tanh.c File Reference

Hyperbolic tangent function. More...

#include "prim.h"

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Functions
double	tanh (double x)
	Hyperbolic tangent function. More...

Variables
static const double	one = 1.0
static const double	two = 2.0
static const double	tiny = 1.0e-300

Detailed Description

Hyperbolic tangent function.

Definition in file tanh.c.

Function Documentation

tanh()

double tanh

(

double

x

)

Hyperbolic tangent function.

Returns

The Hyperbolic Tangent of x

Method
                                   x    -x
                                  e  - e
    0. tanh(x) is defined to be --------—
                                   x    -x
                                  e  + e

    1. reduce x to non-negative by tanh(-x) = -tanh(x)

    2.  0      <= x <= 2**-55 : tanh(x) = x*(one+x)
                                           -t
        2**-55 <  x <=  1     : tanh(x) = --—; t = expm1(-2x)
                                          t + 2
                                                2
        1      <= x <=  22.0  : tanh(x) = 1-  --— ; t=expm1(2x)
                                              t + 2
        22.0   <  x <= INF    : tanh(x) = 1

Special cases
    tanh(NaN) is NaN
    only tanh(0)=0 is exact for finite argument.

Definition at line 81 of file tanh.c.

References expm1(), fabs(), one, tiny, and two.

Referenced by RealNumber::HypTangent().

{
    double t, z;
    int32_t jx, ix;

    /* High word of |x|. */
    GET_HIGH_WORD(jx, x);
    ix = jx & 0x7FFFFFFF;

    /* x is INF or NaN */
    if (ix >= 0x7FF00000)
    {
        if (jx >= 0)
            return one / x + one; /* tanh(+-inf)=+-1 */
        else
            return NAN; /* tanh(NaN) = NaN */
    }

    /* |x| < 22 */
    if (ix < 0x40360000)
    {                             /* |x|<22 */
        if (ix < 0x3C800000)      /* |x|<2**-55 */
            return x * (one + x); /* tanh(small) = small */
        if (ix >= 0x3FF00000)
        { /* |x|>=1 */
            t = expm1(two * fabs(x));
            z = one - two / (t + two);
        }
        else
        {
            t = expm1(-two * fabs(x));
            z = -t / (t + two);
        }
    }
    /* |x| > 22, return +-1 */
    else
    {
        z = one - tiny; /* raised inexact flag */
    }

    return (jx >= 0) ? z : -z;
}

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Variable Documentation

one

const double one = 1.0

static

Definition at line 49 of file tanh.c.

Referenced by tanh().

tiny

const double tiny = 1.0e-300

static

Definition at line 51 of file tanh.c.

Referenced by tanh().

two

const double two = 2.0

static

Definition at line 50 of file tanh.c.

Referenced by tanh().