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4347 lines
131 KiB
C
4347 lines
131 KiB
C
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/* Copyright (C) 2007, 2009 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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#include "bid_internal.h"
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BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_equal, x, y)
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int res;
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int exp_x, exp_y, exp_t;
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UINT128 sig_x, sig_y, sig_t;
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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, non_canon_x, non_canon_y;
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// NaN (CASE1)
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// if either number is NAN, the comparison is unordered,
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// rather than equal : return 0
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if (((x.w[1] & MASK_NAN) == MASK_NAN)
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|| ((y.w[1] & MASK_NAN) == MASK_NAN)) {
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if ((x.w[1] & MASK_SNAN) == MASK_SNAN
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|| (y.w[1] & MASK_SNAN) == MASK_SNAN) {
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*pfpsf |= INVALID_EXCEPTION;
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}
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{
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res = 0;
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BID_RETURN (res);
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}
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}
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// SIMPLE (CASE2)
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// if all the bits are the same, these numbers are equivalent.
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if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
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res = 1;
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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 ((y.w[1] & MASK_INF) == MASK_INF) {
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res = (((x.w[1] ^ y.w[1]) & MASK_SIGN) != MASK_SIGN);
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BID_RETURN (res);
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} else {
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res = 0;
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BID_RETURN (res);
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}
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}
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if ((y.w[1] & MASK_INF) == MASK_INF) {
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res = 0;
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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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// CHECK IF X IS CANONICAL
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// 9999999999999999999999999999999999(decimal) =
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// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
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// [0, 10^34) is the 754r supported canonical range.
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// If the value exceeds that, it is interpreted as 0.
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if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
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|| ((sig_x.w[1] == 0x0001ed09bead87c0ull)
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&& (sig_x.w[0] > 0x378d8e63ffffffffull))
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|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
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non_canon_x = 1;
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else
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non_canon_x = 0;
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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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// CHECK IF Y IS CANONICAL
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// 9999999999999999999999999999999999(decimal) =
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// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
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// [0, 10^34) is the 754r supported canonical range.
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// If the value exceeds that, it is interpreted as 0.
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if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
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|| ((sig_y.w[1] == 0x0001ed09bead87c0ull)
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&& (sig_y.w[0] > 0x378d8e63ffffffffull))
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|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
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non_canon_y = 1;
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else
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non_canon_y = 0;
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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 => therefore
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// ignore the exponent field
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// (Any non-canonical # is considered 0)
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if (non_canon_x || ((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 (non_canon_y || ((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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res = 1;
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BID_RETURN (res);
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} else if ((x_is_zero && !y_is_zero) || (!x_is_zero && y_is_zero)) {
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res = 0;
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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 => not equal : return 0
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if ((x.w[1] ^ y.w[1]) & MASK_SIGN) {
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res = 0;
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BID_RETURN (res);
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}
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// REDUNDANT REPRESENTATIONS (CASE6)
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if (exp_x > exp_y) { // to simplify the loop below,
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SWAP (exp_x, exp_y, exp_t); // put the larger exp in y,
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SWAP (sig_x.w[1], sig_y.w[1], sig_t.w[1]); // and the smaller exp in x
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SWAP (sig_x.w[0], sig_y.w[0], sig_t.w[0]); // and the smaller exp in x
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}
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if (exp_y - exp_x > 33) {
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res = 0;
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BID_RETURN (res);
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} // difference cannot be greater than 10^33
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if (exp_y - exp_x > 19) {
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// recalculate y's significand upwards
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__mul_128x128_to_256 (sig_n_prime256, sig_y,
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ten2k128[exp_y - exp_x - 20]);
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{
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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_x.w[1])
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&& (sig_n_prime256.w[0] == sig_x.w[0]));
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BID_RETURN (res);
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}
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}
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//else{
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// recalculate y's significand upwards
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__mul_64x128_to_192 (sig_n_prime192, ten2k64[exp_y - exp_x], sig_y);
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{
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res = ((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[0] == sig_x.w[0]));
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BID_RETURN (res);
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}
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}
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BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_greater, x,
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y)
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int 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, non_canon_x, non_canon_y;
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// NaN (CASE1)
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// if either number is NAN, the comparison is unordered, rather than
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// equal : return 0
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if (((x.w[1] & MASK_NAN) == MASK_NAN)
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|| ((y.w[1] & MASK_NAN) == MASK_NAN)) {
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if ((x.w[1] & MASK_SNAN) == MASK_SNAN
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|| (y.w[1] & MASK_SNAN) == MASK_SNAN) {
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*pfpsf |= INVALID_EXCEPTION;
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}
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{
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res = 0;
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BID_RETURN (res);
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}
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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 = 0;
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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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if (((x.w[1] & MASK_SIGN) == MASK_SIGN)) {
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res = 0;
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BID_RETURN (res);
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}
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// x is pos infinity, it is greater, unless y is positive infinity =>
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// return y!=pos_infinity
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else {
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res = (((y.w[1] & MASK_INF) != MASK_INF)
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|| ((y.w[1] & MASK_SIGN) == MASK_SIGN));
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BID_RETURN (res);
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}
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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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{
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res = ((y.w[1] & MASK_SIGN) == MASK_SIGN);
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BID_RETURN (res);
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}
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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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// CHECK IF X IS CANONICAL
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// 9999999999999999999999999999999999(decimal) =
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// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
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// [0, 10^34) is the 754r supported canonical range.
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// If the value exceeds that, it is interpreted as 0.
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if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
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|| ((sig_x.w[1] == 0x0001ed09bead87c0ull)
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&& (sig_x.w[0] > 0x378d8e63ffffffffull))
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|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
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non_canon_x = 1;
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else
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non_canon_x = 0;
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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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// CHECK IF Y IS CANONICAL
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// 9999999999999999999999999999999999(decimal) =
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// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
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// [0, 10^34) is the 754r supported canonical range.
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// If the value exceeds that, it is interpreted as 0.
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if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
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|| ((sig_y.w[1] == 0x0001ed09bead87c0ull)
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&& (sig_y.w[0] > 0x378d8e63ffffffffull))
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|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
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non_canon_y = 1;
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else
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non_canon_y = 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 => therefore
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// ignore the exponent field
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// (Any non-canonical # is considered 0)
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if (non_canon_x || ((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 (non_canon_y || ((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 both numbers are zero, neither is greater => return NOTGREATERTHAN
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if (x_is_zero && y_is_zero) {
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res = 0;
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BID_RETURN (res);
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}
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// is x is zero, it is greater if Y is negative
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else if (x_is_zero) {
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res = ((y.w[1] & MASK_SIGN) == MASK_SIGN);
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BID_RETURN (res);
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}
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// is y is zero, X is greater if it is positive
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else if (y_is_zero) {
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res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
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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);
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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
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// of 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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|
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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));
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BID_RETURN (res);
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}
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// if both components are either bigger or smaller,
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// it is clear what needs to be done
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||
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if ((sig_x.w[1] > sig_y.w[1]
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|
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|| (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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{
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res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
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BID_RETURN (res);
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}
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}
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if ((sig_x.w[1] < sig_y.w[1]
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|
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|| (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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{
|
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res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
|
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BID_RETURN (res);
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||
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}
|
||
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}
|
||
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|
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|
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diff = exp_x - exp_y;
|
||
|
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|
||
|
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// 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.w[1] & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // difference cannot be greater than 10^33
|
||
|
|
|
||
|
|
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 = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
//else { //128 by 64 bit multiply -> 192 bits
|
||
|
|
__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])) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
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);
|
||
|
|
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])) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
//else { //128 by 64 bit multiply -> 192 bits
|
||
|
|
// 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])) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int,
|
||
|
|
bid128_quiet_greater_equal, x,
|
||
|
|
y)
|
||
|
|
|
||
|
|
int 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, non_canon_x, non_canon_y;
|
||
|
|
|
||
|
|
// NaN (CASE1)
|
||
|
|
// if either number is NAN, the comparison is unordered,
|
||
|
|
// rather than equal : return 1
|
||
|
|
if (((x.w[1] & MASK_NAN) == MASK_NAN)
|
||
|
|
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) {
|
||
|
|
if ((x.w[1] & MASK_SNAN) == MASK_SNAN
|
||
|
|
|| (y.w[1] & MASK_SNAN) == MASK_SNAN) {
|
||
|
|
*pfpsf |= INVALID_EXCEPTION;
|
||
|
|
}
|
||
|
|
{
|
||
|
|
res = 0;
|
||
|
|
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 = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// INFINITY (CASE3)
|
||
|
|
if ((x.w[1] & MASK_INF) == MASK_INF) {
|
||
|
|
// if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) }
|
||
|
|
if ((x.w[1] & MASK_SIGN) == MASK_SIGN)
|
||
|
|
// x is -inf, so it is less than y unless y is -inf
|
||
|
|
{
|
||
|
|
res = (((y.w[1] & MASK_INF) == MASK_INF)
|
||
|
|
&& (y.w[1] & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
} else
|
||
|
|
// x is pos_inf, no way for it to be less than y
|
||
|
|
{
|
||
|
|
res = 1;
|
||
|
|
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);
|
||
|
|
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;
|
||
|
|
|
||
|
|
// CHECK IF X IS CANONICAL
|
||
|
|
// 9999999999999999999999999999999999(decimal) =
|
||
|
|
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
|
||
|
|
// [0, 10^34) is the 754r supported canonical range.
