forked from KolibriOS/kolibrios
3173 lines
93 KiB
C
3173 lines
93 KiB
C
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/* Copyright (C) 2007-2015 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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static const UINT64 mult_factor[16] = {
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1ull, 10ull, 100ull, 1000ull,
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10000ull, 100000ull, 1000000ull, 10000000ull,
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100000000ull, 1000000000ull, 10000000000ull, 100000000000ull,
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1000000000000ull, 10000000000000ull,
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100000000000000ull, 1000000000000000ull
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};
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#if DECIMAL_CALL_BY_REFERENCE
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void
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bid64_quiet_equal (int *pres, UINT64 * px,
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UINT64 *
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py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
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_EXC_INFO_PARAM) {
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UINT64 x = *px;
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UINT64 y = *py;
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#else
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int
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bid64_quiet_equal (UINT64 x,
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UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
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_EXC_INFO_PARAM) {
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#endif
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int res;
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int exp_x, exp_y, exp_t;
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UINT64 sig_x, sig_y, sig_t;
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char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y, lcv;
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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 & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
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if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) {
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*pfpsf |= INVALID_EXCEPTION; // set exception if sNaN
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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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// SIMPLE (CASE2)
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// if all the bits are the same, these numbers are equivalent.
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if (x == y) {
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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 & MASK_INF) == MASK_INF) && ((y & MASK_INF) == MASK_INF)) {
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res = (((x ^ y) & MASK_SIGN) != MASK_SIGN);
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BID_RETURN (res);
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}
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// ONE INFINITY (CASE3')
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if (((x & MASK_INF) == MASK_INF) || ((y & 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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// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
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if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
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exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
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sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
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if (sig_x > 9999999999999999ull) {
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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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}
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} else {
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exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
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sig_x = (x & MASK_BINARY_SIG1);
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non_canon_x = 0;
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}
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// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
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if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
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exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
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sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
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if (sig_y > 9999999999999999ull) {
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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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}
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} else {
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exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
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sig_y = (y & MASK_BINARY_SIG1);
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non_canon_y = 0;
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}
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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 =>
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// therefore ignore the exponent field
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// (Any non-canonical # is considered 0)
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if (non_canon_x || sig_x == 0) {
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x_is_zero = 1;
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}
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if (non_canon_y || sig_y == 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 ^ y) & 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, sig_y, sig_t); // and the smaller exp in x
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}
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if (exp_y - exp_x > 15) {
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res = 0; // difference cannot be greater than 10^15
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BID_RETURN (res);
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}
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for (lcv = 0; lcv < (exp_y - exp_x); lcv++) {
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// recalculate y's significand upwards
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sig_y = sig_y * 10;
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if (sig_y > 9999999999999999ull) {
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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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res = (sig_y == sig_x);
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BID_RETURN (res);
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}
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#if DECIMAL_CALL_BY_REFERENCE
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void
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bid64_quiet_greater (int *pres, UINT64 * px,
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UINT64 *
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py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
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_EXC_INFO_PARAM) {
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UINT64 x = *px;
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UINT64 y = *py;
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#else
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int
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bid64_quiet_greater (UINT64 x,
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UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
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_EXC_INFO_PARAM) {
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#endif
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int res;
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int exp_x, exp_y;
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UINT64 sig_x, sig_y;
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UINT128 sig_n_prime;
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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 equal :
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// return 0
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if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
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if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) {
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*pfpsf |= INVALID_EXCEPTION; // set exception if sNaN
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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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// 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 == y) {
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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 & 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 & MASK_SIGN) == MASK_SIGN)) {
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res = 0;
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BID_RETURN (res);
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} else {
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// x is pos infinity, it is greater, unless y is positive
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// infinity => return y!=pos_infinity
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res = (((y & MASK_INF) != MASK_INF)
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|| ((y & MASK_SIGN) == MASK_SIGN));
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BID_RETURN (res);
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}
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} else if ((y & MASK_INF) == MASK_INF) {
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// x is finite, so if y is positive infinity, then x is less, return 0
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// if y is negative infinity, then x is greater, return 1
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res = ((y & MASK_SIGN) == MASK_SIGN);
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BID_RETURN (res);
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}
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// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
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if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
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exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
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sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
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if (sig_x > 9999999999999999ull) {
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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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}
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} else {
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exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
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sig_x = (x & MASK_BINARY_SIG1);
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non_canon_x = 0;
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}
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// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
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if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
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exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
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sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
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if (sig_y > 9999999999999999ull) {
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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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}
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} else {
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exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
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sig_y = (y & MASK_BINARY_SIG1);
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non_canon_y = 0;
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}
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// ZERO (CASE4)
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// some properties:
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//(+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater
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//(ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore ignore the
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// exponent field
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// (Any non-canonical # is considered 0)
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if (non_canon_x || sig_x == 0) {
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x_is_zero = 1;
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}
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if (non_canon_y || sig_y == 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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} else if (x_is_zero) {
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// is x is zero, it is greater if Y is negative
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res = ((y & MASK_SIGN) == MASK_SIGN);
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BID_RETURN (res);
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} else if (y_is_zero) {
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// is y is zero, X is greater if it is positive
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res = ((x & 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 ^ y) & MASK_SIGN) == MASK_SIGN) {
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res = ((y & 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 both components are either bigger or smaller,
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// it is clear what needs to be done
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if (sig_x > sig_y && exp_x > exp_y) {
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res = ((x & MASK_SIGN) != MASK_SIGN);
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BID_RETURN (res);
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}
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if (sig_x < sig_y && exp_x < exp_y) {
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res = ((x & MASK_SIGN) == MASK_SIGN);
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BID_RETURN (res);
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}
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// if exp_x is 15 greater than exp_y, no need for compensation
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if (exp_x - exp_y > 15) { // difference cannot be greater than 10^15
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if (x & MASK_SIGN) // if both are negative
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res = 0;
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else // if both are positive
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res = 1;
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BID_RETURN (res);
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}
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// if exp_x is 15 less than exp_y, no need for compensation
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if (exp_y - exp_x > 15) {
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if (x & MASK_SIGN) // if both are negative
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res = 1;
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else // if both are positive
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res = 0;
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BID_RETURN (res);
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}
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// if |exp_x - exp_y| < 15, it comes down to the compensated significand
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if (exp_x > exp_y) { // to simplify the loop below,
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// otherwise adjust the x significand upwards
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__mul_64x64_to_128MACH (sig_n_prime, sig_x,
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mult_factor[exp_x - exp_y]);
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// if postitive, return whichever significand is larger (converse if neg.)
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if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
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res = 0;
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BID_RETURN (res);
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}
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res = (((sig_n_prime.w[1] > 0)
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|| sig_n_prime.w[0] > sig_y) ^ ((x & MASK_SIGN) ==
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MASK_SIGN));
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BID_RETURN (res);
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}
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// adjust the y significand upwards
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__mul_64x64_to_128MACH (sig_n_prime, sig_y,
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mult_factor[exp_y - exp_x]);
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// if postitive, return whichever significand is larger
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// (converse if negative)
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if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
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res = 0;
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BID_RETURN (res);
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}
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res = (((sig_n_prime.w[1] == 0)
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&& (sig_x > sig_n_prime.w[0])) ^ ((x & MASK_SIGN) ==
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MASK_SIGN));
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BID_RETURN (res);
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}
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||
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|
||
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
||
|
|
void
|
||
|
|
bid64_quiet_greater_equal (int *pres, UINT64 * px,
|
||
|
|
UINT64 *
|
||
|
|
py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
||
|
|
_EXC_INFO_PARAM) {
|
||
|
|
UINT64 x = *px;
|
||
|
|
UINT64 y = *py;
|
||
|
|
#else
|
||
|
|
int
|
||
|
|
bid64_quiet_greater_equal (UINT64 x,
|
||
|
|
UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
||
|
|
_EXC_INFO_PARAM) {
|
||
|
|
#endif
|
||
|
|
int res;
|
||
|
|
int exp_x, exp_y;
|
||
|
|
UINT64 sig_x, sig_y;
|
||
|
|
UINT128 sig_n_prime;
|
||
|
|
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 : return 1
|
||
|
|
if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
|
||
|
|
if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) {
|
||
|
|
*pfpsf |= INVALID_EXCEPTION; // set exception if sNaN
|
||
|
|
}
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// SIMPLE (CASE2)
|
||
|
|
// if all the bits are the same, these numbers are equal.
|
||
|
|
if (x == y) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// INFINITY (CASE3)
|
||
|
|
if ((x & MASK_INF) == MASK_INF) {
|
||
|
|
// if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) }
|
||
|
|
if ((x & MASK_SIGN) == MASK_SIGN) {
|
||
|
|
// x is -inf, so it is less than y unless y is -inf
|
||
|
|
res = (((y & MASK_INF) == MASK_INF)
|
||
|
|
&& (y & 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 & MASK_INF) == MASK_INF) {
|
||
|
|
// x is finite, so:
|
||
|
|
// if y is +inf, x<y
|
||
|
|
// if y is -inf, x>y
|
||
|
|
res = ((y & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
||
|
|
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
||
|
|
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
|
||
|
|
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
||
|
|
if (sig_x > 9999999999999999ull) {
|
||
|
|
non_canon_x = 1;
|
||
|
|
} else {
|
||
|
|
non_canon_x = 0;
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
|
||
|
|
sig_x = (x & MASK_BINARY_SIG1);
|
||
|
|
non_canon_x = 0;
|
||
|
|
}
|
||
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
||
|
|
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
||
|
|
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
|
||
|
|
sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
||
|
|
if (sig_y > 9999999999999999ull) {
|
||
|
|
non_canon_y = 1;
|
||
|
|
} else {
|
||
|
|
non_canon_y = 0;
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
|
||
|
|
sig_y = (y & MASK_BINARY_SIG1);
|
||
|
|
non_canon_y = 0;
|
||
|
|
}
|
||
|
|
// ZERO (CASE4)
|
||
|
|
// some properties:
|
||
|
|
// (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater
|
||
|
|
// (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 == 0) {
|
||
|
|
x_is_zero = 1;
|
||
|
|
}
|
||
|
|
if (non_canon_y || sig_y == 0) {
|
||
|
|
y_is_zero = 1;
|
||
|
|
}
|
||
|
|
if (x_is_zero && y_is_zero) {
|
||
|
|
// if both numbers are zero, they are equal
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} else if (x_is_zero) {
|
||
|
|
// if x is zero, it is lessthan if Y is positive
|
||
|
|
res = ((y & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
} else if (y_is_zero) {
|
||
|
|
// if y is zero, X is less if it is negative
|
||
|
|
res = ((x & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// OPPOSITE SIGN (CASE5)
|
||
|
|
// now, if the sign bits differ, x is less than if y is positive
|
||
|
|
if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
|
||
|
|
res = ((y & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// REDUNDANT REPRESENTATIONS (CASE6)
|
||
|
|
// if both components are either bigger or smaller
|
||
|
|
if (sig_x > sig_y && exp_x >= exp_y) {
|
||
|
|
res = ((x & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
if (sig_x < sig_y && exp_x <= exp_y) {
|
||
|
|
res = ((x & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if exp_x is 15 greater than exp_y, no need for compensation
|
||
|
|
if (exp_x - exp_y > 15) {
|
||
|
|
res = ((x & MASK_SIGN) != MASK_SIGN);
|
||
|
|
// difference cannot be greater than 10^15
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if exp_x is 15 less than exp_y, no need for compensation
|
||
|
|
if (exp_y - exp_x > 15) {
|
||
|
|
res = ((x & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if |exp_x - exp_y| < 15, it comes down to the compensated significand
|
||
|
|
if (exp_x > exp_y) { // to simplify the loop below,
|
||
|
|
// otherwise adjust the x significand upwards
|
||
|
|
__mul_64x64_to_128MACH (sig_n_prime, sig_x,
|
||
|
|
mult_factor[exp_x - exp_y]);
|
||
|
|
// return 1 if values are equal
|
||
|
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if postitive, return whichever significand abs is smaller
|
||
|
|
// (converse if negative)
|
||
|
|
res = (((sig_n_prime.w[1] == 0)
|
||
|
|
&& sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) !=
|
||
|
|
MASK_SIGN));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// adjust the y significand upwards
|
||
|
|
__mul_64x64_to_128MACH (sig_n_prime, sig_y,
|
||
|
|
mult_factor[exp_y - exp_x]);
|
||
|
|
// return 0 if values are equal
|
||
|
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if positive, return whichever significand abs is smaller
|
||
|
|
// (converse if negative)
|
||
|
|
res = (((sig_n_prime.w[1] > 0)
|
||
|
|
|| (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) !=
|
||
|
|
MASK_SIGN));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
|
||
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
||
|
|
void
|
||
|
|
bid64_quiet_greater_unordered (int *pres, UINT64 * px,
|
||
|
|
UINT64 *
|
||
|
|
py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
||
|
|
_EXC_INFO_PARAM) {
|
||
|
|
UINT64 x = *px;
|
||
|
|
UINT64 y = *py;
|
||
|
|
#else
|
||
|
|
int
|
||
|
|
bid64_quiet_greater_unordered (UINT64 x,
|
||
|
|
UINT64 y _EXC_FLAGS_PARAM
|
||
|
|
_EXC_MASKS_PARAM _EXC_INFO_PARAM) {
|
||
|
|
#endif
|
||
|
|
int res;
|
||
|
|
int exp_x, exp_y;
|
||
|
|
UINT64 sig_x, sig_y;
|
||
|
|
UINT128 sig_n_prime;
|
||
|
|
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 & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
|
||
|
|
if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) {
|
||
|
|
*pfpsf |= INVALID_EXCEPTION; // set exception if sNaN
|
||
|
|
}
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// SIMPLE (CASE2)
|
||
|
|
// if all the bits are the same, these numbers are equal (not Greater).
