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lightning-sunbird  0.9+nobinonly
Functions | Variables
s_expm1.c File Reference
#include "fdlibm.h"

Go to the source code of this file.

Functions

double fd_expm1 (double x)

Variables

static double one = 1.0
static double really_big = 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 Q1 = -3.33333333333331316428e-02
static double Q2 = 1.58730158725481460165e-03
static double Q3 = -7.93650757867487942473e-05
static double Q4 = 4.00821782732936239552e-06
static double Q5 = -2.01099218183624371326e-07

Function Documentation

double fd_expm1 ( double  x)

Definition at line 171 of file s_expm1.c.

{
        fd_twoints u;
       double y,hi,lo,c,t,e,hxs,hfx,r1;
       int k,xsb;
       unsigned hx;

        u.d = x;
       hx  = __HI(u);       /* high word of 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.d = x;
                  if(((hx&0xfffff)|__LO(u))!=0) 
                       return x+x;         /* NaN */
                  else return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
               }
               if(x > o_threshold) return really_big*really_big; /* 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  = (int)(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 = really_big+x;       /* return x with inexact flags when x!=0 */
           return x - (t-(really_big+x)); 
       }
       else k = 0;

    /* x is now in primary range */
       hfx = 0.5*x;
       hxs = x*hfx;
       r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));
       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 */
               y = one-(e-x);
                u.d = y;
               __HI(u) += (k<<20); /* add k to y's exponent */
                y = u.d;
               return y-one;
           }
           t = one;
           if(k<20) {
                u.d = t;
                     __HI(u) = 0x3ff00000 - (0x200000>>k);  /* t=1-2^-k */
                t = u.d;
                     y = t-(e-x);
                u.d = y;
                     __HI(u) += (k<<20);  /* add k to y's exponent */
                y = u.d;
          } else {
               u.d = t;
                     __HI(u)  = ((0x3ff-k)<<20); /* 2^-k */
                t = u.d;
                     y = x-(e+t);
                     y += one;
                u.d = y;
                     __HI(u) += (k<<20);  /* add k to y's exponent */
                y = u.d;
           }
       }
       return y;
}

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Variable Documentation

double invln2 = 1.44269504088896338700e+00 [static]

Definition at line 160 of file s_expm1.c.

double ln2_hi = 6.93147180369123816490e-01 [static]

Definition at line 158 of file s_expm1.c.

double ln2_lo = 1.90821492927058770002e-10 [static]

Definition at line 159 of file s_expm1.c.

double o_threshold = 7.09782712893383973096e+02 [static]

Definition at line 157 of file s_expm1.c.

double one = 1.0 [static]

Definition at line 154 of file s_expm1.c.

double Q1 = -3.33333333333331316428e-02 [static]

Definition at line 162 of file s_expm1.c.

double Q2 = 1.58730158725481460165e-03 [static]

Definition at line 163 of file s_expm1.c.

double Q3 = -7.93650757867487942473e-05 [static]

Definition at line 164 of file s_expm1.c.

double Q4 = 4.00821782732936239552e-06 [static]

Definition at line 165 of file s_expm1.c.

double Q5 = -2.01099218183624371326e-07 [static]

Definition at line 166 of file s_expm1.c.

double really_big = 1.0e+300 [static]

Definition at line 155 of file s_expm1.c.

double tiny = 1.0e-300 [static]

Definition at line 156 of file s_expm1.c.