sysdeps/ieee754/flt-32/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
  16 #if defined(LIBM_SCCS) && !defined(lint)
  17 static char rcsid[] = "$NetBSD: s_expm1f.c,v 1.5 1995/05/10 20:47:11 jtc Exp $";
  18 #endif
  19
  20 #include "math.h"
  21 #include "math_private.h"
  22
  23 static const volatile float huge = 1.0e+30;
  24 static const volatile float tiny = 1.0e-30;
  25
  26 #ifdef __STDC__
  27 static const float
  28 #else
  29 static float
  30 #endif
  31 one             = 1.0,
  32 o_threshold     = 8.8721679688e+01,/* 0x42b17180 */
  33 ln2_hi          = 6.9313812256e-01,/* 0x3f317180 */
  34 ln2_lo          = 9.0580006145e-06,/* 0x3717f7d1 */
  35 invln2          = 1.4426950216e+00,/* 0x3fb8aa3b */
  36         /* scaled coefficients related to expm1 */
  37 Q1  =  -3.3333335072e-02, /* 0xbd088889 */
  38 Q2  =   1.5873016091e-03, /* 0x3ad00d01 */
  39 Q3  =  -7.9365076090e-05, /* 0xb8a670cd */
  40 Q4  =   4.0082177293e-06, /* 0x36867e54 */
  41 Q5  =  -2.0109921195e-07; /* 0xb457edbb */
  42
  43 #ifdef __STDC__
  44         float __expm1f(float x)
  45 #else
  46         float __expm1f(x)
  47         float x;
  48 #endif
  49 {
  50         float y,hi,lo,c,t,e,hxs,hfx,r1;
  51         int32_t k,xsb;
  52         u_int32_t hx;
  53
  54         GET_FLOAT_WORD(hx,x);
  55         xsb = hx&0x80000000;            /* sign bit of x */
  56         if(xsb==0) y=x; else y= -x;     /* y = |x| */
  57         hx &= 0x7fffffff;               /* high word of |x| */
  58
  59     /* filter out huge and non-finite argument */
  60         if(hx >= 0x4195b844) {                  /* if |x|>=27*ln2 */
  61             if(hx >= 0x42b17218) {              /* if |x|>=88.721... */
  62                 if(hx>0x7f800000)
  63                     return x+x;          /* NaN */
  64                 if(hx==0x7f800000)
  65                     return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
  66                 if(x > o_threshold) return huge*huge; /* overflow */
  67             }
  68             if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */
  69                 if(x+tiny<(float)0.0)   /* raise inexact */
  70                 return tiny-one;        /* return -1 */
  71             }
  72         }
  73
  74     /* argument reduction */
  75         if(hx > 0x3eb17218) {           /* if  |x| > 0.5 ln2 */
  76             if(hx < 0x3F851592) {       /* and |x| < 1.5 ln2 */
  77                 if(xsb==0)
  78                     {hi = x - ln2_hi; lo =  ln2_lo;  k =  1;}
  79                 else
  80                     {hi = x + ln2_hi; lo = -ln2_lo;  k = -1;}
  81             } else {
  82                 k  = invln2*x+((xsb==0)?(float)0.5:(float)-0.5);
  83                 t  = k;
  84                 hi = x - t*ln2_hi;      /* t*ln2_hi is exact here */
  85                 lo = t*ln2_lo;
  86             }
  87             x  = hi - lo;
  88             c  = (hi-x)-lo;
  89         }
  90         else if(hx < 0x33000000) {      /* when |x|<2**-25, return x */
  91             t = huge+x; /* return x with inexact flags when x!=0 */
  92             return x - (t-(huge+x));
  93         }
  94         else k = 0;
  95
  96     /* x is now in primary range */
  97         hfx = (float)0.5*x;
  98         hxs = x*hfx;
  99         r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));
 100         t  = (float)3.0-r1*hfx;
 101         e  = hxs*((r1-t)/((float)6.0 - x*t));
 102         if(k==0) return x - (x*e-hxs);          /* c is 0 */
 103         else {
 104             e  = (x*(e-c)-c);
 105             e -= hxs;
 106             if(k== -1) return (float)0.5*(x-e)-(float)0.5;
 107             if(k==1) {
 108                 if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5));
 109                 else          return  one+(float)2.0*(x-e);
 110             }
 111             if (k <= -2 || k>56) {   /* suffice to return exp(x)-1 */
 112                 int32_t i;
 113                 y = one-(e-x);
 114                 GET_FLOAT_WORD(i,y);
 115                 SET_FLOAT_WORD(y,i+(k<<23));    /* add k to y's exponent */
 116                 return y-one;
 117             }
 118             t = one;
 119             if(k<23) {
 120                 int32_t i;
 121                 SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */
 122                 y = t-(e-x);
 123                 GET_FLOAT_WORD(i,y);
 124                 SET_FLOAT_WORD(y,i+(k<<23));    /* add k to y's exponent */
 125            } else {
 126                 int32_t i;
 127                 SET_FLOAT_WORD(t,((0x7f-k)<<23));       /* 2^-k */
 128                 y = x-(e+t);
 129                 y += one;
 130                 GET_FLOAT_WORD(i,y);
 131                 SET_FLOAT_WORD(y,i+(k<<23));    /* add k to y's exponent */
 132             }
 133         }
 134         return y;
 135 }
 136 weak_alias (__expm1f, expm1f)