test_int (s, 0, "gsl_isnan(inf)");
s = gsl_isnan (-inf);
gsl_test_int (s, 0, "gsl_isnan(-inf)");
s = gsl_isnan (nan);
gsl_test_int (s, 1, "gsl_isnan(nan)");
s = gsl_finite (zero);
gsl_test_int (s, 1, "gsl_finite(0)");
s = gsl_finite (one);
gsl_test_int (s, 1, "gsl_finite(1)");
s = gsl_finite (inf);
gsl_test_int (s, 0, "gsl_finite(inf)");
s = gsl_finite (-inf);
gsl_test_int (s, 0, "gsl_finite(-inf)");
s = gsl_finite (nan);
gsl_test_int (s, 0, "gsl_finite(nan)");
}
#endif
{
double x = gsl_fdiv (2.0, 3.0);
gsl_test_rel (x, 2.0 / 3.0, 4 * GSL_DBL_EPSILON, "gsl_fdiv(2,3)");
}
/* Test constants in gsl_math.h */
{
double x = log(M_E);
gsl_test_rel (x, 1.0, 4 * GSL_DBL_EPSILON, "ln(M_E)");
}
{
double x=pow(2.0,M_LOG2E);
gsl_test_rel (x, exp(1.0), 4 * GSL_DBL_EPSILON, "2^M_LOG2E");
}
{
double x=pow(10.0,M_LOG10E);
gsl_test_rel (x, exp(1.0), 4 * GSL_DBL_EPSILON, "10^M_LOG10E");
}
{
double x=pow(M_SQRT2, 2.0);
gsl_test_rel (x, 2.0, 4 * GSL_DBL_EPSILON, "M_SQRT2^2");
}
{
double x=pow(M_SQRT1_2, 2.0);
gsl_test_rel (x, 1.0/2.0, 4 * GSL_DBL_EPSILON, "M_SQRT1_2");
}
{
double x=pow(M_SQRT3, 2.0);
gsl_test_rel (x, 3.0, 4 * GSL_DBL_EPSILON, "M_SQRT3^2");
}
{
double x = M_PI;
gsl_test_rel (x, 3.1415926535897932384626433832795, 4 * GSL_DBL_EPSILON, "M_PI");
}
{
double x = 2 * M_PI_2;
gsl_test_rel (x, M_PI, 4 * GSL_DBL_EPSILON, "2*M_PI_2");
}
{
double x = 4 * M_PI_4;
gsl_test_rel (x, M_PI, 4 * GSL_DBL_EPSILON, "4*M_PI_4");
}
{
double x = pow(M_SQRTPI, 2.0);
gsl_test_rel (x, M_PI, 4 * GSL_DBL_EPSILON, "M_SQRTPI^2");
}
{
double x = pow(M_2_SQRTPI, 2.0);
gsl_test_rel (x, 4/M_PI, 4 * GSL_DBL_EPSILON, "M_SQRTPI^2");
}
{
double x = M_1_PI;
gsl_test_rel (x, 1/M_PI, 4 * GSL_DBL_EPSILON, "M_1_SQRTPI");
}
{
double x = M_2_PI;
gsl_test_rel (x, 2.0/M_PI, 4 * GSL_DBL_EPSILON, "M_2_PI");
}
{
double x = exp(M_LN10);
gsl_test_rel (x, 10, 4 * GSL_DBL_EPSILON, "exp(M_LN10)");
}
{
double x = exp(M_LN2);
gsl_test_rel (x, 2, 4 * GSL_DBL_EPSILON, "exp(M_LN2)");
}
{
double x = exp(M_LNPI);
gsl_test_rel (x, M_PI, 4 * GSL_DBL_EPSILON, "exp(M_LNPI)");
}
{
double x = M_EULER;
gsl_test_rel (x, 0.5772156649015328606065120900824, 4 * GSL_DBL_EPSILON, "M_EULER");
}
exit (gsl_test_summary ());
}
int
main (void)
{
double y, y_expected;
gsl_ieee_env_setup ();
/* Test for expm1 */
y = gsl_expm1 (0.0); y_expected = 0.0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_expm1(0.0)");
y = gsl_expm1 (1e-10); y_expected = 1.000000000050000000002e-10;
gsl_test_rel (y, y_expected, 1e-15, "gsl_expm1(1e-10)");
y = gsl_expm1 (-1e-10); y_expected = -9.999999999500000000017e-11;
gsl_test_rel (y, y_expected, 1e-15, "gsl_expm1(-1e-10)");
y = gsl_expm1 (0.1); y_expected = 0.1051709180756476248117078264902;
gsl_test_rel (y, y_expected, 1e-15, "gsl_expm1(0.1)");
y = gsl_expm1 (-0.1); y_expected = -0.09516258196404042683575094055356;
gsl_test_rel (y, y_expected, 1e-15, "gsl_expm1(-0.1)");
y = gsl_expm1 (10.0); y_expected = 22025.465794806716516957900645284;
gsl_test_rel (y, y_expected, 1e-15, "gsl_expm1(10.0)");
y = gsl_expm1 (-10.0); y_expected = -0.99995460007023751514846440848444;
gsl_test_rel (y, y_expected, 1e-15, "gsl_expm1(-10.0)");
/* Test for log1p */
y = gsl_log1p (0.0); y_expected = 0.0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_log1p(0.0)");
