Fix a bug about the iSCSI DHCP dependency issue.

[mirror_edk2.git] / StdLib / LibC / Math / e_exp.c

/* @(#)e_exp.c 5.1 93/09/24 */\r
/*\r
 * ====================================================\r
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\r
 *\r
 * Developed at SunPro, a Sun Microsystems, Inc. business.\r
 * Permission to use, copy, modify, and distribute this\r
 * software is freely granted, provided that this notice\r
 * is preserved.\r
 * ====================================================\r
 */\r
#include  <LibConfig.h>\r
#include  <sys/EfiCdefs.h>\r
#if defined(LIBM_SCCS) && !defined(lint)\r
__RCSID("$NetBSD: e_exp.c,v 1.11 2002/05/26 22:01:49 wiz Exp $");\r
#endif\r
\r
#if defined(_MSC_VER)           /* Handle Microsoft VC++ compiler specifics. */\r
  // C4756: overflow in constant arithmetic\r
  #pragma warning ( disable : 4756 )\r
#endif\r
\r
/* __ieee754_exp(x)\r
 * Returns the exponential of x.\r
 *\r
 * Method\r
 *   1. Argument reduction:\r
 *      Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658.\r
 *  Given x, find r and integer k such that\r
 *\r
 *               x = k*ln2 + r,  |r| <= 0.5*ln2.\r
 *\r
 *      Here r will be represented as r = hi-lo for better\r
 *  accuracy.\r
 *\r
 *   2. Approximation of exp(r) by a special rational function on\r
 *  the interval [0,0.34658]:\r
 *  Write\r
 *      R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ...\r
 *      We use a special Reme algorithm on [0,0.34658] to generate\r
 *  a polynomial of degree 5 to approximate R. The maximum error\r
 *  of this polynomial approximation is bounded by 2**-59. In\r
 *  other words,\r
 *      R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5\r
 *    (where z=r*r, and the values of P1 to P5 are listed below)\r
 *  and\r
 *      |                  5          |     -59\r
 *      | 2.0+P1*z+...+P5*z   -  R(z) | <= 2\r
 *      |                             |\r
 *  The computation of exp(r) thus becomes\r
 *                             2*r\r
 *    exp(r) = 1 + -------\r
 *                  R - r\r
 *                                 r*R1(r)\r
 *           = 1 + r + ----------- (for better accuracy)\r
 *                      2 - R1(r)\r
 *  where\r
 *               2       4             10\r
 *    R1(r) = r - (P1*r  + P2*r  + ... + P5*r   ).\r
 *\r
 *   3. Scale back to obtain exp(x):\r
 *  From step 1, we have\r
 *     exp(x) = 2^k * exp(r)\r
 *\r
 * Special cases:\r
 *  exp(INF) is INF, exp(NaN) is NaN;\r
 *  exp(-INF) is 0, and\r
 *  for finite argument, only exp(0)=1 is exact.\r
 *\r
 * Accuracy:\r
 *  according to an error analysis, the error is always less than\r
 *  1 ulp (unit in the last place).\r
 *\r
 * Misc. info.\r
 *  For IEEE double\r
 *      if x >  7.09782712893383973096e+02 then exp(x) overflow\r
 *      if x < -7.45133219101941108420e+02 then exp(x) underflow\r
 *\r
 * Constants:\r
 * The hexadecimal values are the intended ones for the following\r
 * constants. The decimal values may be used, provided that the\r
 * compiler will convert from decimal to binary accurately enough\r
 * to produce the hexadecimal values shown.\r
 */\r
\r
#include "math.h"\r
#include "math_private.h"\r
\r
static const double\r
one = 1.0,\r
halF[2] = {0.5,-0.5,},\r
huge  = 1.0e+300,\r
twom1000= 9.33263618503218878990e-302,     /* 2**-1000=0x01700000,0*/\r
o_threshold=  7.09782712893383973096e+02,  /* 0x40862E42, 0xFEFA39EF */\r
u_threshold= -7.45133219101941108420e+02,  /* 0xc0874910, 0xD52D3051 */\r
ln2HI[2]   ={ 6.93147180369123816490e-01,  /* 0x3fe62e42, 0xfee00000 */\r
       -6.93147180369123816490e-01,},/* 0xbfe62e42, 0xfee00000 */\r
ln2LO[2]   ={ 1.90821492927058770002e-10,  /* 0x3dea39ef, 0x35793c76 */\r
       -1.90821492927058770002e-10,},/* 0xbdea39ef, 0x35793c76 */\r
invln2 =  1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */\r
P1   =  1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */\r
P2   = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */\r
P3   =  6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */\r
P4   = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */\r
P5   =  4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */\r
\r
\r
double\r
__ieee754_exp(double x) /* default IEEE double exp */\r
{\r
  double y,hi,lo,c,t;\r
  int32_t k,xsb;\r
  u_int32_t hx;\r
\r
  hi = lo = 0;\r
  k = 0;\r
  GET_HIGH_WORD(hx,x);\r
  xsb = (hx>>31)&1;   /* sign bit of x */\r
  hx &= 0x7fffffff;   /* high word of |x| */\r
\r
    /* filter out non-finite argument */\r
  if(hx >= 0x40862E42) {      /* if |x|>=709.78... */\r
            if(hx>=0x7ff00000) {\r
          u_int32_t lx;\r
    GET_LOW_WORD(lx,x);\r
    if(((hx&0xfffff)|lx)!=0)\r
         return x+x;    /* NaN */\r
    else return (xsb==0)? x:0.0;  /* exp(+-inf)={inf,0} */\r
      }\r
      if(x > o_threshold) return huge*huge; /* overflow */\r
      if(x < u_threshold) return twom1000*twom1000; /* underflow */\r
  }\r
\r
    /* argument reduction */\r
  if(hx > 0x3fd62e42) {   /* if  |x| > 0.5 ln2 */\r
      if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */\r
    hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;\r
      } else {\r
    k  = (int32_t)(invln2*x+halF[xsb]);\r
    t  = k;\r
    hi = x - t*ln2HI[0];  /* t*ln2HI is exact here */\r
    lo = t*ln2LO[0];\r
      }\r
      x  = hi - lo;\r
  }\r
  else if(hx < 0x3e300000)  { /* when |x|<2**-28 */\r
      if(huge+x>one) return one+x;/* trigger inexact */\r
  }\r
  else k = 0;\r
\r
    /* x is now in primary range */\r
  t  = x*x;\r
  c  = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));\r
  if(k==0)  return one-((x*c)/(c-2.0)-x);\r
  else    y = one-((lo-(x*c)/(2.0-c))-hi);\r
  if(k >= -1021) {\r
      u_int32_t hy;\r
      GET_HIGH_WORD(hy,y);\r
      SET_HIGH_WORD(y,hy+(k<<20));  /* add k to y's exponent */\r
      return y;\r
  } else {\r
      u_int32_t hy;\r
      GET_HIGH_WORD(hy,y);\r
      SET_HIGH_WORD(y,hy+((k+1000)<<20)); /* add k to y's exponent */\r
      return y*twom1000;\r
  }\r
}\r