forked from KolibriOS/kolibrios
955 lines
28 KiB
C
955 lines
28 KiB
C
/* 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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/*****************************************************************************
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* BID64 non-computational functions:
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* - bid64_isSigned
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* - bid64_isNormal
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* - bid64_isSubnormal
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* - bid64_isFinite
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* - bid64_isZero
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* - bid64_isInf
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* - bid64_isSignaling
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* - bid64_isCanonical
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* - bid64_isNaN
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* - bid64_copy
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* - bid64_negate
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* - bid64_abs
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* - bid64_copySign
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* - bid64_class
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* - bid64_sameQuantum
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* - bid64_totalOrder
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* - bid64_totalOrderMag
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* - bid64_radix
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****************************************************************************/
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#if DECIMAL_CALL_BY_REFERENCE
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void
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bid64_isSigned (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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UINT64 x = *px;
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#else
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int
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bid64_isSigned (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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#endif
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int res;
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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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// return 1 iff x is not zero, nor NaN nor subnormal nor infinity
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#if DECIMAL_CALL_BY_REFERENCE
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void
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bid64_isNormal (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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UINT64 x = *px;
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#else
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int
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bid64_isNormal (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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#endif
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int res;
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UINT128 sig_x_prime;
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UINT64 sig_x;
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unsigned int exp_x;
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if ((x & MASK_INF) == MASK_INF) { // x is either INF or NaN
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res = 0;
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} else {
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// decode number into exponent and significand
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if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
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sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
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// check for zero or non-canonical
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if (sig_x > 9999999999999999ull || sig_x == 0) {
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res = 0; // zero or non-canonical
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BID_RETURN (res);
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}
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exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
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} else {
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sig_x = (x & MASK_BINARY_SIG1);
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if (sig_x == 0) {
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res = 0; // zero
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BID_RETURN (res);
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}
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exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
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}
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// if exponent is less than -383, the number may be subnormal
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// if (exp_x - 398 = -383) the number may be subnormal
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if (exp_x < 15) {
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__mul_64x64_to_128MACH (sig_x_prime, sig_x, mult_factor[exp_x]);
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if (sig_x_prime.w[1] == 0
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&& sig_x_prime.w[0] < 1000000000000000ull) {
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res = 0; // subnormal
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} else {
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res = 1; // normal
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}
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} else {
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res = 1; // normal
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}
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}
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BID_RETURN (res);
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}
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// return 1 iff x is not zero, nor NaN nor normal nor infinity
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#if DECIMAL_CALL_BY_REFERENCE
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void
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bid64_isSubnormal (int *pres,
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UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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UINT64 x = *px;
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#else
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int
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bid64_isSubnormal (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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#endif
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int res;
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UINT128 sig_x_prime;
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UINT64 sig_x;
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unsigned int exp_x;
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if ((x & MASK_INF) == MASK_INF) { // x is either INF or NaN
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res = 0;
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} else {
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// decode number into exponent and significand
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if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
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sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
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// check for zero or non-canonical
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if (sig_x > 9999999999999999ull || sig_x == 0) {
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res = 0; // zero or non-canonical
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BID_RETURN (res);
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}
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exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
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} else {
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sig_x = (x & MASK_BINARY_SIG1);
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if (sig_x == 0) {
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res = 0; // zero
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BID_RETURN (res);
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}
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exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
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}
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// if exponent is less than -383, the number may be subnormal
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// if (exp_x - 398 = -383) the number may be subnormal
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if (exp_x < 15) {
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__mul_64x64_to_128MACH (sig_x_prime, sig_x, mult_factor[exp_x]);
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if (sig_x_prime.w[1] == 0
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&& sig_x_prime.w[0] < 1000000000000000ull) {
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res = 1; // subnormal
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} else {
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res = 0; // normal
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}
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} else {
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res = 0; // normal
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}
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}
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BID_RETURN (res);
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}
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//iff x is zero, subnormal or normal (not infinity or NaN)
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#if DECIMAL_CALL_BY_REFERENCE
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void
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bid64_isFinite (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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UINT64 x = *px;
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#else
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int
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bid64_isFinite (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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#endif
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int res;
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res = ((x & MASK_INF) != MASK_INF);
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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_isZero (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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UINT64 x = *px;
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#else
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int
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bid64_isZero (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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#endif
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int res;
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// if infinity or nan, return 0
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if ((x & MASK_INF) == MASK_INF) {
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res = 0;
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} else if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
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// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1]
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// => sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
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// if(sig_x > 9999999999999999ull) {return 1;}
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res =
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(((x & MASK_BINARY_SIG2) | MASK_BINARY_OR2) >
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9999999999999999ull);
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} else {
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res = ((x & MASK_BINARY_SIG1) == 0);
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}
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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_isInf (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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UINT64 x = *px;
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#else
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int
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bid64_isInf (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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#endif
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int res;
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res = ((x & MASK_INF) == MASK_INF) && ((x & MASK_NAN) != MASK_NAN);
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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_isSignaling (int *pres,
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UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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UINT64 x = *px;
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#else
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int
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bid64_isSignaling (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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#endif
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int res;
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res = ((x & MASK_SNAN) == MASK_SNAN);
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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_isCanonical (int *pres,
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UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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UINT64 x = *px;
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#else
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int
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bid64_isCanonical (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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#endif
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int res;
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if ((x & MASK_NAN) == MASK_NAN) { // NaN
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if (x & 0x01fc000000000000ull) {
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res = 0;
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} else if ((x & 0x0003ffffffffffffull) > 999999999999999ull) { // payload
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res = 0;
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} else {
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res = 1;
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}
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} else if ((x & MASK_INF) == MASK_INF) {
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if (x & 0x03ffffffffffffffull) {
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res = 0;
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} else {
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res = 1;
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}
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} else if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // 54-bit coeff.