y = gsl_log1p (1e-10); y_expected = 9.9999999995000000000333333333308e-11;
gsl_test_rel (y, y_expected, 1e-15, "gsl_log1p(1e-10)");
y = gsl_log1p (0.1); y_expected = 0.095310179804324860043952123280765;
gsl_test_rel (y, y_expected, 1e-15, "gsl_log1p(0.1)");
y = gsl_log1p (10.0); y_expected = 2.3978952727983705440619435779651;
gsl_test_rel (y, y_expected, 1e-15, "gsl_log1p(10.0)");
/* Test for gsl_hypot */
y = gsl_hypot (0.0, 0.0) ; y_expected = 0.0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(0.0, 0.0)");
y = gsl_hypot (1e-10, 1e-10) ; y_expected = 1.414213562373095048801688e-10;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(1e-10, 1e-10)");
y = gsl_hypot (1e-38, 1e-38) ; y_expected = 1.414213562373095048801688e-38;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(1e-38, 1e-38)");
y = gsl_hypot (1e-10, -1.0) ; y_expected = 1.000000000000000000005;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(1e-10, -1)");
y = gsl_hypot (-1.0, 1e-10) ; y_expected = 1.000000000000000000005;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(-1, 1e-10)");
y = gsl_hypot (1e307, 1e301) ; y_expected = 1.000000000000499999999999e307;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(1e307, 1e301)");
y = gsl_hypot (1e301, 1e307) ; y_expected = 1.000000000000499999999999e307;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(1e301, 1e307)");
y = gsl_hypot (1e307, 1e307) ; y_expected = 1.414213562373095048801688e307;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(1e307, 1e307)");
/* Test for acosh */
y = gsl_acosh (1.0); y_expected = 0.0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_acosh(1.0)");
y = gsl_acosh (1.1); y_expected = 4.435682543851151891329110663525e-1;
gsl_test_rel (y, y_expected, 1e-15, "gsl_acosh(1.1)");
y = gsl_acosh (10.0); y_expected = 2.9932228461263808979126677137742e0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_acosh(10.0)");
y = gsl_acosh (1e10); y_expected = 2.3718998110500402149594646668302e1;
gsl_test_rel (y, y_expected, 1e-15, "gsl_acosh(1e10)");
/* Test for asinh */
y = gsl_asinh (0.0); y_expected = 0.0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(0.0)");
y = gsl_asinh (1e-10); y_expected = 9.9999999999999999999833333333346e-11;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(1e-10)");
y = gsl_asinh (-1e-10); y_expected = -9.9999999999999999999833333333346e-11;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(1e-10)");
y = gsl_asinh (0.1); y_expected = 9.983407889920756332730312470477e-2;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(0.1)");
y = gsl_asinh (-0.1); y_expected = -9.983407889920756332730312470477e-2;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(-0.1)");
y = gsl_asinh (1.0); y_expected = 8.8137358701954302523260932497979e-1;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(1.0)");
y = gsl_asinh (-1.0); y_expected = -8.8137358701954302523260932497979e-1;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(-1.0)");
y = gsl_asinh (10.0); y_expected = 2.9982229502979697388465955375965e0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(10)");
y = gsl_asinh (-10.0); y_expected = -2.9982229502979697388465955375965e0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(-10)");
