sysdeps/ieee754/flt-32/s_expm1f.c

   1 /* s_expm1f.c -- float version of s_expm1.c.
   2  */
   3
   4 /*
   5  * ====================================================
   6  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   7  *
   8  * Developed at SunPro, a Sun Microsystems, Inc. business.
   9  * Permission to use, copy, modify, and distribute this
  10  * software is freely granted, provided that this notice
  11  * is preserved.
  12  * ====================================================
  13  */
  14
  15 #include <errno.h>
  16 #include <float.h>
  17 #include <math.h>
  18 #include <math-barriers.h>
  19 #include <math_private.h>
  20 #include <math-underflow.h>
  21 #include <libm-alias-float.h>
  22
  23 static const float huge = 1.0e+30;
  24 static const float tiny = 1.0e-30;
  25
  26 static const float
  27 one             = 1.0,
  28 o_threshold     = 8.8721679688e+01,/* 0x42b17180 */
  29 ln2_hi          = 6.9313812256e-01,/* 0x3f317180 */
  30 ln2_lo          = 9.0580006145e-06,/* 0x3717f7d1 */
  31 invln2          = 1.4426950216e+00,/* 0x3fb8aa3b */
  32         /* scaled coefficients related to expm1 */
  33 Q1  =  -3.3333335072e-02, /* 0xbd088889 */
  34 Q2  =   1.5873016091e-03, /* 0x3ad00d01 */
  35 Q3  =  -7.9365076090e-05, /* 0xb8a670cd */
  36 Q4  =   4.0082177293e-06, /* 0x36867e54 */
  37 Q5  =  -2.0109921195e-07; /* 0xb457edbb */
  38
  39 float
  40 __expm1f(float x)
  41 {
  42         float y,hi,lo,c,t,e,hxs,hfx,r1;
  43         int32_t k,xsb;
  44         uint32_t hx;
  45
  46         GET_FLOAT_WORD(hx,x);
  47         xsb = hx&0x80000000;            /* sign bit of x */
  48         if(xsb==0) y=x; else y= -x;     /* y = |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) {
  59                   __set_errno (ERANGE);
  60                   return huge*huge; /* overflow */
  61                 }
  62             }
  63             if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */
  64                 math_force_eval(x+tiny);/* raise inexact */
  65                 return tiny-one;        /* return -1 */
  66             }
  67         }
  68
  69     /* argument reduction */
  70         if(hx > 0x3eb17218) {           /* if  |x| > 0.5 ln2 */
  71             if(hx < 0x3F851592) {       /* and |x| < 1.5 ln2 */
  72                 if(xsb==0)
  73                     {hi = x - ln2_hi; lo =  ln2_lo;  k =  1;}
  74                 else
  75                     {hi = x + ln2_hi; lo = -ln2_lo;  k = -1;}
  76             } else {
  77                 k  = invln2*x+((xsb==0)?(float)0.5:(float)-0.5);
  78                 t  = k;
  79                 hi = x - t*ln2_hi;      /* t*ln2_hi is exact here */
  80                 lo = t*ln2_lo;
  81             }
  82             x  = hi - lo;
  83             c  = (hi-x)-lo;
  84         }
  85         else if(hx < 0x33000000) {      /* when |x|<2**-25, return x */
  86             math_check_force_underflow (x);
  87             t = huge+x; /* return x with inexact flags when x!=0 */
  88             return x - (t-(huge+x));
  89         }
  90         else k = 0;
  91
  92     /* x is now in primary range */
  93         hfx = (float)0.5*x;
  94         hxs = x*hfx;
  95         r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));
  96         t  = (float)3.0-r1*hfx;
  97         e  = hxs*((r1-t)/((float)6.0 - x*t));
  98         if(k==0) return x - (x*e-hxs);          /* c is 0 */
  99         else {
 100             e  = (x*(e-c)-c);
 101             e -= hxs;
 102             if(k== -1) return (float)0.5*(x-e)-(float)0.5;
 103             if(k==1) {
 104                 if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5));
 105                 else          return  one+(float)2.0*(x-e);
 106             }
 107             if (k <= -2 || k>56) {   /* suffice to return exp(x)-1 */
 108                 int32_t i;
 109                 y = one-(e-x);
 110                 GET_FLOAT_WORD(i,y);
 111                 SET_FLOAT_WORD(y,i+(k<<23));    /* add k to y's exponent */
 112                 return y-one;
 113             }
 114             t = one;
 115             if(k<23) {
 116                 int32_t i;
 117                 SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */
 118                 y = t-(e-x);
 119                 GET_FLOAT_WORD(i,y);
 120                 SET_FLOAT_WORD(y,i+(k<<23));    /* add k to y's exponent */
 121            } else {
 122                 int32_t i;
 123                 SET_FLOAT_WORD(t,((0x7f-k)<<23));       /* 2^-k */
 124                 y = x-(e+t);
 125                 y += one;
 126                 GET_FLOAT_WORD(i,y);
 127                 SET_FLOAT_WORD(y,i+(k<<23));    /* add k to y's exponent */
 128             }
 129         }
 130         return y;
 131 }
 132 libm_alias_float (__expm1, expm1)