|
||
|
|
if (x == y) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// INFINITY (CASE3)
|
||
|
|
if ((x & MASK_INF) == MASK_INF) {
|
||
|
|
// if x is neg infinity, there is no way it is greater than y, return 0
|
||
|
|
if (((x & MASK_SIGN) == MASK_SIGN)) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} else {
|
||
|
|
// x is pos infinity, it is greater, unless y is positive infinity =>
|
||
|
|
// return y!=pos_infinity
|
||
|
|
res = (((y & MASK_INF) != MASK_INF)
|
||
|
|
|| ((y & MASK_SIGN) == MASK_SIGN));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
} else if ((y & 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 & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
||
|
|
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
||
|
|
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
|
||
|
|
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
||
|
|
if (sig_x > 9999999999999999ull) {
|
||
|
|
non_canon_x = 1;
|
||
|
|
} else {
|
||
|
|
non_canon_x = 0;
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
|
||
|
|
sig_x = (x & MASK_BINARY_SIG1);
|
||
|
|
non_canon_x = 0;
|
||
|
|
}
|
||
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
||
|
|
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
||
|
|
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
|
||
|
|
sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
||
|
|
if (sig_y > 9999999999999999ull) {
|
||
|
|
non_canon_y = 1;
|
||
|
|
} else {
|
||
|
|
non_canon_y = 0;
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
|
||
|
|
sig_y = (y & MASK_BINARY_SIG1);
|
||
|
|
non_canon_y = 0;
|
||
|
|
}
|
||
|
|
// ZERO (CASE4)
|
||
|
|
// some properties:
|
||
|
|
// (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater
|
||
|
|
// (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 == 0) {
|
||
|
|
x_is_zero = 1;
|
||
|
|
}
|
||
|
|
if (non_canon_y || sig_y == 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);
|
||
|
|
} else if (x_is_zero) {
|
||
|
|
// is x is zero, it is greater if Y is negative
|
||
|
|
res = ((y & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
} else if (y_is_zero) {
|
||
|
|
// is y is zero, X is greater if it is positive
|
||
|
|
res = ((x & 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 ^ y) & MASK_SIGN) == MASK_SIGN) {
|
||
|
|
res = ((y & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// REDUNDANT REPRESENTATIONS (CASE6)
|
||
|
|
// if both components are either bigger or smaller
|
||
|
|
if (sig_x > sig_y && exp_x >= exp_y) {
|
||
|
|
res = ((x & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
if (sig_x < sig_y && exp_x <= exp_y) {
|
||
|
|
res = ((x & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if exp_x is 15 greater than exp_y, no need for compensation
|
||
|
|
if (exp_x - exp_y > 15) {
|
||
|
|
// difference cannot be greater than 10^15
|
||
|
|
res = ((x & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if exp_x is 15 less than exp_y, no need for compensation
|
||
|
|
if (exp_y - exp_x > 15) {
|
||
|
|
res = ((x & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if |exp_x - exp_y| < 15, it comes down to the compensated significand
|
||
|
|
if (exp_x > exp_y) { // to simplify the loop below,
|
||
|
|
// otherwise adjust the x significand upwards
|
||
|
|
__mul_64x64_to_128MACH (sig_n_prime, sig_x,
|
||
|
|
mult_factor[exp_x - exp_y]);
|
||
|
|
// if postitive, return whichever significand is larger
|
||
|
|
// (converse if negative)
|
||
|
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
res = (((sig_n_prime.w[1] > 0)
|
||
|
|
|| sig_n_prime.w[0] > sig_y) ^ ((x & MASK_SIGN) ==
|
||
|
|
MASK_SIGN));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// adjust the y significand upwards
|
||
|
|
__mul_64x64_to_128MACH (sig_n_prime, sig_y,
|
||
|
|
mult_factor[exp_y - exp_x]);
|
||
|
|
// if postitive, return whichever significand is larger (converse if negative)
|
||
|
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
res = (((sig_n_prime.w[1] == 0)
|
||
|
|
&& (sig_x > sig_n_prime.w[0])) ^ ((x & MASK_SIGN) ==
|
||
|
|
MASK_SIGN));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
|
||
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
||
|
|
void
|
||
|
|
bid64_quiet_less (int *pres, UINT64 * px,
|
||
|
|
UINT64 *
|
||
|
|
py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM)
|
||
|
|
{
|
||
|
|
UINT64 x = *px;
|
||
|
|
UINT64 y = *py;
|
||
|
|
#else
|
||
|
|
int
|
||
|
|
bid64_quiet_less (UINT64 x,
|
||
|
|
UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
||
|
|
_EXC_INFO_PARAM) {
|
||
|
|
#endif
|
||
|
|
int res;
|
||
|
|
int exp_x, exp_y;
|
||
|
|
UINT64 sig_x, sig_y;
|
||
|
|
UINT128 sig_n_prime;
|
||
|
|
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 : return 0
|
||
|
|
if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
|
||
|
|
if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) {
|
||
|
|
*pfpsf |= INVALID_EXCEPTION; // set exception if sNaN
|
||
|
|
}
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// SIMPLE (CASE2)
|
||
|
|
// if all the bits are the same, these numbers are equal.
|
||
|
|
if (x == y) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// INFINITY (CASE3)
|
||
|
|
if ((x & MASK_INF) == MASK_INF) {
|
||
|
|
// if x==neg_inf, { res = (y == neg_inf)?0:1; BID_RETURN (res) }
|
||
|
|
if ((x & MASK_SIGN) == MASK_SIGN) {
|
||
|
|
// x is -inf, so it is less than y unless y is -inf
|
||
|
|
res = (((y & MASK_INF) != MASK_INF)
|
||
|
|
|| (y & 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 & MASK_INF) == MASK_INF) {
|
||
|
|
// x is finite, so:
|
||
|
|
// if y is +inf, x<y
|
||
|
|
// if y is -inf, x>y
|
||
|
|
res = ((y & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
||
|
|
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
||
|
|
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
|
||
|
|
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
||
|
|
if (sig_x > 9999999999999999ull) {
|
||
|
|
non_canon_x = 1;
|
||
|
|
} else {
|
||
|
|
non_canon_x = 0;
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
|
||
|
|
sig_x = (x & MASK_BINARY_SIG1);
|
||
|
|
non_canon_x = 0;
|
||
|
|
}
|
||
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
||
|
|
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
||
|
|
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
|
||
|
|
sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
||
|
|
if (sig_y > 9999999999999999ull) {
|
||
|
|
non_canon_y = 1;
|
||
|
|
} else {
|
||
|
|
non_canon_y = 0;
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
|
||
|
|
sig_y = (y & MASK_BINARY_SIG1);
|
||
|
|
non_canon_y = 0;
|
||
|
|
}
|
||
|
|
// ZERO (CASE4)
|
||
|
|
// some properties:
|
||
|
|
// (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater
|
||
|
|
// (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 == 0) {
|
||
|
|
x_is_zero = 1;
|
||
|
|
}
|
||
|
|
if (non_canon_y || sig_y == 0) {
|
||
|
|
y_is_zero = 1;
|
||
|
|
}
|
||
|
|
if (x_is_zero && y_is_zero) {
|
||
|
|
// if both numbers are zero, they are equal
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} else if (x_is_zero) {
|
||
|
|
// if x is zero, it is lessthan if Y is positive
|
||
|
|
res = ((y & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
} else if (y_is_zero) {
|
||
|
|
// if y is zero, X is less if it is negative
|
||
|
|
res = ((x & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// OPPOSITE SIGN (CASE5)
|
||
|
|
// now, if the sign bits differ, x is less than if y is positive
|
||
|
|
if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
|
||
|
|
res = ((y & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// REDUNDANT REPRESENTATIONS (CASE6)
|
||
|
|
// if both components are either bigger or smaller,
|
||
|
|
// it is clear what needs to be done
|
||
|
|
if (sig_x > sig_y && exp_x >= exp_y) {
|
||
|
|
res = ((x & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
if (sig_x < sig_y && exp_x <= exp_y) {
|
||
|
|
res = ((x & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if exp_x is 15 greater than exp_y, no need for compensation
|
||
|
|
if (exp_x - exp_y > 15) {
|
||
|
|
res = ((x & MASK_SIGN) == MASK_SIGN);
|
||
|
|
// difference cannot be greater than 10^15
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if exp_x is 15 less than exp_y, no need for compensation
|
||
|
|
if (exp_y - exp_x > 15) {
|
||
|
|
res = ((x & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if |exp_x - exp_y| < 15, it comes down to the compensated significand
|
||
|
|
if (exp_x > exp_y) { // to simplify the loop below,
|
||
|
|
// otherwise adjust the x significand upwards
|
||
|
|
__mul_64x64_to_128MACH (sig_n_prime, sig_x,
|
||
|
|
mult_factor[exp_x - exp_y]);
|
||
|
|
// return 0 if values are equal
|
||
|
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if postitive, return whichever significand abs is smaller
|
||
|
|
// (converse if negative)
|
||
|
|
res = (((sig_n_prime.w[1] == 0)
|
||
|
|
&& sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) ==
|
||
|
|
MASK_SIGN));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// adjust the y significand upwards
|
||
|
|
__mul_64x64_to_128MACH (sig_n_prime, sig_y,
|
||
|
|
mult_factor[exp_y - exp_x]);
|
||
|
|
// return 0 if values are equal
|
||
|
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if positive, return whichever significand abs is smaller
|
||
|
|
// (converse if negative)
|
||
|
|
res = (((sig_n_prime.w[1] > 0)
|
||
|
|
|| (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) ==
|
||
|
|
MASK_SIGN));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
|
||
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
||
|
|
void
|
||
|
|
bid64_quiet_less_equal (int *pres, UINT64 * px,
|
||
|
|
UINT64 *
|
||
|
|
py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
||
|
|
_EXC_INFO_PARAM) {
|
||
|
|
UINT64 x = *px;
|
||
|
|
UINT64 y = *py;
|
||
|
|
#else
|
||
|
|
int
|
||
|
|
bid64_quiet_less_equal (UINT64 x,
|
||
|
|
UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
||
|
|
_EXC_INFO_PARAM) {
|
||
|
|
#endif
|
||
|
|
int res;
|
||
|
|
int exp_x, exp_y;
|
||
|
|
UINT64 sig_x, sig_y;
|
||
|
|
UINT128 sig_n_prime;
|
||
|
|
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 & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
|
||
|
|
if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) {
|
||
|
|
*pfpsf |= INVALID_EXCEPTION; // set exception if sNaN
|
||
|
|
}
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// SIMPLE (CASE2)
|
||
|
|
// if all the bits are the same, these numbers are equal (LESSEQUAL).