y = gsl_asinh (1e10); y_expected = 2.3718998110500402149599646668302e1;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(1e10)");
y = gsl_asinh (-1e10); y_expected = -2.3718998110500402149599646668302e1;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(-1e10)");
/* Test for atanh */
y = gsl_atanh (0.0); y_expected = 0.0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_atanh(0.0)");
y = gsl_atanh (1e-20); y_expected = 1e-20;
gsl_test_rel (y, y_expected, 1e-15, "gsl_atanh(1e-20)");
y = gsl_atanh (-1e-20); y_expected = -1e-20;
gsl_test_rel (y, y_expected, 1e-15, "gsl_atanh(-1e-20)");
y = gsl_atanh (0.1); y_expected = 1.0033534773107558063572655206004e-1;
gsl_test_rel (y, y_expected, 1e-15, "gsl_atanh(0.1)");
y = gsl_atanh (-0.1); y_expected = -1.0033534773107558063572655206004e-1;
gsl_test_rel (y, y_expected, 1e-15, "gsl_atanh(-0.1)");
y = gsl_atanh (0.9); y_expected = 1.4722194895832202300045137159439e0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_atanh(0.9)");
y = gsl_atanh (-0.9); y_expected = -1.4722194895832202300045137159439e0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_atanh(0.9)");
/* Test for pow_int */
y = gsl_pow_2 (-3.14); y_expected = pow(-3.14, 2.0);
gsl_test_rel (y, y_expected, 1e-15, "gsl_pow_2(-3.14)");
y = gsl_pow_3 (-3.14); y_expected = pow(-3.14, 3.0);
gsl_test_rel (y, y_expected, 1e-15, "gsl_pow_3(-3.14)");
y = gsl_pow_4 (-3.14); y_expected = pow(-3.14, 4.0);
gsl_test_rel (y, y_expected, 1e-15, "gsl_pow_4(-3.14)");
y = gsl_pow_5 (-3.14); y_expected = pow(-3.14, 5.0);
gsl_test_rel (y, y_expected, 1e-15, "gsl_pow_5(-3.14)");
y = gsl_pow_6 (-3.14); y_expected = pow(-3.14, 6.0);
gsl_test_rel (y, y_expected, 1e-15, "gsl_pow_6(-3.14)");
y = gsl_pow_7 (-3.14); y_expected = pow(-3.14, 7.0);
gsl_test_rel (y, y_expected, 1e-15, "gsl_pow_7(-3.14)");
y = gsl_pow_8 (-3.14); y_expected = pow(-3.14, 8.0);
gsl_test_rel (y, y_expected, 1e-15, "gsl_pow_8(-3.14)");
y = gsl_pow_9 (-3.14); y_expected = pow(-3.14, 9.0);
gsl_test_rel (y, y_expected, 1e-15, "gsl_pow_9(-3.14)");
{
int n;
for (n = -9; n < 10; n++) {
y = gsl_pow_int (-3.14, n); y_expected = pow(-3.14, n);
gsl_test_rel (y, y_expected, 1e-15, "gsl_pow_n(-3.14,%d)", n);
}
}
/* Test for isinf, isnan, finite*/
{
double zero, one, inf, nan;
int s;
zero = 0.0;
one = 1.0;
inf = exp(1.0e10);
nan = inf / inf;
s = gsl_isinf(zero);
gsl_test_int (s, 0, "gsl_isinf(0)");
s = gsl_isinf(one);
gsl_test_int (s, 0, "gsl_isinf(1)");
s = gsl_isinf(inf);
gsl_test_int (s, 1, "gsl_isinf(inf)");
s = gsl_isinf(-inf);
gsl_test_int (s, -1, "gsl_isinf(-inf)");
s = gsl_isinf(nan);
gsl_test_int (s, 0, "gsl_isinf(nan)");
s = gsl_isnan(zero);
gsl_test_int (s, 0, "gsl_isnan(0)");
s = gsl_isnan(one);
gsl_test_int (s, 0, "gsl_isnan(1)");
s = gsl_isnan(inf);
gsl_test_int (s, 0, "gsl_isnan(inf)");
s = gsl_isnan(nan);
gsl_test_int (s, 1, "gsl_isnan(nan)");
s = gsl_finite(zero);
gsl_test_int (s, 1, "gsl_finite(0)");
s = gsl_finite(one);
gsl_test_int (s, 1, "gsl_finite(1)");
s = gsl_finite(inf);
gsl_test_int (s, 0, "gsl_finite(inf)");
s = gsl_finite(nan);
gsl_test_int (s, 0, "gsl_finite(nan)");
}
{
double x = gsl_fdiv (2.0, 3.0);
gsl_test_rel (x, 2.0/3.0, 4*GSL_DBL_EPSILON, "gsl_fdiv(2,3)");
}
exit (gsl_test_summary ());
}
/**
* C++ version of gsl_atanh().
* @param x A real value.
* @return atanh( x ).
