nsz Git - libm/blob - src/math/expm1f.c

   1 /* origin: FreeBSD /usr/src/lib/msun/src/s_expm1f.c */
   2 /*
   3  * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
   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 #include "libm.h"
  17
  18 static const float
  19 one         = 1.0,
  20 huge        = 1.0e+30,
  21 tiny        = 1.0e-30,
  22 o_threshold = 8.8721679688e+01, /* 0x42b17180 */
  23 ln2_hi      = 6.9313812256e-01, /* 0x3f317180 */
  24 ln2_lo      = 9.0580006145e-06, /* 0x3717f7d1 */
  25 invln2      = 1.4426950216e+00, /* 0x3fb8aa3b */
  26 /*
  27  * Domain [-0.34568, 0.34568], range ~[-6.694e-10, 6.696e-10]:
  28  * |6 / x * (1 + 2 * (1 / (exp(x) - 1) - 1 / x)) - q(x)| < 2**-30.04
  29  * Scaled coefficients: Qn_here = 2**n * Qn_for_q (see s_expm1.c):
  30  */
  31 Q1 = -3.3333212137e-2, /* -0x888868.0p-28 */
  32 Q2 =  1.5807170421e-3; /*  0xcf3010.0p-33 */
  33
  34 float expm1f(float x)
  35 {
  36         float y,hi,lo,c,t,e,hxs,hfx,r1,twopk;
  37         int32_t k,xsb;
  38         uint32_t hx;
  39
  40         GET_FLOAT_WORD(hx, x);
  41         xsb = hx&0x80000000;  /* sign bit of x */
  42         hx &= 0x7fffffff;     /* high word of |x| */
  43
  44         /* filter out huge and non-finite argument */
  45         if (hx >= 0x4195b844) {  /* if |x|>=27*ln2 */
  46                 if (hx >= 0x42b17218) {  /* if |x|>=88.721... */
  47                         if (hx > 0x7f800000)  /* NaN */
  48                                 return x+x;
  49                         if (hx == 0x7f800000) /* exp(+-inf)={inf,-1} */
  50                                 return xsb==0 ? x : -1.0;
  51                         if (x > o_threshold)
  52                                 return huge*huge; /* overflow */
  53                 }
  54                 if (xsb != 0) {  /* x < -27*ln2 */
  55                         /* raise inexact */
  56                         if (x+tiny < (float)0.0)
  57                                 return tiny-one;  /* return -1 */
  58                 }
  59         }
  60
  61         /* argument reduction */
  62         if (hx > 0x3eb17218) {           /* if  |x| > 0.5 ln2 */
  63                 if (hx < 0x3F851592) {       /* and |x| < 1.5 ln2 */
  64                         if (xsb == 0) {
  65                                 hi = x - ln2_hi;
  66                                 lo = ln2_lo;
  67                                 k =  1;
  68                         } else {
  69                                 hi = x + ln2_hi;
  70                                 lo = -ln2_lo;
  71                                 k = -1;
  72                         }
  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         } 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         } else
  85                 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)  /* c is 0 */
  94                 return x - (x*e-hxs);
  95         SET_FLOAT_WORD(twopk, 0x3f800000+(k<<23));   /* 2^k */
  96         e  = x*(e-c) - c;
  97         e -= hxs;
  98         if (k == -1)
  99                 return (float)0.5*(x-e) - (float)0.5;
 100         if (k == 1) {
 101                 if (x < (float)-0.25)
 102                         return -(float)2.0*(e-(x+(float)0.5));
 103                 return one+(float)2.0*(x-e);
 104         }
 105         if (k <= -2 || k > 56) {   /* suffice to return exp(x)-1 */
 106                 y = one - (e - x);
 107                 if (k == 128)
 108                         y = y*2.0F*0x1p127F;
 109                 else
 110                         y = y*twopk;
 111                 return y - one;
 112         }
 113         t = one;
 114         if (k < 23) {
 115                 SET_FLOAT_WORD(t, 0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */
 116                 y = t - (e - x);
 117                 y = y*twopk;
 118         } else {
 119                 SET_FLOAT_WORD(t, ((0x7f-k)<<23));  /* 2^-k */
 120                 y = x - (e + t);
 121                 y += one;
 122                 y = y*twopk;
 123         }
 124         return y;
 125 }