compiler/stdc/math/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 #ifndef lint
  17 static char rcsid[] = "$FreeBSD: src/lib/msun/src/s_expm1f.c,v 1.12 2011/10/21 06:26:38 das Exp $";
  18 #endif
  19
  20 #include "math.h"
  21 #include "math_private.h"
  22
  23 static const float
  24 one             = 1.0,
  25 tiny            = 1.0e-30,
  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 /*
  31  * Domain [-0.34568, 0.34568], range ~[-6.694e-10, 6.696e-10]:
  32  * |6 / x * (1 + 2 * (1 / (exp(x) - 1) - 1 / x)) - q(x)| < 2**-30.04
  33  * Scaled coefficients: Qn_here = 2**n * Qn_for_q (see s_expm1.c):
  34  */
  35 Q1 = -3.3333212137e-2,          /* -0x888868.0p-28 */
  36 Q2 =  1.5807170421e-3;          /*  0xcf3010.0p-33 */
  37
  38 static const volatile float huge __attribute__ ((__section__(".rodata,\"a\" " SECTIONCOMMENT))) = 1.0e+30;
  39
  40 float
  41 expm1f(float x)
  42 {
  43         float y,hi,lo,c,t,e,hxs,hfx,r1,twopk;
  44         int32_t k,xsb;
  45         uint32_t hx;
  46
  47         GET_FLOAT_WORD(hx,x);
  48         xsb = hx&0x80000000;            /* sign bit of x */
  49         hx &= 0x7fffffff;               /* high word of |x| */
  50
  51     /* filter out huge and non-finite argument */
  52         if(hx >= 0x4195b844) {                  /* if |x|>=27*ln2 */
  53             if(hx >= 0x42b17218) {              /* if |x|>=88.721... */
  54                 if(hx>0x7f800000)
  55                     return x+x;          /* NaN */
  56                 if(hx==0x7f800000)
  57                     return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
  58                 if(x > o_threshold) return huge*huge; /* overflow */
  59             }
  60             if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */
  61                 if(x+tiny<(float)0.0)   /* raise inexact */
  62                 return tiny-one;        /* return -1 */
  63             }
  64         }
  65
  66     /* argument reduction */
  67         if(hx > 0x3eb17218) {           /* if  |x| > 0.5 ln2 */
  68             if(hx < 0x3F851592) {       /* and |x| < 1.5 ln2 */
  69                 if(xsb==0)
  70                     {hi = x - ln2_hi; lo =  ln2_lo;  k =  1;}
  71                 else
  72                     {hi = x + ln2_hi; lo = -ln2_lo;  k = -1;}
  73             } else {
  74                 k  = invln2*x+((xsb==0)?(float)0.5:(float)-0.5);
  75                 t  = k;
  76                 hi = x - t*ln2_hi;      /* t*ln2_hi is exact here */
  77                 lo = t*ln2_lo;
  78             }
  79             STRICT_ASSIGN(float, x, hi - lo);
  80             c  = (hi-x)-lo;
  81         }
  82         else if(hx < 0x33000000) {      /* when |x|<2**-25, return x */
  83             t = huge+x; /* return x with inexact flags when x!=0 */
  84             return x - (t-(huge+x));
  85         }
  86         else k = 0;
  87
  88     /* x is now in primary range */
  89         hfx = (float)0.5*x;
  90         hxs = x*hfx;
  91         r1 = one+hxs*(Q1+hxs*Q2);
  92         t  = (float)3.0-r1*hfx;
  93         e  = hxs*((r1-t)/((float)6.0 - x*t));
  94         if(k==0) return x - (x*e-hxs);          /* c is 0 */
  95         else {
  96             SET_FLOAT_WORD(twopk,0x3f800000+(k<<23));   /* 2^k */
  97             e  = (x*(e-c)-c);
  98             e -= hxs;
  99             if(k== -1) return (float)0.5*(x-e)-(float)0.5;
 100             if(k==1) {
 101                 if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5));
 102                 else          return  one+(float)2.0*(x-e);
 103             }
 104             if (k <= -2 || k>56) {   /* suffice to return exp(x)-1 */
 105                 y = one-(e-x);
 106                 if (k == 128) y = y*2.0F*0x1p127F;
 107                 else y = y*twopk;
 108                 return y-one;
 109             }
 110             t = one;
 111             if(k<23) {
 112                 SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */
 113                 y = t-(e-x);
 114                 y = y*twopk;
 115            } else {
 116                 SET_FLOAT_WORD(t,((0x7f-k)<<23));       /* 2^-k */
 117                 y = x-(e+t);
 118                 y += one;
 119                 y = y*twopk;
 120             }
 121         }
 122         return y;
 123 }