asinh.c File Reference

Inverse hyperbolic sine function. More...

#include "prim.h"

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Functions
double	asinh (double x)
	Inverse hyperbolic sine function. More...

Variables
static const double	one = 1.00000000000000000000e+00
static const double	ln2 = 6.93147180559945286227e-01
static const double	huge = 1.00000000000000000000e+300

Detailed Description

Inverse hyperbolic sine function.

Definition in file asinh.c.

Function Documentation

asinh()

double asinh

(

double

x

)

Inverse hyperbolic sine function.

Method
    Based on
    asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]

    we have
    asinh(x) = x  if  1+x*x=1,
             = sign(x)*(log(x)+ln2)) for large |x|, else
             = sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
             = sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))

Definition at line 68 of file asinh.c.

References fabs(), huge, ln2, log(), log1p(), one, and sqrt().

Referenced by RealNumber::HypArcSine().

{
    double t, w;
    int32_t hx, ix;
    GET_HIGH_WORD(hx, x);
    ix = hx & 0x7fffffff;
    if (ix >= 0x7ff00000)
        return x + x; /* x is inf or NaN */
    if (ix < 0x3e300000)
    { /* |x|<2**-28 */
        if (huge + x > one)
            return x; /* return x inexact except 0 */
    }
    if (ix > 0x41b00000)
    { /* |x| > 2**28 */
        w = log(fabs(x)) + ln2;
    }
    else if (ix > 0x40000000)
    { /* 2**28 > |x| > 2.0 */
        t = fabs(x);
        w = log(2.0 * t + one / (sqrt(x * x + one) + t));
    }
    else
    { /* 2.0 > |x| > 2**-28 */
        t = x * x;
        w = log1p(fabs(x) + t / (one + sqrt(one + t)));
    }
    if (hx > 0)
        return w;
    else
        return -w;
}

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Variable Documentation

huge

const double huge = 1.00000000000000000000e+300

static

Definition at line 51 of file asinh.c.

Referenced by asinh().

ln2

const double ln2 = 6.93147180559945286227e-01

static

Definition at line 50 of file asinh.c.

Referenced by asinh().

one

const double one = 1.00000000000000000000e+00

static

Definition at line 49 of file asinh.c.

Referenced by asinh().