1096 lines
38 KiB
C
1096 lines
38 KiB
C
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/* Copyright (C) 2007-2022 Free Software Foundation, Inc.
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This file is part of GCC.
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GCC is free software; you can redistribute it and/or modify it under
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the terms of the GNU General Public License as published by the Free
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Software Foundation; either version 3, or (at your option) any later
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version.
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GCC is distributed in the hope that it will be useful, but WITHOUT ANY
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WARRANTY; without even the implied warranty of MERCHANTABILITY or
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FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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for more details.
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Under Section 7 of GPL version 3, you are granted additional
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permissions described in the GCC Runtime Library Exception, version
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3.1, as published by the Free Software Foundation.
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You should have received a copy of the GNU General Public License and
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a copy of the GCC Runtime Library Exception along with this program;
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see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
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<http://www.gnu.org/licenses/>. */
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#define BID_128RES
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#include "bid_internal.h"
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/*****************************************************************************
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* BID128 minimum number
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*****************************************************************************/
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#if DECIMAL_CALL_BY_REFERENCE
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void
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bid128_minnum (UINT128 * pres, UINT128 * px,
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UINT128 * py _EXC_FLAGS_PARAM) {
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UINT128 x = *px;
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UINT128 y = *py;
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#else
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UINT128
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bid128_minnum (UINT128 x, UINT128 y _EXC_FLAGS_PARAM) {
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#endif
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UINT128 res;
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int exp_x, exp_y;
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int diff;
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UINT128 sig_x, sig_y;
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UINT192 sig_n_prime192;
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UINT256 sig_n_prime256;
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char x_is_zero = 0, y_is_zero = 0;
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BID_SWAP128 (x);
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BID_SWAP128 (y);
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// check for non-canonical x
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if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
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x.w[1] = x.w[1] & 0xfe003fffffffffffull; // clear out G[6]-G[16]
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// check for non-canonical NaN payload
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if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
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(((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
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(x.w[0] > 0x38c15b09ffffffffull))) {
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x.w[1] = x.w[1] & 0xffffc00000000000ull;
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x.w[0] = 0x0ull;
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}
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} else if ((x.w[1] & MASK_ANY_INF) == MASK_INF) { // x = inf
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x.w[1] = x.w[1] & (MASK_SIGN | MASK_INF);
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x.w[0] = 0x0ull;
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} else { // x is not special
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// check for non-canonical values - treated as zero
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if ((x.w[1] & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // G0_G1=11
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// non-canonical
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x.w[1] = (x.w[1] & MASK_SIGN) | ((x.w[1] << 2) & MASK_EXP);
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x.w[0] = 0x0ull;
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} else { // G0_G1 != 11
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if ((x.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull ||
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((x.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull
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&& x.w[0] > 0x378d8e63ffffffffull)) {
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// x is non-canonical if coefficient is larger than 10^34 -1
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x.w[1] = (x.w[1] & MASK_SIGN) | (x.w[1] & MASK_EXP);
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x.w[0] = 0x0ull;
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} else { // canonical
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;
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}
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}
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}
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// check for non-canonical y
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if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NAN
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y.w[1] = y.w[1] & 0xfe003fffffffffffull; // clear out G[6]-G[16]
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// check for non-canonical NaN payload
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if (((y.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
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(((y.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
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(y.w[0] > 0x38c15b09ffffffffull))) {
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y.w[1] = y.w[1] & 0xffffc00000000000ull;
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y.w[0] = 0x0ull;
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}
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} else if ((y.w[1] & MASK_ANY_INF) == MASK_INF) { // y = inf
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y.w[1] = y.w[1] & (MASK_SIGN | MASK_INF);
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y.w[0] = 0x0ull;
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} else { // y is not special
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// check for non-canonical values - treated as zero
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if ((y.w[1] & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // G0_G1=11
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// non-canonical
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y.w[1] = (y.w[1] & MASK_SIGN) | ((y.w[1] << 2) & MASK_EXP);
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y.w[0] = 0x0ull;
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} else { // G0_G1 != 11
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if ((y.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull ||
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((y.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull
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&& y.w[0] > 0x378d8e63ffffffffull)) {
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// y is non-canonical if coefficient is larger than 10^34 -1
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y.w[1] = (y.w[1] & MASK_SIGN) | (y.w[1] & MASK_EXP);
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y.w[0] = 0x0ull;
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} else { // canonical
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;
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}
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}
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}
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// NaN (CASE1)
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if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
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if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNaN
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// if x is SNAN, then return quiet (x)
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*pfpsf |= INVALID_EXCEPTION; // set exception if SNaN
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x.w[1] = x.w[1] & 0xfdffffffffffffffull; // quietize x
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res = x;
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} else { // x is QNaN
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if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NAN
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if ((y.w[1] & MASK_SNAN) == MASK_SNAN) { // y is SNAN
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*pfpsf |= INVALID_EXCEPTION; // set invalid flag
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}
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res = x;
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} else {
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res = y;
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}
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}
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BID_RETURN (res);
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} else if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NaN, but x is not
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if ((y.w[1] & MASK_SNAN) == MASK_SNAN) {
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*pfpsf |= INVALID_EXCEPTION; // set exception if SNaN
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y.w[1] = y.w[1] & 0xfdffffffffffffffull; // quietize y
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res = y;
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} else {
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// will return x (which is not NaN)
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res = x;
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}
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BID_RETURN (res);
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}
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// SIMPLE (CASE2)
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// if all the bits are the same, these numbers are equal (not Greater).
