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  * $FreeBSD: head/lib/msun/src/s_expm1f.c 251024 2013-05-27 08:50:10Z das $
  15  */
  16
  17 #include <float.h>
  18
  19 #include "math.h"
  20 #include "math_private.h"
  21
  22 static const float
  23 one             = 1.0,
  24 tiny            = 1.0e-30,
  25 o_threshold     = 8.8721679688e+01,/* 0x42b17180 */
  26 ln2_hi          = 6.9313812256e-01,/* 0x3f317180 */
  27 ln2_lo          = 9.0580006145e-06,/* 0x3717f7d1 */
  28 invln2          = 1.4426950216e+00,/* 0x3fb8aa3b */
  29 /*
  30  * Domain [-0.34568, 0.34568], range ~[-6.694e-10, 6.696e-10]:
  31  * |6 / x * (1 + 2 * (1 / (exp(x) - 1) - 1 / x)) - q(x)| < 2**-30.04
  32  * Scaled coefficients: Qn_here = 2**n * Qn_for_q (see s_expm1.c):
  33  */
  34 Q1 = -3.3333212137e-2,          /* -0x888868.0p-28 */
  35 Q2 =  1.5807170421e-3;          /*  0xcf3010.0p-33 */
  36
  37 static volatile float huge = 1.0e+30;
  38
  39 float
  40 expm1f(float x)
  41 {
  42         float y,hi,lo,c,t,e,hxs,hfx,r1,twopk;
  43         int32_t k,xsb;
  44         u_int32_t hx;
  45
  46         GET_FLOAT_WORD(hx,x);
  47         xsb = hx&0x80000000;            /* sign bit of x */
  48         hx &= 0x7fffffff;               /* high word of |x| */
  49
  50     /* filter out huge and non-finite argument */
  51         if(hx >= 0x4195b844) {                  /* if |x|>=27*ln2 */
  52             if(hx >= 0x42b17218) {              /* if |x|>=88.721... */
  53                 if(hx>0x7f800000)
  54                     return x+x;          /* NaN */
  55                 if(hx==0x7f800000)
  56                     return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
  57                 if(x > o_threshold) return huge*huge; /* overflow */
  58             }
  59             if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */
  60                 if(x+tiny<(float)0.0)   /* raise inexact */
  61                 return tiny-one;        /* return -1 */
  62             }
  63         }
  64
  65     /* argument reduction */
  66         if(hx > 0x3eb17218) {           /* if  |x| > 0.5 ln2 */
  67             if(hx < 0x3F851592) {       /* and |x| < 1.5 ln2 */
  68                 if(xsb==0)
  69                     {hi = x - ln2_hi; lo =  ln2_lo;  k =  1;}
  70                 else
  71                     {hi = x + ln2_hi; lo = -ln2_lo;  k = -1;}
  72             } else {
  73                 k  = invln2*x+((xsb==0)?(float)0.5:(float)-0.5);
  74                 t  = k;
  75                 hi = x - t*ln2_hi;      /* t*ln2_hi is exact here */
  76                 lo = t*ln2_lo;
  77             }
  78             STRICT_ASSIGN(float, x, hi - lo);
  79             c  = (hi-x)-lo;
  80         }
  81         else if(hx < 0x33000000) {      /* when |x|<2**-25, return x */
  82             t = huge+x; /* return x with inexact flags when x!=0 */
  83             return x - (t-(huge+x));
  84         }
  85         else k = 0;
  86
  87     /* x is now in primary range */
  88         hfx = (float)0.5*x;
  89         hxs = x*hfx;
  90         r1 = one+hxs*(Q1+hxs*Q2);
  91         t  = (float)3.0-r1*hfx;
  92         e  = hxs*((r1-t)/((float)6.0 - x*t));
  93         if(k==0) return x - (x*e-hxs);          /* c is 0 */
  94         else {
  95             SET_FLOAT_WORD(twopk,0x3f800000+(k<<23));   /* 2^k */
  96             e  = (x*(e-c)-c);
  97             e -= hxs;
  98             if(k== -1) return (float)0.5*(x-e)-(float)0.5;
  99             if(k==1) {
 100                 if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5));
 101                 else          return  one+(float)2.0*(x-e);
 102             }
 103             if (k <= -2 || k>56) {   /* suffice to return exp(x)-1 */
 104                 y = one-(e-x);
 105                 if (k == 128) y = y*2.0F*0x1p127F;
 106                 else y = y*twopk;
 107                 return y-one;
 108             }
 109             t = one;
 110             if(k<23) {
 111                 SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */
 112                 y = t-(e-x);
 113                 y = y*twopk;
 114            } else {
 115                 SET_FLOAT_WORD(t,((0x7f-k)<<23));       /* 2^-k */
 116                 y = x-(e+t);
 117                 y += one;
 118                 y = y*twopk;
 119             }
 120         }
 121         return y;
 122 }