sysdeps/i386/fpu/e_expl.c

   1 /*
   2  * Written by J.T. Conklin <jtc@netbsd.org>.
   3  * Public domain.
   4  *
   5  * Adapted for `long double' by Ulrich Drepper <drepper@cygnus.com>.
   6  */
   7
   8 /*
   9  * The 8087 method for the exponential function is to calculate
  10  *   exp(x) = 2^(x log2(e))
  11  * after separating integer and fractional parts
  12  *   x log2(e) = i + f, |f| <= .5
  13  * 2^i is immediate but f needs to be precise for long double accuracy.
  14  * Suppress range reduction error in computing f by the following.
  15  * Separate x into integer and fractional parts
  16  *   x = xi + xf, |xf| <= .5
  17  * Separate log2(e) into the sum of an exact number c0 and small part c1.
  18  *   c0 + c1 = log2(e) to extra precision
  19  * Then
  20  *   f = (c0 xi - i) + c0 xf + c1 x
  21  * where c0 xi is exact and so also is (c0 xi - i).
  22  * -- moshier@na-net.ornl.gov
  23  */
  24
  25 #include <math_private.h>
  26
  27 static const long double c0 = 1.44268798828125L;
  28 static const long double c1 = 7.05260771340735992468e-6L;
  29
  30 long double
  31 __ieee754_expl (long double x)
  32 {
  33   long double res;
  34
  35 /* I added the following ugly construct because expl(+-Inf) resulted
  36    in NaN.  The ugliness results from the bright minds at Intel.
  37    For the i686 the code can be written better.
  38    -- drepper@cygnus.com.  */
  39   asm ("fxam\n\t"               /* Is NaN or +-Inf?  */
  40        "fstsw   %%ax\n\t"
  41        "movb    $0x45, %%dh\n\t"
  42        "andb    %%ah, %%dh\n\t"
  43        "cmpb    $0x05, %%dh\n\t"
  44        "je      1f\n\t"         /* Is +-Inf, jump.    */
  45        "fldl2e\n\t"             /* 1  log2(e)         */
  46        "fmul %%st(1),%%st\n\t"  /* 1  x log2(e)       */
  47        "frndint\n\t"            /* 1  i               */
  48        "fld %%st(1)\n\t"        /* 2  x               */
  49        "frndint\n\t"            /* 2  xi              */
  50        "fld %%st(1)\n\t"        /* 3  i               */
  51        "fldt %2\n\t"            /* 4  c0              */
  52        "fld %%st(2)\n\t"        /* 5  xi              */
  53        "fmul %%st(1),%%st\n\t"  /* 5  c0 xi           */
  54        "fsubp %%st,%%st(2)\n\t" /* 4  f = c0 xi  - i  */
  55        "fld %%st(4)\n\t"        /* 5  x               */
  56        "fsub %%st(3),%%st\n\t"  /* 5  xf = x - xi     */
  57        "fmulp %%st,%%st(1)\n\t" /* 4  c0 xf           */
  58        "faddp %%st,%%st(1)\n\t" /* 3  f = f + c0 xf   */
  59        "fldt %3\n\t"            /* 4                  */
  60        "fmul %%st(4),%%st\n\t"  /* 4  c1 * x          */
  61        "faddp %%st,%%st(1)\n\t" /* 3  f = f + c1 * x  */
  62        "f2xm1\n\t"              /* 3 2^(fract(x * log2(e))) - 1 */
  63        "fld1\n\t"               /* 4 1.0              */
  64        "faddp\n\t"              /* 3 2^(fract(x * log2(e))) */
  65        "fstp    %%st(1)\n\t"    /* 2  */
  66        "fscale\n\t"             /* 2 scale factor is st(1); e^x */
  67        "fstp    %%st(1)\n\t"    /* 1  */
  68        "fstp    %%st(1)\n\t"    /* 0  */
  69        "jmp 2f\n\t"
  70        "1:\ttestl       $0x200, %%eax\n\t"      /* Test sign.  */
  71        "jz      2f\n\t"         /* If positive, jump.  */
  72        "fstp    %%st\n\t"
  73        "fldz\n\t"               /* Set result to 0.  */
  74        "2:\t\n"
  75        : "=t" (res) : "0" (x), "m" (c0), "m" (c1) : "ax", "dx");
  76   return res;
  77 }