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if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
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res = x;
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BID_RETURN (res);
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}
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// INFINITY (CASE3)
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if ((x.w[1] & MASK_INF) == MASK_INF) {
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// if x is neg infinity, there is no way it is greater than y, return 0
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res = (((x.w[1] & MASK_SIGN) == MASK_SIGN)) ? x : y;
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BID_RETURN (res);
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} else if ((y.w[1] & MASK_INF) == MASK_INF) {
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// x is finite, so if y is positive infinity, then x is less, return 0
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// if y is negative infinity, then x is greater, return 1
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res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x;
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BID_RETURN (res);
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}
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// CONVERT X
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sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
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sig_x.w[0] = x.w[0];
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exp_x = (x.w[1] >> 49) & 0x000000000003fffull;
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// CONVERT Y
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exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
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sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
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sig_y.w[0] = y.w[0];
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// ZERO (CASE4)
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// some properties:
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// (+ZERO == -ZERO) => therefore ignore the sign
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// (ZERO x 10^A == ZERO x 10^B) for any valid A, B => ignore the exponent
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// field
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// (Any non-canonical # is considered 0)
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if ((sig_x.w[1] == 0) && (sig_x.w[0] == 0)) {
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x_is_zero = 1;
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}
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if ((sig_y.w[1] == 0) && (sig_y.w[0] == 0)) {
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y_is_zero = 1;
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}
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if (x_is_zero && y_is_zero) {
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// if both numbers are zero, neither is greater => return either number
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res = x;
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BID_RETURN (res);
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} else if (x_is_zero) {
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// is x is zero, it is greater if Y is negative
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res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x;
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BID_RETURN (res);
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} else if (y_is_zero) {
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// is y is zero, X is greater if it is positive
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res = ((x.w[1] & MASK_SIGN) != MASK_SIGN) ? y : x;
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BID_RETURN (res);
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}
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// OPPOSITE SIGN (CASE5)
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// now, if the sign bits differ, x is greater if y is negative
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if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) {
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res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x;
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BID_RETURN (res);
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}
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// REDUNDANT REPRESENTATIONS (CASE6)
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// if exponents are the same, then we have a simple comparison of
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// the significands
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if (exp_y == exp_x) {
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res = (((sig_x.w[1] > sig_y.w[1])
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|| (sig_x.w[1] == sig_y.w[1]
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&& sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) ==
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MASK_SIGN)) ? y : x;
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BID_RETURN (res);
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}
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// if both components are either bigger or smaller, it is clear what
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// needs to be done
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if (sig_x.w[1] >= sig_y.w[1] && sig_x.w[0] >= sig_y.w[0]
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&& exp_x > exp_y) {
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res = ((x.w[1] & MASK_SIGN) != MASK_SIGN) ? y : x;
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BID_RETURN (res);
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}
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if (sig_x.w[1] <= sig_y.w[1] && sig_x.w[0] <= sig_y.w[0]
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&& exp_x < exp_y) {
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res = ((x.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x;
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BID_RETURN (res);
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}
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diff = exp_x - exp_y;
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// if |exp_x - exp_y| < 33, it comes down to the compensated significand
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if (diff > 0) { // to simplify the loop below,
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// if exp_x is 33 greater than exp_y, no need for compensation
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if (diff > 33) {
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// difference cannot be greater than 10^33
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res = ((x.w[1] & MASK_SIGN) != MASK_SIGN) ? y : x;
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BID_RETURN (res);
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}
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if (diff > 19) { //128 by 128 bit multiply -> 256 bits
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__mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]);
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// if postitive, return whichever significand is larger
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// (converse if negative)
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res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0)
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|| (sig_n_prime256.w[1] > sig_y.w[1])
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|| (sig_n_prime256.w[1] == sig_y.w[1]
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&& sig_n_prime256.w[0] >
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sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) ==
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MASK_SIGN)) ? y : x;
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BID_RETURN (res);
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}
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__mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_x);
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// if postitive, return whichever significand is larger
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// (converse if negative)
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res =
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(((sig_n_prime192.w[2] > 0) || (sig_n_prime192.w[1] > sig_y.w[1])
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|| (sig_n_prime192.w[1] == sig_y.w[1]
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&& sig_n_prime192.w[0] >
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sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)) ? y : x;
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BID_RETURN (res);