*/
inline double atanh( double const x ){ return gsl_atanh( x ); }
int
main (void)
{
double y, y_expected;
int e, e_expected;
gsl_ieee_env_setup ();
/* Test for expm1 */
y = gsl_expm1 (0.0);
y_expected = 0.0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_expm1(0.0)");
y = gsl_expm1 (1e-10);
y_expected = 1.000000000050000000002e-10;
gsl_test_rel (y, y_expected, 1e-15, "gsl_expm1(1e-10)");
y = gsl_expm1 (-1e-10);
y_expected = -9.999999999500000000017e-11;
gsl_test_rel (y, y_expected, 1e-15, "gsl_expm1(-1e-10)");
y = gsl_expm1 (0.1);
y_expected = 0.1051709180756476248117078264902;
gsl_test_rel (y, y_expected, 1e-15, "gsl_expm1(0.1)");
y = gsl_expm1 (-0.1);
y_expected = -0.09516258196404042683575094055356;
gsl_test_rel (y, y_expected, 1e-15, "gsl_expm1(-0.1)");
y = gsl_expm1 (10.0);
y_expected = 22025.465794806716516957900645284;
gsl_test_rel (y, y_expected, 1e-15, "gsl_expm1(10.0)");
y = gsl_expm1 (-10.0);
y_expected = -0.99995460007023751514846440848444;
gsl_test_rel (y, y_expected, 1e-15, "gsl_expm1(-10.0)");
/* Test for log1p */
y = gsl_log1p (0.0);
y_expected = 0.0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_log1p(0.0)");
y = gsl_log1p (1e-10);
y_expected = 9.9999999995000000000333333333308e-11;
gsl_test_rel (y, y_expected, 1e-15, "gsl_log1p(1e-10)");
y = gsl_log1p (0.1);
y_expected = 0.095310179804324860043952123280765;
gsl_test_rel (y, y_expected, 1e-15, "gsl_log1p(0.1)");
y = gsl_log1p (10.0);
y_expected = 2.3978952727983705440619435779651;
gsl_test_rel (y, y_expected, 1e-15, "gsl_log1p(10.0)");
/* Test for gsl_hypot */
y = gsl_hypot (0.0, 0.0);
y_expected = 0.0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(0.0, 0.0)");
y = gsl_hypot (1e-10, 1e-10);
y_expected = 1.414213562373095048801688e-10;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(1e-10, 1e-10)");
y = gsl_hypot (1e-38, 1e-38);
y_expected = 1.414213562373095048801688e-38;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(1e-38, 1e-38)");
y = gsl_hypot (1e-10, -1.0);
y_expected = 1.000000000000000000005;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(1e-10, -1)");
y = gsl_hypot (-1.0, 1e-10);
y_expected = 1.000000000000000000005;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(-1, 1e-10)");
y = gsl_hypot (1e307, 1e301);
y_expected = 1.000000000000499999999999e307;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(1e307, 1e301)");
y = gsl_hypot (1e301, 1e307);
y_expected = 1.000000000000499999999999e307;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(1e301, 1e307)");
y = gsl_hypot (1e307, 1e307);
y_expected = 1.414213562373095048801688e307;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(1e307, 1e307)");
/* Test for acosh */
y = gsl_acosh (1.0);
y_expected = 0.0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_acosh(1.0)");
y = gsl_acosh (1.1);
y_expected = 4.435682543851151891329110663525e-1;
gsl_test_rel (y, y_expected, 1e-15, "gsl_acosh(1.1)");
y = gsl_acosh (10.0);
y_expected = 2.9932228461263808979126677137742e0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_acosh(10.0)");
y = gsl_acosh (1e10);
y_expected = 2.3718998110500402149594646668302e1;
gsl_test_rel (y, y_expected, 1e-15, "gsl_acosh(1e10)");
/* Test for asinh */
y = gsl_asinh (0.0);
y_expected = 0.0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(0.0)");
y = gsl_asinh (1e-10);
y_expected = 9.9999999999999999999833333333346e-11;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(1e-10)");
y = gsl_asinh (-1e-10);
y_expected = -9.9999999999999999999833333333346e-11;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(1e-10)");
y = gsl_asinh (0.1);
y_expected = 9.983407889920756332730312470477e-2;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(0.1)");
y = gsl_asinh (-0.1);
y_expected = -9.983407889920756332730312470477e-2;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(-0.1)");
y = gsl_asinh (1.0);