|
||
|
|
if (x == y) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// INFINITY (CASE3)
|
||
|
|
if ((x & MASK_INF) == MASK_INF) {
|
||
|
|
if (((x & MASK_SIGN) == MASK_SIGN)) {
|
||
|
|
// if x is neg infinity, it must be lessthan or equal to y return 1
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} else {
|
||
|
|
// x is pos infinity, it is greater, unless y is positive infinity =>
|
||
|
|
// return y==pos_infinity
|
||
|
|
res = !(((y & MASK_INF) != MASK_INF)
|
||
|
|
|| ((y & MASK_SIGN) == MASK_SIGN));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
} else if ((y & MASK_INF) == MASK_INF) {
|
||
|
|
// x is finite, so if y is positive infinity, then x is less, return 1
|
||
|
|
// if y is negative infinity, then x is greater, return 0
|
||
|
|
res = ((y & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
||
|
|
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
||
|
|
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
|
||
|
|
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
||
|
|
if (sig_x > 9999999999999999ull) {
|
||
|
|
non_canon_x = 1;
|
||
|
|
} else {
|
||
|
|
non_canon_x = 0;
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
|
||
|
|
sig_x = (x & MASK_BINARY_SIG1);
|
||
|
|
non_canon_x = 0;
|
||
|
|
}
|
||
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
||
|
|
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
||
|
|
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
|
||
|
|
sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
||
|
|
if (sig_y > 9999999999999999ull) {
|
||
|
|
non_canon_y = 1;
|
||
|
|
} else {
|
||
|
|
non_canon_y = 0;
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
|
||
|
|
sig_y = (y & MASK_BINARY_SIG1);
|
||
|
|
non_canon_y = 0;
|
||
|
|
}
|
||
|
|
// ZERO (CASE4)
|
||
|
|
// some properties:
|
||
|
|
// (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater
|
||
|
|
// (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 == 0) {
|
||
|
|
x_is_zero = 1;
|
||
|
|
}
|
||
|
|
if (non_canon_y || sig_y == 0) {
|
||
|
|
y_is_zero = 1;
|
||
|
|
}
|
||
|
|
if (x_is_zero && y_is_zero) {
|
||
|
|
// if both numbers are zero, they are equal -> return 1
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} else if (x_is_zero) {
|
||
|
|
// if x is zero, it is lessthan if Y is positive
|
||
|
|
res = ((y & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
} else if (y_is_zero) {
|
||
|
|
// if y is zero, X is less if it is negative
|
||
|
|
res = ((x & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// OPPOSITE SIGN (CASE5)
|
||
|
|
// now, if the sign bits differ, x is less than if y is positive
|
||
|
|
if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
|
||
|
|
res = ((y & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// REDUNDANT REPRESENTATIONS (CASE6)
|
||
|
|
// if both components are either bigger or smaller
|
||
|
|
if (sig_x > sig_y && exp_x >= exp_y) {
|
||
|
|
res = ((x & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
if (sig_x < sig_y && exp_x <= exp_y) {
|
||
|
|
res = ((x & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if exp_x is 15 greater than exp_y, no need for compensation
|
||
|
|
if (exp_x - exp_y > 15) {
|
||
|
|
res = ((x & MASK_SIGN) == MASK_SIGN);
|
||
|
|
// difference cannot be greater than 10^15
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if exp_x is 15 less than exp_y, no need for compensation
|
||
|
|
if (exp_y - exp_x > 15) {
|
||
|
|
res = ((x & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if |exp_x - exp_y| < 15, it comes down to the compensated significand
|
||
|
|
if (exp_x > exp_y) { // to simplify the loop below,
|
||
|
|
// otherwise adjust the x significand upwards
|
||
|
|
__mul_64x64_to_128MACH (sig_n_prime, sig_x,
|
||
|
|
mult_factor[exp_x - exp_y]);
|
||
|
|
// return 1 if values are equal
|
||
|
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if postitive, return whichever significand abs is smaller
|
||
|
|
// (converse if negative)
|
||
|
|
res = (((sig_n_prime.w[1] == 0)
|
||
|
|
&& sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) ==
|
||
|
|
MASK_SIGN));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// adjust the y significand upwards
|
||
|
|
__mul_64x64_to_128MACH (sig_n_prime, sig_y,
|
||
|
|
mult_factor[exp_y - exp_x]);
|
||
|
|
// return 1 if values are equal
|
||
|
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if positive, return whichever significand abs is smaller
|
||
|
|
// (converse if negative)
|
||
|
|
res = (((sig_n_prime.w[1] > 0)
|
||
|
|
|| (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) ==
|
||
|
|
MASK_SIGN));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
|
||
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
||
|
|
void
|
||
|
|
bid64_quiet_less_unordered (int *pres, UINT64 * px,
|
||
|
|
UINT64 *
|
||
|
|
py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
||
|
|
_EXC_INFO_PARAM) {
|
||
|
|
UINT64 x = *px;
|
||
|
|
UINT64 y = *py;
|
||
|
|
#else
|
||
|
|
int
|
||
|
|
bid64_quiet_less_unordered (UINT64 x,
|
||
|
|
UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
||
|
|
_EXC_INFO_PARAM) {
|
||
|
|
#endif
|
||
|
|
int res;
|
||
|
|
int exp_x, exp_y;
|
||
|
|
UINT64 sig_x, sig_y;
|
||
|
|
UINT128 sig_n_prime;
|
||
|
|
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 : return 0
|
||
|
|
if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
|
||
|
|
if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) {
|
||
|
|
*pfpsf |= INVALID_EXCEPTION; // set exception if sNaN
|
||
|
|
}
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// SIMPLE (CASE2)
|
||
|
|
// if all the bits are the same, these numbers are equal.
|
||
|
|
if (x == y) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// INFINITY (CASE3)
|
||
|
|
if ((x & MASK_INF) == MASK_INF) {
|
||
|
|
// if x==neg_inf, { res = (y == neg_inf)?0:1; BID_RETURN (res) }
|
||
|
|
if ((x & MASK_SIGN) == MASK_SIGN) {
|
||
|
|
// x is -inf, so it is less than y unless y is -inf
|
||
|
|
res = (((y & MASK_INF) != MASK_INF)
|
||
|
|
|| (y & 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 & MASK_INF) == MASK_INF) {
|
||
|
|
// x is finite, so:
|
||
|
|
// if y is +inf, x<y
|
||
|
|
// if y is -inf, x>y
|
||
|
|
res = ((y & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
||
|
|
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
||
|
|
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
|
||
|
|
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
||
|
|
if (sig_x > 9999999999999999ull) {
|
||
|
|
non_canon_x = 1;
|
||
|
|
} else {
|
||
|
|
non_canon_x = 0;
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
|
||
|
|
sig_x = (x & MASK_BINARY_SIG1);
|
||
|
|
non_canon_x = 0;
|
||
|
|
}
|
||
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
||
|
|
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
||
|
|
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
|
||
|
|
sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
||
|
|
if (sig_y > 9999999999999999ull) {
|
||
|
|
non_canon_y = 1;
|
||
|
|
} else {
|
||
|
|
non_canon_y = 0;
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
|
||
|
|
sig_y = (y & MASK_BINARY_SIG1);
|
||
|
|
non_canon_y = 0;
|
||
|
|
}
|
||
|
|
// ZERO (CASE4)
|
||
|
|
// some properties:
|
||
|
|
// (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater
|
||
|
|
// (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 == 0) {
|
||
|
|
x_is_zero = 1;
|
||
|
|
}
|
||
|
|
if (non_canon_y || sig_y == 0) {
|
||
|
|
y_is_zero = 1;
|
||
|
|
}
|
||
|
|
if (x_is_zero && y_is_zero) {
|
||
|
|
// if both numbers are zero, they are equal
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} else if (x_is_zero) {
|
||
|
|
// if x is zero, it is lessthan if Y is positive
|
||
|
|
res = ((y & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
} else if (y_is_zero) {
|
||
|
|
// if y is zero, X is less if it is negative
|
||
|
|
res = ((x & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// OPPOSITE SIGN (CASE5)
|
||
|
|
// now, if the sign bits differ, x is less than if y is positive
|
||
|
|
if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
|
||
|
|
res = ((y & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// REDUNDANT REPRESENTATIONS (CASE6)
|
||
|
|
// if both components are either bigger or smaller
|
||
|
|
if (sig_x > sig_y && exp_x >= exp_y) {
|
||
|
|
res = ((x & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
if (sig_x < sig_y && exp_x <= exp_y) {
|
||
|
|
res = ((x & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if exp_x is 15 greater than exp_y, no need for compensation
|
||
|
|
if (exp_x - exp_y > 15) {
|
||
|
|
res = ((x & MASK_SIGN) == MASK_SIGN);
|
||
|
|
// difference cannot be greater than 10^15
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if exp_x is 15 less than exp_y, no need for compensation
|
||
|
|
if (exp_y - exp_x > 15) {
|
||
|
|
res = ((x & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if |exp_x - exp_y| < 15, it comes down to the compensated significand
|
||
|
|
if (exp_x > exp_y) { // to simplify the loop below,
|
||
|
|
// otherwise adjust the x significand upwards
|
||
|
|
__mul_64x64_to_128MACH (sig_n_prime, sig_x,
|
||
|
|
mult_factor[exp_x - exp_y]);
|
||
|
|
// return 0 if values are equal
|
||
|
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if postitive, return whichever significand abs is smaller
|
||
|
|
// (converse if negative)
|
||
|
|
res = (((sig_n_prime.w[1] == 0)
|
||
|
|
&& sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) ==
|
||
|
|
MASK_SIGN));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// adjust the y significand upwards
|
||
|
|
__mul_64x64_to_128MACH (sig_n_prime, sig_y,
|
||
|
|
mult_factor[exp_y - exp_x]);
|
||
|
|
// return 0 if values are equal
|
||
|
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if positive, return whichever significand abs is smaller
|
||
|
|
// (converse if negative)
|
||
|
|
res = (((sig_n_prime.w[1] > 0)
|
||
|
|
|| (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) ==
|
||
|
|
MASK_SIGN));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
|
||
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
||
|
|
void
|
||
|
|
bid64_quiet_not_equal (int *pres, UINT64 * px,
|
||
|
|
UINT64 *
|
||
|
|
py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
||
|
|
_EXC_INFO_PARAM) {
|
||
|
|
UINT64 x = *px;
|
||
|
|
UINT64 y = *py;
|
||
|
|
#else
|
||
|
|
int
|
||
|
|
bid64_quiet_not_equal (UINT64 x,
|
||
|
|
UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
||
|
|
_EXC_INFO_PARAM) {
|
||
|
|
#endif
|
||
|
|
int res;
|
||
|
|
int exp_x, exp_y, exp_t;
|
||
|
|
UINT64 sig_x, sig_y, sig_t;
|
||
|
|
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y, lcv;
|
||
|
|
|
||
|
|
// NaN (CASE1)
|
||
|
|
// if either number is NAN, the comparison is unordered,
|
||
|
|
// rather than equal : return 1
|
||
|
|
if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
|
||
|
|
if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) {
|
||
|
|
*pfpsf |= INVALID_EXCEPTION; // set exception if sNaN
|
||
|
|
}
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// SIMPLE (CASE2)
|
||
|
|
// if all the bits are the same, these numbers are equivalent.