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}
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diff = exp_y - exp_x;
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// if exp_x is 33 less than exp_y, no need for compensation
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if (diff > 33) {
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res = ((x.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x;
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BID_RETURN (res);
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}
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if (diff > 19) { //128 by 128 bit multiply -> 256 bits
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// adjust the y significand upwards
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__mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]);
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// if postitive, return whichever significand is larger
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// (converse if negative)
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res =
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((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0
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|| (sig_n_prime256.w[1] > sig_x.w[1]
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|| (sig_n_prime256.w[1] == sig_x.w[1]
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&& sig_n_prime256.w[0] >
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sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) ==
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MASK_SIGN)) ? x : y;
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BID_RETURN (res);
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}
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// adjust the y significand upwards
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__mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_y);
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// if postitive, return whichever significand is larger (converse if negative)
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res =
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((sig_n_prime192.w[2] != 0
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|| (sig_n_prime192.w[1] > sig_x.w[1]
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|| (sig_n_prime192.w[1] == sig_x.w[1]
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&& sig_n_prime192.w[0] > sig_x.w[0])))
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^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)) ? x : y;
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BID_RETURN (res);
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}
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/*****************************************************************************
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||
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* BID128 minimum magnitude function - returns greater of two numbers
|
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*****************************************************************************/
|
||
|
|
||
|
#if DECIMAL_CALL_BY_REFERENCE
|
||
|
void
|
||
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bid128_minnum_mag (UINT128 * pres, UINT128 * px,
|
||
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UINT128 * py _EXC_FLAGS_PARAM) {
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UINT128 x = *px;
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UINT128 y = *py;
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#else
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UINT128
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bid128_minnum_mag (UINT128 x, UINT128 y _EXC_FLAGS_PARAM) {
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#endif
|
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||
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UINT128 res;
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int exp_x, exp_y;
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int diff;
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UINT128 sig_x, sig_y;
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UINT192 sig_n_prime192;
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UINT256 sig_n_prime256;
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|
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BID_SWAP128 (x);
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BID_SWAP128 (y);
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||
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// check for non-canonical x
|
||
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if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
|
||
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x.w[1] = x.w[1] & 0xfe003fffffffffffull; // clear out G[6]-G[16]
|
||
|
// check for non-canonical NaN payload
|
||
|
if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
|
||
|
(((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
|
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(x.w[0] > 0x38c15b09ffffffffull))) {
|
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x.w[1] = x.w[1] & 0xffffc00000000000ull;
|
||
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x.w[0] = 0x0ull;
|
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}
|
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} else if ((x.w[1] & MASK_ANY_INF) == MASK_INF) { // x = inf
|
||
|
x.w[1] = x.w[1] & (MASK_SIGN | MASK_INF);
|
||
|
x.w[0] = 0x0ull;
|
||
|
} else { // x is not special
|
||
|
// check for non-canonical values - treated as zero
|
||
|
if ((x.w[1] & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // G0_G1=11
|
||
|
// non-canonical
|
||
|
x.w[1] = (x.w[1] & MASK_SIGN) | ((x.w[1] << 2) & MASK_EXP);
|
||
|
x.w[0] = 0x0ull;
|
||
|
} else { // G0_G1 != 11
|
||
|
if ((x.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull ||
|
||
|
((x.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull
|
||
|
&& x.w[0] > 0x378d8e63ffffffffull)) {
|
||
|
// x is non-canonical if coefficient is larger than 10^34 -1
|
||
|
x.w[1] = (x.w[1] & MASK_SIGN) | (x.w[1] & MASK_EXP);
|
||
|
x.w[0] = 0x0ull;
|
||
|
} else { // canonical
|
||
|
;
|
||
|
}
|
||
|
}
|
||
|
}
|
||
|
// check for non-canonical y
|
||
|
if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NAN
|
||
|
y.w[1] = y.w[1] & 0xfe003fffffffffffull; // clear out G[6]-G[16]
|
||
|
// check for non-canonical NaN payload
|
||
|
if (((y.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
|
||
|
(((y.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
|
||
|
(y.w[0] > 0x38c15b09ffffffffull))) {
|
||
|
y.w[1] = y.w[1] & 0xffffc00000000000ull;
|
||
|
y.w[0] = 0x0ull;
|
||
|
}
|
||
|
} else if ((y.w[1] & MASK_ANY_INF) == MASK_INF) { // y = inf
|
||
|
y.w[1] = y.w[1] & (MASK_SIGN | MASK_INF);
|
||
|
y.w[0] = 0x0ull;
|
||
|
} else { // y is not special
|
||
|
// check for non-canonical values - treated as zero
|
||
|
if ((y.w[1] & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // G0_G1=11
|
||
|
// non-canonical
|
||
|
y.w[1] = (y.w[1] & MASK_SIGN) | ((y.w[1] << 2) & MASK_EXP);
|
||
|
y.w[0] = 0x0ull;
|
||
|
} else { // G0_G1 != 11
|
||
|
if ((y.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull ||
|
||
|
((y.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull
|
||
|
&& y.w[0] > 0x378d8e63ffffffffull)) {
|
||
|
// y is non-canonical if coefficient is larger than 10^34 -1
|
||
|
y.w[1] = (y.w[1] & MASK_SIGN) | (y.w[1] & MASK_EXP);
|
||
|
y.w[0] = 0x0ull;
|
||
|
} else { // canonical
|
||
|
;
|
||
|
}
|
||
|
}
|
||
|
}
|
||
|
|
||
|
// NaN (CASE1)
|
||
|
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
|
||
|
if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNaN
|
||
|
// if x is SNAN, then return quiet (x)
|
||
|
*pfpsf |= INVALID_EXCEPTION; // set exception if SNaN
|
||
|
x.w[1] = x.w[1] & 0xfdffffffffffffffull; // quietize x
|
||
|
res = x;
|
||
|
} else { // x is QNaN
|
||
|
if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NAN
|
||
|
if ((y.w[1] & MASK_SNAN) == MASK_SNAN) { // y is SNAN
|
||
|
*pfpsf |= INVALID_EXCEPTION; // set invalid flag
|
||
|
}
|
||
|
res = x;
|
||
|
} else {
|
||
|
res = y;
|
||
|
}
|
||
|
}
|
||
|
BID_RETURN (res);
|
||
|
} else if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NaN, but x is not
|
||
|
if ((y.w[1] & MASK_SNAN) == MASK_SNAN) {
|
||
|
*pfpsf |= INVALID_EXCEPTION; // set exception if SNaN
|
||
|
y.w[1] = y.w[1] & 0xfdffffffffffffffull; // quietize y
|
||
|
res = y;
|
||
|
} else {
|
||
|
// will return x (which is not NaN)
|
||
|
res = x;
|
||
|
}
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
// SIMPLE (CASE2)
|
||
|
// if all the bits are the same, these numbers are equal (not Greater).
|
||
|
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
|
||
|
res = y;
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
// INFINITY (CASE3)
|
||
|
if ((x.w[1] & MASK_INF) == MASK_INF) {
|
||
|
// if x infinity, it has maximum magnitude.
|
||
|
// Check if magnitudes are equal. If x is negative, return it.
