// SPDX-License-Identifier: GPL-2.0
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/*---------------------------------------------------------------------------+
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| poly_2xm1.c |
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| Function to compute 2^x-1 by a polynomial approximation. |
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| Copyright (C) 1992,1993,1994,1997 |
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| W. Metzenthen, 22 Parker St, Ormond, Vic 3163, Australia |
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| E-mail billm@suburbia.net |
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+---------------------------------------------------------------------------*/
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#include "exception.h"
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#include "reg_constant.h"
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#include "fpu_emu.h"
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#include "fpu_system.h"
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#include "control_w.h"
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#include "poly.h"
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#define HIPOWER 11
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static const unsigned long long lterms[HIPOWER] = {
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0x0000000000000000LL, /* This term done separately as 12 bytes */
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0xf5fdeffc162c7543LL,
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0x1c6b08d704a0bfa6LL,
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0x0276556df749cc21LL,
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0x002bb0ffcf14f6b8LL,
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0x0002861225ef751cLL,
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0x00001ffcbfcd5422LL,
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0x00000162c005d5f1LL,
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0x0000000da96ccb1bLL,
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0x0000000078d1b897LL,
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0x000000000422b029LL
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};
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static const Xsig hiterm = MK_XSIG(0xb17217f7, 0xd1cf79ab, 0xc8a39194);
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/* Four slices: 0.0 : 0.25 : 0.50 : 0.75 : 1.0,
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These numbers are 2^(1/4), 2^(1/2), and 2^(3/4)
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*/
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static const Xsig shiftterm0 = MK_XSIG(0, 0, 0);
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static const Xsig shiftterm1 = MK_XSIG(0x9837f051, 0x8db8a96f, 0x46ad2318);
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static const Xsig shiftterm2 = MK_XSIG(0xb504f333, 0xf9de6484, 0x597d89b3);
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static const Xsig shiftterm3 = MK_XSIG(0xd744fcca, 0xd69d6af4, 0x39a68bb9);
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static const Xsig *shiftterm[] = { &shiftterm0, &shiftterm1,
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&shiftterm2, &shiftterm3
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};
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/*--- poly_2xm1() -----------------------------------------------------------+
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| Requires st(0) which is TAG_Valid and < 1. |
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+---------------------------------------------------------------------------*/
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int poly_2xm1(u_char sign, FPU_REG *arg, FPU_REG *result)
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{
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long int exponent, shift;
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unsigned long long Xll;
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Xsig accumulator, Denom, argSignif;
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u_char tag;
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exponent = exponent16(arg);
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#ifdef PARANOID
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if (exponent >= 0) { /* Don't want a |number| >= 1.0 */
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/* Number negative, too large, or not Valid. */
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EXCEPTION(EX_INTERNAL | 0x127);
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return 1;
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}
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#endif /* PARANOID */
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argSignif.lsw = 0;
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XSIG_LL(argSignif) = Xll = significand(arg);
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if (exponent == -1) {
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shift = (argSignif.msw & 0x40000000) ? 3 : 2;
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/* subtract 0.5 or 0.75 */
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exponent -= 2;
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XSIG_LL(argSignif) <<= 2;
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Xll <<= 2;
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} else if (exponent == -2) {
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shift = 1;
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/* subtract 0.25 */
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exponent--;
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XSIG_LL(argSignif) <<= 1;
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Xll <<= 1;
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} else
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shift = 0;
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if (exponent < -2) {
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/* Shift the argument right by the required places. */
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if (FPU_shrx(&Xll, -2 - exponent) >= 0x80000000U)
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Xll++; /* round up */
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}
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accumulator.lsw = accumulator.midw = accumulator.msw = 0;
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polynomial_Xsig(&accumulator, &Xll, lterms, HIPOWER - 1);
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mul_Xsig_Xsig(&accumulator, &argSignif);
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shr_Xsig(&accumulator, 3);
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mul_Xsig_Xsig(&argSignif, &hiterm); /* The leading term */
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add_two_Xsig(&accumulator, &argSignif, &exponent);
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if (shift) {
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/* The argument is large, use the identity:
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f(x+a) = f(a) * (f(x) + 1) - 1;
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*/
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shr_Xsig(&accumulator, -exponent);
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accumulator.msw |= 0x80000000; /* add 1.0 */
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mul_Xsig_Xsig(&accumulator, shiftterm[shift]);
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accumulator.msw &= 0x3fffffff; /* subtract 1.0 */
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exponent = 1;
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}
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if (sign != SIGN_POS) {
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/* The argument is negative, use the identity:
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f(-x) = -f(x) / (1 + f(x))
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*/
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Denom.lsw = accumulator.lsw;
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XSIG_LL(Denom) = XSIG_LL(accumulator);
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if (exponent < 0)
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shr_Xsig(&Denom, -exponent);
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else if (exponent > 0) {
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/* exponent must be 1 here */
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XSIG_LL(Denom) <<= 1;
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if (Denom.lsw & 0x80000000)
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XSIG_LL(Denom) |= 1;
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(Denom.lsw) <<= 1;
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}
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Denom.msw |= 0x80000000; /* add 1.0 */
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div_Xsig(&accumulator, &Denom, &accumulator);
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}
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/* Convert to 64 bit signed-compatible */
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exponent += round_Xsig(&accumulator);
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result = &st(0);
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significand(result) = XSIG_LL(accumulator);
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setexponent16(result, exponent);
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tag = FPU_round(result, 1, 0, FULL_PRECISION, sign);
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setsign(result, sign);
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FPU_settag0(tag);
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return 0;
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}
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