|
||
|
|
if (x == y) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// INFINITY (CASE3)
|
||
|
|
if (((x & MASK_INF) == MASK_INF) && ((y & MASK_INF) == MASK_INF)) {
|
||
|
|
res = (((x ^ y) & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// ONE INFINITY (CASE3')
|
||
|
|
if (((x & MASK_INF) == MASK_INF) || ((y & MASK_INF) == MASK_INF)) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
||
|
|
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
||
|
|
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
|
||
|
|
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
||
|
|
if (sig_x > 9999999999999999ull) {
|
||
|
|
non_canon_x = 1;
|
||
|
|
} else {
|
||
|
|
non_canon_x = 0;
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
|
||
|
|
sig_x = (x & MASK_BINARY_SIG1);
|
||
|
|
non_canon_x = 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
||
|
|
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
||
|
|
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
|
||
|
|
sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
||
|
|
if (sig_y > 9999999999999999ull) {
|
||
|
|
non_canon_y = 1;
|
||
|
|
} else {
|
||
|
|
non_canon_y = 0;
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
|
||
|
|
sig_y = (y & MASK_BINARY_SIG1);
|
||
|
|
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 == 0) {
|
||
|
|
x_is_zero = 1;
|
||
|
|
}
|
||
|
|
if (non_canon_y || sig_y == 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 1
|
||
|
|
if ((x ^ y) & 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, sig_y, sig_t); // and the smaller exp in x
|
||
|
|
}
|
||
|
|
|
||
|
|
if (exp_y - exp_x > 15) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// difference cannot be greater than 10^16
|
||
|
|
|
||
|
|
for (lcv = 0; lcv < (exp_y - exp_x); lcv++) {
|
||
|
|
|
||
|
|
// recalculate y's significand upwards
|
||
|
|
sig_y = sig_y * 10;
|
||
|
|
if (sig_y > 9999999999999999ull) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
{
|
||
|
|
res = sig_y != sig_x;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
|
||
|
|
}
|
||
|
|
|
||
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
||
|
|
void
|
||
|
|
bid64_quiet_not_greater (int *pres, UINT64 * px,
|
||
|
|
UINT64 *
|
||
|
|
py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
||
|
|
_EXC_INFO_PARAM) {
|
||
|
|
UINT64 x = *px;
|
||
|
|
UINT64 y = *py;
|
||
|
|
#else
|
||
|
|
int
|
||
|
|
bid64_quiet_not_greater (UINT64 x,
|
||
|
|
UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
||
|
|
_EXC_INFO_PARAM) {
|
||
|
|
#endif
|
||
|
|
int res;
|
||
|
|
int exp_x, exp_y;
|
||
|
|
UINT64 sig_x, sig_y;
|
||
|
|
UINT128 sig_n_prime;
|
||
|
|
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 & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
|
||
|
|
if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) {
|
||
|
|
*pfpsf |= INVALID_EXCEPTION; // set exception if sNaN
|
||
|
|
}
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// SIMPLE (CASE2)
|
||
|
|
// if all the bits are the same, these numbers are equal (LESSEQUAL).
|
||
|
|
if (x == y) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// INFINITY (CASE3)
|
||
|
|
if ((x & MASK_INF) == MASK_INF) {
|
||
|
|
// if x is neg infinity, it must be lessthan or equal to y return 1
|
||
|
|
if (((x & 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 & MASK_INF) != MASK_INF)
|
||
|
|
|| ((y & MASK_SIGN) == MASK_SIGN));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
} else if ((y & MASK_INF) == MASK_INF) {
|
||
|
|
// x is finite, so if y is positive infinity, then x is less, return 1
|
||
|
|
// if y is negative infinity, then x is greater, return 0
|
||
|
|
{
|
||
|
|
res = ((y & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
||
|
|
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
||
|
|
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
|
||
|
|
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
||
|
|
if (sig_x > 9999999999999999ull) {
|
||
|
|
non_canon_x = 1;
|
||
|
|
} else {
|
||
|
|
non_canon_x = 0;
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
|
||
|
|
sig_x = (x & MASK_BINARY_SIG1);
|
||
|
|
non_canon_x = 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
||
|
|
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
||
|
|
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
|
||
|
|
sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
||
|
|
if (sig_y > 9999999999999999ull) {
|
||
|
|
non_canon_y = 1;
|
||
|
|
} else {
|
||
|
|
non_canon_y = 0;
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
|
||
|
|
sig_y = (y & MASK_BINARY_SIG1);
|
||
|
|
non_canon_y = 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
// ZERO (CASE4)
|
||
|
|
// some properties:
|
||
|
|
// (+ZERO==-ZERO) => therefore ignore the sign, and neither
|
||
|
|
// number is greater
|
||
|
|
// (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 == 0) {
|
||
|
|
x_is_zero = 1;
|
||
|
|
}
|
||
|
|
if (non_canon_y || sig_y == 0) {
|
||
|
|
y_is_zero = 1;
|
||
|
|
}
|
||
|
|
// if both numbers are zero, they are equal -> return 1
|
||
|
|
if (x_is_zero && y_is_zero) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if x is zero, it is lessthan if Y is positive
|
||
|
|
else if (x_is_zero) {
|
||
|
|
res = ((y & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if y is zero, X is less if it is negative
|
||
|
|
else if (y_is_zero) {
|
||
|
|
res = ((x & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// OPPOSITE SIGN (CASE5)
|
||
|
|
// now, if the sign bits differ, x is less than if y is positive
|
||
|
|
if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
|
||
|
|
res = ((y & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// REDUNDANT REPRESENTATIONS (CASE6)
|
||
|
|
// if both components are either bigger or smaller
|
||
|
|
if (sig_x > sig_y && exp_x >= exp_y) {
|
||
|
|
res = ((x & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
if (sig_x < sig_y && exp_x <= exp_y) {
|
||
|
|
res = ((x & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if exp_x is 15 greater than exp_y, no need for compensation
|
||
|
|
if (exp_x - exp_y > 15) {
|
||
|
|
res = ((x & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// difference cannot be greater than 10^15
|
||
|
|
|
||
|
|
// if exp_x is 15 less than exp_y, no need for compensation
|
||
|
|
if (exp_y - exp_x > 15) {
|
||
|
|
res = ((x & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if |exp_x - exp_y| < 15, it comes down to the compensated significand
|
||
|
|
if (exp_x > exp_y) { // to simplify the loop below,
|
||
|
|
|
||
|
|
// otherwise adjust the x significand upwards
|
||
|
|
__mul_64x64_to_128MACH (sig_n_prime, sig_x,
|
||
|
|
mult_factor[exp_x - exp_y]);
|
||
|
|
|
||
|
|
// return 1 if values are equal
|
||
|
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if postitive, return whichever significand abs is smaller
|
||
|
|
// (converse if negative)
|
||
|
|
{
|
||
|
|
res = (((sig_n_prime.w[1] == 0)
|
||
|
|
&& sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) ==
|
||
|
|
MASK_SIGN));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
// adjust the y significand upwards
|
||
|
|
__mul_64x64_to_128MACH (sig_n_prime, sig_y,
|
||
|
|
mult_factor[exp_y - exp_x]);
|
||
|
|
|
||
|
|
// return 1 if values are equal
|
||
|
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if positive, return whichever significand abs is smaller
|
||
|
|
// (converse if negative)
|
||
|
|
{
|
||
|
|
res = (((sig_n_prime.w[1] > 0)
|
||
|
|
|| (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) ==
|
||
|
|
MASK_SIGN));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
||
|
|
void
|
||
|
|
bid64_quiet_not_less (int *pres, UINT64 * px,
|
||
|
|
UINT64 *
|
||
|
|
py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
||
|
|
_EXC_INFO_PARAM) {
|
||
|
|
UINT64 x = *px;
|
||
|
|
UINT64 y = *py;
|
||
|
|
#else
|
||
|
|
int
|
||
|
|
bid64_quiet_not_less (UINT64 x,
|
||
|
|
UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
||
|
|
_EXC_INFO_PARAM) {
|
||
|
|
#endif
|
||
|
|
int res;
|
||
|
|
int exp_x, exp_y;
|
||
|
|
UINT64 sig_x, sig_y;
|
||
|
|
UINT128 sig_n_prime;
|
||
|
|
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 : return 1
|
||
|
|
if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
|
||
|
|
if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) {
|
||
|
|
*pfpsf |= INVALID_EXCEPTION; // set exception if sNaN
|
||
|
|
}
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// SIMPLE (CASE2)
|
||
|
|
// if all the bits are the same, these numbers are equal.