|
||
|
|
// If the value exceeds that, it is interpreted as 0.
|
||
|
|
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
|
||
|
|
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull)
|
||
|
|
&& (sig_x.w[0] > 0x378d8e63ffffffffull))
|
||
|
|
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
|
||
|
|
non_canon_x = 1;
|
||
|
|
else
|
||
|
|
non_canon_x = 0;
|
||
|
|
|
||
|
|
// CONVERT Y
|
||
|
|
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
|
||
|
|
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
|
||
|
|
sig_y.w[0] = y.w[0];
|
||
|
|
|
||
|
|
// CHECK IF Y IS CANONICAL
|
||
|
|
// 9999999999999999999999999999999999(decimal) =
|
||
|
|
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
|
||
|
|
// [0, 10^34) is the 754r supported canonical range.
|
||
|
|
// If the value exceeds that, it is interpreted as 0.
|
||
|
|
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
|
||
|
|
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull)
|
||
|
|
&& (sig_y.w[0] > 0x378d8e63ffffffffull))
|
||
|
|
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
|
||
|
|
non_canon_y = 1;
|
||
|
|
else
|
||
|
|
non_canon_y = 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 (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) {
|
||
|
|
x_is_zero = 1;
|
||
|
|
}
|
||
|
|
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) {
|
||
|
|
y_is_zero = 1;
|
||
|
|
}
|
||
|
|
// if both numbers are zero, neither is greater => return NOTGREATERTHAN
|
||
|
|
if (x_is_zero && y_is_zero) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// is x is zero, it is greater if Y is negative
|
||
|
|
else if (x_is_zero) {
|
||
|
|
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// is y is zero, X is greater if it is positive
|
||
|
|
else if (y_is_zero) {
|
||
|
|
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
|
||
|
|
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);
|
||
|
|
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));
|
||
|
|
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[0] >= sig_y.w[0]
|
||
|
|
&& exp_x > exp_y) {
|
||
|
|
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
if (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);
|
||
|
|
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) {
|
||
|
|
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // difference cannot be greater than 10^33
|
||
|
|
|
||
|
|
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 = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 1
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
//else { //128 by 64 bit multiply -> 192 bits
|
||
|
|
__mul_64x128_to192 (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])) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 1
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
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);
|
||
|
|
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])) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 1
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
//else { //128 by 64 bit multiply -> 192 bits
|
||
|
|
// adjust the y significand upwards
|
||
|
|
__mul_64x128_to192 (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])) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 1
|
||
|
|
{
|
||
|
|
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);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int,
|
||
|
|
bid128_quiet_greater_unordered,
|
||
|
|
x, y)
|
||
|
|
|
||
|
|
int 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, non_canon_x, non_canon_y;
|
||
|
|
|
||
|
|
// NaN (CASE1)
|
||
|
|
// if either number is NAN, the comparison is unordered,
|
||
|
|
// rather than
|
||
|
|
// equal : return 1
|
||
|
|
if (((x.w[1] & MASK_NAN) == MASK_NAN)
|
||
|
|
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) {
|
||
|
|
if ((x.w[1] & MASK_SNAN) == MASK_SNAN
|
||
|
|
|| (y.w[1] & MASK_SNAN) == MASK_SNAN) {
|
||
|
|
*pfpsf |= INVALID_EXCEPTION;
|
||
|
|
}
|
||
|
|
{
|
||
|
|
res = 1;
|
||
|
|
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 = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// INFINITY (CASE3)
|
||
|
|
if ((x.w[1] & MASK_INF) == MASK_INF) {
|
||
|
|
// if x is neg infinity, there is no way it is greater than y, return 0
|
||
|
|
if (((x.w[1] & MASK_SIGN) == MASK_SIGN)) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// x is pos infinity, it is greater, unless y is positive infinity =>
|
||
|
|
// return y!=pos_infinity
|
||
|
|
else {
|
||
|
|
res = (((y.w[1] & MASK_INF) != MASK_INF)
|
||
|
|
|| ((y.w[1] & MASK_SIGN) == MASK_SIGN));
|
||
|
|
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);
|
||
|
|
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;
|
||
|
|
|
||
|
|
// CHECK IF X IS CANONICAL
|
||
|
|
// 9999999999999999999999999999999999(decimal) =
|
||
|
|
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
|
||
|
|
// [0, 10^34) is the 754r supported canonical range.
|
||
|
|
// If the value exceeds that, it is interpreted as 0.
|
||
|
|
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
|
||
|
|
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull)
|
||
|
|
&& (sig_x.w[0] > 0x378d8e63ffffffffull))
|
||
|
|
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
|
||
|
|
non_canon_x = 1;
|
||
|
|
else
|
||
|
|
non_canon_x = 0;
|
||
|
|
|
||
|
|
// CONVERT Y
|
||
|
|
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
|
||
|
|
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
|
||
|
|
sig_y.w[0] = y.w[0];
|
||
|
|
|
||
|
|
// CHECK IF Y IS CANONICAL
|
||
|
|
// 9999999999999999999999999999999999(decimal) =
|
||
|
|
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
|
||
|
|
// [0, 10^34) is the 754r supported canonical range.
|
||
|
|
// If the value exceeds that, it is interpreted as 0.
|
||
|
|
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
|
||
|
|
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull)
|
||
|
|
&& (sig_y.w[0] > 0x378d8e63ffffffffull))
|
||
|
|
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
|
||
|
|
non_canon_y = 1;
|
||
|
|
else
|
||
|
|
non_canon_y = 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 (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) {
|
||
|
|
x_is_zero = 1;
|
||
|
|
}
|
||
|
|
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) {
|
||
|
|
y_is_zero = 1;
|
||
|
|
}
|
||
|
|
// if both numbers are zero, neither is greater => return NOTGREATERTHAN
|
||
|
|
if (x_is_zero && y_is_zero) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// is x is zero, it is greater if Y is negative
|
||
|
|
else if (x_is_zero) {
|
||
|
|
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// is y is zero, X is greater if it is positive
|
||
|
|
else if (y_is_zero) {
|
||
|
|
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
|
||
|
|
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);
|
||
|
|
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));
|
||
|
|
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[0] >= sig_y.w[0]
|
||
|
|
&& exp_x > exp_y) {
|
||
|
|
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
if (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);
|
||
|
|
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) {
|
||
|
|
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // difference cannot be greater than 10^33
|
||
|
|
|
||
|
|
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 = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
//else { //128 by 64 bit multiply -> 192 bits
|
||
|
|
__mul_64x128_to192 (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])) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
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);
|
||
|
|
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])) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
//else { //128 by 64 bit multiply -> 192 bits
|
||
|
|
// adjust the y significand upwards
|
||
|
|
__mul_64x128_to192 (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])) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_less, x, y)
|
||
|
|
|
||
|
|
int 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, non_canon_x, non_canon_y;
|
||
|
|
|
||
|
|
// NaN (CASE1)
|
||
|
|
// if either number is NAN, the comparison is unordered,
|
||
|
|
// rather than equal : return 0
|
||
|
|
if (((x.w[1] & MASK_NAN) == MASK_NAN)
|
||
|
|
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) {
|
||
|
|
if ((x.w[1] & MASK_SNAN) == MASK_SNAN
|
||
|
|
|| (y.w[1] & MASK_SNAN) == MASK_SNAN) {
|
||
|
|
*pfpsf |= INVALID_EXCEPTION;
|
||
|
|
}
|
||
|
|
{
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
// SIMPLE (CASE2)
|
||
|
|
// if all the bits are the same, these numbers are equal.
|
||
|
|
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// INFINITY (CASE3)
|
||
|
|
if ((x.w[1] & MASK_INF) == MASK_INF) {
|
||
|
|
// if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) }
|
||
|
|
if ((x.w[1] & MASK_SIGN) == MASK_SIGN)
|
||
|
|
// x is -inf, so it is less than y unless y is -inf
|
||
|
|
{
|
||
|
|
res = (((y.w[1] & MASK_INF) != MASK_INF)
|
||
|
|
|| (y.w[1] & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
} else
|
||
|
|
// x is pos_inf, no way for it to be less than y
|
||
|
|
{
|
||
|
|
res = 0;
|
||
|
|
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);
|
||
|
|
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;
|
||
|
|
|
||
|
|
// CHECK IF X IS CANONICAL
|
||
|
|
// 9999999999999999999999999999999999(decimal) =
|
||
|
|
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
|
||
|
|
// [0, 10^34) is the 754r supported canonical range.
|
||
|
|
// If the value exceeds that, it is interpreted as 0.
|
||
|
|
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
|
||
|
|
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull)
|
||
|
|
&& (sig_x.w[0] > 0x378d8e63ffffffffull))
|
||
|
|
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
|
||
|
|
non_canon_x = 1;
|
||
|
|
else
|
||
|
|
non_canon_x = 0;
|
||
|
|
|
||
|
|
// CONVERT Y
|
||
|
|
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
|
||
|
|
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
|
||
|
|
sig_y.w[0] = y.w[0];
|
||
|
|
|
||
|
|
// CHECK IF Y IS CANONICAL
|
||
|
|
// 9999999999999999999999999999999999(decimal) =
|
||
|
|
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
|
||
|
|
// [0, 10^34) is the 754r supported canonical range.
