log10.c File Reference

Base 10 logarithm function. More...

#include "prim.h"

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Functions
double	log10 (double x)
	Base 10 logarithm function. More...

Variables
static const double	two54 = 1.80143985094819840000e+16
static const double	ivln10 = 4.34294481903251816668e-01
static const double	log10_2hi = 3.01029995663611771306e-01
static const double	log10_2lo = 3.69423907715893078616e-13
static double	zero = 0.0

Detailed Description

Base 10 logarithm function.

Definition in file log10.c.

Function Documentation

log10()

double log10

(

double

x

)

Base 10 logarithm function.

Method:
Let log10_2hi = leading 40 bits of log10(2) and
    log10_2lo = log10(2) - log10_2hi,
    ivln10    = 1/log(10) rounded.
Then
    n = ilogb(x),
    if(n<0)  n = n+1;
    x = scalbn(x,-n);
    log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))

Note 1:
To guarantee log10(10**n)=n, where 10**n is normal, the rounding
mode must set to Round-to-Nearest.

Note 2:
[1/log(10)] rounded to 53 bits has error .198 ulps;
log10 is monotonic at all binary break points.

Special cases:
log10(x) is NaN with signal if x < 0;
log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
log10(NaN) is that NaN with no signal;
log10(10**N) = N  for N=0,1,...,22.

Constants:
The hexadecimal values are the intended ones for the following constants.
The decimal values may be used, provided that the compiler will convert
from decimal to binary accurately enough to produce the hexadecimal values
shown.

Definition at line 93 of file log10.c.

References ivln10, log(), log10_2hi, log10_2lo, two54, and zero.

Referenced by DecimalSystem::GetText(), and RealNumber::Log10().

{
    double y,z;
    int32_t i,k,hx;
    uint32_t lx;

    EXTRACT_WORDS(hx,lx,x);

    k=0;
    if (hx < 0x00100000) {                  /* x < 2**-1022  */
        if (((hx&0x7fffffff)|lx)==0)
            return -two54/zero;             /* log(+-0)=-inf */
        if (hx<0) return (x-x)/zero;        /* log(-#) = NaN */
        k -= 54;
        x *= two54; /* subnormal number, scale up x */
        GET_HIGH_WORD(hx, x);              /* high word of x */
    }
    if (hx >= 0x7ff00000) return x+x;
    k += (hx>>20)-1023;
    i  = ((uint32_t)k&0x80000000)>>31;
    hx = (hx&0x000fffff)|((0x3ff-i)<<20);
    y  = (double)(k+i);
    SET_HIGH_WORD(x,hx);
    z  = y*log10_2lo + ivln10*log(x);
    return  z+y*log10_2hi;
}

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Variable Documentation

ivln10

const double ivln10 = 4.34294481903251816668e-01

static

Definition at line 50 of file log10.c.

Referenced by log10().

log10_2hi

const double log10_2hi = 3.01029995663611771306e-01

static

Definition at line 51 of file log10.c.

Referenced by log10().

log10_2lo

const double log10_2lo = 3.69423907715893078616e-13

static

Definition at line 52 of file log10.c.

Referenced by log10().

two54

const double two54 = 1.80143985094819840000e+16

static

Definition at line 49 of file log10.c.

Referenced by log10().

zero

double zero = 0.0

static

Definition at line 54 of file log10.c.

Referenced by log10().