|
||
|
|
if (x == y) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// INFINITY (CASE3)
|
||
|
|
if ((x & MASK_INF) == MASK_INF) {
|
||
|
|
// if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) }
|
||
|
|
if ((x & MASK_SIGN) == MASK_SIGN)
|
||
|
|
// x is -inf, so it is less than y unless y is -inf
|
||
|
|
{
|
||
|
|
res = (((y & MASK_INF) == MASK_INF)
|
||
|
|
&& (y & 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 & MASK_INF) == MASK_INF) {
|
||
|
|
// x is finite, so:
|
||
|
|
// if y is +inf, x<y
|
||
|
|
// if y is -inf, x>y
|
||
|
|
{
|
||
|
|
res = ((y & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
||
|
|
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
||
|
|
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
|
||
|
|
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
||
|
|
if (sig_x > 9999999999999999ull) {
|
||
|
|
non_canon_x = 1;
|
||
|
|
} else {
|
||
|
|
non_canon_x = 0;
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
|
||
|
|
sig_x = (x & MASK_BINARY_SIG1);
|
||
|
|
non_canon_x = 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
||
|
|
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
||
|
|
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
|
||
|
|
sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
||
|
|
if (sig_y > 9999999999999999ull) {
|
||
|
|
non_canon_y = 1;
|
||
|
|
} else {
|
||
|
|
non_canon_y = 0;
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
|
||
|
|
sig_y = (y & MASK_BINARY_SIG1);
|
||
|
|
non_canon_y = 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
// ZERO (CASE4)
|
||
|
|
// some properties:
|
||
|
|
// (+ZERO==-ZERO) => therefore ignore the sign, and neither
|
||
|
|
// number is greater
|
||
|
|
// (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 == 0) {
|
||
|
|
x_is_zero = 1;
|
||
|
|
}
|
||
|
|
if (non_canon_y || sig_y == 0) {
|
||
|
|
y_is_zero = 1;
|
||
|
|
}
|
||
|
|
// if both numbers are zero, they are equal
|
||
|
|
if (x_is_zero && y_is_zero) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if x is zero, it is lessthan if Y is positive
|
||
|
|
else if (x_is_zero) {
|
||
|
|
res = ((y & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if y is zero, X is less if it is negative
|
||
|
|
else if (y_is_zero) {
|
||
|
|
res = ((x & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// OPPOSITE SIGN (CASE5)
|
||
|
|
// now, if the sign bits differ, x is less than if y is positive
|
||
|
|
if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
|
||
|
|
res = ((y & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// REDUNDANT REPRESENTATIONS (CASE6)
|
||
|
|
// if both components are either bigger or smaller
|
||
|
|
if (sig_x > sig_y && exp_x >= exp_y) {
|
||
|
|
res = ((x & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
if (sig_x < sig_y && exp_x <= exp_y) {
|
||
|
|
res = ((x & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if exp_x is 15 greater than exp_y, no need for compensation
|
||
|
|
if (exp_x - exp_y > 15) {
|
||
|
|
res = ((x & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// difference cannot be greater than 10^15
|
||
|
|
|
||
|
|
// if exp_x is 15 less than exp_y, no need for compensation
|
||
|
|
if (exp_y - exp_x > 15) {
|
||
|
|
res = ((x & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if |exp_x - exp_y| < 15, it comes down to the compensated significand
|
||
|
|
if (exp_x > exp_y) { // to simplify the loop below,
|
||
|
|
|
||
|
|
// otherwise adjust the x significand upwards
|
||
|
|
__mul_64x64_to_128MACH (sig_n_prime, sig_x,
|
||
|
|
mult_factor[exp_x - exp_y]);
|
||
|
|
|
||
|
|
// return 0 if values are equal
|
||
|
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if postitive, return whichever significand abs is smaller
|
||
|
|
// (converse if negative)
|
||
|
|
{
|
||
|
|
res = (((sig_n_prime.w[1] == 0)
|
||
|
|
&& sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) !=
|
||
|
|
MASK_SIGN));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
// adjust the y significand upwards
|
||
|
|
__mul_64x64_to_128MACH (sig_n_prime, sig_y,
|
||
|
|
mult_factor[exp_y - exp_x]);
|
||
|
|
|
||
|
|
// return 0 if values are equal
|
||
|
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if positive, return whichever significand abs is smaller
|
||
|
|
// (converse if negative)
|
||
|
|
{
|
||
|
|
res = (((sig_n_prime.w[1] > 0)
|
||
|
|
|| (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) !=
|
||
|
|
MASK_SIGN));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
||
|
|
void
|
||
|
|
bid64_quiet_ordered (int *pres, UINT64 * px,
|
||
|
|
UINT64 *
|
||
|
|
py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
||
|
|
_EXC_INFO_PARAM) {
|
||
|
|
UINT64 x = *px;
|
||
|
|
UINT64 y = *py;
|
||
|
|
#else
|
||
|
|
int
|
||
|
|
bid64_quiet_ordered (UINT64 x,
|
||
|
|
UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
||
|
|
_EXC_INFO_PARAM) {
|
||
|
|
#endif
|
||
|
|
int res;
|
||
|
|
|
||
|
|
// NaN (CASE1)
|
||
|
|
// if either number is NAN, the comparison is ordered, rather than equal : return 0
|
||
|
|
if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
|
||
|
|
if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) {
|
||
|
|
*pfpsf |= INVALID_EXCEPTION; // set exception if sNaN
|
||
|
|
}
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} else {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
||
|
|
void
|
||
|
|
bid64_quiet_unordered (int *pres, UINT64 * px,
|
||
|
|
UINT64 *
|
||
|
|
py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
||
|
|
_EXC_INFO_PARAM) {
|
||
|
|
UINT64 x = *px;
|
||
|
|
UINT64 y = *py;
|
||
|
|
#else
|
||
|
|
int
|
||
|
|
bid64_quiet_unordered (UINT64 x,
|
||
|
|
UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
||
|
|
_EXC_INFO_PARAM) {
|
||
|
|
#endif
|
||
|
|
int res;
|
||
|
|
|
||
|
|
// NaN (CASE1)
|
||
|
|
// if either number is NAN, the comparison is unordered,
|
||
|
|
// rather than equal : return 0
|
||
|
|
if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
|
||
|
|
if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) {
|
||
|
|
*pfpsf |= INVALID_EXCEPTION; // set exception if sNaN
|
||
|
|
}
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
} else {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
||
|
|
void
|
||
|
|
bid64_signaling_greater (int *pres, UINT64 * px,
|
||
|
|
UINT64 *
|
||
|
|
py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
||
|
|
_EXC_INFO_PARAM) {
|
||
|
|
UINT64 x = *px;
|
||
|
|
UINT64 y = *py;
|
||
|
|
#else
|
||
|
|
int
|
||
|
|
bid64_signaling_greater (UINT64 x,
|
||
|
|
UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
||
|
|
_EXC_INFO_PARAM) {
|
||
|
|
#endif
|
||
|
|
int res;
|
||
|
|
int exp_x, exp_y;
|
||
|
|
UINT64 sig_x, sig_y;
|
||
|
|
UINT128 sig_n_prime;
|
||
|
|
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 & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
|
||
|
|
*pfpsf |= INVALID_EXCEPTION; // set invalid exception if NaN
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// SIMPLE (CASE2)
|
||
|
|
// if all the bits are the same, these numbers are equal (not Greater).
|
||
|
|
if (x == y) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// INFINITY (CASE3)
|
||
|
|
if ((x & MASK_INF) == MASK_INF) {
|
||
|
|
// if x is neg infinity, there is no way it is greater than y, return 0
|
||
|
|
if (((x & 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 & MASK_INF) != MASK_INF)
|
||
|
|
|| ((y & MASK_SIGN) == MASK_SIGN));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
} else if ((y & 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 & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
||
|
|
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
||
|
|
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
|
||
|
|
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
||
|
|
if (sig_x > 9999999999999999ull) {
|
||
|
|
non_canon_x = 1;
|
||
|
|
} else {
|
||
|
|
non_canon_x = 0;
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
|
||
|
|
sig_x = (x & MASK_BINARY_SIG1);
|
||
|
|
non_canon_x = 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
||
|
|
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
||
|
|
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
|
||
|
|
sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
||
|
|
if (sig_y > 9999999999999999ull) {
|
||
|
|
non_canon_y = 1;
|
||
|
|
} else {
|
||
|
|
non_canon_y = 0;
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
|
||
|
|
sig_y = (y & MASK_BINARY_SIG1);
|
||
|
|
non_canon_y = 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
// ZERO (CASE4)
|
||
|
|
// some properties:
|
||
|
|
// (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater
|
||
|
|
// (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 == 0) {
|
||
|
|
x_is_zero = 1;
|
||
|
|
}
|
||
|
|
if (non_canon_y || sig_y == 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 & 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 & 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 ^ y) & MASK_SIGN) == MASK_SIGN) {
|
||
|
|
res = ((y & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// REDUNDANT REPRESENTATIONS (CASE6)
|
||
|
|
|
||
|
|
// if both components are either bigger or smaller
|
||
|
|
if (sig_x > sig_y && exp_x >= exp_y) {
|
||
|
|
res = ((x & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
if (sig_x < sig_y && exp_x <= exp_y) {
|
||
|
|
res = ((x & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if exp_x is 15 greater than exp_y, no need for compensation
|
||
|
|
if (exp_x - exp_y > 15) {
|
||
|
|
res = ((x & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// difference cannot be greater than 10^15
|
||
|
|
|
||
|
|
// if exp_x is 15 less than exp_y, no need for compensation
|
||
|
|
if (exp_y - exp_x > 15) {
|
||
|
|
res = ((x & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if |exp_x - exp_y| < 15, it comes down to the compensated significand
|
||
|
|
if (exp_x > exp_y) { // to simplify the loop below,
|
||
|
|
|
||
|
|
// otherwise adjust the x significand upwards
|
||
|
|
__mul_64x64_to_128MACH (sig_n_prime, sig_x,
|
||
|
|
mult_factor[exp_x - exp_y]);
|
||
|
|
|
||
|
|
|
||
|
|
// if postitive, return whichever significand is larger
|
||
|
|
// (converse if negative)
|
||
|
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
|
||
|
|
{
|
||
|
|
res = (((sig_n_prime.w[1] > 0)
|
||
|
|
|| sig_n_prime.w[0] > sig_y) ^ ((x & MASK_SIGN) ==
|
||
|
|
MASK_SIGN));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
// adjust the y significand upwards
|
||
|
|
__mul_64x64_to_128MACH (sig_n_prime, sig_y,
|
||
|
|
mult_factor[exp_y - exp_x]);
|
||
|
|
|
||
|
|
// if postitive, return whichever significand is larger
|
||
|
|
// (converse if negative)
|
||
|
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
{
|
||
|
|
res = (((sig_n_prime.w[1] == 0)
|
||
|
|
&& (sig_x > sig_n_prime.w[0])) ^ ((x & MASK_SIGN) ==
|
||
|
|
MASK_SIGN));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
||
|
|
void
|
||
|
|
bid64_signaling_greater_equal (int *pres, UINT64 * px,
|
||
|
|
UINT64 *
|
||
|
|
py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
||
|
|
_EXC_INFO_PARAM) {
|
||
|
|
UINT64 x = *px;
|
||
|
|
UINT64 y = *py;
|
||
|
|
#else
|
||
|
|
int
|
||
|
|
bid64_signaling_greater_equal (UINT64 x,
|
||
|
|
UINT64 y _EXC_FLAGS_PARAM
|
||
|
|
_EXC_MASKS_PARAM _EXC_INFO_PARAM) {
|
||
|
|
#endif
|
||
|
|
int res;
|
||
|
|
int exp_x, exp_y;
|
||
|
|
UINT64 sig_x, sig_y;
|
||
|
|
UINT128 sig_n_prime;
|
||
|
|
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 : return 1
|
||
|
|
if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
|
||
|
|
*pfpsf |= INVALID_EXCEPTION; // set invalid exception if NaN
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// SIMPLE (CASE2)
|
||
|
|
// if all the bits are the same, these numbers are equal.