|
||
|
|
// If the value exceeds that, it is interpreted as 0.
|
||
|
|
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
|
||
|
|
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull)
|
||
|
|
&& (sig_y.w[0] > 0x378d8e63ffffffffull))
|
||
|
|
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
|
||
|
|
non_canon_y = 1;
|
||
|
|
else
|
||
|
|
non_canon_y = 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 (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) {
|
||
|
|
x_is_zero = 1;
|
||
|
|
}
|
||
|
|
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) {
|
||
|
|
y_is_zero = 1;
|
||
|
|
}
|
||
|
|
// if both numbers are zero, neither is greater => return NOTGREATERTHAN
|
||
|
|
if (x_is_zero && y_is_zero) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// is x is zero, it is greater if Y is negative
|
||
|
|
else if (x_is_zero) {
|
||
|
|
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// is y is zero, X is greater if it is positive
|
||
|
|
else if (y_is_zero) {
|
||
|
|
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
|
||
|
|
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);
|
||
|
|
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));
|
||
|
|
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);
|
||
|
|
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);
|
||
|
|
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) {
|
||
|
|
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // difference cannot be greater than 10^33
|
||
|
|
|
||
|
|
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 = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
//else { //128 by 64 bit multiply -> 192 bits
|
||
|
|
__mul_64x128_to192 (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])) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
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);
|
||
|
|
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])) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 1
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
//else { //128 by 64 bit multiply -> 192 bits
|
||
|
|
// adjust the y significand upwards
|
||
|
|
__mul_64x128_to192 (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])) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_less_equal,
|
||
|
|
x, y)
|
||
|
|
|
||
|
|
int 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, non_canon_x, non_canon_y;
|
||
|
|
|
||
|
|
// NaN (CASE1)
|
||
|
|
// if either number is NAN, the comparison is unordered,
|
||
|
|
// rather than equal : return 0
|
||
|
|
if (((x.w[1] & MASK_NAN) == MASK_NAN)
|
||
|
|
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) {
|
||
|
|
if ((x.w[1] & MASK_SNAN) == MASK_SNAN
|
||
|
|
|| (y.w[1] & MASK_SNAN) == MASK_SNAN) {
|
||
|
|
*pfpsf |= INVALID_EXCEPTION;
|
||
|
|
}
|
||
|
|
{
|
||
|
|
res = 0;
|
||
|
|
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 = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// INFINITY (CASE3)
|
||
|
|
if ((x.w[1] & MASK_INF) == MASK_INF) {
|
||
|
|
// if x is neg infinity, there is no way it is greater than y, return 1
|
||
|
|
if (((x.w[1] & MASK_SIGN) == MASK_SIGN)) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// x is pos infinity, it is greater, unless y is positive infinity =>
|
||
|
|
// return y!=pos_infinity
|
||
|
|
else {
|
||
|
|
res = (((y.w[1] & MASK_INF) == MASK_INF)
|
||
|
|
&& ((y.w[1] & MASK_SIGN) != MASK_SIGN));
|
||
|
|
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);
|
||
|
|
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;
|
||
|
|
|
||
|
|
// CHECK IF X IS CANONICAL
|
||
|
|
// 9999999999999999999999999999999999(decimal) =
|
||
|
|
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
|
||
|
|
// [0, 10^34) is the 754r supported canonical range.
|
||
|
|
// If the value exceeds that, it is interpreted as 0.
|
||
|
|
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
|
||
|
|
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull)
|
||
|
|
&& (sig_x.w[0] > 0x378d8e63ffffffffull))
|
||
|
|
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
|
||
|
|
non_canon_x = 1;
|
||
|
|
else
|
||
|
|
non_canon_x = 0;
|
||
|
|
|
||
|
|
// CONVERT Y
|
||
|
|
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
|
||
|
|
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
|
||
|
|
sig_y.w[0] = y.w[0];
|
||
|
|
|
||
|
|
// CHECK IF Y IS CANONICAL
|
||
|
|
// 9999999999999999999999999999999999(decimal) =
|
||
|
|
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
|
||
|
|
// [0, 10^34) is the 754r supported canonical range.
|
||
|
|
// If the value exceeds that, it is interpreted as 0.
|
||
|
|
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
|
||
|
|
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull)
|
||
|
|
&& (sig_y.w[0] > 0x378d8e63ffffffffull))
|
||
|
|
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
|
||
|
|
non_canon_y = 1;
|
||
|
|
else
|
||
|
|
non_canon_y = 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 (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) {
|
||
|
|
x_is_zero = 1;
|
||
|
|
}
|
||
|
|
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) {
|
||
|
|
y_is_zero = 1;
|
||
|
|
}
|
||
|
|
// if both numbers are zero, neither is greater => return NOTGREATERTHAN
|
||
|
|
if (x_is_zero && y_is_zero) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// is x is zero, it is greater if Y is negative
|
||
|
|
else if (x_is_zero) {
|
||
|
|
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// is y is zero, X is greater if it is positive
|
||
|
|
else if (y_is_zero) {
|
||
|
|
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
|
||
|
|
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);
|
||
|
|
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));
|
||
|
|
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);
|
||
|
|
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);
|
||
|
|
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) {
|
||
|
|
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // difference cannot be greater than 10^33
|
||
|
|
|
||
|
|
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 = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
//else { //128 by 64 bit multiply -> 192 bits
|
||
|
|
__mul_64x128_to192 (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])) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
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);
|
||
|
|
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])) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
//else { //128 by 64 bit multiply -> 192 bits
|
||
|
|
// adjust the y significand upwards
|
||
|
|
__mul_64x128_to192 (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])) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int,
|
||
|
|
bid128_quiet_less_unordered,
|
||
|
|
x, y)
|
||
|
|
|
||
|
|
int 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, non_canon_x, non_canon_y;
|
||
|
|
|
||
|
|
// NaN (CASE1)
|
||
|
|
// if either number is NAN, the comparison is unordered
|
||
|
|
if (((x.w[1] & MASK_NAN) == MASK_NAN)
|
||
|
|
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) {
|
||
|
|
if ((x.w[1] & MASK_SNAN) == MASK_SNAN
|
||
|
|
|| (y.w[1] & MASK_SNAN) == MASK_SNAN) {
|
||
|
|
*pfpsf |= INVALID_EXCEPTION;
|
||
|
|
}
|
||
|
|
{
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
// SIMPLE (CASE2)
|
||
|
|
// if all the bits are the same, these numbers are equal.
|
||
|
|
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// INFINITY (CASE3)
|
||
|
|
if ((x.w[1] & MASK_INF) == MASK_INF) {
|
||
|
|
// if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) }
|
||
|
|
if ((x.w[1] & MASK_SIGN) == MASK_SIGN)
|
||
|
|
// x is -inf, so it is less than y unless y is -inf
|
||
|
|
{
|
||
|
|
res = (((y.w[1] & MASK_INF) != MASK_INF)
|
||
|
|
|| (y.w[1] & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
} else
|
||
|
|
// x is pos_inf, no way for it to be less than y
|
||
|
|
{
|
||
|
|
res = 0;
|
||
|
|
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);
|
||
|
|
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;
|
||
|
|
|
||
|
|
// CHECK IF X IS CANONICAL
|
||
|
|
// 9999999999999999999999999999999999(decimal) =
|
||
|
|
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
|
||
|
|
// [0, 10^34) is the 754r supported canonical range.
|
||
|
|
// If the value exceeds that, it is interpreted as 0.
|
||
|
|
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
|
||
|
|
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull)
|
||
|
|
&& (sig_x.w[0] > 0x378d8e63ffffffffull))
|
||
|
|
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
|
||
|
|
non_canon_x = 1;
|
||
|
|
else
|
||
|
|
non_canon_x = 0;
|
||
|
|
|
||
|
|
// CONVERT Y
|
||
|
|
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
|
||
|
|
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
|
||
|
|
sig_y.w[0] = y.w[0];
|
||
|
|
|
||
|
|
// CHECK IF Y IS CANONICAL
|
||
|
|
// 9999999999999999999999999999999999(decimal) =
|
||
|
|
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
|
||
|
|
// [0, 10^34) is the 754r supported canonical range.
|
||
|
|
// If the value exceeds that, it is interpreted as 0.