|
||
|
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN
|
||
|
&& (y.w[1] & MASK_INF) == MASK_INF) ? x : y;
|
||
|
BID_RETURN (res);
|
||
|
} else if ((y.w[1] & MASK_INF) == MASK_INF) {
|
||
|
// x is finite, so if y is infinity, then x is less in magnitude
|
||
|
res = x;
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
// CONVERT X
|
||
|
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
|
||
|
sig_x.w[0] = x.w[0];
|
||
|
exp_x = (x.w[1] >> 49) & 0x000000000003fffull;
|
||
|
|
||
|
// CONVERT Y
|
||
|
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
|
||
|
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
|
||
|
sig_y.w[0] = y.w[0];
|
||
|
|
||
|
// ZERO (CASE4)
|
||
|
// some properties:
|
||
|
// (+ZERO == -ZERO) => therefore ignore the sign
|
||
|
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B =>
|
||
|
// therefore ignore the exponent field
|
||
|
// (Any non-canonical # is considered 0)
|
||
|
if ((sig_x.w[1] == 0) && (sig_x.w[0] == 0)) {
|
||
|
res = x;
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
if ((sig_y.w[1] == 0) && (sig_y.w[0] == 0)) {
|
||
|
res = y;
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
// REDUNDANT REPRESENTATIONS (CASE6)
|
||
|
// check if exponents are the same and significands are the same
|
||
|
if (exp_y == exp_x && sig_x.w[1] == sig_y.w[1]
|
||
|
&& sig_x.w[0] == sig_y.w[0]) {
|
||
|
if (x.w[1] & 0x8000000000000000ull) { // x is negative
|
||
|
res = x;
|
||
|
BID_RETURN (res);
|
||
|
} else {
|
||
|
res = y;
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
} else if (((sig_x.w[1] > sig_y.w[1] || (sig_x.w[1] == sig_y.w[1]
|
||
|
&& sig_x.w[0] > sig_y.w[0]))
|
||
|
&& exp_x == exp_y)
|
||
|
|| ((sig_x.w[1] > sig_y.w[1]
|
||
|
|| (sig_x.w[1] == sig_y.w[1]
|
||
|
&& sig_x.w[0] >= sig_y.w[0]))
|
||
|
&& exp_x > exp_y)) {
|
||
|
// if both components are either bigger or smaller, it is clear what
|
||
|
// needs to be done; also if the magnitudes are equal
|
||
|
res = y;
|
||
|
BID_RETURN (res);
|
||
|
} else if (((sig_y.w[1] > sig_x.w[1] || (sig_y.w[1] == sig_x.w[1]
|
||
|
&& sig_y.w[0] > sig_x.w[0]))
|
||
|
&& exp_y == exp_x)
|
||
|
|| ((sig_y.w[1] > sig_x.w[1]
|
||
|
|| (sig_y.w[1] == sig_x.w[1]
|
||
|
&& sig_y.w[0] >= sig_x.w[0]))
|
||
|
&& exp_y > exp_x)) {
|
||
|
res = x;
|
||
|
BID_RETURN (res);
|
||
|
} else {
|
||
|
; // continue
|
||
|
}
|
||
|
diff = exp_x - exp_y;
|
||
|
// if |exp_x - exp_y| < 33, it comes down to the compensated significand
|
||
|
if (diff > 0) { // to simplify the loop below,
|
||
|
// if exp_x is 33 greater than exp_y, no need for compensation
|
||
|
if (diff > 33) {
|
||
|
res = y; // difference cannot be greater than 10^33
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
if (diff > 19) { //128 by 128 bit multiply -> 256 bits
|
||
|
__mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]);
|
||
|
// if positive, return whichever significand is larger
|
||
|
// (converse if negative)
|
||
|
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
|
||
|
&& sig_n_prime256.w[1] == sig_y.w[1]
|
||
|
&& (sig_n_prime256.w[0] == sig_y.w[0])) {
|
||
|
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x; // if equal
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
res = (((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0)
|
||
|
|| (sig_n_prime256.w[1] > sig_y.w[1])
|
||
|
|| (sig_n_prime256.w[1] == sig_y.w[1]
|
||
|
&& sig_n_prime256.w[0] > sig_y.w[0])) ? y : x;
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
__mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_x);
|
||
|
// if positive, return whichever significand is larger
|
||
|
// (converse if negative)
|
||
|
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1]
|
||
|
&& (sig_n_prime192.w[0] == sig_y.w[0])) {
|
||
|
// if = in magnitude, return +, (if possible)
|
||
|
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x;
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
res = ((sig_n_prime192.w[2] > 0)
|
||
|
|| (sig_n_prime192.w[1] > sig_y.w[1])
|
||
|
|| (sig_n_prime192.w[1] == sig_y.w[1]
|
||
|
&& sig_n_prime192.w[0] > sig_y.w[0])) ? y : x;
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
diff = exp_y - exp_x;
|
||
|
// if exp_x is 33 less than exp_y, no need for compensation
|
||
|
if (diff > 33) {
|
||
|
res = x;
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
if (diff > 19) { //128 by 128 bit multiply -> 256 bits
|
||
|
// adjust the y significand upwards
|
||
|
__mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]);
|
||
|
// if positive, return whichever significand is larger
|
||
|
// (converse if negative)
|
||
|
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
|
||
|
&& sig_n_prime256.w[1] == sig_x.w[1]
|
||
|
&& (sig_n_prime256.w[0] == sig_x.w[0])) {
|
||
|
// if = in magnitude, return +, (if possible)
|
||
|
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x;
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
res = (sig_n_prime256.w[3] == 0 && sig_n_prime256.w[2] == 0
|
||
|
&& (sig_n_prime256.w[1] < sig_x.w[1]
|
||
|
|| (sig_n_prime256.w[1] == sig_x.w[1]
|
||
|
&& sig_n_prime256.w[0] < sig_x.w[0]))) ? y : x;
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
// adjust the y significand upwards
|
||
|
__mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_y);
|