|
||
|
|
if (x == y) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// INFINITY (CASE3)
|
||
|
|
if ((x & MASK_INF) == MASK_INF) {
|
||
|
|
// if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) }
|
||
|
|
if ((x & MASK_SIGN) == MASK_SIGN)
|
||
|
|
// x is -inf, so it is less than y unless y is -inf
|
||
|
|
{
|
||
|
|
res = (((y & MASK_INF) == MASK_INF)
|
||
|
|
&& (y & 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 & MASK_INF) == MASK_INF) {
|
||
|
|
// x is finite, so:
|
||
|
|
// if y is +inf, x<y
|
||
|
|
// if y is -inf, x>y
|
||
|
|
{
|
||
|
|
res = ((y & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
||
|
|
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
||
|
|
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
|
||
|
|
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
||
|
|
if (sig_x > 9999999999999999ull) {
|
||
|
|
non_canon_x = 1;
|
||
|
|
} else {
|
||
|
|
non_canon_x = 0;
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
|
||
|
|
sig_x = (x & MASK_BINARY_SIG1);
|
||
|
|
non_canon_x = 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
||
|
|
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
||
|
|
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
|
||
|
|
sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
||
|
|
if (sig_y > 9999999999999999ull) {
|
||
|
|
non_canon_y = 1;
|
||
|
|
} else {
|
||
|
|
non_canon_y = 0;
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
|
||
|
|
sig_y = (y & MASK_BINARY_SIG1);
|
||
|
|
non_canon_y = 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
// ZERO (CASE4)
|
||
|
|
// some properties:
|
||
|
|
// (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater
|
||
|
|
// (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 == 0) {
|
||
|
|
x_is_zero = 1;
|
||
|
|
}
|
||
|
|
if (non_canon_y || sig_y == 0) {
|
||
|
|
y_is_zero = 1;
|
||
|
|
}
|
||
|
|
// if both numbers are zero, they are equal
|
||
|
|
if (x_is_zero && y_is_zero) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if x is zero, it is lessthan if Y is positive
|
||
|
|
else if (x_is_zero) {
|
||
|
|
res = ((y & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if y is zero, X is less if it is negative
|
||
|
|
else if (y_is_zero) {
|
||
|
|
res = ((x & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// OPPOSITE SIGN (CASE5)
|
||
|
|
// now, if the sign bits differ, x is less than if y is positive
|
||
|
|
if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
|
||
|
|
res = ((y & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// REDUNDANT REPRESENTATIONS (CASE6)
|
||
|
|
// if both components are either bigger or smaller
|
||
|
|
if (sig_x > sig_y && exp_x >= exp_y) {
|
||
|
|
res = ((x & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
if (sig_x < sig_y && exp_x <= exp_y) {
|
||
|
|
res = ((x & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if exp_x is 15 greater than exp_y, no need for compensation
|
||
|
|
if (exp_x - exp_y > 15) {
|
||
|
|
res = ((x & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// difference cannot be greater than 10^15
|
||
|
|
|
||
|
|
// if exp_x is 15 less than exp_y, no need for compensation
|
||
|
|
if (exp_y - exp_x > 15) {
|
||
|
|
res = ((x & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if |exp_x - exp_y| < 15, it comes down to the compensated significand
|
||
|
|
if (exp_x > exp_y) { // to simplify the loop below,
|
||
|
|
|
||
|
|
// otherwise adjust the x significand upwards
|
||
|
|
__mul_64x64_to_128MACH (sig_n_prime, sig_x,
|
||
|
|
mult_factor[exp_x - exp_y]);
|
||
|
|
|
||
|
|
// return 1 if values are equal
|
||
|
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if postitive, return whichever significand abs is smaller
|
||
|
|
// (converse if negative)
|
||
|
|
{
|
||
|
|
res = (((sig_n_prime.w[1] == 0)
|
||
|
|
&& sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) !=
|
||
|
|
MASK_SIGN));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
// adjust the y significand upwards
|
||
|
|
__mul_64x64_to_128MACH (sig_n_prime, sig_y,
|
||
|
|
mult_factor[exp_y - exp_x]);
|
||
|
|
|
||
|
|
// return 0 if values are equal
|
||
|
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if positive, return whichever significand abs is smaller
|
||
|
|
// (converse if negative)
|
||
|
|
{
|
||
|
|
res = (((sig_n_prime.w[1] > 0)
|
||
|
|
|| (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) !=
|
||
|
|
MASK_SIGN));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
||
|
|
void
|
||
|
|
bid64_signaling_greater_unordered (int *pres, UINT64 * px,
|
||
|
|
UINT64 *
|
||
|
|
py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
||
|
|
_EXC_INFO_PARAM) {
|
||
|
|
UINT64 x = *px;
|
||
|
|
UINT64 y = *py;
|
||
|
|
#else
|
||
|
|
int
|
||
|
|
bid64_signaling_greater_unordered (UINT64 x,
|
||
|
|
UINT64 y _EXC_FLAGS_PARAM
|
||
|
|
_EXC_MASKS_PARAM _EXC_INFO_PARAM) {
|
||
|
|
#endif
|
||
|
|
int res;
|
||
|
|
int exp_x, exp_y;
|
||
|
|
UINT64 sig_x, sig_y;
|
||
|
|
UINT128 sig_n_prime;
|
||
|
|
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 & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
|
||
|
|
*pfpsf |= INVALID_EXCEPTION; // set invalid exception if NaN
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// SIMPLE (CASE2)
|
||
|
|
// if all the bits are the same, these numbers are equal (not Greater).
|
||
|
|
if (x == y) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// INFINITY (CASE3)
|
||
|
|
if ((x & MASK_INF) == MASK_INF) {
|
||
|
|
// if x is neg infinity, there is no way it is greater than y, return 0
|
||
|
|
if (((x & 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 & MASK_INF) != MASK_INF)
|
||
|
|
|| ((y & MASK_SIGN) == MASK_SIGN));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
} else if ((y & 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 & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
||
|
|
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
||
|
|
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
|
||
|
|
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
||
|
|
if (sig_x > 9999999999999999ull) {
|
||
|
|
non_canon_x = 1;
|
||
|
|
} else {
|
||
|
|
non_canon_x = 0;
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
|
||
|
|
sig_x = (x & MASK_BINARY_SIG1);
|
||
|
|
non_canon_x = 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
||
|
|
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
||
|
|
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
|
||
|
|
sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
||
|
|
if (sig_y > 9999999999999999ull) {
|
||
|
|
non_canon_y = 1;
|
||
|
|
} else {
|
||
|
|
non_canon_y = 0;
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
|
||
|
|
sig_y = (y & MASK_BINARY_SIG1);
|
||
|
|
non_canon_y = 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
// ZERO (CASE4)
|
||
|
|
// some properties:
|
||
|
|
// (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater
|
||
|
|
// (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 == 0) {
|
||
|
|
x_is_zero = 1;
|
||
|
|
}
|
||
|
|
if (non_canon_y || sig_y == 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 & 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 & 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 ^ y) & MASK_SIGN) == MASK_SIGN) {
|
||
|
|
res = ((y & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// REDUNDANT REPRESENTATIONS (CASE6)
|
||
|
|
|
||
|
|
// if both components are either bigger or smaller
|
||
|
|
if (sig_x > sig_y && exp_x >= exp_y) {
|
||
|
|
res = ((x & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
if (sig_x < sig_y && exp_x <= exp_y) {
|
||
|
|
res = ((x & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if exp_x is 15 greater than exp_y, no need for compensation
|
||
|
|
if (exp_x - exp_y > 15) {
|
||
|
|
res = ((x & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// difference cannot be greater than 10^15
|
||
|
|
|
||
|
|
// if exp_x is 15 less than exp_y, no need for compensation
|
||
|
|
if (exp_y - exp_x > 15) {
|
||
|
|
res = ((x & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if |exp_x - exp_y| < 15, it comes down to the compensated significand
|
||
|
|
if (exp_x > exp_y) { // to simplify the loop below,
|
||
|
|
|
||
|
|
// otherwise adjust the x significand upwards
|
||
|
|
__mul_64x64_to_128MACH (sig_n_prime, sig_x,
|
||
|
|
mult_factor[exp_x - exp_y]);
|
||
|
|
|
||
|
|
// if postitive, return whichever significand is larger
|
||
|
|
// (converse if negative)
|
||
|
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
|
||
|
|
{
|
||
|
|
res = (((sig_n_prime.w[1] > 0)
|
||
|
|
|| sig_n_prime.w[0] > sig_y) ^ ((x & MASK_SIGN) ==
|
||
|
|
MASK_SIGN));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
// adjust the y significand upwards
|
||
|
|
__mul_64x64_to_128MACH (sig_n_prime, sig_y,
|
||
|
|
mult_factor[exp_y - exp_x]);
|
||
|
|
|
||
|
|
// if postitive, return whichever significand is larger
|
||
|
|
// (converse if negative)
|
||
|
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
{
|
||
|
|
res = (((sig_n_prime.w[1] == 0)
|
||
|
|
&& (sig_x > sig_n_prime.w[0])) ^ ((x & MASK_SIGN) ==
|
||
|
|
MASK_SIGN));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
||
|
|
void
|
||
|
|
bid64_signaling_less (int *pres, UINT64 * px,
|
||
|
|
UINT64 *
|
||
|
|
py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
||
|
|
_EXC_INFO_PARAM) {
|
||
|
|
UINT64 x = *px;
|
||
|
|
UINT64 y = *py;
|
||
|
|
#else
|
||
|
|
int
|
||
|
|
bid64_signaling_less (UINT64 x,
|
||
|
|
UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
||
|
|
_EXC_INFO_PARAM) {
|
||
|
|
#endif
|
||
|
|
int res;
|
||
|
|
int exp_x, exp_y;
|
||
|
|
UINT64 sig_x, sig_y;
|
||
|
|
UINT128 sig_n_prime;
|
||
|
|
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 : return 0
|
||
|
|
if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
|
||
|
|
*pfpsf |= INVALID_EXCEPTION; // set invalid exception if NaN
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// SIMPLE (CASE2)
|
||
|
|
// if all the bits are the same, these numbers are equal.
|
||
|
|
if (x == y) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// INFINITY (CASE3)
|
||
|
|
if ((x & MASK_INF) == MASK_INF) {
|
||
|
|
// if x==neg_inf, { res = (y == neg_inf)?0:1; BID_RETURN (res) }
|
||
|
|
if ((x & MASK_SIGN) == MASK_SIGN)
|
||
|
|
// x is -inf, so it is less than y unless y is -inf
|
||
|
|
{
|
||
|
|
res = (((y & MASK_INF) != MASK_INF)
|
||
|
|
|| (y & 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 & MASK_INF) == MASK_INF) {
|
||
|
|
// x is finite, so:
|
||
|
|
// if y is +inf, x<y
|
||
|
|
// if y is -inf, x>y
|
||
|
|
{
|
||
|
|
res = ((y & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
||
|
|
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
||
|
|
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
|
||
|
|
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
||
|
|
if (sig_x > 9999999999999999ull) {
|
||
|
|
non_canon_x = 1;
|
||
|
|
} else {
|
||
|
|
non_canon_x = 0;
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
|
||
|
|
sig_x = (x & MASK_BINARY_SIG1);
|
||
|
|
non_canon_x = 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
||
|
|
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
||
|
|
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
|
||
|
|
sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
||
|
|
if (sig_y > 9999999999999999ull) {
|
||
|
|
non_canon_y = 1;
|
||
|
|
} else {
|
||
|
|
non_canon_y = 0;
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
|
||
|
|
sig_y = (y & MASK_BINARY_SIG1);
|
||
|
|
non_canon_y = 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
// ZERO (CASE4)
|
||
|
|
// some properties:
|
||
|
|
// (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater
|
||
|
|
// (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 == 0) {
|
||
|
|
x_is_zero = 1;
|
||
|
|
}
|
||
|
|
if (non_canon_y || sig_y == 0) {
|
||
|
|
y_is_zero = 1;
|
||
|
|
}
|
||
|
|
// if both numbers are zero, they are equal
|
||
|
|
if (x_is_zero && y_is_zero) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if x is zero, it is lessthan if Y is positive
|
||
|
|
else if (x_is_zero) {
|
||
|
|
res = ((y & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if y is zero, X is less if it is negative
|
||
|
|
else if (y_is_zero) {
|
||
|
|
res = ((x & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// OPPOSITE SIGN (CASE5)
|
||
|
|
// now, if the sign bits differ, x is less than if y is positive
|
||
|
|
if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
|
||
|
|
res = ((y & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// REDUNDANT REPRESENTATIONS (CASE6)
|
||
|
|
// if both components are either bigger or smaller
|
||
|
|
if (sig_x > sig_y && exp_x >= exp_y) {
|
||
|
|
res = ((x & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
if (sig_x < sig_y && exp_x <= exp_y) {
|
||
|
|
res = ((x & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if exp_x is 15 greater than exp_y, no need for compensation
|
||
|
|
if (exp_x - exp_y > 15) {
|
||
|
|
res = ((x & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// difference cannot be greater than 10^15
|
||
|
|
|
||
|
|
// if exp_x is 15 less than exp_y, no need for compensation
|
||
|
|
if (exp_y - exp_x > 15) {
|
||
|
|
res = ((x & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if |exp_x - exp_y| < 15, it comes down to the compensated significand
|
||
|
|
if (exp_x > exp_y) { // to simplify the loop below,
|
||
|
|
|
||
|
|
// otherwise adjust the x significand upwards
|
||
|
|
__mul_64x64_to_128MACH (sig_n_prime, sig_x,
|
||
|
|
mult_factor[exp_x - exp_y]);
|
||
|
|
|
||
|
|
// return 0 if values are equal
|
||
|
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if postitive, return whichever significand abs is smaller
|
||
|
|
// (converse if negative)
|
||
|
|
{
|
||
|
|
res = (((sig_n_prime.w[1] == 0)
|
||
|
|
&& sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) ==
|
||
|
|
MASK_SIGN));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
// adjust the y significand upwards
|
||
|
|
__mul_64x64_to_128MACH (sig_n_prime, sig_y,
|
||
|
|
mult_factor[exp_y - exp_x]);
|
||
|
|
|
||
|
|
// return 0 if values are equal
|
||
|
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if positive, return whichever significand abs is smaller
|
||
|
|
// (converse if negative)
|
||
|
|
{
|
||
|
|
res = (((sig_n_prime.w[1] > 0)
|
||
|
|
|| (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) ==
|
||
|
|
MASK_SIGN));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
||
|
|
void
|
||
|
|
bid64_signaling_less_equal (int *pres, UINT64 * px,
|
||
|
|
UINT64 *
|
||
|
|
py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
||
|
|
_EXC_INFO_PARAM) {
|
||
|
|
UINT64 x = *px;
|
||
|
|
UINT64 y = *py;
|
||
|
|
#else
|
||
|
|
int
|
||
|
|
bid64_signaling_less_equal (UINT64 x,
|
||
|
|
UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
||
|
|
_EXC_INFO_PARAM) {
|
||
|
|
#endif
|
||
|
|
int res;
|
||
|
|
int exp_x, exp_y;
|
||
|
|
UINT64 sig_x, sig_y;
|
||
|
|
UINT128 sig_n_prime;
|
||
|
|
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 & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
|
||
|
|
*pfpsf |= INVALID_EXCEPTION; // set invalid exception if NaN
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// SIMPLE (CASE2)
|
||
|
|
// if all the bits are the same, these numbers are equal (LESSEQUAL).