|
||
|
|
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
|
||
|
|
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull)
|
||
|
|
&& (sig_y.w[0] > 0x378d8e63ffffffffull))
|
||
|
|
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
|
||
|
|
non_canon_y = 1;
|
||
|
|
else
|
||
|
|
non_canon_y = 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 (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) {
|
||
|
|
x_is_zero = 1;
|
||
|
|
}
|
||
|
|
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) {
|
||
|
|
y_is_zero = 1;
|
||
|
|
}
|
||
|
|
// if both numbers are zero, neither is greater => return NOTGREATERTHAN
|
||
|
|
if (x_is_zero && y_is_zero) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// is x is zero, it is greater if Y is negative
|
||
|
|
else if (x_is_zero) {
|
||
|
|
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// is y is zero, X is greater if it is positive
|
||
|
|
else if (y_is_zero) {
|
||
|
|
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
|
||
|
|
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);
|
||
|
|
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));
|
||
|
|
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);
|
||
|
|
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);
|
||
|
|
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) {
|
||
|
|
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // difference cannot be greater than 10^33
|
||
|
|
|
||
|
|
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 = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
//else { //128 by 64 bit multiply -> 192 bits
|
||
|
|
__mul_64x128_to192 (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])) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
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);
|
||
|
|
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])) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 1
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
//else { //128 by 64 bit multiply -> 192 bits
|
||
|
|
// adjust the y significand upwards
|
||
|
|
__mul_64x128_to192 (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])) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_not_equal,
|
||
|
|
x, y)
|
||
|
|
|
||
|
|
int res;
|
||
|
|
int exp_x, exp_y, exp_t;
|
||
|
|
UINT128 sig_x, sig_y, sig_t;
|
||
|
|
UINT192 sig_n_prime192;
|
||
|
|
UINT256 sig_n_prime256;
|
||
|
|
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y;
|
||
|
|
|
||
|
|
// NaN (CASE1)
|
||
|
|
// if either number is NAN, the comparison is unordered,
|
||
|
|
// rather than equal : return 0
|
||
|
|
if (((x.w[1] & MASK_NAN) == MASK_NAN)
|
||
|
|
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) {
|
||
|
|
if ((x.w[1] & MASK_SNAN) == MASK_SNAN
|
||
|
|
|| (y.w[1] & MASK_SNAN) == MASK_SNAN) {
|
||
|
|
*pfpsf |= INVALID_EXCEPTION;
|
||
|
|
}
|
||
|
|
{
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
// SIMPLE (CASE2)
|
||
|
|
// if all the bits are the same, these numbers are equivalent.
|
||
|
|
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// INFINITY (CASE3)
|
||
|
|
if ((x.w[1] & MASK_INF) == MASK_INF) {
|
||
|
|
if ((y.w[1] & MASK_INF) == MASK_INF) {
|
||
|
|
res = (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
} else {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
if ((y.w[1] & MASK_INF) == MASK_INF) {
|
||
|
|
res = 1;
|
||
|
|
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;
|
||
|
|
|
||
|
|
// CHECK IF X IS CANONICAL
|
||
|
|
// 9999999999999999999999999999999999(decimal) =
|
||
|
|
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
|
||
|
|
// [0, 10^34) is the 754r supported canonical range.
|
||
|
|
// If the value exceeds that, it is interpreted as 0.
|
||
|
|
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
|
||
|
|
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull)
|
||
|
|
&& (sig_x.w[0] > 0x378d8e63ffffffffull))
|
||
|
|
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
|
||
|
|
non_canon_x = 1;
|
||
|
|
else
|
||
|
|
non_canon_x = 0;
|
||
|
|
|
||
|
|
// CONVERT Y
|
||
|
|
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
|
||
|
|
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
|
||
|
|
sig_y.w[0] = y.w[0];
|
||
|
|
|
||
|
|
// CHECK IF Y IS CANONICAL
|
||
|
|
// 9999999999999999999999999999999999(decimal) =
|
||
|
|
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
|
||
|
|
// [0, 10^34) is the 754r supported canonical range.
|
||
|
|
// If the value exceeds that, it is interpreted as 0.
|
||
|
|
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
|
||
|
|
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull)
|
||
|
|
&& (sig_y.w[0] > 0x378d8e63ffffffffull))
|
||
|
|
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
|
||
|
|
non_canon_y = 1;
|
||
|
|
else
|
||
|
|
non_canon_y = 0;
|
||
|
|
|
||
|
|
// 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 (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) {
|
||
|
|
x_is_zero = 1;
|
||
|
|
}
|
||
|
|
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) {
|
||
|
|
y_is_zero = 1;
|
||
|
|
}
|
||
|
|
|
||
|
|
if (x_is_zero && y_is_zero) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} else if ((x_is_zero && !y_is_zero) || (!x_is_zero && y_is_zero)) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// OPPOSITE SIGN (CASE5)
|
||
|
|
// now, if the sign bits differ => not equal : return 0
|
||
|
|
if ((x.w[1] ^ y.w[1]) & MASK_SIGN) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// REDUNDANT REPRESENTATIONS (CASE6)
|
||
|
|
if (exp_x > exp_y) { // to simplify the loop below,
|
||
|
|
SWAP (exp_x, exp_y, exp_t); // put the larger exp in y,
|
||
|
|
SWAP (sig_x.w[1], sig_y.w[1], sig_t.w[1]); // and the smaller exp in x
|
||
|
|
SWAP (sig_x.w[0], sig_y.w[0], sig_t.w[0]); // and the smaller exp in x
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
if (exp_y - exp_x > 33) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // difference cannot be greater than 10^33
|
||
|
|
|
||
|
|
if (exp_y - exp_x > 19) {
|
||
|
|
// recalculate y's significand upwards
|
||
|
|
__mul_128x128_to_256 (sig_n_prime256, sig_y,
|
||
|
|
ten2k128[exp_y - exp_x - 20]);
|
||
|
|
{
|
||
|
|
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[0] != sig_x.w[0]));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
|
||
|
|
}
|
||
|
|
//else{
|
||
|
|
// recalculate y's significand upwards
|
||
|
|
__mul_64x128_to192 (sig_n_prime192, ten2k64[exp_y - exp_x], sig_y);
|
||
|
|
{
|
||
|
|
res = ((sig_n_prime192.w[2] != 0)
|
||
|
|
|| (sig_n_prime192.w[1] != sig_x.w[1])
|
||
|
|
|| (sig_n_prime192.w[0] != sig_x.w[0]));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_not_greater,
|
||
|
|
x, y)
|
||
|
|
|
||
|
|
int 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, non_canon_x, non_canon_y;
|
||
|
|
|
||
|
|
// NaN (CASE1)
|
||
|
|
// if either number is NAN, the comparison is unordered,
|
||
|
|
// rather than equal : return 0
|
||
|
|
if (((x.w[1] & MASK_NAN) == MASK_NAN)
|
||
|
|
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) {
|
||
|
|
if ((x.w[1] & MASK_SNAN) == MASK_SNAN
|
||
|
|
|| (y.w[1] & MASK_SNAN) == MASK_SNAN) {
|
||
|
|
*pfpsf |= INVALID_EXCEPTION;
|
||
|
|
}
|
||
|
|
{
|
||
|
|
res = 1;
|
||
|
|
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 = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// INFINITY (CASE3)
|
||
|
|
if ((x.w[1] & MASK_INF) == MASK_INF) {
|
||
|
|
// if x is neg infinity, there is no way it is greater than y, return 1
|
||
|
|
if (((x.w[1] & MASK_SIGN) == MASK_SIGN)) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// x is pos infinity, it is greater, unless y is positive infinity => return y!=pos_infinity
|
||
|
|
else {
|
||
|
|
res = (((y.w[1] & MASK_INF) == MASK_INF)
|
||
|
|
&& ((y.w[1] & MASK_SIGN) != MASK_SIGN));
|
||
|
|
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);
|
||
|
|
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;
|
||
|
|
|
||
|
|
// CHECK IF X IS CANONICAL
|
||
|
|
// 9999999999999999999999999999999999(decimal) =
|
||
|
|
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
|
||
|
|
// [0, 10^34) is the 754r supported canonical range.
|
||
|
|
// If the value exceeds that, it is interpreted as 0.
|
||
|
|
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
|
||
|
|
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull)
|
||
|
|
&& (sig_x.w[0] > 0x378d8e63ffffffffull))
|
||
|
|
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
|
||
|
|
non_canon_x = 1;
|
||
|
|
else
|
||
|
|
non_canon_x = 0;
|
||
|
|
|
||
|
|
// CONVERT Y
|
||
|
|
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
|
||
|
|
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
|
||
|
|
sig_y.w[0] = y.w[0];
|
||
|
|
|
||
|
|
// CHECK IF Y IS CANONICAL
|
||
|
|
// 9999999999999999999999999999999999(decimal) =
|
||
|
|
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
|
||
|
|
// [0, 10^34) is the 754r supported canonical range.
|
||
|
|
// If the value exceeds that, it is interpreted as 0.
