kernel/arch/x86/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 #define HIPOWER 11
  21 static const unsigned long long lterms[HIPOWER] = {
  22         0x0000000000000000LL,   /* This term done separately as 12 bytes */
  23         0xf5fdeffc162c7543LL,
  24         0x1c6b08d704a0bfa6LL,
  25         0x0276556df749cc21LL,
  26         0x002bb0ffcf14f6b8LL,
  27         0x0002861225ef751cLL,
  28         0x00001ffcbfcd5422LL,
  29         0x00000162c005d5f1LL,
  30         0x0000000da96ccb1bLL,
  31         0x0000000078d1b897LL,
  32         0x000000000422b029LL
  33 };
  34
  35 static const Xsig hiterm = MK_XSIG(0xb17217f7, 0xd1cf79ab, 0xc8a39194);
  36
  37 /* Four slices: 0.0 : 0.25 : 0.50 : 0.75 : 1.0,
  38    These numbers are 2^(1/4), 2^(1/2), and 2^(3/4)
  39  */
  40 static const Xsig shiftterm0 = MK_XSIG(0, 0, 0);
  41 static const Xsig shiftterm1 = MK_XSIG(0x9837f051, 0x8db8a96f, 0x46ad2318);
  42 static const Xsig shiftterm2 = MK_XSIG(0xb504f333, 0xf9de6484, 0x597d89b3);
  43 static const Xsig shiftterm3 = MK_XSIG(0xd744fcca, 0xd69d6af4, 0x39a68bb9);
  44
  45 static const Xsig *shiftterm[] = { &shiftterm0, &shiftterm1,
  46         &shiftterm2, &shiftterm3
  47 };
  48
  49 /*--- poly_2xm1() -----------------------------------------------------------+
  50  | Requires st(0) which is TAG_Valid and < 1.                                |
  51  +---------------------------------------------------------------------------*/
  52 int poly_2xm1(u_char sign, FPU_REG *arg, FPU_REG *result)
  53 {
  54         long int exponent, shift;
  55         unsigned long long Xll;
  56         Xsig accumulator, Denom, argSignif;
  57         u_char tag;
  58
  59         exponent = exponent16(arg);
  60
  61 #ifdef PARANOID
  62         if (exponent >= 0) {    /* Don't want a |number| >= 1.0 */
  63                 /* Number negative, too large, or not Valid. */
  64                 EXCEPTION(EX_INTERNAL | 0x127);
  65                 return 1;
  66         }
  67 #endif /* PARANOID */
  68
  69         argSignif.lsw = 0;
  70         XSIG_LL(argSignif) = Xll = significand(arg);
  71
  72         if (exponent == -1) {
  73                 shift = (argSignif.msw & 0x40000000) ? 3 : 2;
  74                 /* subtract 0.5 or 0.75 */
  75                 exponent -= 2;
  76                 XSIG_LL(argSignif) <<= 2;
  77                 Xll <<= 2;
  78         } else if (exponent == -2) {
  79                 shift = 1;
  80                 /* subtract 0.25 */
  81                 exponent--;
  82                 XSIG_LL(argSignif) <<= 1;
  83                 Xll <<= 1;
  84         } else
  85                 shift = 0;
  86
  87         if (exponent < -2) {
  88                 /* Shift the argument right by the required places. */
  89                 if (FPU_shrx(&Xll, -2 - exponent) >= 0x80000000U)
  90                         Xll++;  /* round up */
  91         }
  92
  93         accumulator.lsw = accumulator.midw = accumulator.msw = 0;
  94         polynomial_Xsig(&accumulator, &Xll, lterms, HIPOWER - 1);
  95         mul_Xsig_Xsig(&accumulator, &argSignif);
  96         shr_Xsig(&accumulator, 3);
  97
  98         mul_Xsig_Xsig(&argSignif, &hiterm);     /* The leading term */
  99         add_two_Xsig(&accumulator, &argSignif, &exponent);
 100
 101         if (shift) {
 102                 /* The argument is large, use the identity:
 103                    f(x+a) = f(a) * (f(x) + 1) - 1;
 104                  */
 105                 shr_Xsig(&accumulator, -exponent);
 106                 accumulator.msw |= 0x80000000;  /* add 1.0 */
 107                 mul_Xsig_Xsig(&accumulator, shiftterm[shift]);
 108                 accumulator.msw &= 0x3fffffff;  /* subtract 1.0 */
 109                 exponent = 1;
 110         }
 111
 112         if (sign != SIGN_POS) {
 113                 /* The argument is negative, use the identity:
 114                    f(-x) = -f(x) / (1 + f(x))
 115                  */
 116                 Denom.lsw = accumulator.lsw;
 117                 XSIG_LL(Denom) = XSIG_LL(accumulator);
 118                 if (exponent < 0)
 119                         shr_Xsig(&Denom, -exponent);
 120                 else if (exponent > 0) {
 121                         /* exponent must be 1 here */
 122                         XSIG_LL(Denom) <<= 1;
 123                         if (Denom.lsw & 0x80000000)
 124                                 XSIG_LL(Denom) |= 1;
 125                         (Denom.lsw) <<= 1;
 126                 }
 127                 Denom.msw |= 0x80000000;        /* add 1.0 */
 128                 div_Xsig(&accumulator, &Denom, &accumulator);
 129         }
 130
 131         /* Convert to 64 bit signed-compatible */
 132         exponent += round_Xsig(&accumulator);
 133
 134         result = &st(0);
 135         significand(result) = XSIG_LL(accumulator);
 136         setexponent16(result, exponent);
 137
 138         tag = FPU_round(result, 1, 0, FULL_PRECISION, sign);
 139
 140         setsign(result, sign);
 141         FPU_settag0(tag);
 142
 143         return 0;
 144
 145 }