double gsl_pow_int(double x, int n)
{
unsigned int un;
if(n < 0) {
x = 1.0/x;
un = -n;
} else {
un = n;
}
return gsl_pow_uint(x, un);
}
/**
* Evaluate the one-dimensional polynomial vector field at a given state.
* \param[in] state State at which to evaluate the vector field.
* \param[out] field Vector resulting from the evaluation of the vector field.
*/
void
polynomial1D::evalField(gsl_vector *state, gsl_vector *field)
{
double tmp;
double stateScal = gsl_vector_get(state, 0);
// One-dimensional polynomial field:
tmp = gsl_vector_get(coeff, 0);
for (size_t c = 1; c < degree + 1; c++)
{
tmp += gsl_vector_get(coeff, c) * gsl_pow_uint(stateScal, c);
}
gsl_vector_set(field, 0, tmp);
return;
}
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 ());
}
double annihilation(double theta, void *par)
{
double Z1_, Z2_, Z3_, Z4_, Z5_, Z6_, Z7_, Z8_, Z9_;
double trace_numerator, trace_denominator;
double p, w1, w2, kin, xi;
double E = *(double *) par;
p = sqrt(E*E-m*m);
w1 = m*(m+E)/(m+E-p*cos(theta));
w2 = E+m-w1;
kin = alpha*alpha*w1*w1/(2*p*(m+E));
xi = 1-cos(theta/2);
Z1_=gsl_pow_uint(w1,2);
Z2_=gsl_pow_uint(w2,3);
Z3_=Z1_*Z2_;
Z4_=gsl_pow_uint(w2,5);
Z3_=Z3_ + Z4_;
Z3_=2*Z3_;
Z5_=xi*Z4_;
Z5_= - Z3_ + Z5_;
Z5_=xi*Z5_;
Z3_=Z3_ + Z5_;
Z5_=gsl_pow_uint(w1,3);
Z3_=Z5_*Z3_;
Z6_=gsl_pow_uint(w2,2);
Z7_=Z6_*w1;
Z8_= - Z2_ + Z7_;
Z8_=w1*Z8_;
Z6_=gsl_pow_uint(Z6_,2);
Z8_= - 3*Z6_ + Z8_;
Z8_=w1*Z8_;
Z8_= - Z4_ + Z8_;
Z8_=xi*Z8_;
Z7_=2*Z2_ + Z7_;
Z7_=w1*Z7_;
Z7_=Z6_ + Z7_;
Z9_=2*xi;
Z7_=m*Z7_*Z9_;
Z7_=Z7_ + Z8_;
Z1_=Z1_*Z7_;
Z2_= - w1*Z2_;
Z2_= - Z6_ + Z2_;
Z2_=Z2_*Z5_;
Z1_=4*Z2_ + Z1_;
Z1_=m*Z1_;
Z1_=2*Z3_ + Z1_;
Z1_=m*Z1_;
Z2_=Z6_*w1;
Z2_=Z2_ + Z4_;
Z3_=2 - xi;
Z2_=Z9_*Z2_*Z3_*gsl_pow_uint(w1,4);
Z1_=Z2_ + Z1_;
trace_numerator = 128*Z1_*gsl_pow_uint(m,3);
Z1_=2 - xi;
Z2_=w1*w2;
trace_denominator = 32*gsl_pow_uint(Z2_,3)*Z1_*gsl_pow_uint(m,4);
return 0.5*MeV2mBn*kin*trace_numerator/trace_denominator;
}
int
gsl_filter_gaussian_kernel(const double alpha, const size_t order, const int normalize, gsl_vector * kernel)
{
const size_t N = kernel->size;
if (alpha <= 0.0)
{
GSL_ERROR("alpha must be positive", GSL_EDOM);
}
else if (order > GSL_FILTER_GAUSSIAN_MAX_ORDER)
{
GSL_ERROR("derivative order is too large", GSL_EDOM);
}
else
{
const double half = 0.5 * (N - 1.0); /* (N - 1) / 2 */
double sum = 0.0;
size_t i;
/* check for quick return */
if (N == 1)
{
if (order == 0)
gsl_vector_set(kernel, 0, 1.0);
else
gsl_vector_set(kernel, 0, 0.0);
return GSL_SUCCESS;
}
for (i = 0; i < N; ++i)
{
double xi = ((double)i - half) / half;
double yi = alpha * xi;
double gi = exp(-0.5 * yi * yi);
gsl_vector_set(kernel, i, gi);
sum += gi;
}
/* normalize so sum(kernel) = 1 */
if (normalize)
gsl_vector_scale(kernel, 1.0 / sum);
if (order > 0)
{
const double beta = -0.5 * alpha * alpha;
double q[GSL_FILTER_GAUSSIAN_MAX_ORDER + 1];
size_t k;
/*
* Need to calculate derivatives of the Gaussian window; define
*
* w(n) = C * exp [ p(n) ]
*
* p(n) = beta * n^2
* beta = -1/2 * ( alpha / ((N-1)/2) )^2
*
* Then:
*
* d^k/dn^k w(n) = q_k(n) * w(n)
*
* where q_k(n) is a degree-k polynomial in n, which satisfies:
*
* q_k(n) = d/dn q_{k-1}(n) + q_{k-1}(n) * dp(n)/dn
* q_0(n) = 1 / half^{order}
*/
/* initialize q_0(n) = 1 / half^{order} */
q[0] = 1.0 / gsl_pow_uint(half, order);
for (i = 1; i <= GSL_FILTER_GAUSSIAN_MAX_ORDER; ++i)
q[i] = 0.0;
/* loop through derivative orders and calculate q_k(n) for k = 1,...,order */
for (k = 1; k <= order; ++k)
{
double qm1 = q[0];
q[0] = q[1];
for (i = 1; i <= k; ++i)
{
double tmp = q[i];
q[i] = (i + 1.0) * q[i + 1] + /* d/dn q_{k-1} */
2.0 * beta * qm1; /* q_{k-1}(n) p'(n) */
qm1 = tmp;
}
}
/* now set w(n) := q(n) * w(n) */
for (i = 0; i < N; ++i)
{
double xi = ((double)i - half) / half;
double qn = gsl_poly_eval(q, order + 1, xi);
double *wn = gsl_vector_ptr(kernel, i);
*wn *= qn;
}
}
return GSL_SUCCESS;
}
}