||
|
// if positive, return whichever significand is larger (converse if negative)
|
||
|
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1]
|
||
|
&& (sig_n_prime192.w[0] == sig_x.w[0])) {
|
||
|
// if = in magnitude, return +, if possible)
|
||
|
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x;
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
res = (sig_n_prime192.w[2] == 0
|
||
|
&& (sig_n_prime192.w[1] < sig_x.w[1]
|
||
|
|| (sig_n_prime192.w[1] == sig_x.w[1]
|
||
|
&& sig_n_prime192.w[0] < sig_x.w[0]))) ? y : x;
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
|
||
|
/*****************************************************************************
|
||
|
* BID128 maximum function - returns greater of two numbers
|
||
|
*****************************************************************************/
|
||
|
|
||
|
#if DECIMAL_CALL_BY_REFERENCE
|
||
|
void
|
||
|
bid128_maxnum (UINT128 * pres, UINT128 * px,
|
||
|
UINT128 * py _EXC_FLAGS_PARAM) {
|
||
|
UINT128 x = *px;
|
||
|
UINT128 y = *py;
|
||
|
#else
|
||
|
UINT128
|
||
|
bid128_maxnum (UINT128 x, UINT128 y _EXC_FLAGS_PARAM) {
|
||
|
#endif
|
||
|
|
||
|
UINT128 res;
|
||
|
int exp_x, exp_y;
|
||
|
int diff;
|
||
|
UINT128 sig_x, sig_y;
|
||
|
UINT192 sig_n_prime192;
|
||
|
UINT256 sig_n_prime256;
|
||
|
char x_is_zero = 0, y_is_zero = 0;
|
||
|
|
||
|
BID_SWAP128 (x);
|
||
|
BID_SWAP128 (y);
|
||
|
|
||
|
// check for non-canonical x
|
||
|
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
|
||
|
x.w[1] = x.w[1] & 0xfe003fffffffffffull; // clear out G[6]-G[16]
|
||
|
// check for non-canonical NaN payload
|
||
|
if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
|
||
|
(((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
|
||
|
(x.w[0] > 0x38c15b09ffffffffull))) {
|
||
|
x.w[1] = x.w[1] & 0xffffc00000000000ull;
|
||
|
x.w[0] = 0x0ull;
|
||
|
}
|
||
|
} else if ((x.w[1] & MASK_ANY_INF) == MASK_INF) { // x = inf
|
||
|
x.w[1] = x.w[1] & (MASK_SIGN | MASK_INF);
|
||
|
x.w[0] = 0x0ull;
|
||
|
} else { // x is not special
|
||
|
// check for non-canonical values - treated as zero
|
||
|
if ((x.w[1] & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // G0_G1=11
|
||
|
// non-canonical
|
||
|
x.w[1] = (x.w[1] & MASK_SIGN) | ((x.w[1] << 2) & MASK_EXP);
|
||
|
x.w[0] = 0x0ull;
|
||
|
} else { // G0_G1 != 11
|
||
|
if ((x.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull ||
|
||
|
((x.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull
|
||
|
&& x.w[0] > 0x378d8e63ffffffffull)) {
|
||
|
// x is non-canonical if coefficient is larger than 10^34 -1
|
||
|
x.w[1] = (x.w[1] & MASK_SIGN) | (x.w[1] & MASK_EXP);
|
||
|
x.w[0] = 0x0ull;
|
||
|
} else { // canonical
|
||
|
;
|
||
|
}
|
||
|
}
|
||
|
}
|
||
|
// check for non-canonical y
|
||
|
if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NAN
|
||
|
y.w[1] = y.w[1] & 0xfe003fffffffffffull; // clear out G[6]-G[16]
|
||
|
// check for non-canonical NaN payload
|
||
|
if (((y.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
|
||
|
(((y.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
|
||
|
(y.w[0] > 0x38c15b09ffffffffull))) {
|
||
|
y.w[1] = y.w[1] & 0xffffc00000000000ull;
|
||
|
y.w[0] = 0x0ull;
|
||
|
}
|
||
|
} else if ((y.w[1] & MASK_ANY_INF) == MASK_INF) { // y = inf
|
||
|
y.w[1] = y.w[1] & (MASK_SIGN | MASK_INF);
|
||
|
y.w[0] = 0x0ull;
|
||
|
} else { // y is not special
|
||
|
// check for non-canonical values - treated as zero
|
||
|
if ((y.w[1] & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // G0_G1=11
|
||
|
// non-canonical
|
||
|
y.w[1] = (y.w[1] & MASK_SIGN) | ((y.w[1] << 2) & MASK_EXP);
|
||
|
y.w[0] = 0x0ull;
|
||
|
} else { // G0_G1 != 11
|
||
|
if ((y.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull ||
|
||
|
((y.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull
|
||
|
&& y.w[0] > 0x378d8e63ffffffffull)) {
|
||
|
// y is non-canonical if coefficient is larger than 10^34 -1
|
||
|
y.w[1] = (y.w[1] & MASK_SIGN) | (y.w[1] & MASK_EXP);
|
||
|
y.w[0] = 0x0ull;
|
||
|
} else { // canonical
|
||
|
;
|
||
|
}
|
||
|
}
|
||
|
}
|
||
|
|
||
|
// NaN (CASE1)
|
||
|
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
|
||
|
if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNaN
|
||
|
// if x is SNAN, then return quiet (x)
|
||
|
*pfpsf |= INVALID_EXCEPTION; // set exception if SNaN
|
||
|
x.w[1] = x.w[1] & 0xfdffffffffffffffull; // quietize x
|
||
|
res = x;
|
||
|
} else { // x is QNaN
|
||
|
if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NAN
|
||
|
if ((y.w[1] & MASK_SNAN) == MASK_SNAN) { // y is SNAN
|
||
|
*pfpsf |= INVALID_EXCEPTION; // set invalid flag
|
||
|
}
|
||
|
res = x;
|
||
|
} else {
|
||
|
res = y;
|
||
|
}
|
||
|
}
|
||
|
BID_RETURN (res);
|
||
|
} else if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NaN, but x is not
|
||
|
if ((y.w[1] & MASK_SNAN) == MASK_SNAN) {
|
||
|
*pfpsf |= INVALID_EXCEPTION; // set exception if SNaN
|
||
|
y.w[1] = y.w[1] & 0xfdffffffffffffffull; // quietize y
|
||
|
res = y;
|
||
|
} else {
|
||
|
// will return x (which is not NaN)
|
||
|
res = x;
|
||
|
}
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
// SIMPLE (CASE2)
|
||
|
// if all the bits are the same, these numbers are equal (not Greater).
