lib/libm/src/s_expm1f.c

   1 /* s_expm1f.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  * $NetBSD: s_expm1f.c,v 1.10 2002/05/26 22:01:55 wiz Exp $
  16  * $DragonFly: src/lib/libm/src/s_expm1f.c,v 1.1 2005/07/26 21:15:20 joerg Exp $
  17  */
  18
  19 #include <math.h>
  20 #include "math_private.h"
  21
  22 static const float huge = 1.0e+30, tiny = 1.0e-30;
  23
  24 static const float
  25 one             = 1.0,
  26 o_threshold     = 8.8721679688e+01,/* 0x42b17180 */
  27 ln2_hi          = 6.9313812256e-01,/* 0x3f317180 */
  28 ln2_lo          = 9.0580006145e-06,/* 0x3717f7d1 */
  29 invln2          = 1.4426950216e+00,/* 0x3fb8aa3b */
  30         /* scaled coefficients related to expm1 */
  31 Q1  =  -3.3333335072e-02, /* 0xbd088889 */
  32 Q2  =   1.5873016091e-03, /* 0x3ad00d01 */
  33 Q3  =  -7.9365076090e-05, /* 0xb8a670cd */
  34 Q4  =   4.0082177293e-06, /* 0x36867e54 */
  35 Q5  =  -2.0109921195e-07; /* 0xb457edbb */
  36
  37 float
  38 expm1f(float x)
  39 {
  40         float y,hi,lo,c,t,e,hxs,hfx,r1;
  41         int32_t k,xsb;
  42         u_int32_t hx;
  43
  44         c = 0;
  45         GET_FLOAT_WORD(hx,x);
  46         xsb = hx&0x80000000;            /* sign bit of x */
  47         hx &= 0x7fffffff;               /* high word of |x| */
  48
  49     /* filter out huge and non-finite argument */
  50         if(hx >= 0x4195b844) {                  /* if |x|>=27*ln2 */
  51             if(hx >= 0x42b17218) {              /* if |x|>=88.721... */
  52                 if(hx>0x7f800000)
  53                     return x+x;          /* NaN */
  54                 if(hx==0x7f800000)
  55                     return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
  56                 if(x > o_threshold) return huge*huge; /* overflow */
  57             }
  58             if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */
  59                 if(x+tiny<(float)0.0)   /* raise inexact */
  60                 return tiny-one;        /* return -1 */
  61             }
  62         }
  63
  64     /* argument reduction */
  65         if(hx > 0x3eb17218) {           /* if  |x| > 0.5 ln2 */
  66             if(hx < 0x3F851592) {       /* and |x| < 1.5 ln2 */
  67                 if(xsb==0)
  68                     {hi = x - ln2_hi; lo =  ln2_lo;  k =  1;}
  69                 else
  70                     {hi = x + ln2_hi; lo = -ln2_lo;  k = -1;}
  71             } else {
  72                 k  = invln2*x+((xsb==0)?(float)0.5:(float)-0.5);
  73                 t  = k;
  74                 hi = x - t*ln2_hi;      /* t*ln2_hi is exact here */
  75                 lo = t*ln2_lo;
  76             }
  77             x  = hi - lo;
  78             c  = (hi-x)-lo;
  79         }
  80         else if(hx < 0x33000000) {      /* when |x|<2**-25, return x */
  81             t = huge+x; /* return x with inexact flags when x!=0 */
  82             return x - (t-(huge+x));
  83         }
  84         else k = 0;
  85
  86     /* x is now in primary range */
  87         hfx = (float)0.5*x;
  88         hxs = x*hfx;
  89         r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));
  90         t  = (float)3.0-r1*hfx;
  91         e  = hxs*((r1-t)/((float)6.0 - x*t));
  92         if(k==0) return x - (x*e-hxs);          /* c is 0 */
  93         else {
  94             e  = (x*(e-c)-c);
  95             e -= hxs;
  96             if(k== -1) return (float)0.5*(x-e)-(float)0.5;
  97             if(k==1)  {
  98                 if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5));
  99                 else          return  one+(float)2.0*(x-e);
 100             }
 101             if (k <= -2 || k>56) {   /* suffice to return exp(x)-1 */
 102                 int32_t i;
 103                 y = one-(e-x);
 104                 GET_FLOAT_WORD(i,y);
 105                 SET_FLOAT_WORD(y,i+(k<<23));    /* add k to y's exponent */
 106                 return y-one;
 107             }
 108             if(k<23) {
 109                 int32_t i;
 110                 SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */
 111                 y = t-(e-x);
 112                 GET_FLOAT_WORD(i,y);
 113                 SET_FLOAT_WORD(y,i+(k<<23));    /* add k to y's exponent */
 114            } else {
 115                 int32_t i;
 116                 SET_FLOAT_WORD(t,((0x7f-k)<<23));       /* 2^-k */
 117                 y = x-(e+t);
 118                 y += one;
 119                 GET_FLOAT_WORD(i,y);
 120                 SET_FLOAT_WORD(y,i+(k<<23));    /* add k to y's exponent */
 121             }
 122         }
 123         return y;
 124 }