itcompat.cpp
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#include <itpp/base/itcompat.h>
#include <itpp/base/itassert.h>
#include <limits>
#ifndef HAVE_TGAMMA
// "True" gamma function
double tgamma(double x)
{
double s = (2.50662827510730 + 190.9551718930764 / (x + 1)
- 216.8366818437280 / (x + 2) + 60.19441764023333
/ (x + 3) - 3.08751323928546 / (x + 4) + 0.00302963870525
/ (x + 5) - 0.00001352385959072596 / (x + 6)) / x;
if (s < 0)
return -exp((x + 0.5) * log(x + 5.5) - x - 5.5 + log(-s));
else
return exp((x + 0.5) * log(x + 5.5) - x - 5.5 + log(s));
}
#endif
#if !defined(HAVE_LGAMMA) || (HAVE_DECL_SIGNGAM != 1)
// The sign of the Gamma function is returned in the external integer
// signgam declared in <math.h>. It is 1 when the Gamma function is positive
// or zero, -1 when it is negative. However, MinGW definition of lgamma()
// function does not use the global signgam variable.
int signgam;
// Logarithm of an absolute value of gamma function
double lgamma(double x)
{
double gam = tgamma(x);
signgam = (gam < 0) ? -1 : 1;
return log(fabs(gam));
}
#endif
#ifndef HAVE_CBRT
// Cubic root
double cbrt(double x) { return std::pow(x, 1.0 / 3.0); }
#endif
#ifndef HAVE_EXPM1
#ifndef M_LN2
#define M_LN2 0.69314718055994530941723212146 // ln(2)
#endif
// Implementation taken from GSL (http://www.gnu.org/software/gsl/)
double expm1(double x)
{
/* FIXME: this should be improved */
if (std::fabs(x) < M_LN2) {
/* Compute the taylor series S = x + (1/2!) x^2 + (1/3!) x^3 + ... */
double i = 1.0;
double sum = x;
double term = x / 1.0;
do {
i++;
term *= x / i;
sum += term;
}
while (std::fabs(term) > (std::fabs(sum)
* std::numeric_limits<double>::epsilon()));
return sum;
}
else {
return std::exp(x) - 1.0;
}
}
#endif // HAVE_EXPM1
#ifndef HAVE_ERFC
// Complementary error function
double erfc(double Y)
{
int ISW, I;
double P[4], Q[3], P1[6], Q1[5], P2[4], Q2[3];
double XMIN, XLARGE, SQRPI;
double X, RES, XSQ, XNUM, XDEN, XI, XBIG, ERFCret;
P[1] = 0.3166529;
P[2] = 1.722276;
P[3] = 21.38533;
Q[1] = 7.843746;
Q[2] = 18.95226;
P1[1] = 0.5631696;
P1[2] = 3.031799;
P1[3] = 6.865018;
P1[4] = 7.373888;
P1[5] = 4.318779e-5;
Q1[1] = 5.354217;
Q1[2] = 12.79553;
Q1[3] = 15.18491;
Q1[4] = 7.373961;
P2[1] = 5.168823e-2;
P2[2] = 0.1960690;
P2[3] = 4.257996e-2;
Q2[1] = 0.9214524;
Q2[2] = 0.1509421;
XMIN = 1.0E-5;
XLARGE = 4.1875E0;
XBIG = 9.0;
SQRPI = 0.5641896;
X = Y;
ISW = 1;
if (X < 0) {
ISW = -1;
X = -X;
}
if (X < 0.477) {
if (X >= XMIN) {
XSQ = X * X;
XNUM = (P[1] * XSQ + P[2]) * XSQ + P[3];
XDEN = (XSQ + Q[1]) * XSQ + Q[2];
RES = X * XNUM / XDEN;
}
else RES = X * P[3] / Q[2];
if (ISW == -1) RES = -RES;
RES = 1.0 - RES;
goto slut;
}
if (X > 4.0) {
if (ISW > 0) goto ulf;
if (X < XLARGE) goto eva;
RES = 2.0;
goto slut;
}
XSQ = X * X;
XNUM = P1[5] * X + P1[1];
XDEN = X + Q1[1];
for (I = 2;I <= 4;I++) {
XNUM = XNUM * X + P1[I];
XDEN = XDEN * X + Q1[I];
}
RES = XNUM / XDEN;
goto elin;
ulf:
if (X > XBIG) goto fred;
eva:
XSQ = X * X;
XI = 1.0 / XSQ;
XNUM = (P2[1] * XI + P2[2]) * XI + P2[3];
XDEN = XI + Q2[1] * XI + Q2[2];
RES = (SQRPI + XI * XNUM / XDEN) / X;
elin:
RES = RES * exp(-XSQ);
if (ISW == -1) RES = 2.0 - RES;
goto slut;
fred:
RES = 0.0;
slut:
ERFCret = RES;
return ERFCret;
}
#endif
#ifndef HAVE_ASINH
// Arcus sinhyp
double asinh(double x)
{
return ((x >= 0) ? std::log(x + std::sqrt(x * x + 1))
: -std::log(-x + std::sqrt(x * x + 1)));
}
#endif
#ifndef HAVE_ACOSH
// Arcus coshyp
double acosh(double x)
{
it_error_if(x < 1, "acosh(): Argument out of range");
return std::log(x + std::sqrt(x * x - 1.0));
}
#endif
#ifndef HAVE_ATANH
// Arcus tanhyp
double atanh(double x)
{
it_error_if(std::fabs(x) >= 1, "atanh(): Argument out of range");
return 0.5 * std::log((x + 1) / (x - 1));
}
#endif
#ifndef HAVE_RINT
double rint(double x)
{
// zero or NaN case
if ((x == 0.0) || (x != x))
return x;
// negative case
bool neg = false;
if (x < 0.0) {
x = -x;
neg = true;
}
double y = std::floor(x + 0.5);
int i = static_cast<int>(y);
if ((y - x >= 0.5) && (i & 1))
--y;
return neg ? -y : y;
}
#endif // HAVE_RINT
itpp::erfc
vec erfc(const vec &x)
Complementary error function.
Definition error.cpp:240
it_error_if
#define it_error_if(t, s)
Abort if t is true.
Definition itassert.h:117
itpp::asinh
vec asinh(const vec &x)
Inverse sine hyperbolic function.
Definition trig_hyp.cpp:36
itpp::acosh
vec acosh(const vec &x)
Inverse cosine hyperbolic function.
Definition trig_hyp.cpp:40
itpp::atanh
vec atanh(const vec &x)
Inverse tan hyperbolic function.
Definition trig_hyp.cpp:44
itpp::log
vec log(const vec &x)
The natural logarithm of the elements.
Definition log_exp.h:241
itpp::exp
vec exp(const vec &x)
Exp of the elements of a vector x.
Definition log_exp.h:155
itpp::sum
T sum(const Vec< T > &v)
Sum of all elements in the vector.
Definition matfunc.h:59
itpp::sqrt
vec sqrt(const vec &x)
Square root of the elements.
Definition elem_math.h:123
itassert.h
Error handling functions - header file.
itcompat.h
IT++ compatibility types and functions.
std
STL namespace.

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