newlib/libm/common/sf_expm1.c

   1 /* sf_expm1.c -- float version of s_expm1.c.
   2  * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
   3  */
   4
   5 /*
   6  * ====================================================
   7  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   8  *
   9  * Developed at SunPro, a Sun Microsystems, Inc. business.
  10  * Permission to use, copy, modify, and distribute this
  11  * software is freely granted, provided that this notice
  12  * is preserved.
  13  * ====================================================
  14  */
  15
  16 #include "fdlibm.h"
  17
  18 #ifdef __v810__
  19 #define const
  20 #endif
  21
  22 #ifdef __STDC__
  23 static const float
  24 #else
  25 static float
  26 #endif
  27 one             = 1.0,
  28 huge            = 1.0e+30,
  29 tiny            = 1.0e-30,
  30 o_threshold     = 8.8721679688e+01,/* 0x42b17180 */
  31 ln2_hi          = 6.9313812256e-01,/* 0x3f317180 */
  32 ln2_lo          = 9.0580006145e-06,/* 0x3717f7d1 */
  33 invln2          = 1.4426950216e+00,/* 0x3fb8aa3b */
  34         /* scaled coefficients related to expm1 */
  35 Q1  =  -3.3333335072e-02, /* 0xbd088889 */
  36 Q2  =   1.5873016091e-03, /* 0x3ad00d01 */
  37 Q3  =  -7.9365076090e-05, /* 0xb8a670cd */
  38 Q4  =   4.0082177293e-06, /* 0x36867e54 */
  39 Q5  =  -2.0109921195e-07; /* 0xb457edbb */
  40
  41 #ifdef __STDC__
  42         float expm1f(float x)
  43 #else
  44         float expm1f(x)
  45         float x;
  46 #endif
  47 {
  48         float y,hi,lo,c,t,e,hxs,hfx,r1;
  49         __int32_t k,xsb;
  50         __uint32_t hx;
  51
  52         GET_FLOAT_WORD(hx,x);
  53         xsb = hx&0x80000000;            /* sign bit of x */
  54         if(xsb==0) y=x; else y= -x;     /* y = |x| */
  55         hx &= 0x7fffffff;               /* high word of |x| */
  56
  57     /* filter out huge and non-finite argument */
  58         if(hx >= 0x4195b844) {                  /* if |x|>=27*ln2 */
  59             if(hx >= 0x42b17218) {              /* if |x|>=88.721... */
  60                 if(hx>0x7f800000)
  61                     return x+x;          /* NaN */
  62                 if(hx==0x7f800000)
  63                     return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
  64                 if(x > o_threshold) return huge*huge; /* overflow */
  65             }
  66             if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */
  67                 if(x+tiny<(float)0.0)   /* raise inexact */
  68                 return tiny-one;        /* return -1 */
  69             }
  70         }
  71
  72     /* argument reduction */
  73         if(hx > 0x3eb17218) {           /* if  |x| > 0.5 ln2 */
  74             if(hx < 0x3F851592) {       /* and |x| < 1.5 ln2 */
  75                 if(xsb==0)
  76                     {hi = x - ln2_hi; lo =  ln2_lo;  k =  1;}
  77                 else
  78                     {hi = x + ln2_hi; lo = -ln2_lo;  k = -1;}
  79             } else {
  80                 k  = invln2*x+((xsb==0)?(float)0.5:(float)-0.5);
  81                 t  = k;
  82                 hi = x - t*ln2_hi;      /* t*ln2_hi is exact here */
  83                 lo = t*ln2_lo;
  84             }
  85             x  = hi - lo;
  86             c  = (hi-x)-lo;
  87         }
  88         else if(hx < 0x33000000) {      /* when |x|<2**-25, return x */
  89             t = huge+x; /* return x with inexact flags when x!=0 */
  90             return x - (t-(huge+x));
  91         }
  92         else k = 0;
  93
  94     /* x is now in primary range */
  95         hfx = (float)0.5*x;
  96         hxs = x*hfx;
  97         r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));
  98         t  = (float)3.0-r1*hfx;
  99         e  = hxs*((r1-t)/((float)6.0 - x*t));
 100         if(k==0) return x - (x*e-hxs);          /* c is 0 */
 101         else {
 102             e  = (x*(e-c)-c);
 103             e -= hxs;
 104             if(k== -1) return (float)0.5*(x-e)-(float)0.5;
 105             if(k==1)
 106                 if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5));
 107                 else          return  one+(float)2.0*(x-e);
 108             if (k <= -2 || k>56) {   /* suffice to return exp(x)-1 */
 109                 __int32_t i;
 110                 y = one-(e-x);
 111                 GET_FLOAT_WORD(i,y);
 112                 SET_FLOAT_WORD(y,i+(k<<23));    /* add k to y's exponent */
 113                 return y-one;
 114             }
 115             t = one;
 116             if(k<23) {
 117                 __int32_t i;
 118                 SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */
 119                 y = t-(e-x);
 120                 GET_FLOAT_WORD(i,y);
 121                 SET_FLOAT_WORD(y,i+(k<<23));    /* add k to y's exponent */
 122            } else {
 123                 __int32_t i;
 124                 SET_FLOAT_WORD(t,((0x7f-k)<<23));       /* 2^-k */
 125                 y = x-(e+t);
 126                 y += one;
 127                 GET_FLOAT_WORD(i,y);
 128                 SET_FLOAT_WORD(y,i+(k<<23));    /* add k to y's exponent */
 129             }
 130         }
 131         return y;
 132 }
 133
 134 #ifdef _DOUBLE_IS_32BITS
 135
 136 #ifdef __STDC__
 137         double expm1(double x)
 138 #else
 139         double expm1(x)
 140         double x;
 141 #endif
 142 {
 143         return (double) expm1f((float) x);
 144 }
 145
 146 #endif /* defined(_DOUBLE_IS_32BITS) */