y_expected = 8.8137358701954302523260932497979e-1;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(1.0)");
y = gsl_asinh (-1.0);
y_expected = -8.8137358701954302523260932497979e-1;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(-1.0)");
y = gsl_asinh (10.0);
y_expected = 2.9982229502979697388465955375965e0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(10)");
y = gsl_asinh (-10.0);
y_expected = -2.9982229502979697388465955375965e0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(-10)");
y = gsl_asinh (1e10);
y_expected = 2.3718998110500402149599646668302e1;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(1e10)");
y = gsl_asinh (-1e10);
y_expected = -2.3718998110500402149599646668302e1;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(-1e10)");
/* Test for atanh */
y = gsl_atanh (0.0);
y_expected = 0.0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_atanh(0.0)");
y = gsl_atanh (1e-20);
y_expected = 1e-20;
gsl_test_rel (y, y_expected, 1e-15, "gsl_atanh(1e-20)");
y = gsl_atanh (-1e-20);
y_expected = -1e-20;
gsl_test_rel (y, y_expected, 1e-15, "gsl_atanh(-1e-20)");
y = gsl_atanh (0.1);
y_expected = 1.0033534773107558063572655206004e-1;
gsl_test_rel (y, y_expected, 1e-15, "gsl_atanh(0.1)");
y = gsl_atanh (-0.1);
y_expected = -1.0033534773107558063572655206004e-1;
gsl_test_rel (y, y_expected, 1e-15, "gsl_atanh(-0.1)");
y = gsl_atanh (0.9);
y_expected = 1.4722194895832202300045137159439e0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_atanh(0.9)");
y = gsl_atanh (-0.9);
y_expected = -1.4722194895832202300045137159439e0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_atanh(0.9)");
/* Test for pow_int */
y = gsl_pow_2 (-3.14);
y_expected = pow (-3.14, 2.0);
gsl_test_rel (y, y_expected, 1e-15, "gsl_pow_2(-3.14)");
y = gsl_pow_3 (-3.14);
y_expected = pow (-3.14, 3.0);
gsl_test_rel (y, y_expected, 1e-15, "gsl_pow_3(-3.14)");
y = gsl_pow_4 (-3.14);
y_expected = pow (-3.14, 4.0);
gsl_test_rel (y, y_expected, 1e-15, "gsl_pow_4(-3.14)");
y = gsl_pow_5 (-3.14);
y_expected = pow (-3.14, 5.0);
gsl_test_rel (y, y_expected, 1e-15, "gsl_pow_5(-3.14)");
y = gsl_pow_6 (-3.14);
y_expected = pow (-3.14, 6.0);
gsl_test_rel (y, y_expected, 1e-15, "gsl_pow_6(-3.14)");
y = gsl_pow_7 (-3.14);
y_expected = pow (-3.14, 7.0);
gsl_test_rel (y, y_expected, 1e-15, "gsl_pow_7(-3.14)");
y = gsl_pow_8 (-3.14);
y_expected = pow (-3.14, 8.0);
gsl_test_rel (y, y_expected, 1e-15, "gsl_pow_8(-3.14)");
y = gsl_pow_9 (-3.14);
y_expected = pow (-3.14, 9.0);
gsl_test_rel (y, y_expected, 1e-15, "gsl_pow_9(-3.14)");
{
int n;
for (n = -9; n < 10; n++)
{
y = gsl_pow_int (-3.14, n);
y_expected = pow (-3.14, n);
gsl_test_rel (y, y_expected, 1e-15, "gsl_pow_n(-3.14,%d)", n);
}
}
/* Test for ldexp */
y = gsl_ldexp (M_PI, -2);
y_expected = M_PI_4;
gsl_test_rel (y, y_expected, 1e-15, "gsl_ldexp(pi,-2)");
y = gsl_ldexp (1.0, 2);
y_expected = 4.000000;
gsl_test_rel (y, y_expected, 1e-15, "gsl_ldexp(1.0,2)");
y = gsl_ldexp (0.0, 2);
y_expected = 0.0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_ldexp(0.0,2)");
/* Test for frexp */
y = gsl_frexp (M_PI, &e);
y_expected = M_PI_4;
e_expected = 2;
gsl_test_rel (y, y_expected, 1e-15, "gsl_frexp(pi) fraction");
gsl_test_int (e, e_expected, "gsl_frexp(pi) exponent");
y = gsl_frexp (2.0, &e);
y_expected = 0.5;
e_expected = 2;
gsl_test_rel (y, y_expected, 1e-15, "gsl_frexp(2.0) fraction");
gsl_test_int (e, e_expected, "gsl_frexp(2.0) exponent");
y = gsl_frexp (1.0 / 4.0, &e);
y_expected = 0.5;
e_expected = -1;
gsl_test_rel (y, y_expected, 1e-15, "gsl_frexp(0.25) fraction");
gsl_test_int (e, e_expected, "gsl_frexp(0.25) exponent");
y = gsl_frexp (1.0 / 4.0 - 4.0 * GSL_DBL_EPSILON, &e);
y_expected = 0.999999999999996447;
e_expected = -2;
gsl_test_rel (y, y_expected, 1e-15, "gsl_frexp(0.25-eps) fraction");
gsl_test_int (e, e_expected, "gsl_frexp(0.25-eps) exponent");
/* Test for approximate floating point comparison */
{
double x, y;
int i;
x = M_PI;
