log1p.c File Reference

#include "prim.h"

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Functions
double	log1p (double x)

Variables
static const double	ln2_hi = 6.93147180369123816490e-01
static const double	ln2_lo = 1.90821492927058770002e-10
static const double	two54 = 1.80143985094819840000e+16
static const double	Lp1 = 6.666666666666735130e-01
static const double	Lp2 = 3.999999999940941908e-01
static const double	Lp3 = 2.857142874366239149e-01
static const double	Lp4 = 2.222219843214978396e-01
static const double	Lp5 = 1.818357216161805012e-01
static const double	Lp6 = 1.531383769920937332e-01
static const double	Lp7 = 1.479819860511658591e-01
static double	zero = 0.0

Function Documentation

log1p()

double log1p

(

double

x

)

Definition at line 122 of file log1p.c.

References ln2_hi, ln2_lo, Lp1, Lp2, Lp3, Lp4, Lp5, Lp6, Lp7, two54, and zero.

Referenced by acosh(), asinh(), and atanh().

{
    double hfsq,f,c,s,z,R,u;
    int32_t k,hx,hu,ax;

    f = 0.0;
    c = 0.0;
    hu = 0;

    GET_HIGH_WORD(hx,x); /* high word of x */
    ax = hx&0x7fffffff;

    k = 1;
    if (hx < 0x3FDA827A) {          /* x < 0.41422  */
        if(ax>=0x3ff00000) {        /* x <= -1.0 */
            if(x==-1.0) return -two54/zero; /* log1p(-1)=+inf */
            else return (x-x)/(x-x);    /* log1p(x<-1)=NaN */
        }
        if(ax<0x3e200000) {         /* |x| < 2**-29 */
            if(two54+x>zero         /* raise inexact */
                    &&ax<0x3c900000)        /* |x| < 2**-54 */
                return x;
            else
                return x - x*x*0.5;
        }
        if(hx>0||hx<=((int)0xbfd2bec3)) {
            k=0;
            f=x;
            hu=1;
        }   /* -0.2929<x<0.41422 */
    }
    if (hx >= 0x7ff00000) return x+x;
    if(k!=0) {
        if(hx<0x43400000) {
            u  = 1.0+x;
            GET_HIGH_WORD(hu,u); /* high word of u */
            k  = (hu>>20)-1023;
            c  = (k>0)? 1.0-(u-x):x-(u-1.0);/* correction term */
            c /= u;
        } else {
            u  = x;
            GET_HIGH_WORD(hu,u); /* high word of u */
            k  = (hu>>20)-1023;
            c  = 0;
        }
        hu &= 0x000fffff;
        if(hu<0x6a09e) {
            SET_HIGH_WORD(u, hu|0x3ff00000);    /* normalize u */
        } else {
            k += 1;
            SET_HIGH_WORD(u, hu|0x3fe00000);    /* normalize u/2 */
            hu = (0x00100000-hu)>>2;
        }
        f = u-1.0;
    }
    hfsq=0.5*f*f;
    if(hu==0) { /* |f| < 2**-20 */
        if(f==zero) {
            if(k==0) return zero;
            else {
                c += k*ln2_lo;
                return k*ln2_hi+c;
            }
        }
        R = hfsq*(1.0-0.66666666666666666*f);
        if(k==0) return f-R;
        else
            return k*ln2_hi-((R-(k*ln2_lo+c))-f);
    }
    s = f/(2.0+f);
    z = s*s;
    R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7))))));
    if(k==0) return f-(hfsq-s*(hfsq+R));
    else
        return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f);
}

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Variable Documentation

ln2_hi

const double ln2_hi = 6.93147180369123816490e-01

static

Definition at line 109 of file log1p.c.

Referenced by log1p().

ln2_lo

const double ln2_lo = 1.90821492927058770002e-10

static

Definition at line 110 of file log1p.c.

Referenced by log1p().

Lp1

const double Lp1 = 6.666666666666735130e-01

static

Definition at line 112 of file log1p.c.

Referenced by log1p().

Lp2

const double Lp2 = 3.999999999940941908e-01

static

Definition at line 113 of file log1p.c.

Referenced by log1p().

Lp3

const double Lp3 = 2.857142874366239149e-01

static

Definition at line 114 of file log1p.c.

Referenced by log1p().

Lp4

const double Lp4 = 2.222219843214978396e-01

static

Definition at line 115 of file log1p.c.

Referenced by log1p().

Lp5

const double Lp5 = 1.818357216161805012e-01

static

Definition at line 116 of file log1p.c.

Referenced by log1p().

Lp6

const double Lp6 = 1.531383769920937332e-01

static

Definition at line 117 of file log1p.c.

Referenced by log1p().

Lp7

const double Lp7 = 1.479819860511658591e-01

static

Definition at line 118 of file log1p.c.

Referenced by log1p().

two54

const double two54 = 1.80143985094819840000e+16

static

Definition at line 111 of file log1p.c.

Referenced by log1p().

zero

double zero = 0.0

static

Definition at line 120 of file log1p.c.

Referenced by log1p().