arch/i386/math-emu/poly_2xm1.c

   1 /*---------------------------------------------------------------------------+
   2  |  poly_2xm1.c                                                              |
   3  |                                                                           |
   4  | Function to compute 2^x-1 by a polynomial approximation.                  |
   5  |                                                                           |
   6  | Copyright (C) 1992,1993,1994,1997                                         |
   7  |                  W. Metzenthen, 22 Parker St, Ormond, Vic 3163, Australia |
   8  |                  E-mail   billm@suburbia.net                              |
   9  |                                                                           |
  10  |                                                                           |
  11  +---------------------------------------------------------------------------*/
  12
  13 #include "exception.h"
  14 #include "reg_constant.h"
  15 #include "fpu_emu.h"
  16 #include "fpu_system.h"
  17 #include "control_w.h"
  18 #include "poly.h"
  19
  20
  21 #define HIPOWER 11
  22 static const unsigned long long lterms[HIPOWER] =
  23 {
  24   0x0000000000000000LL,  /* This term done separately as 12 bytes */
  25   0xf5fdeffc162c7543LL,
  26   0x1c6b08d704a0bfa6LL,
  27   0x0276556df749cc21LL,
  28   0x002bb0ffcf14f6b8LL,
  29   0x0002861225ef751cLL,
  30   0x00001ffcbfcd5422LL,
  31   0x00000162c005d5f1LL,
  32   0x0000000da96ccb1bLL,
  33   0x0000000078d1b897LL,
  34   0x000000000422b029LL
  35 };
  36
  37 static const Xsig hiterm = MK_XSIG(0xb17217f7, 0xd1cf79ab, 0xc8a39194);
  38
  39 /* Four slices: 0.0 : 0.25 : 0.50 : 0.75 : 1.0,
  40    These numbers are 2^(1/4), 2^(1/2), and 2^(3/4)
  41  */
  42 static const Xsig shiftterm0 = MK_XSIG(0, 0, 0);
  43 static const Xsig shiftterm1 = MK_XSIG(0x9837f051, 0x8db8a96f, 0x46ad2318);
  44 static const Xsig shiftterm2 = MK_XSIG(0xb504f333, 0xf9de6484, 0x597d89b3);
  45 static const Xsig shiftterm3 = MK_XSIG(0xd744fcca, 0xd69d6af4, 0x39a68bb9);
  46
  47 static const Xsig *shiftterm[] = { &shiftterm0, &shiftterm1,
  48                                      &shiftterm2, &shiftterm3 };
  49
  50
  51 /*--- poly_2xm1() -----------------------------------------------------------+
  52  | Requires st(0) which is TAG_Valid and < 1.                                |
  53  +---------------------------------------------------------------------------*/
  54 int     poly_2xm1(u_char sign, FPU_REG *arg, FPU_REG *result)
  55 {
  56   long int              exponent, shift;
  57   unsigned long long    Xll;
  58   Xsig                  accumulator, Denom, argSignif;
  59   u_char                tag;
  60
  61   exponent = exponent16(arg);
  62
  63 #ifdef PARANOID
  64   if ( exponent >= 0 )          /* Don't want a |number| >= 1.0 */
  65     {
  66       /* Number negative, too large, or not Valid. */
  67       EXCEPTION(EX_INTERNAL|0x127);
  68       return 1;
  69     }
  70 #endif /* PARANOID */
  71
  72   argSignif.lsw = 0;
  73   XSIG_LL(argSignif) = Xll = significand(arg);
  74
  75   if ( exponent == -1 )
  76     {
  77       shift = (argSignif.msw & 0x40000000) ? 3 : 2;
  78       /* subtract 0.5 or 0.75 */
  79       exponent -= 2;
  80       XSIG_LL(argSignif) <<= 2;
  81       Xll <<= 2;
  82     }
  83   else if ( exponent == -2 )
  84     {
  85       shift = 1;
  86       /* subtract 0.25 */
  87       exponent--;
  88       XSIG_LL(argSignif) <<= 1;
  89       Xll <<= 1;
  90     }
  91   else
  92     shift = 0;
  93
  94   if ( exponent < -2 )
  95     {
  96       /* Shift the argument right by the required places. */
  97       if ( FPU_shrx(&Xll, -2-exponent) >= 0x80000000U )
  98         Xll++;  /* round up */
  99     }
 100
 101   accumulator.lsw = accumulator.midw = accumulator.msw = 0;
 102   polynomial_Xsig(&accumulator, &Xll, lterms, HIPOWER-1);
 103   mul_Xsig_Xsig(&accumulator, &argSignif);
 104   shr_Xsig(&accumulator, 3);
 105
 106   mul_Xsig_Xsig(&argSignif, &hiterm);   /* The leading term */
 107   add_two_Xsig(&accumulator, &argSignif, &exponent);
 108
 109   if ( shift )
 110     {
 111       /* The argument is large, use the identity:
 112          f(x+a) = f(a) * (f(x) + 1) - 1;
 113          */
 114       shr_Xsig(&accumulator, - exponent);
 115       accumulator.msw |= 0x80000000;      /* add 1.0 */
 116       mul_Xsig_Xsig(&accumulator, shiftterm[shift]);
 117       accumulator.msw &= 0x3fffffff;      /* subtract 1.0 */
 118       exponent = 1;
 119     }
 120
 121   if ( sign != SIGN_POS )
 122     {
 123       /* The argument is negative, use the identity:
 124              f(-x) = -f(x) / (1 + f(x))
 125          */
 126       Denom.lsw = accumulator.lsw;
 127       XSIG_LL(Denom) = XSIG_LL(accumulator);
 128       if ( exponent < 0 )
 129         shr_Xsig(&Denom, - exponent);
 130       else if ( exponent > 0 )
 131         {
 132           /* exponent must be 1 here */
 133           XSIG_LL(Denom) <<= 1;
 134           if ( Denom.lsw & 0x80000000 )
 135             XSIG_LL(Denom) |= 1;
 136           (Denom.lsw) <<= 1;
 137         }
 138       Denom.msw |= 0x80000000;      /* add 1.0 */
 139       div_Xsig(&accumulator, &Denom, &accumulator);
 140     }
 141
 142   /* Convert to 64 bit signed-compatible */
 143   exponent += round_Xsig(&accumulator);
 144
 145   result = &st(0);
 146   significand(result) = XSIG_LL(accumulator);
 147   setexponent16(result, exponent);
 148
 149   tag = FPU_round(result, 1, 0, FULL_PRECISION, sign);
 150
 151   setsign(result, sign);
 152   FPU_settag0(tag);
 153
 154   return 0;
 155
 156 }