|
||
|
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
|
||
|
res = x;
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
// INFINITY (CASE3)
|
||
|
if ((x.w[1] & MASK_INF) == MASK_INF) {
|
||
|
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x;
|
||
|
BID_RETURN (res);
|
||
|
} else if ((y.w[1] & MASK_INF) == MASK_INF) {
|
||
|
// x is finite, so if y is positive infinity, then x is less, return 0
|
||
|
// if y is negative infinity, then x is greater, return 1
|
||
|
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? x : y;
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
// CONVERT X
|
||
|
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
|
||
|
sig_x.w[0] = x.w[0];
|
||
|
exp_x = (x.w[1] >> 49) & 0x000000000003fffull;
|
||
|
|
||
|
// CONVERT Y
|
||
|
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
|
||
|
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
|
||
|
sig_y.w[0] = y.w[0];
|
||
|
|
||
|
// ZERO (CASE4)
|
||
|
// some properties:
|
||
|
// (+ZERO == -ZERO) => therefore ignore the sign
|
||
|
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B =>
|
||
|
// therefore ignore the exponent field
|
||
|
// (Any non-canonical # is considered 0)
|
||
|
if ((sig_x.w[1] == 0) && (sig_x.w[0] == 0)) {
|
||
|
x_is_zero = 1;
|
||
|
}
|
||
|
if ((sig_y.w[1] == 0) && (sig_y.w[0] == 0)) {
|
||
|
y_is_zero = 1;
|
||
|
}
|
||
|
|
||
|
if (x_is_zero && y_is_zero) {
|
||
|
// if both numbers are zero, neither is greater => return either number
|
||
|
res = x;
|
||
|
BID_RETURN (res);
|
||
|
} else if (x_is_zero) {
|
||
|
// is x is zero, it is greater if Y is negative
|
||
|
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? x : y;
|
||
|
BID_RETURN (res);
|
||
|
} else if (y_is_zero) {
|
||
|
// is y is zero, X is greater if it is positive
|
||
|
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN) ? x : y;
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
// OPPOSITE SIGN (CASE5)
|
||
|
// now, if the sign bits differ, x is greater if y is negative
|
||
|
if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) {
|
||
|
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? x : y;
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
// REDUNDANT REPRESENTATIONS (CASE6)
|
||
|
// if exponents are the same, then we have a simple comparison of
|
||
|
// the significands
|
||
|
if (exp_y == exp_x) {
|
||
|
res = (((sig_x.w[1] > sig_y.w[1]) || (sig_x.w[1] == sig_y.w[1] &&
|
||
|
sig_x.w[0] >= sig_y.w[0])) ^
|
||
|
((x.w[1] & MASK_SIGN) == MASK_SIGN)) ? x : y;
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
// if both components are either bigger or smaller, it is clear what
|
||
|
// needs to be done
|
||
|
if ((sig_x.w[1] > sig_y.w[1]
|
||
|
|| (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0]))
|
||
|
&& exp_x >= exp_y) {
|
||
|
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN) ? x : y;
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
if ((sig_x.w[1] < sig_y.w[1]
|
||
|
|| (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0]))
|
||
|
&& exp_x <= exp_y) {
|
||
|
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN) ? x : y;
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
diff = exp_x - exp_y;
|
||
|
// if |exp_x - exp_y| < 33, it comes down to the compensated significand
|
||
|
if (diff > 0) { // to simplify the loop below,
|
||
|
// if exp_x is 33 greater than exp_y, no need for compensation
|
||
|
if (diff > 33) {
|
||
|
// difference cannot be greater than 10^33
|
||
|
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN) ? x : y;
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
if (diff > 19) { //128 by 128 bit multiply -> 256 bits
|
||
|
__mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]);
|
||
|
// if postitive, return whichever significand is larger
|
||
|
// (converse if negative)
|
||
|
res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0)
|
||
|
|| (sig_n_prime256.w[1] > sig_y.w[1])
|
||
|
|| (sig_n_prime256.w[1] == sig_y.w[1]
|
||
|
&& sig_n_prime256.w[0] >
|
||
|
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) ==
|
||
|
MASK_SIGN)) ? x : y;
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
__mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_x);
|
||
|
// if postitive, return whichever significand is larger
|
||
|
// (converse if negative)
|
||
|
res =
|
||
|
(((sig_n_prime192.w[2] > 0) || (sig_n_prime192.w[1] > sig_y.w[1])
|
||
|
|| (sig_n_prime192.w[1] == sig_y.w[1]
|
||
|
&& sig_n_prime192.w[0] >
|
||
|
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)) ? x : y;
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
diff = exp_y - exp_x;
|
||
|
// if exp_x is 33 less than exp_y, no need for compensation
|
||
|
if (diff > 33) {
|
||
|
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN) ? x : y;
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
if (diff > 19) { //128 by 128 bit multiply -> 256 bits
|
||
|
// adjust the y significand upwards
|
||
|
__mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]);
|
||
|
// if postitive, return whichever significand is larger
|
||
|
// (converse if negative)
|
||
|
res =
|
||
|
((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0
|
||
|
|| (sig_n_prime256.w[1] > sig_x.w[1]
|
||
|
|| (sig_n_prime256.w[1] == sig_x.w[1]
|
||
|