|
||
|
|
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
|
||
|
|
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull)
|
||
|
|
&& (sig_y.w[0] > 0x378d8e63ffffffffull))
|
||
|
|
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
|
||
|
|
non_canon_y = 1;
|
||
|
|
else
|
||
|
|
non_canon_y = 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 (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) {
|
||
|
|
x_is_zero = 1;
|
||
|
|
}
|
||
|
|
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) {
|
||
|
|
y_is_zero = 1;
|
||
|
|
}
|
||
|
|
// if both numbers are zero, neither is greater => return NOTGREATERTHAN
|
||
|
|
if (x_is_zero && y_is_zero) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// is x is zero, it is greater if Y is negative
|
||
|
|
else if (x_is_zero) {
|
||
|
|
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// is y is zero, X is greater if it is positive
|
||
|
|
else if (y_is_zero) {
|
||
|
|
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
|
||
|
|
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);
|
||
|
|
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));
|
||
|
|
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);
|
||
|
|
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);
|
||
|
|
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) {
|
||
|
|
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // difference cannot be greater than 10^33
|
||
|
|
|
||
|
|
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 = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
//else { //128 by 64 bit multiply -> 192 bits
|
||
|
|
__mul_64x128_to192 (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])) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
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);
|
||
|
|
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])) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
//else { //128 by 64 bit multiply -> 192 bits
|
||
|
|
// adjust the y significand upwards
|
||
|
|
__mul_64x128_to192 (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])) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_not_less, x,
|
||
|
|
y)
|
||
|
|
|
||
|
|
int 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, non_canon_x, non_canon_y;
|
||
|
|
|
||
|
|
// NaN (CASE1)
|
||
|
|
// if either number is NAN, the comparison is unordered,
|
||
|
|
// rather than equal : return 1
|
||
|
|
if (((x.w[1] & MASK_NAN) == MASK_NAN)
|
||
|
|
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) {
|
||
|
|
if ((x.w[1] & MASK_SNAN) == MASK_SNAN
|
||
|
|
|| (y.w[1] & MASK_SNAN) == MASK_SNAN) {
|
||
|
|
*pfpsf |= INVALID_EXCEPTION;
|
||
|
|
}
|
||
|
|
{
|
||
|
|
res = 1;
|
||
|
|
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 = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// INFINITY (CASE3)
|
||
|
|
if ((x.w[1] & MASK_INF) == MASK_INF) {
|
||
|
|
// if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) }
|
||
|
|
if ((x.w[1] & MASK_SIGN) == MASK_SIGN)
|
||
|
|
// x is -inf, so it is less than y unless y is -inf
|
||
|
|
{
|
||
|
|
res = (((y.w[1] & MASK_INF) == MASK_INF)
|
||
|
|
&& (y.w[1] & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
} else
|
||
|
|
// x is pos_inf, no way for it to be less than y
|
||
|
|
{
|
||
|
|
res = 1;
|
||
|
|
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);
|
||
|
|
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;
|
||
|
|
|
||
|
|
// CHECK IF X IS CANONICAL
|
||
|
|
// 9999999999999999999999999999999999(decimal) =
|
||
|
|
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
|
||
|
|
// [0, 10^34) is the 754r supported canonical range.
|
||
|
|
// If the value exceeds that, it is interpreted as 0.
|
||
|
|
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
|
||
|
|
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull)
|
||
|
|
&& (sig_x.w[0] > 0x378d8e63ffffffffull))
|
||
|
|
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
|
||
|
|
non_canon_x = 1;
|
||
|
|
else
|
||
|
|
non_canon_x = 0;
|
||
|
|
|
||
|
|
// CONVERT Y
|
||
|
|
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
|
||
|
|
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
|
||
|
|
sig_y.w[0] = y.w[0];
|
||
|
|
|
||
|
|
// CHECK IF Y IS CANONICAL
|
||
|
|
// 9999999999999999999999999999999999(decimal) =
|
||
|
|
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
|
||
|
|
// [0, 10^34) is the 754r supported canonical range.
|
||
|
|
// If the value exceeds that, it is interpreted as 0.
|
||
|
|
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
|
||
|
|
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull)
|
||
|
|
&& (sig_y.w[0] > 0x378d8e63ffffffffull))
|
||
|
|
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
|
||
|
|
non_canon_y = 1;
|
||
|
|
else
|
||
|
|
non_canon_y = 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 (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) {
|
||
|
|
x_is_zero = 1;
|
||
|
|
}
|
||
|
|
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) {
|
||
|
|
y_is_zero = 1;
|
||
|
|
}
|
||
|
|
// if both numbers are zero, neither is greater => return NOTGREATERTHAN
|
||
|
|
if (x_is_zero && y_is_zero) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// is x is zero, it is greater if Y is negative
|
||
|
|
else if (x_is_zero) {
|
||
|
|
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// is y is zero, X is greater if it is positive
|
||
|
|
else if (y_is_zero) {
|
||
|
|
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
|
||
|
|
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);
|
||
|
|
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));
|
||
|
|
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[0] >= sig_y.w[0]
|
||
|
|
&& exp_x > exp_y) {
|
||
|
|
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
if (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);
|
||
|
|
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) {
|
||
|
|
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // difference cannot be greater than 10^33
|
||
|
|
|
||
|
|
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 = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 1
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
//else { //128 by 64 bit multiply -> 192 bits
|
||
|
|
__mul_64x128_to192 (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])) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 1
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
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);
|
||
|
|
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])) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 1
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
//else { //128 by 64 bit multiply -> 192 bits
|
||
|
|
// adjust the y significand upwards
|
||
|
|
__mul_64x128_to192 (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])) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 1
|
||
|
|
{
|
||
|
|
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);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_ordered, x,
|
||
|
|
y)
|
||
|
|
|
||
|
|
int res;
|
||
|
|
|
||
|
|
// NaN (CASE1)
|
||
|
|
// if either number is NAN, the comparison is ordered : return 1
|
||
|
|
if (((x.w[1] & MASK_NAN) == MASK_NAN)
|
||
|
|
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) {
|
||
|
|
if ((x.w[1] & MASK_SNAN) == MASK_SNAN
|
||
|
|
|| (y.w[1] & MASK_SNAN) == MASK_SNAN) {
|
||
|
|
*pfpsf |= INVALID_EXCEPTION;
|
||
|
|
}
|
||
|
|
{
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
{
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_unordered,
|
||
|
|
x, y)
|
||
|
|
|
||
|
|
int res;
|
||
|
|
|
||
|
|
// NaN (CASE1)
|
||
|
|
// if either number is NAN, the comparison is unordered : return 1
|
||
|
|
if (((x.w[1] & MASK_NAN) == MASK_NAN)
|
||
|
|
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) {
|
||
|
|
if ((x.w[1] & MASK_SNAN) == MASK_SNAN
|
||
|
|
|| (y.w[1] & MASK_SNAN) == MASK_SNAN) {
|
||
|
|
*pfpsf |= INVALID_EXCEPTION;
|
||
|
|
}
|
||
|
|
{
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
{
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_signaling_greater,
|
||
|
|
x, y)
|
||
|
|
|
||
|
|
int 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, non_canon_x, non_canon_y;
|
||
|
|
|
||
|
|
// NaN (CASE1)
|
||
|
|
// if either number is NAN, the comparison is unordered,
|
||
|
|
// rather than equal : return 0
|
||
|
|
if (((x.w[1] & MASK_NAN) == MASK_NAN)
|
||
|
|
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) {
|
||
|
|
*pfpsf |= INVALID_EXCEPTION;
|
||
|
|
{
|
||
|
|
res = 0;
|
||
|
|
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 = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// INFINITY (CASE3)
|
||
|
|
if ((x.w[1] & MASK_INF) == MASK_INF) {
|
||
|
|
// if x is neg infinity, there is no way it is greater than y, return 0
|
||
|
|
if (((x.w[1] & MASK_SIGN) == MASK_SIGN)) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// x is pos infinity, it is greater, unless y is positive infinity => return y!=pos_infinity
|
||
|
|
else {
|
||
|
|
res = (((y.w[1] & MASK_INF) != MASK_INF)
|
||
|
|
|| ((y.w[1] & MASK_SIGN) == MASK_SIGN));
|
||
|
|
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);
|
||
|
|
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;
|
||
|
|
|
||
|
|
// CHECK IF X IS CANONICAL
|
||
|
|
// 9999999999999999999999999999999999(decimal) =
|
||
|
|
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
|
||
|
|
// [0, 10^34) is the 754r supported canonical range.
|
||
|
|
// If the value exceeds that, it is interpreted as 0.
|
||
|
|
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
|
||
|
|
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull)
|
||
|
|
&& (sig_x.w[0] > 0x378d8e63ffffffffull))
|
||
|
|
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
|
||
|
|
non_canon_x = 1;
|
||
|
|
else
|
||
|
|
non_canon_x = 0;
|
||
|
|
|
||
|
|
// CONVERT Y
|
||
|
|
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
|
||
|
|
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
|
||
|
|
sig_y.w[0] = y.w[0];
|
||
|
|
|
||
|
|
// CHECK IF Y IS CANONICAL
|
||
|
|
// 9999999999999999999999999999999999(decimal) =
|
||
|
|
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
|
||
|
|
// [0, 10^34) is the 754r supported canonical range.
|
||
|
|
// If the value exceeds that, it is interpreted as 0.
