arch/x86/math-emu/poly_2xm1.c

   1 // SPDX-License-Identifier: GPL-2.0
   2 /*---------------------------------------------------------------------------+
   3  |  poly_2xm1.c                                                              |
   4  |                                                                           |
   5  | Function to compute 2^x-1 by a polynomial approximation.                  |
   6  |                                                                           |
   7  | Copyright (C) 1992,1993,1994,1997                                         |
   8  |                  W. Metzenthen, 22 Parker St, Ormond, Vic 3163, Australia |
   9  |                  E-mail   billm@suburbia.net                              |
  10  |                                                                           |
  11  |                                                                           |
  12  +---------------------------------------------------------------------------*/
  13
  14 #include "exception.h"
  15 #include "reg_constant.h"
  16 #include "fpu_emu.h"
  17 #include "fpu_system.h"
  18 #include "control_w.h"
  19 #include "poly.h"
  20
  21 #define HIPOWER 11
  22 static const unsigned long long lterms[HIPOWER] = {
  23         0x0000000000000000LL,   /* This term done separately as 12 bytes */
  24         0xf5fdeffc162c7543LL,
  25         0x1c6b08d704a0bfa6LL,
  26         0x0276556df749cc21LL,
  27         0x002bb0ffcf14f6b8LL,
  28         0x0002861225ef751cLL,
  29         0x00001ffcbfcd5422LL,
  30         0x00000162c005d5f1LL,
  31         0x0000000da96ccb1bLL,
  32         0x0000000078d1b897LL,
  33         0x000000000422b029LL
  34 };
  35
  36 static const Xsig hiterm = MK_XSIG(0xb17217f7, 0xd1cf79ab, 0xc8a39194);
  37
  38 /* Four slices: 0.0 : 0.25 : 0.50 : 0.75 : 1.0,
  39    These numbers are 2^(1/4), 2^(1/2), and 2^(3/4)
  40  */
  41 static const Xsig shiftterm0 = MK_XSIG(0, 0, 0);
  42 static const Xsig shiftterm1 = MK_XSIG(0x9837f051, 0x8db8a96f, 0x46ad2318);
  43 static const Xsig shiftterm2 = MK_XSIG(0xb504f333, 0xf9de6484, 0x597d89b3);
  44 static const Xsig shiftterm3 = MK_XSIG(0xd744fcca, 0xd69d6af4, 0x39a68bb9);
  45
  46 static const Xsig *shiftterm[] = { &shiftterm0, &shiftterm1,
  47         &shiftterm2, &shiftterm3
  48 };
  49
  50 /*--- poly_2xm1() -----------------------------------------------------------+
  51  | Requires st(0) which is TAG_Valid and < 1.                                |
  52  +---------------------------------------------------------------------------*/
  53 int poly_2xm1(u_char sign, FPU_REG *arg, FPU_REG *result)
  54 {
  55         long int exponent, shift;
  56         unsigned long long Xll;
  57         Xsig accumulator, Denom, argSignif;
  58         u_char tag;
  59
  60         exponent = exponent16(arg);
  61
  62 #ifdef PARANOID
  63         if (exponent >= 0) {    /* Don't want a |number| >= 1.0 */
  64                 /* Number negative, too large, or not Valid. */
  65                 EXCEPTION(EX_INTERNAL | 0x127);
  66                 return 1;
  67         }
  68 #endif /* PARANOID */
  69
  70         argSignif.lsw = 0;
  71         XSIG_LL(argSignif) = Xll = significand(arg);
  72
  73         if (exponent == -1) {
  74                 shift = (argSignif.msw & 0x40000000) ? 3 : 2;
  75                 /* subtract 0.5 or 0.75 */
  76                 exponent -= 2;
  77                 XSIG_LL(argSignif) <<= 2;
  78                 Xll <<= 2;
  79         } else if (exponent == -2) {
  80                 shift = 1;
  81                 /* subtract 0.25 */
  82                 exponent--;
  83                 XSIG_LL(argSignif) <<= 1;
  84                 Xll <<= 1;
  85         } else
  86                 shift = 0;
  87
  88         if (exponent < -2) {
  89                 /* Shift the argument right by the required places. */
  90                 if (FPU_shrx(&Xll, -2 - exponent) >= 0x80000000U)
  91                         Xll++;  /* round up */
  92         }
  93
  94         accumulator.lsw = accumulator.midw = accumulator.msw = 0;
  95         polynomial_Xsig(&accumulator, &Xll, lterms, HIPOWER - 1);
  96         mul_Xsig_Xsig(&accumulator, &argSignif);
  97         shr_Xsig(&accumulator, 3);
  98
  99         mul_Xsig_Xsig(&argSignif, &hiterm);     /* The leading term */
 100         add_two_Xsig(&accumulator, &argSignif, &exponent);
 101
 102         if (shift) {
 103                 /* The argument is large, use the identity:
 104                    f(x+a) = f(a) * (f(x) + 1) - 1;
 105                  */
 106                 shr_Xsig(&accumulator, -exponent);
 107                 accumulator.msw |= 0x80000000;  /* add 1.0 */
 108                 mul_Xsig_Xsig(&accumulator, shiftterm[shift]);
 109                 accumulator.msw &= 0x3fffffff;  /* subtract 1.0 */
 110                 exponent = 1;
 111         }
 112
 113         if (sign != SIGN_POS) {
 114                 /* The argument is negative, use the identity:
 115                    f(-x) = -f(x) / (1 + f(x))
 116                  */
 117                 Denom.lsw = accumulator.lsw;
 118                 XSIG_LL(Denom) = XSIG_LL(accumulator);
 119                 if (exponent < 0)
 120                         shr_Xsig(&Denom, -exponent);
 121                 else if (exponent > 0) {
 122                         /* exponent must be 1 here */
 123                         XSIG_LL(Denom) <<= 1;
 124                         if (Denom.lsw & 0x80000000)
 125                                 XSIG_LL(Denom) |= 1;
 126                         (Denom.lsw) <<= 1;
 127                 }
 128                 Denom.msw |= 0x80000000;        /* add 1.0 */
 129                 div_Xsig(&accumulator, &Denom, &accumulator);
 130         }
 131
 132         /* Convert to 64 bit signed-compatible */
 133         exponent += round_Xsig(&accumulator);
 134
 135         result = &st(0);
 136         significand(result) = XSIG_LL(accumulator);
 137         setexponent16(result, exponent);
 138
 139         tag = FPU_round(result, 1, 0, FULL_PRECISION, sign);
 140
 141         setsign(result, sign);
 142         FPU_settag0(tag);
 143
 144         return 0;
 145
 146 }