&& sig_n_prime256.w[0] >
|
||
|
sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) !=
|
||
|
MASK_SIGN)) ? x : y;
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
// adjust the y significand upwards
|
||
|
__mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_y);
|
||
|
// if postitive, return whichever significand is larger (converse if negative)
|
||
|
res =
|
||
|
((sig_n_prime192.w[2] != 0
|
||
|
|| (sig_n_prime192.w[1] > sig_x.w[1]
|
||
|
|| (sig_n_prime192.w[1] == sig_x.w[1]
|
||
|
&& sig_n_prime192.w[0] >
|
||
|
sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) !=
|
||
|
MASK_SIGN)) ? x : y;
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
|
||
|
/*****************************************************************************
|
||
|
* BID128 maximum magnitude function - returns greater of two numbers
|
||
|
*****************************************************************************/
|
||
|
|
||
|
#if DECIMAL_CALL_BY_REFERENCE
|
||
|
void
|
||
|
bid128_maxnum_mag (UINT128 * pres, UINT128 * px,
|
||
|
UINT128 * py _EXC_FLAGS_PARAM) {
|
||
|
UINT128 x = *px;
|
||
|
UINT128 y = *py;
|
||
|
#else
|
||
|
UINT128
|
||
|
bid128_maxnum_mag (UINT128 x, UINT128 y _EXC_FLAGS_PARAM) {
|
||
|
#endif
|
||
|
|
||
|
UINT128 res;
|
||
|
int exp_x, exp_y;
|
||
|
int diff;
|
||
|
UINT128 sig_x, sig_y;
|
||
|
UINT192 sig_n_prime192;
|
||
|
UINT256 sig_n_prime256;
|
||
|
|
||
|
BID_SWAP128 (x);
|
||
|
BID_SWAP128 (y);
|
||
|
|
||
|
// check for non-canonical x
|
||
|
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
|
||
|
x.w[1] = x.w[1] & 0xfe003fffffffffffull; // clear out G[6]-G[16]
|
||
|
// check for non-canonical NaN payload
|
||
|
if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
|
||
|
(((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
|
||
|
(x.w[0] > 0x38c15b09ffffffffull))) {
|
||
|
x.w[1] = x.w[1] & 0xffffc00000000000ull;
|
||
|
x.w[0] = 0x0ull;
|
||
|
}
|
||
|
} else if ((x.w[1] & MASK_ANY_INF) == MASK_INF) { // x = inf
|
||
|
x.w[1] = x.w[1] & (MASK_SIGN | MASK_INF);
|
||
|
x.w[0] = 0x0ull;
|
||
|
} else { // x is not special
|
||
|
// check for non-canonical values - treated as zero
|
||
|
if ((x.w[1] & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // G0_G1=11
|
||
|
// non-canonical
|
||
|
x.w[1] = (x.w[1] & MASK_SIGN) | ((x.w[1] << 2) & MASK_EXP);
|
||
|
x.w[0] = 0x0ull;
|
||
|
} else { // G0_G1 != 11
|
||
|
if ((x.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull ||
|
||
|
((x.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull
|
||
|
&& x.w[0] > 0x378d8e63ffffffffull)) {
|
||
|
// x is non-canonical if coefficient is larger than 10^34 -1
|
||
|
x.w[1] = (x.w[1] & MASK_SIGN) | (x.w[1] & MASK_EXP);
|
||
|
x.w[0] = 0x0ull;
|
||
|
} else { // canonical
|
||
|
;
|
||
|
}
|
||
|
}
|
||
|
}
|
||
|
// check for non-canonical y
|
||
|
if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NAN
|
||
|
y.w[1] = y.w[1] & 0xfe003fffffffffffull; // clear out G[6]-G[16]
|
||
|
// check for non-canonical NaN payload
|
||
|
if (((y.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
|
||
|
(((y.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
|
||
|
(y.w[0] > 0x38c15b09ffffffffull))) {
|
||
|
y.w[1] = y.w[1] & 0xffffc00000000000ull;
|
||
|
y.w[0] = 0x0ull;
|
||
|
}
|
||
|
} else if ((y.w[1] & MASK_ANY_INF) == MASK_INF) { // y = inf
|
||
|
y.w[1] = y.w[1] & (MASK_SIGN | MASK_INF);
|
||
|
y.w[0] = 0x0ull;
|
||
|
} else { // y is not special
|
||
|
// check for non-canonical values - treated as zero
|
||
|
if ((y.w[1] & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // G0_G1=11
|
||
|
// non-canonical
|
||
|
y.w[1] = (y.w[1] & MASK_SIGN) | ((y.w[1] << 2) & MASK_EXP);
|
||
|
y.w[0] = 0x0ull;
|
||
|
} else { // G0_G1 != 11
|
||
|
if ((y.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull ||
|
||
|
((y.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull &&
|
||
|
y.w[0] > 0x378d8e63ffffffffull)) {
|
||
|
// y is non-canonical if coefficient is larger than 10^34 -1
|
||
|
y.w[1] = (y.w[1] & MASK_SIGN) | (y.w[1] & MASK_EXP);
|
||
|
y.w[0] = 0x0ull;
|
||
|
} else { // canonical
|
||
|
;
|
||
|
}
|
||
|
}
|
||
|
}
|
||
|
|
||
|
// NaN (CASE1)
|
||
|
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
|
||
|
if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNaN
|
||
|
// if x is SNAN, then return quiet (x)
|
||
|
*pfpsf |= INVALID_EXCEPTION; // set exception if SNaN
|
||
|
x.w[1] = x.w[1] & 0xfdffffffffffffffull; // quietize x
|
||
|
res = x;
|
||
|
} else { // x is QNaN
|
||
|
if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NAN
|
||
|
if ((y.w[1] & MASK_SNAN) == MASK_SNAN) { // y is SNAN
|
||
|
*pfpsf |= INVALID_EXCEPTION; // set invalid flag
|
||
|
}
|
||
|
res = x;
|
||
|
} else {
|
||
|
res = y;
|
||
|
}
|
||
|
}
|
||
|
BID_RETURN (res);
|
||
|
} else if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NaN, but x is not
|
||
|
if ((y.w[1] & MASK_SNAN) == MASK_SNAN) {
|
||
|
*pfpsf |= INVALID_EXCEPTION; // set exception if SNaN
|
||
|
y.w[1] = y.w[1] & 0xfdffffffffffffffull; // quietize y
|
||
|
res = y;
|
||
|
} else {
|
||
|
// will return x (which is not NaN)
|
||
|
res = x;
|
||
|
}
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
// SIMPLE (CASE2)
|
||
|
// if all the bits are the same, these numbers are equal (not Greater).
