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

   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
  21static 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
  35static 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 */
  40static const Xsig shiftterm0 = MK_XSIG(0, 0, 0);
  41static const Xsig shiftterm1 = MK_XSIG(0x9837f051, 0x8db8a96f, 0x46ad2318);
  42static const Xsig shiftterm2 = MK_XSIG(0xb504f333, 0xf9de6484, 0x597d89b3);
  43static const Xsig shiftterm3 = MK_XSIG(0xd744fcca, 0xd69d6af4, 0x39a68bb9);
  44
  45static const Xsig *shiftterm[] = { &shiftterm0, &shiftterm1,
  46        &shiftterm2, &shiftterm3
  47};
  48
  49/*--- poly_2xm1() -----------------------------------------------------------+
  50 | Requires st(0) which is TAG_Valid and < 1.                                |
  51 +---------------------------------------------------------------------------*/
  52int 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}
 146