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 huge        = 1.0e+30,
  20 tiny        = 1.0e-30,
  21 o_threshold = 8.8721679688e+01, /* 0x42b17180 */
  22 ln2_hi      = 6.9313812256e-01, /* 0x3f317180 */
  23 ln2_lo      = 9.0580006145e-06, /* 0x3717f7d1 */
  24 invln2      = 1.4426950216e+00, /* 0x3fb8aa3b */
  25 /*
  26  * Domain [-0.34568, 0.34568], range ~[-6.694e-10, 6.696e-10]:
  27  * |6 / x * (1 + 2 * (1 / (exp(x) - 1) - 1 / x)) - q(x)| < 2**-30.04
  28  * Scaled coefficients: Qn_here = 2**n * Qn_for_q (see s_expm1.c):
  29  */
  30 Q1 = -3.3333212137e-2, /* -0x888868.0p-28 */
  31 Q2 =  1.5807170421e-3; /*  0xcf3010.0p-33 */
  32
  33 float expm1f(float x)
  34 {
  35         float y,hi,lo,c,t,e,hxs,hfx,r1,twopk;
  36         int32_t k,xsb;
  37         uint32_t hx;
  38
  39         GET_FLOAT_WORD(hx, x);
  40         xsb = hx&0x80000000;  /* sign bit of x */
  41         hx &= 0x7fffffff;     /* high word of |x| */
  42
  43         /* filter out huge and non-finite argument */
  44         if (hx >= 0x4195b844) {  /* if |x|>=27*ln2 */
  45                 if (hx >= 0x42b17218) {  /* if |x|>=88.721... */
  46                         if (hx > 0x7f800000)  /* NaN */
  47                                 return x+x;
  48                         if (hx == 0x7f800000) /* exp(+-inf)={inf,-1} */
  49                                 return xsb==0 ? x : -1.0;
  50                         if (x > o_threshold)
  51                                 return huge*huge; /* overflow */
  52                 }
  53                 if (xsb != 0) {  /* x < -27*ln2 */
  54                         /* raise inexact */
  55                         if (x+tiny < 0.0f)
  56                                 return tiny-1.0f;  /* return -1 */
  57                 }
  58         }
  59
  60         /* argument reduction */
  61         if (hx > 0x3eb17218) {           /* if  |x| > 0.5 ln2 */
  62                 if (hx < 0x3F851592) {       /* and |x| < 1.5 ln2 */
  63                         if (xsb == 0) {
  64                                 hi = x - ln2_hi;
  65                                 lo = ln2_lo;
  66                                 k =  1;
  67                         } else {
  68                                 hi = x + ln2_hi;
  69                                 lo = -ln2_lo;
  70                                 k = -1;
  71                         }
  72                 } else {
  73                         k  = invln2*x + (xsb==0 ? 0.5f : -0.5f);
  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         } else if (hx < 0x33000000) {  /* when |x|<2**-25, return x */
  81                 t = huge+x; /* return x with inexact flags when x!=0 */
  82                 return x - (t-(huge+x));
  83         } else
  84                 k = 0;
  85
  86         /* x is now in primary range */
  87         hfx = 0.5f*x;
  88         hxs = x*hfx;
  89         r1 = 1.0f+hxs*(Q1+hxs*Q2);
  90         t  = 3.0f - r1*hfx;
  91         e  = hxs*((r1-t)/(6.0f - x*t));
  92         if (k == 0)  /* c is 0 */
  93                 return x - (x*e-hxs);
  94         SET_FLOAT_WORD(twopk, 0x3f800000+(k<<23));   /* 2^k */
  95         e  = x*(e-c) - c;
  96         e -= hxs;
  97         if (k == -1)
  98                 return 0.5f*(x-e) - 0.5f;
  99         if (k == 1) {
 100                 if (x < -0.25f)
 101                         return -2.0f*(e-(x+0.5f));
 102                 return 1.0f + 2.0f*(x-e);
 103         }
 104         if (k <= -2 || k > 56) {   /* suffice to return exp(x)-1 */
 105                 y = 1.0f - (e - x);
 106                 if (k == 128)
 107                         y = y*2.0f*0x1p127f;
 108                 else
 109                         y = y*twopk;
 110                 return y - 1.0f;
 111         }
 112         t = 1.0f;
 113         if (k < 23) {
 114                 SET_FLOAT_WORD(t, 0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */
 115                 y = t - (e - x);
 116                 y = y*twopk;
 117         } else {
 118                 SET_FLOAT_WORD(t, (0x7f-k)<<23);  /* 2^-k */
 119                 y = x - (e + t);
 120                 y += 1.0f;
 121                 y = y*twopk;
 122         }
 123         return y;
 124 }