|
||
|
|
if (x == y) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// INFINITY (CASE3)
|
||
|
|
if ((x & MASK_INF) == MASK_INF) {
|
||
|
|
// if x is neg infinity, it must be lessthan or equal to y return 1
|
||
|
|
if (((x & 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 & MASK_INF) != MASK_INF)
|
||
|
|
|| ((y & MASK_SIGN) == MASK_SIGN));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
} else if ((y & MASK_INF) == MASK_INF) {
|
||
|
|
// x is finite, so if y is positive infinity, then x is less, return 1
|
||
|
|
// if y is negative infinity, then x is greater, return 0
|
||
|
|
{
|
||
|
|
res = ((y & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
||
|
|
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
||
|
|
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
|
||
|
|
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
||
|
|
if (sig_x > 9999999999999999ull) {
|
||
|
|
non_canon_x = 1;
|
||
|
|
} else {
|
||
|
|
non_canon_x = 0;
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
|
||
|
|
sig_x = (x & MASK_BINARY_SIG1);
|
||
|
|
non_canon_x = 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
||
|
|
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
||
|
|
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
|
||
|
|
sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
||
|
|
if (sig_y > 9999999999999999ull) {
|
||
|
|
non_canon_y = 1;
|
||
|
|
} else {
|
||
|
|
non_canon_y = 0;
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
|
||
|
|
sig_y = (y & MASK_BINARY_SIG1);
|
||
|
|
non_canon_y = 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
// ZERO (CASE4)
|
||
|
|
// some properties:
|
||
|
|
// (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater
|
||
|
|
// (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 == 0) {
|
||
|
|
x_is_zero = 1;
|
||
|
|
}
|
||
|
|
if (non_canon_y || sig_y == 0) {
|
||
|
|
y_is_zero = 1;
|
||
|
|
}
|
||
|
|
// if both numbers are zero, they are equal -> return 1
|
||
|
|
if (x_is_zero && y_is_zero) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if x is zero, it is lessthan if Y is positive
|
||
|
|
else if (x_is_zero) {
|
||
|
|
res = ((y & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if y is zero, X is less if it is negative
|
||
|
|
else if (y_is_zero) {
|
||
|
|
res = ((x & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// OPPOSITE SIGN (CASE5)
|
||
|
|
// now, if the sign bits differ, x is less than if y is positive
|
||
|
|
if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
|
||
|
|
res = ((y & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// REDUNDANT REPRESENTATIONS (CASE6)
|
||
|
|
// if both components are either bigger or smaller
|
||
|
|
if (sig_x > sig_y && exp_x >= exp_y) {
|
||
|
|
res = ((x & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
if (sig_x < sig_y && exp_x <= exp_y) {
|
||
|
|
res = ((x & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if exp_x is 15 greater than exp_y, no need for compensation
|
||
|
|
if (exp_x - exp_y > 15) {
|
||
|
|
res = ((x & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// difference cannot be greater than 10^15
|
||
|
|
|
||
|
|
// if exp_x is 15 less than exp_y, no need for compensation
|
||
|
|
if (exp_y - exp_x > 15) {
|
||
|
|
res = ((x & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if |exp_x - exp_y| < 15, it comes down to the compensated significand
|
||
|
|
if (exp_x > exp_y) { // to simplify the loop below,
|
||
|
|
|
||
|
|
// otherwise adjust the x significand upwards
|
||
|
|
__mul_64x64_to_128MACH (sig_n_prime, sig_x,
|
||
|
|
mult_factor[exp_x - exp_y]);
|
||
|
|
|
||
|
|
// return 1 if values are equal
|
||
|
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if postitive, return whichever significand abs is smaller
|
||
|
|
// (converse if negative)
|
||
|
|
{
|
||
|
|
res = (((sig_n_prime.w[1] == 0)
|
||
|
|
&& sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) ==
|
||
|
|
MASK_SIGN));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
// adjust the y significand upwards
|
||
|
|
__mul_64x64_to_128MACH (sig_n_prime, sig_y,
|
||
|
|
mult_factor[exp_y - exp_x]);
|
||
|
|
|
||
|
|
// return 1 if values are equal
|
||
|
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if positive, return whichever significand abs is smaller
|
||
|
|
// (converse if negative)
|
||
|
|
{
|
||
|
|
res = (((sig_n_prime.w[1] > 0)
|
||
|
|
|| (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) ==
|
||
|
|
MASK_SIGN));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
||
|
|
void
|
||
|
|
bid64_signaling_less_unordered (int *pres, UINT64 * px,
|
||
|
|
UINT64 *
|
||
|
|
py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
||
|
|
_EXC_INFO_PARAM) {
|
||
|
|
UINT64 x = *px;
|
||
|
|
UINT64 y = *py;
|
||
|
|
#else
|
||
|
|
int
|
||
|
|
bid64_signaling_less_unordered (UINT64 x,
|
||
|
|
UINT64 y _EXC_FLAGS_PARAM
|
||
|
|
_EXC_MASKS_PARAM _EXC_INFO_PARAM) {
|
||
|
|
#endif
|
||
|
|
int res;
|
||
|
|
int exp_x, exp_y;
|
||
|
|
UINT64 sig_x, sig_y;
|
||
|
|
UINT128 sig_n_prime;
|
||
|
|
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 : return 0
|
||
|
|
if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
|
||
|
|
*pfpsf |= INVALID_EXCEPTION; // set invalid exception if NaN
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// SIMPLE (CASE2)
|
||
|
|
// if all the bits are the same, these numbers are equal.
|
||
|
|
if (x == y) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// INFINITY (CASE3)
|
||
|
|
if ((x & MASK_INF) == MASK_INF) {
|
||
|
|
// if x==neg_inf, { res = (y == neg_inf)?0:1; BID_RETURN (res) }
|
||
|
|
if ((x & MASK_SIGN) == MASK_SIGN)
|
||
|
|
// x is -inf, so it is less than y unless y is -inf
|
||
|
|
{
|
||
|
|
res = (((y & MASK_INF) != MASK_INF)
|
||
|
|
|| (y & 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 & MASK_INF) == MASK_INF) {
|
||
|
|
// x is finite, so:
|
||
|
|
// if y is +inf, x<y
|
||
|
|
// if y is -inf, x>y
|
||
|
|
{
|
||
|
|
res = ((y & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
||
|
|
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
||
|
|
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
|
||
|
|
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
||
|
|
if (sig_x > 9999999999999999ull) {
|
||
|
|
non_canon_x = 1;
|
||
|
|
} else {
|
||
|
|
non_canon_x = 0;
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
|
||
|
|
sig_x = (x & MASK_BINARY_SIG1);
|
||
|
|
non_canon_x = 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
||
|
|
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
||
|
|
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
|
||
|
|
sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
||
|
|
if (sig_y > 9999999999999999ull) {
|
||
|
|
non_canon_y = 1;
|
||
|
|
} else {
|
||
|
|
non_canon_y = 0;
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
|
||
|
|
sig_y = (y & MASK_BINARY_SIG1);
|
||
|
|
non_canon_y = 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
// ZERO (CASE4)
|
||
|
|
// some properties:
|
||
|
|
// (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater
|
||
|
|
// (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 == 0) {
|
||
|
|
x_is_zero = 1;
|
||
|
|
}
|
||
|
|
if (non_canon_y || sig_y == 0) {
|
||
|
|
y_is_zero = 1;
|
||
|
|
}
|
||
|
|
// if both numbers are zero, they are equal
|
||
|
|
if (x_is_zero && y_is_zero) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if x is zero, it is lessthan if Y is positive
|
||
|
|
else if (x_is_zero) {
|
||
|
|
res = ((y & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if y is zero, X is less if it is negative
|
||
|
|
else if (y_is_zero) {
|
||
|
|
res = ((x & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// OPPOSITE SIGN (CASE5)
|
||
|
|
// now, if the sign bits differ, x is less than if y is positive
|
||
|
|
if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
|
||
|
|
res = ((y & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// REDUNDANT REPRESENTATIONS (CASE6)
|
||
|
|
// if both components are either bigger or smaller
|
||
|
|
if (sig_x > sig_y && exp_x >= exp_y) {
|
||
|
|
res = ((x & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
if (sig_x < sig_y && exp_x <= exp_y) {
|
||
|
|
res = ((x & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if exp_x is 15 greater than exp_y, no need for compensation
|
||
|
|
if (exp_x - exp_y > 15) {
|
||
|
|
res = ((x & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// difference cannot be greater than 10^15
|
||
|
|
|
||
|
|
// if exp_x is 15 less than exp_y, no need for compensation
|
||
|
|
if (exp_y - exp_x > 15) {
|
||
|
|
res = ((x & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if |exp_x - exp_y| < 15, it comes down to the compensated significand
|
||
|
|
if (exp_x > exp_y) { // to simplify the loop below,
|
||
|
|
|
||
|
|
// otherwise adjust the x significand upwards
|
||
|
|
__mul_64x64_to_128MACH (sig_n_prime, sig_x,
|
||
|
|
mult_factor[exp_x - exp_y]);
|
||
|
|
|
||
|
|
// return 0 if values are equal
|
||
|
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if postitive, return whichever significand abs is smaller
|
||
|
|
// (converse if negative)
|
||
|
|
{
|
||
|
|
res = (((sig_n_prime.w[1] == 0)
|
||
|
|
&& sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) ==
|
||
|
|
MASK_SIGN));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
// adjust the y significand upwards
|
||
|
|
__mul_64x64_to_128MACH (sig_n_prime, sig_y,
|
||
|
|
mult_factor[exp_y - exp_x]);
|
||
|
|
|
||
|
|
// return 0 if values are equal
|
||
|
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
|
||
|
|
res = 0;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if positive, return whichever significand abs is smaller
|
||
|
|
// (converse if negative)
|
||
|
|
{
|
||
|
|
res = (((sig_n_prime.w[1] > 0)
|
||
|
|
|| (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) ==
|
||
|
|
MASK_SIGN));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
||
|
|
void
|
||
|
|
bid64_signaling_not_greater (int *pres, UINT64 * px,
|
||
|
|
UINT64 *
|
||
|
|
py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
||
|
|
_EXC_INFO_PARAM) {
|
||
|
|
UINT64 x = *px;
|
||
|
|
UINT64 y = *py;
|
||
|
|
#else
|
||
|
|
int
|
||
|
|
bid64_signaling_not_greater (UINT64 x,
|
||
|
|
UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
||
|
|
_EXC_INFO_PARAM) {
|
||
|
|
#endif
|
||
|
|
int res;
|
||
|
|
int exp_x, exp_y;
|
||
|
|
UINT64 sig_x, sig_y;
|
||
|
|
UINT128 sig_n_prime;
|
||
|
|
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 & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
|
||
|
|
*pfpsf |= INVALID_EXCEPTION; // set invalid exception if NaN
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// SIMPLE (CASE2)
|
||
|
|
// if all the bits are the same, these numbers are equal (LESSEQUAL).