y = 22.0 / 7.0;
/* test the basic function */
for (i = 0; i < 10; i++)
{
double tol = pow (10, -i);
int res = gsl_fcmp (x, y, tol);
gsl_test_int (res, -(i >= 4), "gsl_fcmp(%.5f,%.5f,%g)", x, y, tol);
}
for (i = 0; i < 10; i++)
{
double tol = pow (10, -i);
int res = gsl_fcmp (y, x, tol);
gsl_test_int (res, (i >= 4), "gsl_fcmp(%.5f,%.5f,%g)", y, x, tol);
}
}
#if HAVE_IEEE_COMPARISONS
/* Test for isinf, isnan, finite */
{
double zero, one, inf, nan;
int s;
zero = 0.0;
one = 1.0;
inf = exp (1.0e10);
nan = inf / inf;
s = gsl_isinf (zero);
gsl_test_int (s, 0, "gsl_isinf(0)");
s = gsl_isinf (one);
gsl_test_int (s, 0, "gsl_isinf(1)");
s = gsl_isinf (inf);
gsl_test_int (s, 1, "gsl_isinf(inf)");
s = gsl_isinf (-inf);
gsl_test_int (s, -1, "gsl_isinf(-inf)");
s = gsl_isinf (nan);
gsl_test_int (s, 0, "gsl_isinf(nan)");
s = gsl_isnan (zero);
gsl_test_int (s, 0, "gsl_isnan(0)");
s = gsl_isnan (one);
gsl_test_int (s, 0, "gsl_isnan(1)");
s = gsl_isnan (inf);
gsl_test_int (s, 0, "gsl_isnan(inf)");
s = gsl_isnan (nan);
gsl_test_int (s, 1, "gsl_isnan(nan)");
s = gsl_finite (zero);
gsl_test_int (s, 1, "gsl_finite(0)");
s = gsl_finite (one);
gsl_test_int (s, 1, "gsl_finite(1)");
s = gsl_finite (inf);
gsl_test_int (s, 0, "gsl_finite(inf)");
s = gsl_finite (nan);
gsl_test_int (s, 0, "gsl_finite(nan)");
}
#endif
{
double x = gsl_fdiv (2.0, 3.0);
gsl_test_rel (x, 2.0 / 3.0, 4 * GSL_DBL_EPSILON, "gsl_fdiv(2,3)");
}
exit (gsl_test_summary ());
}
double datanh(double x){
return gsl_atanh(x);
}
float satanh(float x){
return gsl_atanh(x);
}
void
multimin(size_t n,double *x,double *fun,
const unsigned *type, const double *xmin,const double *xmax,
void (*f) (const size_t,const double *,void *,double *),
void (* df) (const size_t,const double *, void *,double *),
void (* fdf) (const size_t,const double *, void *,double *,double *),
void *fparams,
const struct multimin_params oparams)
{
unsigned iter=0;
int status;
size_t i;
double dtmp1;
const gsl_multimin_fdfminimizer_type *Tfdf;
const gsl_multimin_fminimizer_type *Tf;
const char *Tname;
gsl_vector * y = gsl_vector_alloc (n);
/* set the algorithm */
switch(oparams.method){
case 0:/* Fletcher-Reeves conjugate gradient */
Tfdf = gsl_multimin_fdfminimizer_conjugate_fr;
Tname = Tfdf->name;
break;
case 1:/* Polak-Ribiere conjugate gradient */
Tfdf = gsl_multimin_fdfminimizer_conjugate_pr;
Tname = Tfdf->name;
break;
case 2:/* Vector Broyden-Fletcher-Goldfarb-Shanno method */
Tfdf = gsl_multimin_fdfminimizer_vector_bfgs;
Tname = Tfdf->name;
break;
case 3:/* Steepest descent algorithm */
Tfdf =gsl_multimin_fdfminimizer_steepest_descent;
Tname = Tfdf->name;
break;
case 4:/* Simplex */
Tf = gsl_multimin_fminimizer_nmsimplex2;
Tname = Tf->name;
break;
case 5:/* Vector Broyden-Fletcher-Goldfarb-Shanno2 method */
Tfdf = gsl_multimin_fdfminimizer_vector_bfgs2;
Tname = Tfdf->name;
break;
default:
fprintf(stderr,"Optimization method not recognized. Try -h\n");
exit(EXIT_FAILURE);
}
/* --- OUPUT ---------------------------------- */
if(oparams.verbosity>0){
fprintf(stderr,"#--- MULTIMIN START\n");
fprintf(stderr,"# method %s\n",Tname);
if(oparams.method<4 || oparams.method==5){
fprintf(stderr,"# initial step size %g\n", oparams.step_size);
fprintf(stderr,"# line minimization tolerance %g\n",oparams.tol);
fprintf(stderr,"# maximum number of iterations %u\n",oparams.maxiter);
fprintf(stderr,"# precision %g\n",oparams.epsabs);
}
else{
fprintf(stderr,"# maximum number of iterations %u\n",oparams.maxiter);
fprintf(stderr,"# maximum simplex size %g\n",oparams.maxsize);
}
}
/* -------------------------------------------- */
/* compute values of y for initial condition */
for(i=0;i<n;i++){
if(type==NULL)
SET(y,i,x[i]);
else
switch(type[i]){
case 0:/* (-inf,+inf) */
SET(y,i,x[i]);
break;
case 1:/* [a,+inf) */
SET(y,i,sqrt( x[i]-xmin[i] ));
break;
case 2:/* (-inf,a] */
SET(y,i,sqrt( xmax[i]-x[i] ));
break;
case 3:/* [a,b] */
dtmp1 = (xmax[i]>xmin[i]?
