log10.c File Reference

#include <math.h>
#include <stdint.h>

Include dependency graph for log10.c:

Go to the source code of this file.

Functions
double	log10 (double x)

Variables
static const double	ivln10hi = 4.34294481878168880939e-01
static const double	ivln10lo = 2.50829467116452752298e-11
static const double	log10_2hi = 3.01029995663611771306e-01
static const double	log10_2lo = 3.69423907715893078616e-13
static const double	Lg1 = 6.666666666666735130e-01
static const double	Lg2 = 3.999999999940941908e-01
static const double	Lg3 = 2.857142874366239149e-01
static const double	Lg4 = 2.222219843214978396e-01
static const double	Lg5 = 1.818357216161805012e-01
static const double	Lg6 = 1.531383769920937332e-01
static const double	Lg7 = 1.479819860511658591e-01

Function Documentation

log10()

double log10

(

double

x

)

Definition at line 50 of file log10.c.

{
    union {double f; uint64_t i;} u = {x};
    double_t hfsq,f,s,z,R,w,t1,t2,dk,y,hi,lo,val_hi,val_lo;
    uint32_t hx;
    int k;
 
    hx = u.i>>32;
    k = 0;
    if (hx < 0x00100000 || hx>>31) {
        if (u.i<<1 == 0)
            return -1/(x*x);  /* log(+-0)=-inf */
        if (hx>>31)
            return (x-x)/0.0; /* log(-#) = NaN */
        /* subnormal number, scale x up */
        k -= 54;
        x *= 0x1p54;
        u.f = x;
        hx = u.i>>32;
    } else if (hx >= 0x7ff00000) {
        return x;
    } else if (hx == 0x3ff00000 && u.i<<32 == 0)
        return 0;
 
    /* reduce x into [sqrt(2)/2, sqrt(2)] */
    hx += 0x3ff00000 - 0x3fe6a09e;
    k += (int)(hx>>20) - 0x3ff;
    hx = (hx&0x000fffff) + 0x3fe6a09e;
    u.i = (uint64_t)hx<<32 | (u.i&0xffffffff);
    x = u.f;
 
    f = x - 1.0;
    hfsq = 0.5*f*f;
    s = f/(2.0+f);
    z = s*s;
    w = z*z;
    t1 = w*(Lg2+w*(Lg4+w*Lg6));
    t2 = z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
    R = t2 + t1;
 
    /* See log2.c for details. */
    /* hi+lo = f - hfsq + s*(hfsq+R) ~ log(1+f) */
    hi = f - hfsq;
    u.f = hi;
    u.i &= (uint64_t)-1<<32;
    hi = u.f;
    lo = f - hi - hfsq + s*(hfsq+R);
 
    /* val_hi+val_lo ~ log10(1+f) + k*log10(2) */
    val_hi = hi*ivln10hi;
    dk = k;
    y = dk*log10_2hi;
    val_lo = dk*log10_2lo + (lo+hi)*ivln10lo + lo*ivln10hi;
 
    /*
     * Extra precision in for adding y is not strictly needed
     * since there is no very large cancellation near x = sqrt(2) or
     * x = 1/sqrt(2), but we do it anyway since it costs little on CPUs
     * with some parallelism and it reduces the error for many args.
     */
    w = y + val_hi;
    val_lo += (y - w) + val_hi;
    val_hi = w;
 
    return val_lo + val_hi;
}

Referenced by log10f(), and log10l().

Variable Documentation

ivln10hi

const double ivln10hi = 4.34294481878168880939e-01

static

Definition at line 38 of file log10.c.

Referenced by log10().

ivln10lo

const double ivln10lo = 2.50829467116452752298e-11

static

Definition at line 39 of file log10.c.

Referenced by log10().

Lg1

const double Lg1 = 6.666666666666735130e-01

static

Definition at line 42 of file log10.c.

Referenced by log10().

Lg2

const double Lg2 = 3.999999999940941908e-01

static

Definition at line 43 of file log10.c.

Referenced by log10().

Lg3

const double Lg3 = 2.857142874366239149e-01

static

Definition at line 44 of file log10.c.

Referenced by log10().

Lg4

const double Lg4 = 2.222219843214978396e-01

static

Definition at line 45 of file log10.c.

Referenced by log10().

Lg5

const double Lg5 = 1.818357216161805012e-01

static

Definition at line 46 of file log10.c.

Referenced by log10().

Lg6

const double Lg6 = 1.531383769920937332e-01

static

Definition at line 47 of file log10.c.

Referenced by log10().

Lg7

const double Lg7 = 1.479819860511658591e-01

static

Definition at line 48 of file log10.c.

Referenced by log10().

log10_2hi

const double log10_2hi = 3.01029995663611771306e-01

static

Definition at line 40 of file log10.c.

Referenced by log10().

log10_2lo

const double log10_2lo = 3.69423907715893078616e-13

static

Definition at line 41 of file log10.c.

Referenced by log10().