toolchain/gcc/newlib/libm/math/ef_exp.c

   1 /* ef_exp.c -- float version of e_exp.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  */
  15
  16 #include "fdlibm.h"
  17
  18 #ifdef __v810__
  19 #define const
  20 #endif
  21
  22 #ifdef __STDC__
  23 static const float
  24 #else
  25 static float
  26 #endif
  27 one     = 1.0,
  28 halF[2] = {0.5,-0.5,},
  29 huge    = 1.0e+30,
  30 twom100 = 7.8886090522e-31,      /* 2**-100=0x0d800000 */
  31 ln2HI[2]   ={ 6.9313812256e-01,         /* 0x3f317180 */
  32              -6.9313812256e-01,},       /* 0xbf317180 */
  33 ln2LO[2]   ={ 9.0580006145e-06,         /* 0x3717f7d1 */
  34              -9.0580006145e-06,},       /* 0xb717f7d1 */
  35 invln2 =  1.4426950216e+00,             /* 0x3fb8aa3b */
  36 P1   =  1.6666667163e-01, /* 0x3e2aaaab */
  37 P2   = -2.7777778450e-03, /* 0xbb360b61 */
  38 P3   =  6.6137559770e-05, /* 0x388ab355 */
  39 P4   = -1.6533901999e-06, /* 0xb5ddea0e */
  40 P5   =  4.1381369442e-08; /* 0x3331bb4c */
  41
  42 #ifdef __STDC__
  43         float __ieee754_expf(float x)   /* default IEEE double exp */
  44 #else
  45         float __ieee754_expf(x) /* default IEEE double exp */
  46         float x;
  47 #endif
  48 {
  49         float y,hi,lo,c,t;
  50         __int32_t k,xsb,sx;
  51         __uint32_t hx;
  52
  53         GET_FLOAT_WORD(sx,x);
  54         xsb = (sx>>31)&1;               /* sign bit of x */
  55         hx = sx & 0x7fffffff;           /* high word of |x| */
  56
  57     /* filter out non-finite argument */
  58         if(FLT_UWORD_IS_NAN(hx))
  59             return x+x;         /* NaN */
  60         if(FLT_UWORD_IS_INFINITE(hx))
  61             return (xsb==0)? x:0.0;             /* exp(+-inf)={inf,0} */
  62         if(sx > FLT_UWORD_LOG_MAX)
  63             return huge*huge; /* overflow */
  64         if(sx < 0 && hx > FLT_UWORD_LOG_MIN)
  65             return twom100*twom100; /* underflow */
  66
  67     /* argument reduction */
  68         if(hx > 0x3eb17218) {           /* if  |x| > 0.5 ln2 */
  69             if(hx < 0x3F851592) {       /* and |x| < 1.5 ln2 */
  70                 hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
  71             } else {
  72                 k  = invln2*x+halF[xsb];
  73                 t  = k;
  74                 hi = x - t*ln2HI[0];    /* t*ln2HI is exact here */
  75                 lo = t*ln2LO[0];
  76             }
  77             x  = hi - lo;
  78         }
  79         else if(hx < 0x31800000)  {     /* when |x|<2**-28 */
  80             if(huge+x>one) return one+x;/* trigger inexact */
  81         }
  82         else k = 0;
  83
  84     /* x is now in primary range */
  85         t  = x*x;
  86         c  = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
  87         if(k==0)        return one-((x*c)/(c-(float)2.0)-x);
  88         else            y = one-((lo-(x*c)/((float)2.0-c))-hi);
  89         if(k >= -125) {
  90             __uint32_t hy;
  91             GET_FLOAT_WORD(hy,y);
  92             SET_FLOAT_WORD(y,hy+(k<<23));       /* add k to y's exponent */
  93             return y;
  94         } else {
  95             __uint32_t hy;
  96             GET_FLOAT_WORD(hy,y);
  97             SET_FLOAT_WORD(y,hy+((k+100)<<23)); /* add k to y's exponent */
  98             return y*twom100;
  99         }
 100 }