libc-top-half/musl/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 ln2_hi      = 6.9313812256e-01, /* 0x3f317180 */
  20 ln2_lo      = 9.0580006145e-06, /* 0x3717f7d1 */
  21 invln2      = 1.4426950216e+00, /* 0x3fb8aa3b */
  22 /*
  23  * Domain [-0.34568, 0.34568], range ~[-6.694e-10, 6.696e-10]:
  24  * |6 / x * (1 + 2 * (1 / (exp(x) - 1) - 1 / x)) - q(x)| < 2**-30.04
  25  * Scaled coefficients: Qn_here = 2**n * Qn_for_q (see s_expm1.c):
  26  */
  27 Q1 = -3.3333212137e-2, /* -0x888868.0p-28 */
  28 Q2 =  1.5807170421e-3; /*  0xcf3010.0p-33 */
  29
  30 float expm1f(float x)
  31 {
  32         float_t y,hi,lo,c,t,e,hxs,hfx,r1,twopk;
  33         union {float f; uint32_t i;} u = {x};
  34         uint32_t hx = u.i & 0x7fffffff;
  35         int k, sign = u.i >> 31;
  36
  37         /* filter out huge and non-finite argument */
  38         if (hx >= 0x4195b844) {  /* if |x|>=27*ln2 */
  39                 if (hx > 0x7f800000)  /* NaN */
  40                         return x;
  41                 if (sign)
  42                         return -1;
  43                 if (hx > 0x42b17217) { /* x > log(FLT_MAX) */
  44                         x *= 0x1p127f;
  45                         return x;
  46                 }
  47         }
  48
  49         /* argument reduction */
  50         if (hx > 0x3eb17218) {           /* if  |x| > 0.5 ln2 */
  51                 if (hx < 0x3F851592) {       /* and |x| < 1.5 ln2 */
  52                         if (!sign) {
  53                                 hi = x - ln2_hi;
  54                                 lo = ln2_lo;
  55                                 k =  1;
  56                         } else {
  57                                 hi = x + ln2_hi;
  58                                 lo = -ln2_lo;
  59                                 k = -1;
  60                         }
  61                 } else {
  62                         k  = invln2*x + (sign ? -0.5f : 0.5f);
  63                         t  = k;
  64                         hi = x - t*ln2_hi;      /* t*ln2_hi is exact here */
  65                         lo = t*ln2_lo;
  66                 }
  67                 x = hi-lo;
  68                 c = (hi-x)-lo;
  69         } else if (hx < 0x33000000) {  /* when |x|<2**-25, return x */
  70                 if (hx < 0x00800000)
  71                         FORCE_EVAL(x*x);
  72                 return x;
  73         } else
  74                 k = 0;
  75
  76         /* x is now in primary range */
  77         hfx = 0.5f*x;
  78         hxs = x*hfx;
  79         r1 = 1.0f+hxs*(Q1+hxs*Q2);
  80         t  = 3.0f - r1*hfx;
  81         e  = hxs*((r1-t)/(6.0f - x*t));
  82         if (k == 0)  /* c is 0 */
  83                 return x - (x*e-hxs);
  84         e  = x*(e-c) - c;
  85         e -= hxs;
  86         /* exp(x) ~ 2^k (x_reduced - e + 1) */
  87         if (k == -1)
  88                 return 0.5f*(x-e) - 0.5f;
  89         if (k == 1) {
  90                 if (x < -0.25f)
  91                         return -2.0f*(e-(x+0.5f));
  92                 return 1.0f + 2.0f*(x-e);
  93         }
  94         u.i = (0x7f+k)<<23;  /* 2^k */
  95         twopk = u.f;
  96         if (k < 0 || k > 56) {   /* suffice to return exp(x)-1 */
  97                 y = x - e + 1.0f;
  98                 if (k == 128)
  99                         y = y*2.0f*0x1p127f;
 100                 else
 101                         y = y*twopk;
 102                 return y - 1.0f;
 103         }
 104         u.i = (0x7f-k)<<23;  /* 2^-k */
 105         if (k < 23)
 106                 y = (x-e+(1-u.f))*twopk;
 107         else
 108                 y = (x-(e+u.f)+1)*twopk;
 109         return y;
 110 }