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