|
||
|
|
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
|
||
|
|
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull)
|
||
|
|
&& (sig_y.w[0] > 0x378d8e63ffffffffull))
|
||
|
|
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
|
||
|
|
non_canon_y = 1;
|
||
|
|
else
|
||
|
|
non_canon_y = 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 (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) {
|
||
|
|
x_is_zero = 1;
|
||
|
|
}
|
||
|
|
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) {
|
||
|
|
y_is_zero = 1;
|
||
|
|
}
|
||
|
|
// if both numbers are zero, neither is greater => return NOTGREATERTHAN
|
||
|
|
if (x_is_zero && y_is_zero) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// is x is zero, it is greater if Y is negative
|
||
|
|
else if (x_is_zero) {
|
||
|
|
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// is y is zero, X is greater if it is positive
|
||
|
|
else if (y_is_zero) {
|
||
|
|
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
|
||
|
|
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);
|
||
|
|
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));
|
||
|
|
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);
|
||
|
|
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);
|
||
|
|
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) {
|
||
|
|
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // difference cannot be greater than 10^33
|
||
|
|
|
||
|
|
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 = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
//else { //128 by 64 bit multiply -> 192 bits
|
||
|
|
__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])) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
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);
|
||
|
|
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])) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
//else { //128 by 64 bit multiply -> 192 bits
|
||
|
|
// 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])) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int,
|
||
|
|
bid128_signaling_greater_equal,
|
||
|
|
x, y)
|
||
|
|
|
||
|
|
int 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, non_canon_x, non_canon_y;
|
||
|
|
|
||
|
|
// NaN (CASE1)
|
||
|
|
// if either number is NAN, the comparison is unordered,
|
||
|
|
// rather than equal : return 1
|
||
|
|
if (((x.w[1] & MASK_NAN) == MASK_NAN)
|
||
|
|
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) {
|
||
|
|
*pfpsf |= INVALID_EXCEPTION;
|
||
|
|
{
|
||
|
|
res = 0;
|
||
|
|
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 = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// INFINITY (CASE3)
|
||
|
|
if ((x.w[1] & MASK_INF) == MASK_INF) {
|
||
|
|
// if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) }
|
||
|
|
if ((x.w[1] & MASK_SIGN) == MASK_SIGN)
|
||
|
|
// x is -inf, so it is less than y unless y is -inf
|
||
|
|
{
|
||
|
|
res = (((y.w[1] & MASK_INF) == MASK_INF)
|
||
|
|
&& (y.w[1] & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
} else
|
||
|
|
// x is pos_inf, no way for it to be less than y
|
||
|
|
{
|
||
|
|
res = 1;
|
||
|
|
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);
|
||
|
|
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;
|
||
|
|
|
||
|
|
// CHECK IF X IS CANONICAL
|
||
|
|
// 9999999999999999999999999999999999(decimal) =
|
||
|
|
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
|
||
|
|
// [0, 10^34) is the 754r supported canonical range.
|
||
|
|
// If the value exceeds that, it is interpreted as 0.
|
||
|
|
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
|
||
|
|
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull)
|
||
|
|
&& (sig_x.w[0] > 0x378d8e63ffffffffull))
|
||
|
|
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
|
||
|
|
non_canon_x = 1;
|
||
|
|
else
|
||
|
|
non_canon_x = 0;
|
||
|
|
|
||
|
|
// CONVERT Y
|
||
|
|
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
|
||
|
|
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
|
||
|
|
sig_y.w[0] = y.w[0];
|
||
|
|
|
||
|
|
// CHECK IF Y IS CANONICAL
|
||
|
|
// 9999999999999999999999999999999999(decimal) =
|
||
|
|
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
|
||
|
|
// [0, 10^34) is the 754r supported canonical range.
|
||
|
|
// If the value exceeds that, it is interpreted as 0.
|
||
|
|
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
|
||
|
|
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull)
|
||
|
|
&& (sig_y.w[0] > 0x378d8e63ffffffffull))
|
||
|
|
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
|
||
|
|
non_canon_y = 1;
|
||
|
|
else
|
||
|
|
non_canon_y = 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 (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) {
|
||
|
|
x_is_zero = 1;
|
||
|
|
}
|
||
|
|
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) {
|
||
|
|
y_is_zero = 1;
|
||
|
|
}
|
||
|
|
// if both numbers are zero, neither is greater => return NOTGREATERTHAN
|
||
|
|
if (x_is_zero && y_is_zero) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// is x is zero, it is greater if Y is negative
|
||
|
|
else if (x_is_zero) {
|
||
|
|
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// is y is zero, X is greater if it is positive
|
||
|
|
else if (y_is_zero) {
|
||
|
|
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
|
||
|
|
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);
|
||
|
|
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));
|
||
|
|
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[0] >= sig_y.w[0]
|
||
|
|
&& exp_x > exp_y) {
|
||
|
|
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
if (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);
|
||
|
|
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) {
|
||
|
|
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // difference cannot be greater than 10^33
|
||
|
|
|
||
|
|
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 = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 1
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
//else { //128 by 64 bit multiply -> 192 bits
|
||
|
|
__mul_64x128_to192 (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])) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 1
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
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);
|
||
|
|
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])) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 1
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
//else { //128 by 64 bit multiply -> 192 bits
|
||
|
|
// adjust the y significand upwards
|
||
|
|
__mul_64x128_to192 (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])) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 1
|
||
|
|
{
|
||
|
|
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);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int,
|
||
|
|
bid128_signaling_greater_unordered,
|
||
|
|
x, y)
|
||
|
|
|
||
|
|
int 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, non_canon_x, non_canon_y;
|
||
|
|
|
||
|
|
// NaN (CASE1)
|
||
|
|
// if either number is NAN, the comparison is unordered,
|
||
|
|
// rather than equal : return 1
|
||
|
|
if (((x.w[1] & MASK_NAN) == MASK_NAN)
|
||
|
|
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) {
|
||
|
|
*pfpsf |= INVALID_EXCEPTION;
|
||
|
|
{
|
||
|
|
res = 1;
|
||
|
|
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 = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// INFINITY (CASE3)
|
||
|
|
if ((x.w[1] & MASK_INF) == MASK_INF) {
|
||
|
|
// if x is neg infinity, there is no way it is greater than y, return 0
|
||
|
|
if (((x.w[1] & MASK_SIGN) == MASK_SIGN)) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// x is pos infinity, it is greater, unless y is positive infinity => return y!=pos_infinity
|
||
|
|
else {
|
||
|
|
res = (((y.w[1] & MASK_INF) != MASK_INF)
|
||
|
|
|| ((y.w[1] & MASK_SIGN) == MASK_SIGN));
|
||
|
|
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);
|
||
|
|
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;
|
||
|
|
|
||
|
|
// CHECK IF X IS CANONICAL
|
||
|
|
// 9999999999999999999999999999999999(decimal) =
|
||
|
|
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
|
||
|
|
// [0, 10^34) is the 754r supported canonical range.
|
||
|
|
// If the value exceeds that, it is interpreted as 0.
|
||
|
|
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
|
||
|
|
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull)
|
||
|
|
&& (sig_x.w[0] > 0x378d8e63ffffffffull))
|
||
|
|
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
|
||
|
|
non_canon_x = 1;
|
||
|
|
else
|
||
|
|
non_canon_x = 0;
|
||
|
|
|
||
|
|
// CONVERT Y
|
||
|
|
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
|
||
|
|
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
|
||
|
|
sig_y.w[0] = y.w[0];
|
||
|
|
|
||
|
|
// CHECK IF Y IS CANONICAL
|
||
|
|
// 9999999999999999999999999999999999(decimal) =
|
||
|
|
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
|
||
|
|
// [0, 10^34) is the 754r supported canonical range.
|
||
|
|
// If the value exceeds that, it is interpreted as 0.
|
||
|
|
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
|
||
|
|
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull)
|
||
|
|
&& (sig_y.w[0] > 0x378d8e63ffffffffull))
|
||
|
|
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
|
||
|
|
non_canon_y = 1;
|
||
|
|
else
|
||
|
|
non_canon_y = 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 (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) {
|
||
|
|
x_is_zero = 1;
|
||
|
|
}
|
||
|
|
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) {
|
||
|
|
y_is_zero = 1;
|
||
|
|
}
|
||
|
|
// if both numbers are zero, neither is greater => return NOTGREATERTHAN
|
||
|
|
if (x_is_zero && y_is_zero) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// is x is zero, it is greater if Y is negative
|
||
|
|
else if (x_is_zero) {
|
||
|
|
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// is y is zero, X is greater if it is positive
|
||
|
|
else if (y_is_zero) {
|
||
|
|
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
|
||
|
|
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);
|
||
|
|
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));
|
||
|
|
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[0] >= sig_y.w[0]
|
||
|
|
&& exp_x > exp_y) {
|
||
|
|
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
if (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);
|
||
|
|
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) {
|
||
|
|
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // difference cannot be greater than 10^33
|
||
|
|
|
||
|
|
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 = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
//else { //128 by 64 bit multiply -> 192 bits
|
||
|
|
__mul_64x128_to192 (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])) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
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);
|
||
|
|
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])) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
//else { //128 by 64 bit multiply -> 192 bits
|
||
|
|
// adjust the y significand upwards
|
||
|
|
__mul_64x128_to192 (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])) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_signaling_less, x,
|
||
|
|
y)
|
||
|
|
|
||
|
|
int 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, non_canon_x, non_canon_y;
|
||
|
|
|
||
|
|
// NaN (CASE1)
|
||
|
|
// if either number is NAN, the comparison is unordered,
|
||
|
|
// rather than equal : return 0
|
||
|
|
if (((x.w[1] & MASK_NAN) == MASK_NAN)
|
||
|
|
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) {
|
||
|
|
*pfpsf |= INVALID_EXCEPTION;
|
||
|
|
{
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
// SIMPLE (CASE2)
|
||
|
|
// if all the bits are the same, these numbers are equal.
|
||
|
|
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// INFINITY (CASE3)
|
||
|
|
if ((x.w[1] & MASK_INF) == MASK_INF) {
|
||
|
|
// if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) }
|
||
|
|
if ((x.w[1] & MASK_SIGN) == MASK_SIGN)
|
||
|
|
// x is -inf, so it is less than y unless y is -inf
|
||
|
|
{
|
||
|
|
res = (((y.w[1] & MASK_INF) != MASK_INF)
|
||
|
|
|| (y.w[1] & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
} else
|
||
|
|
// x is pos_inf, no way for it to be less than y
|
||
|
|
{
|
||
|
|
res = 0;
|
||
|
|
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);
|
||
|
|
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;
|
||
|
|
|
||
|
|
// CHECK IF X IS CANONICAL
|
||
|
|
// 9999999999999999999999999999999999(decimal) =
|
||
|
|
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
|
||
|
|
// [0, 10^34) is the 754r supported canonical range.
