// SPDX-License-Identifier: GPL-2.0
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/*---------------------------------------------------------------------------+
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| poly_l2.c |
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| Compute the base 2 log of a FPU_REG, using 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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static void log2_kernel(FPU_REG const *arg, u_char argsign,
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Xsig * accum_result, long int *expon);
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/*--- poly_l2() -------------------------------------------------------------+
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| Base 2 logarithm by a polynomial approximation. |
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+---------------------------------------------------------------------------*/
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void poly_l2(FPU_REG *st0_ptr, FPU_REG *st1_ptr, u_char st1_sign)
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{
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long int exponent, expon, expon_expon;
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Xsig accumulator, expon_accum, yaccum;
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u_char sign, argsign;
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FPU_REG x;
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int tag;
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exponent = exponent16(st0_ptr);
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/* From st0_ptr, make a number > sqrt(2)/2 and < sqrt(2) */
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if (st0_ptr->sigh > (unsigned)0xb504f334) {
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/* Treat as sqrt(2)/2 < st0_ptr < 1 */
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significand(&x) = -significand(st0_ptr);
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setexponent16(&x, -1);
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exponent++;
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argsign = SIGN_NEG;
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} else {
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/* Treat as 1 <= st0_ptr < sqrt(2) */
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x.sigh = st0_ptr->sigh - 0x80000000;
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x.sigl = st0_ptr->sigl;
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setexponent16(&x, 0);
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argsign = SIGN_POS;
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}
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tag = FPU_normalize_nuo(&x);
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if (tag == TAG_Zero) {
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expon = 0;
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accumulator.msw = accumulator.midw = accumulator.lsw = 0;
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} else {
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log2_kernel(&x, argsign, &accumulator, &expon);
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}
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if (exponent < 0) {
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sign = SIGN_NEG;
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exponent = -exponent;
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} else
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sign = SIGN_POS;
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expon_accum.msw = exponent;
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expon_accum.midw = expon_accum.lsw = 0;
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if (exponent) {
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expon_expon = 31 + norm_Xsig(&expon_accum);
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shr_Xsig(&accumulator, expon_expon - expon);
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if (sign ^ argsign)
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negate_Xsig(&accumulator);
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add_Xsig_Xsig(&accumulator, &expon_accum);
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} else {
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expon_expon = expon;
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sign = argsign;
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}
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yaccum.lsw = 0;
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XSIG_LL(yaccum) = significand(st1_ptr);
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mul_Xsig_Xsig(&accumulator, &yaccum);
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expon_expon += round_Xsig(&accumulator);
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if (accumulator.msw == 0) {
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FPU_copy_to_reg1(&CONST_Z, TAG_Zero);
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return;
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}
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significand(st1_ptr) = XSIG_LL(accumulator);
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setexponent16(st1_ptr, expon_expon + exponent16(st1_ptr) + 1);
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tag = FPU_round(st1_ptr, 1, 0, FULL_PRECISION, sign ^ st1_sign);
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FPU_settagi(1, tag);
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set_precision_flag_up(); /* 80486 appears to always do this */
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return;
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}
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/*--- poly_l2p1() -----------------------------------------------------------+
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| Base 2 logarithm by a polynomial approximation. |
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| log2(x+1) |
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+---------------------------------------------------------------------------*/
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int poly_l2p1(u_char sign0, u_char sign1,
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FPU_REG * st0_ptr, FPU_REG * st1_ptr, FPU_REG * dest)
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{
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u_char tag;
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long int exponent;
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Xsig accumulator, yaccum;
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if (exponent16(st0_ptr) < 0) {
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log2_kernel(st0_ptr, sign0, &accumulator, &exponent);
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yaccum.lsw = 0;
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XSIG_LL(yaccum) = significand(st1_ptr);
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mul_Xsig_Xsig(&accumulator, &yaccum);
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exponent += round_Xsig(&accumulator);
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exponent += exponent16(st1_ptr) + 1;
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if (exponent < EXP_WAY_UNDER)
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exponent = EXP_WAY_UNDER;
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significand(dest) = XSIG_LL(accumulator);
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setexponent16(dest, exponent);
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tag = FPU_round(dest, 1, 0, FULL_PRECISION, sign0 ^ sign1);
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FPU_settagi(1, tag);
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if (tag == TAG_Valid)
