LXR linux/arch/x86/math-emu/poly

   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
  22static 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
  36static 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 */
  41static const Xsig shiftterm0 = MK_XSIG(0, 0, 0);
  42static const Xsig shiftterm1 = MK_XSIG(0x9837f051, 0x8db8a96f, 0x46ad2318);
  43static const Xsig shiftterm2 = MK_XSIG(0xb504f333, 0xf9de6484, 0x597d89b3);
  44static const Xsig shiftterm3 = MK_XSIG(0xd744fcca, 0xd69d6af4, 0x39a68bb9);
  45
  46static const Xsig *shiftterm[] = { &shiftterm0, &shiftterm1,
  47        &shiftterm2, &shiftterm3
  48};
  49
  50/*--- poly_2xm1() -----------------------------------------------------------+
  51 | Requires st(0) which is TAG_Valid and < 1.                                |
  52 +---------------------------------------------------------------------------*/
  53int 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}
 147