|
||
|
|
if (x == y) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// INFINITY (CASE3)
|
||
|
|
if ((x & MASK_INF) == MASK_INF) {
|
||
|
|
// if x is neg infinity, it must be lessthan or equal to y return 1
|
||
|
|
if (((x & 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 & MASK_INF) != MASK_INF)
|
||
|
|
|| ((y & MASK_SIGN) == MASK_SIGN));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
} else if ((y & MASK_INF) == MASK_INF) {
|
||
|
|
// x is finite, so if y is positive infinity, then x is less, return 1
|
||
|
|
// if y is negative infinity, then x is greater, return 0
|
||
|
|
{
|
||
|
|
res = ((y & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
||
|
|
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
||
|
|
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
|
||
|
|
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
||
|
|
if (sig_x > 9999999999999999ull) {
|
||
|
|
non_canon_x = 1;
|
||
|
|
} else {
|
||
|
|
non_canon_x = 0;
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
|
||
|
|
sig_x = (x & MASK_BINARY_SIG1);
|
||
|
|
non_canon_x = 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
||
|
|
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
||
|
|
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
|
||
|
|
sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
||
|
|
if (sig_y > 9999999999999999ull) {
|
||
|
|
non_canon_y = 1;
|
||
|
|
} else {
|
||
|
|
non_canon_y = 0;
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
|
||
|
|
sig_y = (y & MASK_BINARY_SIG1);
|
||
|
|
non_canon_y = 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
// ZERO (CASE4)
|
||
|
|
// some properties:
|
||
|
|
// (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater
|
||
|
|
// (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 == 0) {
|
||
|
|
x_is_zero = 1;
|
||
|
|
}
|
||
|
|
if (non_canon_y || sig_y == 0) {
|
||
|
|
y_is_zero = 1;
|
||
|
|
}
|
||
|
|
// if both numbers are zero, they are equal -> return 1
|
||
|
|
if (x_is_zero && y_is_zero) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if x is zero, it is lessthan if Y is positive
|
||
|
|
else if (x_is_zero) {
|
||
|
|
res = ((y & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if y is zero, X is less if it is negative
|
||
|
|
else if (y_is_zero) {
|
||
|
|
res = ((x & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// OPPOSITE SIGN (CASE5)
|
||
|
|
// now, if the sign bits differ, x is less than if y is positive
|
||
|
|
if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
|
||
|
|
res = ((y & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// REDUNDANT REPRESENTATIONS (CASE6)
|
||
|
|
// if both components are either bigger or smaller
|
||
|
|
if (sig_x > sig_y && exp_x >= exp_y) {
|
||
|
|
res = ((x & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
if (sig_x < sig_y && exp_x <= exp_y) {
|
||
|
|
res = ((x & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if exp_x is 15 greater than exp_y, no need for compensation
|
||
|
|
if (exp_x - exp_y > 15) {
|
||
|
|
res = ((x & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// difference cannot be greater than 10^15
|
||
|
|
|
||
|
|
// if exp_x is 15 less than exp_y, no need for compensation
|
||
|
|
if (exp_y - exp_x > 15) {
|
||
|
|
res = ((x & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if |exp_x - exp_y| < 15, it comes down to the compensated significand
|
||
|
|
if (exp_x > exp_y) { // to simplify the loop below,
|
||
|
|
|
||
|
|
// otherwise adjust the x significand upwards
|
||
|
|
__mul_64x64_to_128MACH (sig_n_prime, sig_x,
|
||
|
|
mult_factor[exp_x - exp_y]);
|
||
|
|
|
||
|
|
// return 1 if values are equal
|
||
|
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if postitive, return whichever significand abs is smaller
|
||
|
|
// (converse if negative)
|
||
|
|
{
|
||
|
|
res = (((sig_n_prime.w[1] == 0)
|
||
|
|
&& sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) ==
|
||
|
|
MASK_SIGN));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
// adjust the y significand upwards
|
||
|
|
__mul_64x64_to_128MACH (sig_n_prime, sig_y,
|
||
|
|
mult_factor[exp_y - exp_x]);
|
||
|
|
|
||
|
|
// return 1 if values are equal
|
||
|
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if positive, return whichever significand abs is smaller
|
||
|
|
// (converse if negative)
|
||
|
|
{
|
||
|
|
res = (((sig_n_prime.w[1] > 0)
|
||
|
|
|| (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) ==
|
||
|
|
MASK_SIGN));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
||
|
|
void
|
||
|
|
bid64_signaling_not_less (int *pres, UINT64 * px,
|
||
|
|
UINT64 *
|
||
|
|
py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
||
|
|
_EXC_INFO_PARAM) {
|
||
|
|
UINT64 x = *px;
|
||
|
|
UINT64 y = *py;
|
||
|
|
#else
|
||
|
|
int
|
||
|
|
bid64_signaling_not_less (UINT64 x,
|
||
|
|
UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
||
|
|
_EXC_INFO_PARAM) {
|
||
|
|
#endif
|
||
|
|
int res;
|
||
|
|
int exp_x, exp_y;
|
||
|
|
UINT64 sig_x, sig_y;
|
||
|
|
UINT128 sig_n_prime;
|
||
|
|
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 : return 1
|
||
|
|
if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
|
||
|
|
*pfpsf |= INVALID_EXCEPTION; // set invalid exception if NaN
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// SIMPLE (CASE2)
|
||
|
|
// if all the bits are the same, these numbers are equal.
|
||
|
|
if (x == y) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// INFINITY (CASE3)
|
||
|
|
if ((x & MASK_INF) == MASK_INF) {
|
||
|
|
// if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) }
|
||
|
|
if ((x & MASK_SIGN) == MASK_SIGN)
|
||
|
|
// x is -inf, so it is less than y unless y is -inf
|
||
|
|
{
|
||
|
|
res = (((y & MASK_INF) == MASK_INF)
|
||
|
|
&& (y & 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 & MASK_INF) == MASK_INF) {
|
||
|
|
// x is finite, so:
|
||
|
|
// if y is +inf, x<y
|
||
|
|
// if y is -inf, x>y
|
||
|
|
{
|
||
|
|
res = ((y & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
||
|
|
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
||
|
|
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
|
||
|
|
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
||
|
|
if (sig_x > 9999999999999999ull) {
|
||
|
|
non_canon_x = 1;
|
||
|
|
} else {
|
||
|
|
non_canon_x = 0;
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
|
||
|
|
sig_x = (x & MASK_BINARY_SIG1);
|
||
|
|
non_canon_x = 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
||
|
|
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
||
|
|
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
|
||
|
|
sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
||
|
|
if (sig_y > 9999999999999999ull) {
|
||
|
|
non_canon_y = 1;
|
||
|
|
} else {
|
||
|
|
non_canon_y = 0;
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
|
||
|
|
sig_y = (y & MASK_BINARY_SIG1);
|
||
|
|
non_canon_y = 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
// ZERO (CASE4)
|
||
|
|
// some properties:
|
||
|
|
// (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater
|
||
|
|
// (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 == 0) {
|
||
|
|
x_is_zero = 1;
|
||
|
|
}
|
||
|
|
if (non_canon_y || sig_y == 0) {
|
||
|
|
y_is_zero = 1;
|
||
|
|
}
|
||
|
|
// if both numbers are zero, they are equal
|
||
|
|
if (x_is_zero && y_is_zero) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if x is zero, it is lessthan if Y is positive
|
||
|
|
else if (x_is_zero) {
|
||
|
|
res = ((y & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if y is zero, X is less if it is negative
|
||
|
|
else if (y_is_zero) {
|
||
|
|
res = ((x & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// OPPOSITE SIGN (CASE5)
|
||
|
|
// now, if the sign bits differ, x is less than if y is positive
|
||
|
|
if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
|
||
|
|
res = ((y & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// REDUNDANT REPRESENTATIONS (CASE6)
|
||
|
|
// if both components are either bigger or smaller
|
||
|
|
if (sig_x > sig_y && exp_x >= exp_y) {
|
||
|
|
res = ((x & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
if (sig_x < sig_y && exp_x <= exp_y) {
|
||
|
|
res = ((x & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if exp_x is 15 greater than exp_y, no need for compensation
|
||
|
|
if (exp_x - exp_y > 15) {
|
||
|
|
res = ((x & MASK_SIGN) != MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// difference cannot be greater than 10^15
|
||
|
|
|
||
|
|
// if exp_x is 15 less than exp_y, no need for compensation
|
||
|
|
if (exp_y - exp_x > 15) {
|
||
|
|
res = ((x & MASK_SIGN) == MASK_SIGN);
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if |exp_x - exp_y| < 15, it comes down to the compensated significand
|
||
|
|
if (exp_x > exp_y) { // to simplify the loop below,
|
||
|
|
|
||
|
|
// otherwise adjust the x significand upwards
|
||
|
|
__mul_64x64_to_128MACH (sig_n_prime, sig_x,
|
||
|
|
mult_factor[exp_x - exp_y]);
|
||
|
|
|
||
|
|
// return 0 if values are equal
|
||
|
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if postitive, return whichever significand abs is smaller
|
||
|
|
// (converse if negative)
|
||
|
|
{
|
||
|
|
res = (((sig_n_prime.w[1] == 0)
|
||
|
|
&& sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) !=
|
||
|
|
MASK_SIGN));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
// adjust the y significand upwards
|
||
|
|
__mul_64x64_to_128MACH (sig_n_prime, sig_y,
|
||
|
|
mult_factor[exp_y - exp_x]);
|
||
|
|
|
||
|
|
// return 0 if values are equal
|
||
|
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
|
||
|
|
res = 1;
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
// if positive, return whichever significand abs is smaller
|
||
|
|
// (converse if negative)
|
||
|
|
{
|
||
|
|
res = (((sig_n_prime.w[1] > 0)
|
||
|
|
|| (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) !=
|
||
|
|
MASK_SIGN));
|
||
|
|
BID_RETURN (res);
|
||
|
|
}
|
||
|
|
}
|