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set_precision_flag_up(); /* 80486 appears to always do this */
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} else {
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/* The magnitude of st0_ptr is far too large. */
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if (sign0 != SIGN_POS) {
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/* Trying to get the log of a negative number. */
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#ifdef PECULIAR_486 /* Stupid 80486 doesn't worry about log(negative). */
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changesign(st1_ptr);
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#else
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if (arith_invalid(1) < 0)
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return 1;
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#endif /* PECULIAR_486 */
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}
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/* 80486 appears to do this */
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if (sign0 == SIGN_NEG)
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set_precision_flag_down();
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else
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set_precision_flag_up();
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}
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if (exponent(dest) <= EXP_UNDER)
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EXCEPTION(EX_Underflow);
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return 0;
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}
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#undef HIPOWER
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#define HIPOWER 10
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static const unsigned long long logterms[HIPOWER] = {
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0x2a8eca5705fc2ef0LL,
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0xf6384ee1d01febceLL,
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0x093bb62877cdf642LL,
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0x006985d8a9ec439bLL,
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0x0005212c4f55a9c8LL,
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0x00004326a16927f0LL,
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0x0000038d1d80a0e7LL,
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0x0000003141cc80c6LL,
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0x00000002b1668c9fLL,
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0x000000002c7a46aaLL
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};
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static const unsigned long leadterm = 0xb8000000;
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/*--- log2_kernel() ---------------------------------------------------------+
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| Base 2 logarithm by a polynomial approximation. |
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| log2(x+1) |
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+---------------------------------------------------------------------------*/
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static void log2_kernel(FPU_REG const *arg, u_char argsign, Xsig *accum_result,
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long int *expon)
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{
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long int exponent, adj;
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unsigned long long Xsq;
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Xsig accumulator, Numer, Denom, argSignif, arg_signif;
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exponent = exponent16(arg);
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Numer.lsw = Denom.lsw = 0;
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XSIG_LL(Numer) = XSIG_LL(Denom) = significand(arg);
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if (argsign == SIGN_POS) {
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shr_Xsig(&Denom, 2 - (1 + exponent));
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Denom.msw |= 0x80000000;
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div_Xsig(&Numer, &Denom, &argSignif);
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} else {
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shr_Xsig(&Denom, 1 - (1 + exponent));
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negate_Xsig(&Denom);
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if (Denom.msw & 0x80000000) {
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div_Xsig(&Numer, &Denom, &argSignif);
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exponent++;
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} else {
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/* Denom must be 1.0 */
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argSignif.lsw = Numer.lsw;
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argSignif.midw = Numer.midw;
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argSignif.msw = Numer.msw;
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}
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}
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#ifndef PECULIAR_486
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/* Should check here that |local_arg| is within the valid range */
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if (exponent >= -2) {
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if ((exponent > -2) || (argSignif.msw > (unsigned)0xafb0ccc0)) {
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/* The argument is too large */
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}
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}
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#endif /* PECULIAR_486 */
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arg_signif.lsw = argSignif.lsw;
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XSIG_LL(arg_signif) = XSIG_LL(argSignif);
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adj = norm_Xsig(&argSignif);
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accumulator.lsw = argSignif.lsw;
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XSIG_LL(accumulator) = XSIG_LL(argSignif);
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mul_Xsig_Xsig(&accumulator, &accumulator);
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shr_Xsig(&accumulator, 2 * (-1 - (1 + exponent + adj)));
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Xsq = XSIG_LL(accumulator);
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if (accumulator.lsw & 0x80000000)
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Xsq++;
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accumulator.msw = accumulator.midw = accumulator.lsw = 0;
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/* Do the basic fixed point polynomial evaluation */
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polynomial_Xsig(&accumulator, &Xsq, logterms, HIPOWER - 1);
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mul_Xsig_Xsig(&accumulator, &argSignif);
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shr_Xsig(&accumulator, 6 - adj);
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mul32_Xsig(&arg_signif, leadterm);
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add_two_Xsig(&accumulator, &arg_signif, &exponent);
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*expon = exponent + 1;
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accum_result->lsw = accumulator.lsw;
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accum_result->midw = accumulator.midw;
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accum_result->msw = accumulator.msw;
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}
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