|
||
|
|
// If the value exceeds that, it is interpreted as 0.
|
||
|
|
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
|
||
|
|
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull)
|
||
|
|
&& (sig_x.w[0] > 0x378d8e63ffffffffull))
|
||
|
|
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
|
||
|
|
non_canon_x = 1;
|
||
|
|
else
|
||
|
|
non_canon_x = 0;
|
||
|
|
|
||
|
|
// CONVERT Y
|
||
|
|
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
|
||
|
|
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
|
||
|
|
sig_y.w[0] = y.w[0];
|
||
|
|
|
||
|
|
// CHECK IF Y IS CANONICAL
|
||
|
|
// 9999999999999999999999999999999999(decimal) =
|
||
|
|
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
|
||
|
|
// [0, 10^34) is the 754r supported canonical range.
|
||
|
|
// If the value exceeds that, it is interpreted as 0.
|
||
|
|
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
|
||
|
|
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull)
|
||
|
|
&& (sig_y.w[0] > 0x378d8e63ffffffffull))
|
||
|
|
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
|
||
|
|
non_canon_y = 1;
|
||
|
|
else
|
||
|
|
non_canon_y = 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 (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) {
|
||
|
|
x_is_zero = 1;
|
||
|
|
}
|
||
|
|
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) {
|
||
|
|
y_is_zero = 1;
|
||
|
|
}
|
||
|
|
// if both numbers are zero, neither is greater => return NOTGREATERTHAN
|
||
|
|
if (x_is_zero && y_is_zero) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// is x is zero, it is greater if Y is negative
|
||
|
|
else if (x_is_zero) {
|
||
|
|
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// is y is zero, X is greater if it is positive
|
||
|
|
else if (y_is_zero) {
|
||
|
|
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
|
||
|
|
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);
|
||
|
|
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));
|
||
|
|
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);
|
||
|
|
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);
|
||
|
|
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) {
|
||
|
|
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // difference cannot be greater than 10^33
|
||
|
|
|
||
|
|
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 = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
//else { //128 by 64 bit multiply -> 192 bits
|
||
|
|
__mul_64x128_to192 (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])) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
diff = exp_y - exp_x;
|
||
|
|
|
||
|
|
// if exp_x is 33 less than exp_y, |x| < |y|, return 1 if positive
|
||
|
|
if (diff > 33) {
|
||
|
|
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
|
||
|
|
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])) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 1
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
//else { //128 by 64 bit multiply -> 192 bits
|
||
|
|
// adjust the y significand upwards
|
||
|
|
__mul_64x128_to192 (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])) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int,
|
||
|
|
bid128_signaling_less_equal,
|
||
|
|
x, y)
|
||
|
|
|
||
|
|
int 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, non_canon_x, non_canon_y;
|
||
|
|
|
||
|
|
// NaN (CASE1)
|
||
|
|
// if either number is NAN, the comparison is unordered,
|
||
|
|
// rather than equal : return 0
|
||
|
|
if (((x.w[1] & MASK_NAN) == MASK_NAN)
|
||
|
|
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) {
|
||
|
|
*pfpsf |= INVALID_EXCEPTION;
|
||
|
|
{
|
||
|
|
res = 0;
|
||
|
|
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 = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// INFINITY (CASE3)
|
||
|
|
if ((x.w[1] & MASK_INF) == MASK_INF) {
|
||
|
|
// if x is neg infinity, there is no way it is greater than y, return 1
|
||
|
|
if (((x.w[1] & MASK_SIGN) == MASK_SIGN)) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// x is pos infinity, it is greater, unless y is positive infinity => return y!=pos_infinity
|
||
|
|
else {
|
||
|
|
res = (((y.w[1] & MASK_INF) == MASK_INF)
|
||
|
|
&& ((y.w[1] & MASK_SIGN) != MASK_SIGN));
|
||
|
|
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);
|
||
|
|
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;
|
||
|
|
|
||
|
|
// CHECK IF X IS CANONICAL
|
||
|
|
// 9999999999999999999999999999999999(decimal) =
|
||
|
|
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
|
||
|
|
// [0, 10^34) is the 754r supported canonical range.
|
||
|
|
// If the value exceeds that, it is interpreted as 0.
|
||
|
|
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
|
||
|
|
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull)
|
||
|
|
&& (sig_x.w[0] > 0x378d8e63ffffffffull))
|
||
|
|
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
|
||
|
|
non_canon_x = 1;
|
||
|
|
else
|
||
|
|
non_canon_x = 0;
|
||
|
|
|
||
|
|
// CONVERT Y
|
||
|
|
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
|
||
|
|
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
|
||
|
|
sig_y.w[0] = y.w[0];
|
||
|
|
|
||
|
|
// CHECK IF Y IS CANONICAL
|
||
|
|
// 9999999999999999999999999999999999(decimal) =
|
||
|
|
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
|
||
|
|
// [0, 10^34) is the 754r supported canonical range.
|
||
|
|
// If the value exceeds that, it is interpreted as 0.
|
||
|
|
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
|
||
|
|
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull)
|
||
|
|
&& (sig_y.w[0] > 0x378d8e63ffffffffull))
|
||
|
|
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
|
||
|
|
non_canon_y = 1;
|
||
|
|
else
|
||
|
|
non_canon_y = 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 (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) {
|
||
|
|
x_is_zero = 1;
|
||
|
|
}
|
||
|
|
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) {
|
||
|
|
y_is_zero = 1;
|
||
|
|
}
|
||
|
|
// if both numbers are zero, neither is greater => return NOTGREATERTHAN
|
||
|
|
if (x_is_zero && y_is_zero) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// is x is zero, it is greater if Y is negative
|
||
|
|
else if (x_is_zero) {
|
||
|
|
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// is y is zero, X is greater if it is positive
|
||
|
|
else if (y_is_zero) {
|
||
|
|
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
|
||
|
|
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);
|
||
|
|
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));
|
||
|
|
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);
|
||
|
|
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);
|
||
|
|
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) {
|
||
|
|
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // difference cannot be greater than 10^33
|
||
|
|
|
||
|
|
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 = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
//else { //128 by 64 bit multiply -> 192 bits
|
||
|
|
__mul_64x128_to192 (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])) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
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);
|
||
|
|
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])) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
//else { //128 by 64 bit multiply -> 192 bits
|
||
|
|
// adjust the y significand upwards
|
||
|
|
__mul_64x128_to192 (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])) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int,
|
||
|
|
bid128_signaling_less_unordered,
|
||
|
|
x, y)
|
||
|
|
|
||
|
|
int 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, non_canon_x, non_canon_y;
|
||
|
|
|
||
|
|
// NaN (CASE1)
|
||
|
|
// if either number is NAN, the comparison is unordered
|
||
|
|
if (((x.w[1] & MASK_NAN) == MASK_NAN)
|
||
|
|
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) {
|
||
|
|
*pfpsf |= INVALID_EXCEPTION;
|
||
|
|
{
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
// SIMPLE (CASE2)
|
||
|
|
// if all the bits are the same, these numbers are equal.
|
||
|
|
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// INFINITY (CASE3)
|
||
|
|
if ((x.w[1] & MASK_INF) == MASK_INF) {
|
||
|
|
// if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) }
|
||
|
|
if ((x.w[1] & MASK_SIGN) == MASK_SIGN)
|
||
|
|
// x is -inf, so it is less than y unless y is -inf
|
||
|
|
{
|
||
|
|
res = (((y.w[1] & MASK_INF) != MASK_INF)
|
||
|
|
|| (y.w[1] & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
} else
|
||
|
|
// x is pos_inf, no way for it to be less than y
|
||
|
|
{
|
||
|
|
res = 0;
|
||
|
|
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);
|
||
|
|
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;
|
||
|
|
|
||
|
|
// CHECK IF X IS CANONICAL
|
||
|
|
// 9999999999999999999999999999999999(decimal) =
|
||
|
|
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
|
||
|
|
// [0, 10^34) is the 754r supported canonical range.
|
||
|
|
// If the value exceeds that, it is interpreted as 0.
|
||
|
|
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
|
||
|
|
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull)
|
||
|
|
&& (sig_x.w[0] > 0x378d8e63ffffffffull))
|
||
|
|
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
|
||
|
|
non_canon_x = 1;
|
||
|
|
else
|
||
|
|
non_canon_x = 0;
|
||
|
|
|
||
|
|
// CONVERT Y
|
||
|
|
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
|
||
|
|
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
|
||
|
|
sig_y.w[0] = y.w[0];
|
||
|
|
|
||
|
|
// CHECK IF Y IS CANONICAL
|
||
|
|
// 9999999999999999999999999999999999(decimal) =
|
||
|
|
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
|
||
|
|
// [0, 10^34) is the 754r supported canonical range.
|
||
|
|
// If the value exceeds that, it is interpreted as 0.
