log.c File Reference

#include <math.h>
#include <stdint.h>
#include "libm.h"
#include "log_data.h"

Include dependency graph for log.c:

Go to the source code of this file.

Macros
#define	T   __log_data.tab
#define	T2   __log_data.tab2
#define	B   __log_data.poly1
#define	A   __log_data.poly
#define	Ln2hi   __log_data.ln2hi
#define	Ln2lo   __log_data.ln2lo
#define	N   (1 << LOG_TABLE_BITS)
#define	OFF   0x3fe6000000000000
#define	LO   asuint64(1.0 - 0x1p-4)
#define	HI   asuint64(1.0 + 0x1.09p-4)

Functions
static uint32_t	top16 (double x)
double	log (double x)

Macro Definition Documentation

A

#define A   __log_data.poly

Definition at line 30 of file log.c.

B

#define B   __log_data.poly1

Definition at line 29 of file log.c.

HI

#define HI   asuint64(1.0 + 0x1.09p-4)

Ln2hi

#define Ln2hi   __log_data.ln2hi

Definition at line 31 of file log.c.

Ln2lo

#define Ln2lo   __log_data.ln2lo

Definition at line 32 of file log.c.

LO

#define LO   asuint64(1.0 - 0x1p-4)

N

#define N   (1 << LOG_TABLE_BITS)

Definition at line 33 of file log.c.

OFF

#define OFF   0x3fe6000000000000

Definition at line 34 of file log.c.

T

#define T   __log_data.tab

Definition at line 27 of file log.c.

T2

#define T2   __log_data.tab2

Definition at line 28 of file log.c.

Function Documentation

log()

double log

(

double

x

)

Definition at line 42 of file log.c.

{
    double_t w, z, r, r2, r3, y, invc, logc, kd, hi, lo;
    uint64_t ix, iz, tmp;
    uint32_t top;
    int k, i;
 
    ix = asuint64(x);
    top = top16(x);
#define LO asuint64(1.0 - 0x1p-4)
#define HI asuint64(1.0 + 0x1.09p-4)
    if (predict_false(ix - LO < HI - LO)) {
        /* Handle close to 1.0 inputs separately.  */
        /* Fix sign of zero with downward rounding when x==1.  */
        if (WANT_ROUNDING && predict_false(ix == asuint64(1.0)))
            return 0;
        r = x - 1.0;
        r2 = r * r;
        r3 = r * r2;
        y = r3 *
            (B[1] + r * B[2] + r2 * B[3] +
             r3 * (B[4] + r * B[5] + r2 * B[6] +
               r3 * (B[7] + r * B[8] + r2 * B[9] + r3 * B[10])));
        /* Worst-case error is around 0.507 ULP.  */
        w = r * 0x1p27;
        double_t rhi = r + w - w;
        double_t rlo = r - rhi;
        w = rhi * rhi * B[0]; /* B[0] == -0.5.  */
        hi = r + w;
        lo = r - hi + w;
        lo += B[0] * rlo * (rhi + r);
        y += lo;
        y += hi;
        return eval_as_double(y);
    }
    if (predict_false(top - 0x0010 >= 0x7ff0 - 0x0010)) {
        /* x < 0x1p-1022 or inf or nan.  */
        if (ix * 2 == 0)
            return __math_divzero(1);
        if (ix == asuint64(INFINITY)) /* log(inf) == inf.  */
            return x;
        if ((top & 0x8000) || (top & 0x7ff0) == 0x7ff0)
            return __math_invalid(x);
        /* x is subnormal, normalize it.  */
        ix = asuint64(x * 0x1p52);
        ix -= 52ULL << 52;
    }
 
    /* x = 2^k z; where z is in range [OFF,2*OFF) and exact.
       The range is split into N subintervals.
       The ith subinterval contains z and c is near its center.  */
    tmp = ix - OFF;
    i = (tmp >> (52 - LOG_TABLE_BITS)) % N;
    k = (int64_t)tmp >> 52; /* arithmetic shift */
    iz = ix - (tmp & 0xfffULL << 52);
    invc = T[i].invc;
    logc = T[i].logc;
    z = asdouble(iz);
 
    /* log(x) = log1p(z/c-1) + log(c) + k*Ln2.  */
    /* r ~= z/c - 1, |r| < 1/(2*N).  */
#if __FP_FAST_FMA
    /* rounding error: 0x1p-55/N.  */
    r = __builtin_fma(z, invc, -1.0);
#else
    /* rounding error: 0x1p-55/N + 0x1p-66.  */
    r = (z - T2[i].chi - T2[i].clo) * invc;
#endif
    kd = (double_t)k;
 
    /* hi + lo = r + log(c) + k*Ln2.  */
    w = kd * Ln2hi + logc;
    hi = w + r;
    lo = w - hi + r + kd * Ln2lo;
 
    /* log(x) = lo + (log1p(r) - r) + hi.  */
    r2 = r * r; /* rounding error: 0x1p-54/N^2.  */
    /* Worst case error if |y| > 0x1p-5:
       0.5 + 4.13/N + abs-poly-error*2^57 ULP (+ 0.002 ULP without fma)
       Worst case error if |y| > 0x1p-4:
       0.5 + 2.06/N + abs-poly-error*2^56 ULP (+ 0.001 ULP without fma).  */
    y = lo + r2 * A[0] +
        r * r2 * (A[1] + r * A[2] + r2 * (A[3] + r * A[4])) + hi;
    return eval_as_double(y);
}

top16()

static uint32_t top16 ( double  x )

inlinestatic

Definition at line 37 of file log.c.

{
    return asuint64(x) >> 48;
}

Referenced by log().