(2.*x[i]-xmax[i]-xmin[i])/(xmax[i]-xmin[i]) : 0);
/* dtmp1 = (2.*x[i]-xmax[i]-xmin[i])/(xmax[i]-xmin[i]); */
SET(y,i,asin( dtmp1 ));
break;
case 4:/* (a,+inf) */
SET(y,i,log( x[i]-xmin[i] ));
break;
case 5:/* (-inf,a) */
SET(y,i,log( xmax[i]-x[i] ));
break;
case 6:/* (a,b) */
dtmp1 = (2.*x[i]-xmax[i]-xmin[i])/(xmax[i]-xmin[i]);
SET(y,i,gsl_atanh ( dtmp1 ));
break;
case 7:/* (a,b) second approach */
dtmp1 = (2.*x[i]-xmax[i]-xmin[i])/(xmax[i]-xmin[i]);
SET(y,i, dtmp1/sqrt(1-dtmp1*dtmp1));
break;
case 8:/* (a,+inf) second approach */
dtmp1 = x[i]-xmin[i];
SET(y,i, dtmp1-1./(4.*dtmp1));
break;
}
}
/* --- OUPUT ---------------------------------- */
if(oparams.verbosity>1){
fprintf(stderr,"# - variables initial value and boundaries\n");
for(i=0;i<n;i++){
if(type==NULL)
fprintf(stderr,"# x[%d]=%e (-inf,+inf) -> %e\n",(int) i,x[i],GET(y,i));
else
switch(type[i]){
case 0:/* (-inf,+inf) */
fprintf(stderr,"# x[%d]=%e (-inf,+inf) -> %e\n",(int) i,x[i],GET(y,i));
break;
case 1:/* [a,+inf) */
fprintf(stderr,"# x[%d]=%e [%g,+inf) -> %e\n",(int) i,x[i],xmin[i],GET(y,i));
break;
case 2:/* (-inf,a] */
fprintf(stderr,"# x[%d]=%e (-inf,%g] -> %e\n",(int) i,x[i],xmax[i],GET(y,i));
break;
case 3:/* [a,b] */
fprintf(stderr,"# x[%d]=%e [%g,%g] -> %e\n",(int) i,x[i],xmin[i],xmax[i],GET(y,i));
break;
case 4:/* (a,+inf) */
fprintf(stderr,"# x[%d]=%e (%g,+inf) -> %e\n",(int) i,x[i],xmin[i],GET(y,i));
break;
case 5:/* (-inf,a) */
fprintf(stderr,"# x[%d]=%e (-inf,%g) -> %e\n",(int) i,x[i],xmax[i],GET(y,i));
break;
case 6:/* (a,b) */
case 7:
fprintf(stderr,"# x[%d]=%e (%g,%g) -> %e\n",(int) i,x[i],xmin[i],xmax[i],GET(y,i));
break;
case 8:/* [a,+inf) */
fprintf(stderr,"# x[%d]=%e (%g,+inf) -> %e\n",(int) i,x[i],xmin[i],GET(y,i));
break;
}
}
{
double res;
fprintf(stderr,"# - function initial value\n");
f(n,x,fparams,&res);
fprintf(stderr,"# f=%e\n",res);
}
}
/* -------------------------------------------- */
if(oparams.method<4 || oparams.method==5){/* methods with derivatives */
struct g_params gparams;
gsl_multimin_function_fdf GdG;
gsl_multimin_fdfminimizer *s = gsl_multimin_fdfminimizer_alloc (Tfdf,n);
/* set the parameters of the new function */
gparams.n = n;
gparams.type = type;
gparams.xmin = xmin;
gparams.xmax = xmax;
gparams.f = f;
gparams.df = df;
gparams.fdf = fdf;
gparams.fparams = fparams;
/* set the function to solve */
GdG.f=g;
GdG.df=dg;
GdG.fdf=gdg;
GdG.n=n;
GdG.params=(void *) &gparams;
/* initialize minimizer */
status=gsl_multimin_fdfminimizer_set(s,&GdG,y,oparams.step_size,oparams.tol);
if(status)
{
fprintf(stderr,"#ERROR: %s\n",gsl_strerror (status));
exit(EXIT_FAILURE);
}
/* +++++++++++++++++++++++++++++++++++++++++++++++ */
if(oparams.verbosity>2)
fprintf(stderr,"# - start minimization \n");
/* +++++++++++++++++++++++++++++++++++++++++++++++ */
do
{
iter++;
status = gsl_multimin_fdfminimizer_iterate (s);
/* +++++++++++++++++++++++++++++++++++++++++++++++ */
if(oparams.verbosity>2){
fprintf(stderr,"# [%d]",iter);
fprintf(stderr," g=%+12.6e y=( ",s->f);
for(i=0;i<n;i++)
fprintf(stderr,"%+12.6e ",GET(s->x,i));
fprintf(stderr,") dg=( ");
for(i=0;i<n;i++)
fprintf(stderr,"%+12.6e ",GET(s->gradient,i));
fprintf(stderr,") |dg|=%12.6e ",gsl_blas_dnrm2 (s->gradient));
fprintf(stderr,"|dx|=%12.6e\n",gsl_blas_dnrm2 (s->dx));
}
/* +++++++++++++++++++++++++++++++++++++++++++++++ */
if(status == GSL_ENOPROG){
fprintf(stderr,"# status: %s\n",gsl_strerror (status));
break;
}
if(status){
fprintf(stderr,"#WARNING: %s\n", gsl_strerror (status));
break;
}
/* { */
/* const double eps = oparams.epsabs; */
