acosh.c File Reference

Inverse hyperbolic cosine function. More...

#include "prim.h"

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Functions
double	acosh (double x)
	Inverse hyperbolic cosine function. More...

Variables
static const double	one = 1.0
static const double	ln2 = 6.93147180559945286227e-01

Detailed Description

Inverse hyperbolic cosine function.

Definition in file acosh.c.

Function Documentation

acosh()

double acosh

(

double

x

)

Inverse hyperbolic cosine function.

Based on
    acosh(x) = log [ x + sqrt(x*x-1) ]

we have
    acosh(x) = log(x)+ln2, if x is large; else
    acosh(x) = log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
    acosh(x) = log1p(t+sqrt(2.0*t+t*t)); where t=x-1

Special cases
    acosh(x) is NaN if x<1
    acosh(NaN) is NaN

Definition at line 69 of file acosh.c.

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

Referenced by RealNumber::HypArcCosine().

{
    double t;
    int32_t hx, lx;

    GET_HIGH_WORD(hx, x);
    GET_LOW_WORD(lx, x);

    // x < 1
    if (hx < 0x3FF00000)
    {
        return NAN;
    }

    // x > 2**28
    if (hx >= 0x41B00000)
    {
        // x is inf or NaN
        if (hx >= 0x7FF00000)
        {
            return NAN;
        }

        // acosh(huge) = log(2x)
        return log(x) + ln2;
    }

    // acosh(1) = 0
    if (((hx - 0x3FF00000) | lx) == 0)
    {
        return 0.0;
    }

    // 2**28 > x > 2
    if (hx > 0x40000000)
    {
        t = x * x;
        return log(2.0 * x - one / (x + sqrt(t - one)));
    }

    // 1 < x < 2
    t = x - one;
    return log1p(t + sqrt(2.0 * t + t * t));
}

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Variable Documentation

ln2

const double ln2 = 6.93147180559945286227e-01

static

Definition at line 50 of file acosh.c.

Referenced by acosh().

one

const double one = 1.0

static

Definition at line 49 of file acosh.c.

Referenced by acosh().