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glibc  2.9
Functions | Variables
s_log1p.c File Reference
#include "math.h"
#include "math_private.h"
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Functions

double __log1p (double x)

Variables

static double ln2_hi = 6.93147180369123816490e-01
static double ln2_lo = 1.90821492927058770002e-10
static double two54 = 1.80143985094819840000e+16
static double Lp []
static double zero = 0.0

Function Documentation

double __log1p ( double  x)

Definition at line 113 of file s_log1p.c.

{
       double hfsq,f,c,s,z,R,u,z2,z4,z6,R1,R2,R3,R4;
       int32_t k,hx,hu,ax;

       GET_HIGH_WORD(hx,x);
       ax = hx&0x7fffffff;

       k = 1;
       if (hx < 0x3FDA827A) {                    /* x < 0.41422  */
           if(ax>=0x3ff00000) {           /* x <= -1.0 */
              if(x==-1.0) return -two54/(x-x);/* log1p(-1)=+inf */
              else return (x-x)/(x-x);    /* log1p(x<-1)=NaN */
           }
           if(ax<0x3e200000) {                   /* |x| < 2**-29 */
              if(two54+x>zero                    /* raise inexact */
                   &&ax<0x3c900000)              /* |x| < 2**-54 */
                  return x;
              else
                  return x - x*x*0.5;
           }
           if(hx>0||hx<=((int32_t)0xbfd2bec3)) {
              k=0;f=x;hu=1;}       /* -0.2929<x<0.41422 */
       }
       if (hx >= 0x7ff00000) return x+x;
       if(k!=0) {
           if(hx<0x43400000) {
              u  = 1.0+x;
              GET_HIGH_WORD(hu,u);
               k  = (hu>>20)-1023;
               c  = (k>0)? 1.0-(u-x):x-(u-1.0);/* correction term */
              c /= u;
           } else {
              u  = x;
              GET_HIGH_WORD(hu,u);
               k  = (hu>>20)-1023;
              c  = 0;
           }
           hu &= 0x000fffff;
           if(hu<0x6a09e) {
               SET_HIGH_WORD(u,hu|0x3ff00000);   /* normalize u */
           } else {
               k += 1;
              SET_HIGH_WORD(u,hu|0x3fe00000);    /* normalize u/2 */
               hu = (0x00100000-hu)>>2;
           }
           f = u-1.0;
       }
       hfsq=0.5*f*f;
       if(hu==0) {   /* |f| < 2**-20 */
           if(f==zero) {
             if(k==0) return zero;
                     else {c += k*ln2_lo; return k*ln2_hi+c;}
           }
           R = hfsq*(1.0-0.66666666666666666*f);
           if(k==0) return f-R; else
                   return k*ln2_hi-((R-(k*ln2_lo+c))-f);
       }
       s = f/(2.0+f);
       z = s*s;
#ifdef DO_NOT_USE_THIS
       R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7))))));
#else
       R1 = z*Lp[1]; z2=z*z;
       R2 = Lp[2]+z*Lp[3]; z4=z2*z2;
       R3 = Lp[4]+z*Lp[5]; z6=z4*z2;
       R4 = Lp[6]+z*Lp[7];
       R = R1 + z2*R2 + z4*R3 + z6*R4;
#endif
       if(k==0) return f-(hfsq-s*(hfsq+R)); else
               return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f);
}

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Variable Documentation

double ln2_hi = 6.93147180369123816490e-01 [static]

Definition at line 93 of file s_log1p.c.

double ln2_lo = 1.90821492927058770002e-10 [static]

Definition at line 94 of file s_log1p.c.

double Lp[] [static]
Initial value:
 {0.0, 6.666666666666735130e-01,  
 3.999999999940941908e-01,  
 2.857142874366239149e-01,  
 2.222219843214978396e-01,  
 1.818357216161805012e-01,  
 1.531383769920937332e-01,  
 1.479819860511658591e-01}

Definition at line 96 of file s_log1p.c.

double two54 = 1.80143985094819840000e+16 [static]

Definition at line 95 of file s_log1p.c.

double zero = 0.0 [static]

Definition at line 107 of file s_log1p.c.