|
||
|
|
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
|
||
|
|
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull)
|
||
|
|
&& (sig_y.w[0] > 0x378d8e63ffffffffull))
|
||
|
|
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
|
||
|
|
non_canon_y = 1;
|
||
|
|
else
|
||
|
|
non_canon_y = 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 (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) {
|
||
|
|
x_is_zero = 1;
|
||
|
|
}
|
||
|
|
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) {
|
||
|
|
y_is_zero = 1;
|
||
|
|
}
|
||
|
|
// if both numbers are zero, neither is greater => return NOTGREATERTHAN
|
||
|
|
if (x_is_zero && y_is_zero) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// is x is zero, it is greater if Y is negative
|
||
|
|
else if (x_is_zero) {
|
||
|
|
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// is y is zero, X is greater if it is positive
|
||
|
|
else if (y_is_zero) {
|
||
|
|
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
|
||
|
|
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);
|
||
|
|
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));
|
||
|
|
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);
|
||
|
|
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);
|
||
|
|
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) {
|
||
|
|
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // difference cannot be greater than 10^33
|
||
|
|
|
||
|
|
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 = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
//else { //128 by 64 bit multiply -> 192 bits
|
||
|
|
__mul_64x128_to192 (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])) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
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);
|
||
|
|
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])) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 1
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
//else { //128 by 64 bit multiply -> 192 bits
|
||
|
|
// adjust the y significand upwards
|
||
|
|
__mul_64x128_to192 (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])) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int,
|
||
|
|
bid128_signaling_not_greater,
|
||
|
|
x, y)
|
||
|
|
|
||
|
|
int 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, non_canon_x, non_canon_y;
|
||
|
|
|
||
|
|
// NaN (CASE1)
|
||
|
|
// if either number is NAN, the comparison is unordered,
|
||
|
|
// rather than equal : return 0
|
||
|
|
if (((x.w[1] & MASK_NAN) == MASK_NAN)
|
||
|
|
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) {
|
||
|
|
*pfpsf |= INVALID_EXCEPTION;
|
||
|
|
{
|
||
|
|
res = 1;
|
||
|
|
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 = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// INFINITY (CASE3)
|
||
|
|
if ((x.w[1] & MASK_INF) == MASK_INF) {
|
||
|
|
// if x is neg infinity, there is no way it is greater than y, return 1
|
||
|
|
if (((x.w[1] & MASK_SIGN) == MASK_SIGN)) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// x is pos infinity, it is greater, unless y is positive infinity => return y!=pos_infinity
|
||
|
|
else {
|
||
|
|
res = (((y.w[1] & MASK_INF) == MASK_INF)
|
||
|
|
&& ((y.w[1] & MASK_SIGN) != MASK_SIGN));
|
||
|
|
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);
|
||
|
|
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;
|
||
|
|
|
||
|
|
// CHECK IF X IS CANONICAL
|
||
|
|
// 9999999999999999999999999999999999(decimal) =
|
||
|
|
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
|
||
|
|
// [0, 10^34) is the 754r supported canonical range.
|
||
|
|
// If the value exceeds that, it is interpreted as 0.
|
||
|
|
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
|
||
|
|
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull)
|
||
|
|
&& (sig_x.w[0] > 0x378d8e63ffffffffull))
|
||
|
|
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
|
||
|
|
non_canon_x = 1;
|
||
|
|
else
|
||
|
|
non_canon_x = 0;
|
||
|
|
|
||
|
|
// CONVERT Y
|
||
|
|
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
|
||
|
|
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
|
||
|
|
sig_y.w[0] = y.w[0];
|
||
|
|
|
||
|
|
// CHECK IF Y IS CANONICAL
|
||
|
|
// 9999999999999999999999999999999999(decimal) =
|
||
|
|
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
|
||
|
|
// [0, 10^34) is the 754r supported canonical range.
|
||
|
|
// If the value exceeds that, it is interpreted as 0.
|
||
|
|
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
|
||
|
|
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull)
|
||
|
|
&& (sig_y.w[0] > 0x378d8e63ffffffffull))
|
||
|
|
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
|
||
|
|
non_canon_y = 1;
|
||
|
|
else
|
||
|
|
non_canon_y = 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 (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) {
|
||
|
|
x_is_zero = 1;
|
||
|
|
}
|
||
|
|
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) {
|
||
|
|
y_is_zero = 1;
|
||
|
|
}
|
||
|
|
// if both numbers are zero, neither is greater => return NOTGREATERTHAN
|
||
|
|
if (x_is_zero && y_is_zero) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// is x is zero, it is greater if Y is negative
|
||
|
|
else if (x_is_zero) {
|
||
|
|
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// is y is zero, X is greater if it is positive
|
||
|
|
else if (y_is_zero) {
|
||
|
|
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
|
||
|
|
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);
|
||
|
|
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));
|
||
|
|
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);
|
||
|
|
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);
|
||
|
|
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) {
|
||
|
|
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // difference cannot be greater than 10^33
|
||
|
|
|
||
|
|
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 = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
//else { //128 by 64 bit multiply -> 192 bits
|
||
|
|
__mul_64x128_to192 (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])) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
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);
|
||
|
|
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])) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
//else { //128 by 64 bit multiply -> 192 bits
|
||
|
|
// adjust the y significand upwards
|
||
|
|
__mul_64x128_to192 (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])) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 0
|
||
|
|
{
|
||
|
|
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);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int,
|
||
|
|
bid128_signaling_not_less, x,
|
||
|
|
y)
|
||
|
|
|
||
|
|
int 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, non_canon_x, non_canon_y;
|
||
|
|
|
||
|
|
// NaN (CASE1)
|
||
|
|
// if either number is NAN, the comparison is unordered,
|
||
|
|
// rather than equal : return 1
|
||
|
|
if (((x.w[1] & MASK_NAN) == MASK_NAN)
|
||
|
|
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) {
|
||
|
|
*pfpsf |= INVALID_EXCEPTION;
|
||
|
|
{
|
||
|
|
res = 1;
|
||
|
|
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 = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// INFINITY (CASE3)
|
||
|
|
if ((x.w[1] & MASK_INF) == MASK_INF) {
|
||
|
|
// if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) }
|
||
|
|
if ((x.w[1] & MASK_SIGN) == MASK_SIGN)
|
||
|
|
// x is -inf, so it is less than y unless y is -inf
|
||
|
|
{
|
||
|
|
res = (((y.w[1] & MASK_INF) == MASK_INF)
|
||
|
|
&& (y.w[1] & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
} else
|
||
|
|
// x is pos_inf, no way for it to be less than y
|
||
|
|
{
|
||
|
|
res = 1;
|
||
|
|
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);
|
||
|
|
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;
|
||
|
|
|
||
|
|
// CHECK IF X IS CANONICAL
|
||
|
|
// 9999999999999999999999999999999999(decimal) =
|
||
|
|
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
|
||
|
|
// [0, 10^34) is the 754r supported canonical range.
|
||
|
|
// If the value exceeds that, it is interpreted as 0.
|
||
|
|
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
|
||
|
|
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull)
|
||
|
|
&& (sig_x.w[0] > 0x378d8e63ffffffffull))
|
||
|
|
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
|
||
|
|
non_canon_x = 1;
|
||
|
|
else
|
||
|
|
non_canon_x = 0;
|
||
|
|
|
||
|
|
// CONVERT Y
|
||
|
|
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
|
||
|
|
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
|
||
|
|
sig_y.w[0] = y.w[0];
|
||
|
|
|
||
|
|
// CHECK IF Y IS CANONICAL
|
||
|
|
// 9999999999999999999999999999999999(decimal) =
|
||
|
|
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
|
||
|
|
// [0, 10^34) is the 754r supported canonical range.
|
||
|
|
// If the value exceeds that, it is interpreted as 0.
|
||
|
|
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
|
||
|
|
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull)
|
||
|
|
&& (sig_y.w[0] > 0x378d8e63ffffffffull))
|
||
|
|
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
|
||
|
|
non_canon_y = 1;
|
||
|
|
else
|
||
|
|
non_canon_y = 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 (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) {
|
||
|
|
x_is_zero = 1;
|
||
|
|
}
|
||
|
|
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) {
|
||
|
|
y_is_zero = 1;
|
||
|
|
}
|
||
|
|
// if both numbers are zero, neither is greater => return NOTGREATERTHAN
|
||
|
|
if (x_is_zero && y_is_zero) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// is x is zero, it is greater if Y is negative
|
||
|
|
else if (x_is_zero) {
|
||
|
|
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// is y is zero, X is greater if it is positive
|
||
|
|
else if (y_is_zero) {
|
||
|
|
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
|
||
|
|
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);
|
||
|
|
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));
|
||
|
|
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[0] >= sig_y.w[0]
|
||
|
|
&& exp_x > exp_y) {
|
||
|
|
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
if (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);
|
||
|
|
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) {
|
||
|
|
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // difference cannot be greater than 10^33
|
||
|
|
|
||
|
|
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 = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 1
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
//else { //128 by 64 bit multiply -> 192 bits
|
||
|
|
__mul_64x128_to192 (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])) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 1
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
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);
|
||
|
|
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])) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 1
|
||
|
|
{
|
||
|
|
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));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
//else { //128 by 64 bit multiply -> 192 bits
|
||
|
|
// adjust the y significand upwards
|
||
|
|
__mul_64x128_to192 (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])) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} // if equal, return 1
|
||
|
|
{
|
||
|
|
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);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|