|
||
|
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
|
||
|
res = y;
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
// INFINITY (CASE3)
|
||
|
if ((x.w[1] & MASK_INF) == MASK_INF) {
|
||
|
// if x infinity, it has maximum magnitude
|
||
|
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN
|
||
|
&& (y.w[1] & MASK_INF) == MASK_INF) ? y : x;
|
||
|
BID_RETURN (res);
|
||
|
} else if ((y.w[1] & MASK_INF) == MASK_INF) {
|
||
|
// x is finite, so if y is positive infinity, then x is less, return 0
|
||
|
// if y is negative infinity, then x is greater, return 1
|
||
|
res = y;
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
// CONVERT X
|
||
|
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
|
||
|
sig_x.w[0] = x.w[0];
|
||
|
exp_x = (x.w[1] >> 49) & 0x000000000003fffull;
|
||
|
|
||
|
// CONVERT Y
|
||
|
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
|
||
|
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
|
||
|
sig_y.w[0] = y.w[0];
|
||
|
|
||
|
// ZERO (CASE4)
|
||
|
// some properties:
|
||
|
// (+ZERO == -ZERO) => therefore ignore the sign
|
||
|
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B =>
|
||
|
// therefore ignore the exponent field
|
||
|
// (Any non-canonical # is considered 0)
|
||
|
if ((sig_x.w[1] == 0) && (sig_x.w[0] == 0)) {
|
||
|
res = y;
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
if ((sig_y.w[1] == 0) && (sig_y.w[0] == 0)) {
|
||
|
res = x;
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
// REDUNDANT REPRESENTATIONS (CASE6)
|
||
|
if (exp_y == exp_x && sig_x.w[1] == sig_y.w[1]
|
||
|
&& sig_x.w[0] == sig_y.w[0]) {
|
||
|
// check if exponents are the same and significands are the same
|
||
|
if (x.w[1] & 0x8000000000000000ull) { // x is negative
|
||
|
res = y;
|
||
|
BID_RETURN (res);
|
||
|
} else {
|
||
|
res = x;
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
} else if (((sig_x.w[1] > sig_y.w[1] || (sig_x.w[1] == sig_y.w[1]
|
||
|
&& sig_x.w[0] > sig_y.w[0]))
|
||
|
&& exp_x == exp_y)
|
||
|
|| ((sig_x.w[1] > sig_y.w[1]
|
||
|
|| (sig_x.w[1] == sig_y.w[1]
|
||
|
&& sig_x.w[0] >= sig_y.w[0]))
|
||
|
&& exp_x > exp_y)) {
|
||
|
// if both components are either bigger or smaller, it is clear what
|
||
|
// needs to be done; also if the magnitudes are equal
|
||
|
res = x;
|
||
|
BID_RETURN (res);
|
||
|
} else if (((sig_y.w[1] > sig_x.w[1] || (sig_y.w[1] == sig_x.w[1]
|
||
|
&& sig_y.w[0] > sig_x.w[0]))
|
||
|
&& exp_y == exp_x)
|
||
|
|| ((sig_y.w[1] > sig_x.w[1]
|
||
|
|| (sig_y.w[1] == sig_x.w[1]
|
||
|
&& sig_y.w[0] >= sig_x.w[0]))
|
||
|
&& exp_y > exp_x)) {
|
||
|
res = y;
|
||
|
BID_RETURN (res);
|
||
|
} else {
|
||
|
; // continue
|
||
|
}
|
||
|
diff = exp_x - exp_y;
|
||
|
// if |exp_x - exp_y| < 33, it comes down to the compensated significand
|
||
|
if (diff > 0) { // to simplify the loop below,
|
||
|
// if exp_x is 33 greater than exp_y, no need for compensation
|
||
|
if (diff > 33) {
|
||
|
res = x; // difference cannot be greater than 10^33
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
if (diff > 19) { //128 by 128 bit multiply -> 256 bits
|
||
|
__mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]);
|
||
|
// if postitive, return whichever significand is larger
|
||
|
// (converse if negative)
|
||
|
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
|
||
|
&& sig_n_prime256.w[1] == sig_y.w[1]
|
||
|
&& (sig_n_prime256.w[0] == sig_y.w[0])) {
|
||
|
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? x : y; // if equal
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
res = (((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0)
|
||
|
|| (sig_n_prime256.w[1] > sig_y.w[1])
|
||
|
|| (sig_n_prime256.w[1] == sig_y.w[1]
|
||
|
&& sig_n_prime256.w[0] > sig_y.w[0])) ? x : y;
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
__mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_x);
|
||
|
// if postitive, return whichever significand is larger (converse if negative)
|
||
|
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1]
|
||
|
&& (sig_n_prime192.w[0] == sig_y.w[0])) {
|
||
|
// if equal, return positive magnitude
|
||
|
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? x : y;
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
res = ((sig_n_prime192.w[2] > 0)
|
||
|
|| (sig_n_prime192.w[1] > sig_y.w[1])
|
||
|
|| (sig_n_prime192.w[1] == sig_y.w[1]
|
||
|
&& sig_n_prime192.w[0] > sig_y.w[0])) ? x : y;
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
diff = exp_y - exp_x;
|
||
|
// if exp_x is 33 less than exp_y, no need for compensation
|
||
|
if (diff > 33) {
|
||
|
res = y;
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
if (diff > 19) { //128 by 128 bit multiply -> 256 bits
|
||
|
// adjust the y significand upwards
|
||
|
__mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]);
|
||
|
// if postitive, return whichever significand is larger
|
||
|
// (converse if negative)
|
||
|
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
|
||
|
&& sig_n_prime256.w[1] == sig_x.w[1]
|
||
|
&& (sig_n_prime256.w[0] == sig_x.w[0])) {
|
||
|
// if equal, return positive (if possible)
|
||
|
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? x : y;
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
res = (sig_n_prime256.w[3] == 0 && sig_n_prime256.w[2] == 0
|
||
|
&& (sig_n_prime256.w[1] < sig_x.w[1]
|
||
|
|| (sig_n_prime256.w[1] == sig_x.w[1]
|
||
|
&& sig_n_prime256.w[0] < sig_x.w[0]))) ? x : y;
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
// adjust the y significand upwards
|
||
|
__mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_y);
|
||
|
// if postitive, return whichever significand is larger (converse if negative)
|
||
|
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1]
|
||
|
&& (sig_n_prime192.w[0] == sig_x.w[0])) {
|
||
|
// if equal, return positive (if possible)
|
||
|
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? x : y;
|
||
|
BID_RETURN (res);
|
||
|
}
|
||
|
res = (sig_n_prime192.w[2] == 0
|
||
|
&& (sig_n_prime192.w[1] < sig_x.w[1]
|
||
|
|| (sig_n_prime192.w[1] == sig_x.w[1]
|
||
|
&& sig_n_prime192.w[0] < sig_x.w[0]))) ? x : y;
|
||
|
BID_RETURN (res);
|
||
|
}
|