/* const double norm_x = gsl_blas_dnrm2 (s->x); */
/* const double norm_dx = gsl_blas_dnrm2 (s->dx); */
/* const double norm_g = gsl_blas_dnrm2 (s->gradient); */
/* if( norm_dx < eps && norm_dx < norm_x*eps && norm_g < eps ) */
/* status = GSL_SUCCESS; */
/* else */
/* status = GSL_CONTINUE; */
/* fprintf(stderr,"|x|=%f |dx|=%f |dg|=%f\n",norm_x,norm_dx,norm_g); */
/* } */
status = gsl_multimin_test_gradient (s->gradient,oparams.epsabs);
}
while (status == GSL_CONTINUE && iter < oparams.maxiter);
gsl_vector_memcpy (y,s->x);
*fun=s->f;
gsl_multimin_fdfminimizer_free (s);
}
else{ /* methods without derivatives */
gsl_vector *ss = gsl_vector_alloc (n);
struct g_params gparams;
gsl_multimin_function G;
gsl_multimin_fminimizer *s=gsl_multimin_fminimizer_alloc (Tf,n);
/* set the parameters of the new function */
gparams.n = n;
gparams.type = type;
gparams.xmin = xmin;
gparams.xmax = xmax;
gparams.f = f;
gparams.fparams = fparams;
/* set the function to solve */
G.f=g;
G.n=n;
G.params=(void *) &gparams;
/* Initial vertex size vector */
{
/* size_t i; */
/* dg(y,&gparams,ss); */
/* gsl_vector_set_all (ss,1); */
/* for(i=0;i<n;i++) */
/* SET(ss,i,fabs(GET(ss,i))); */
/* gsl_vector_add_constant (ss,oparams.maxsize); */
gsl_vector_set_all (ss,oparams.step_size+oparams.maxsize);
}
/* --- OUPUT ---------------------------------- */
if(oparams.verbosity>0){
size_t i;
fprintf(stderr,"# initial simplex sizes\n");
fprintf(stderr,"# ");
for(i=0;i<n;i++)
fprintf(stderr," %g", GET(ss,i));
fprintf(stderr,"\n");
}
/* -------------------------------------------- */
/* Initialize minimizer */
status=gsl_multimin_fminimizer_set(s,&G,y,ss);
do
{
status = gsl_multimin_fminimizer_iterate(s);
const double size = gsl_multimin_fminimizer_size (s);
iter++;
/* +++++++++++++++++++++++++++++++++++++++++++++++ */
if(oparams.verbosity>2){
fprintf(stderr,"# g=%g y=( ",s->fval);
for(i=0;i<n;i++)
fprintf(stderr,"%g ",GET(s->x,i));
fprintf(stderr,") ");
fprintf(stderr," simplex size=%g ",size);
fprintf(stderr,"\n");
}
/* +++++++++++++++++++++++++++++++++++++++++++++++ */
status=gsl_multimin_test_size (size,oparams.maxsize);
}
while (status == GSL_CONTINUE && iter < oparams.maxiter);
gsl_vector_memcpy (y, s->x);
*fun=s->fval;
gsl_multimin_fminimizer_free (s);
gsl_vector_free(ss);
}
/* compute values of x */
for(i=0;i<n;i++){
if(type==NULL) /* (-inf,+inf) */
x[i]=GET(y,i);
else
switch(type[i]){
case 0:/* (-inf,+inf) */
x[i]=GET(y,i);
break;
case 1:/* [a,+inf) */
x[i]=xmin[i]+GET(y,i)*GET(y,i);
break;
case 2:/* (-inf,a] */
x[i]=xmax[i]-GET(y,i)*GET(y,i);
break;
case 3:/* [a,b] */
dtmp1 = sin( GET(y,i) );
x[i]=.5*(xmin[i]*(1-dtmp1) +xmax[i]*(1+dtmp1));
break;
case 4:/* (a,+inf) */
dtmp1 = exp( GET(y,i) );
x[i]=xmin[i]+dtmp1;
break;
case 5:/* (-inf,a) */
dtmp1 = -exp( GET(y,i) );
x[i]=xmax[i]+dtmp1;
break;
case 6:/* (a,b) */
dtmp1 = tanh( GET(y,i) );
x[i]=.5*(xmin[i]*(1-dtmp1) +xmax[i]*(1+dtmp1));
break;
case 7:/* (a,b) second approach */
dtmp1 = GET(y,i) ;
dtmp1 = dtmp1/sqrt(1.+dtmp1*dtmp1);
x[i]=.5*(xmin[i]*(1-dtmp1) +xmax[i]*(1+dtmp1));
break;
case 8:/* (a,+inf) second approach */
dtmp1 = sqrt(1.+GET(y,i)*GET(y,i));
x[i]= xmin[i] + .5*(dtmp1+GET(y,i));
break;
}
}
/* --- OUPUT ---------------------------------- */
if(oparams.verbosity>0){
fprintf(stderr,"# - end minimization\n");
fprintf(stderr,"# iterations %u\n",iter);
for(i=0;i<n;i++)
fprintf(stderr,"# %e -> x[%zd]=%e\n",GET(y,i),i,x[i]);
fprintf(stderr,"#--- MULTIMIN END --- \n");
}
/* -------------------------------------------- */
gsl_vector_free (y);
}
