Back to index

glibc  2.9
Defines | Functions | Variables
s_expm1.c File Reference
#include "math.h"
#include "math_private.h"
This graph shows which files directly or indirectly include this file:

Go to the source code of this file.

Defines

#define one   Q[0]

Functions

double __expm1 (double x)

Variables

static double huge = 1.0e+300
static double tiny = 1.0e-300
static double o_threshold = 7.09782712893383973096e+02
static double ln2_hi = 6.93147180369123816490e-01
static double ln2_lo = 1.90821492927058770002e-10
static double invln2 = 1.44269504088896338700e+00
static double Q []

Define Documentation

#define one   Q[0]

Definition at line 117 of file s_expm1.c.


Function Documentation

double __expm1 ( double  x)

Definition at line 139 of file s_expm1.c.

{
       double y,hi,lo,c,t,e,hxs,hfx,r1,h2,h4,R1,R2,R3;
       int32_t k,xsb;
       u_int32_t hx;

       GET_HIGH_WORD(hx,x);
       xsb = hx&0x80000000;        /* sign bit of x */
       if(xsb==0) y=x; else y= -x; /* y = |x| */
       hx &= 0x7fffffff;           /* high word of |x| */

    /* filter out huge and non-finite argument */
       if(hx >= 0x4043687A) {                    /* if |x|>=56*ln2 */
           if(hx >= 0x40862E42) {         /* if |x|>=709.78... */
                if(hx>=0x7ff00000) {
                  u_int32_t low;
                  GET_LOW_WORD(low,x);
                  if(((hx&0xfffff)|low)!=0)
                       return x+x;         /* NaN */
                  else return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
               }
               if(x > o_threshold) return huge*huge; /* overflow */
           }
           if(xsb!=0) { /* x < -56*ln2, return -1.0 with inexact */
              if(x+tiny<0.0)              /* raise inexact */
              return tiny-one;     /* return -1 */
           }
       }

    /* argument reduction */
       if(hx > 0x3fd62e42) {              /* if  |x| > 0.5 ln2 */
           if(hx < 0x3FF0A2B2) {   /* and |x| < 1.5 ln2 */
              if(xsb==0)
                  {hi = x - ln2_hi; lo =  ln2_lo;  k =  1;}
              else
                  {hi = x + ln2_hi; lo = -ln2_lo;  k = -1;}
           } else {
              k  = invln2*x+((xsb==0)?0.5:-0.5);
              t  = k;
              hi = x - t*ln2_hi;   /* t*ln2_hi is exact here */
              lo = t*ln2_lo;
           }
           x  = hi - lo;
           c  = (hi-x)-lo;
       }
       else if(hx < 0x3c900000) {         /* when |x|<2**-54, return x */
           t = huge+x;      /* return x with inexact flags when x!=0 */
           return x - (t-(huge+x));
       }
       else k = 0;

    /* x is now in primary range */
       hfx = 0.5*x;
       hxs = x*hfx;
#ifdef DO_NOT_USE_THIS
       r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));
#else
       R1 = one+hxs*Q[1]; h2 = hxs*hxs;
       R2 = Q[2]+hxs*Q[3]; h4 = h2*h2;
       R3 = Q[4]+hxs*Q[5];
       r1 = R1 + h2*R2 + h4*R3;
#endif
       t  = 3.0-r1*hfx;
       e  = hxs*((r1-t)/(6.0 - x*t));
       if(k==0) return x - (x*e-hxs);            /* c is 0 */
       else {
           e  = (x*(e-c)-c);
           e -= hxs;
           if(k== -1) return 0.5*(x-e)-0.5;
           if(k==1) {
                     if(x < -0.25) return -2.0*(e-(x+0.5));
                     else         return  one+2.0*(x-e);
           }
           if (k <= -2 || k>56) {   /* suffice to return exp(x)-1 */
               u_int32_t high;
               y = one-(e-x);
              GET_HIGH_WORD(high,y);
              SET_HIGH_WORD(y,high+(k<<20));     /* add k to y's exponent */
               return y-one;
           }
           t = one;
           if(k<20) {
               u_int32_t high;
               SET_HIGH_WORD(t,0x3ff00000 - (0x200000>>k));  /* t=1-2^-k */
                     y = t-(e-x);
              GET_HIGH_WORD(high,y);
              SET_HIGH_WORD(y,high+(k<<20));     /* add k to y's exponent */
          } else {
               u_int32_t high;
              SET_HIGH_WORD(t,((0x3ff-k)<<20));  /* 2^-k */
                     y = x-(e+t);
                     y += one;
              GET_HIGH_WORD(high,y);
              SET_HIGH_WORD(y,high+(k<<20));     /* add k to y's exponent */
           }
       }
       return y;
}

Here is the caller graph for this function:


Variable Documentation

double huge = 1.0e+300 [static]

Definition at line 123 of file s_expm1.c.

double invln2 = 1.44269504088896338700e+00 [static]

Definition at line 128 of file s_expm1.c.

double ln2_hi = 6.93147180369123816490e-01 [static]

Definition at line 126 of file s_expm1.c.

double ln2_lo = 1.90821492927058770002e-10 [static]

Definition at line 127 of file s_expm1.c.

double o_threshold = 7.09782712893383973096e+02 [static]

Definition at line 125 of file s_expm1.c.

double Q[] [static]
Initial value:
  {1.0, -3.33333333333331316428e-02, 
   1.58730158725481460165e-03, 
  -7.93650757867487942473e-05, 
   4.00821782732936239552e-06, 
  -2.01099218183624371326e-07}

Definition at line 130 of file s_expm1.c.

double tiny = 1.0e-300 [static]

Definition at line 124 of file s_expm1.c.