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res =
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(((x & MASK_BINARY_SIG2) | MASK_BINARY_OR2) <=
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9999999999999999ull);
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} else { // 53-bit coeff.
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res = 1;
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}
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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_isNaN (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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UINT64 x = *px;
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#else
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int
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bid64_isNaN (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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#endif
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int res;
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res = ((x & MASK_NAN) == MASK_NAN);
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BID_RETURN (res);
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}
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// copies a floating-point operand x to destination y, with no change
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#if DECIMAL_CALL_BY_REFERENCE
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void
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bid64_copy (UINT64 * pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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UINT64 x = *px;
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#else
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UINT64
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bid64_copy (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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#endif
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UINT64 res;
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res = x;
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BID_RETURN (res);
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}
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// copies a floating-point operand x to destination y, reversing the sign
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#if DECIMAL_CALL_BY_REFERENCE
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void
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bid64_negate (UINT64 * pres,
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UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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UINT64 x = *px;
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#else
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UINT64
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bid64_negate (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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#endif
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UINT64 res;
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res = x ^ MASK_SIGN;
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BID_RETURN (res);
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}
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// copies a floating-point operand x to destination y, changing the sign to positive
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#if DECIMAL_CALL_BY_REFERENCE
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void
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bid64_abs (UINT64 * pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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UINT64 x = *px;
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#else
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UINT64
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bid64_abs (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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#endif
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UINT64 res;
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res = x & ~MASK_SIGN;
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BID_RETURN (res);
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}
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// copies operand x to destination in the same format as x, but
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// with the sign of y
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#if DECIMAL_CALL_BY_REFERENCE
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void
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bid64_copySign (UINT64 * pres, UINT64 * px,
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UINT64 * py _EXC_MASKS_PARAM _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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UINT64
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bid64_copySign (UINT64 x, UINT64 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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#endif
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UINT64 res;
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res = (x & ~MASK_SIGN) | (y & MASK_SIGN);
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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_class (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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UINT64 x = *px;
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#else
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int
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bid64_class (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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#endif
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int res;
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UINT128 sig_x_prime;
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UINT64 sig_x;
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int exp_x;
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if ((x & MASK_NAN) == MASK_NAN) {
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// is the NaN signaling?
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if ((x & MASK_SNAN) == MASK_SNAN) {
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res = signalingNaN;
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BID_RETURN (res);
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}
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// if NaN and not signaling, must be quietNaN
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res = quietNaN;
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BID_RETURN (res);
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} else if ((x & MASK_INF) == MASK_INF) {
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// is the Infinity negative?
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if ((x & MASK_SIGN) == MASK_SIGN) {
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res = negativeInfinity;
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} else {
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// otherwise, must be positive infinity
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res = positiveInfinity;
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}
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BID_RETURN (res);
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} else if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
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// decode number into exponent and significand
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sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
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// check for zero or non-canonical
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if (sig_x > 9999999999999999ull || sig_x == 0) {
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if ((x & MASK_SIGN) == MASK_SIGN) {
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res = negativeZero;
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} else {
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res = positiveZero;
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}
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BID_RETURN (res);
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}
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exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
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} else {
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sig_x = (x & MASK_BINARY_SIG1);
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if (sig_x == 0) {
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res =
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((x & MASK_SIGN) == MASK_SIGN) ? negativeZero : positiveZero;
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BID_RETURN (res);
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}
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exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
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}
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// if exponent is less than -383, number may be subnormal
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// if (exp_x - 398 < -383)
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if (exp_x < 15) { // sig_x *10^exp_x
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__mul_64x64_to_128MACH (sig_x_prime, sig_x, mult_factor[exp_x]);
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if (sig_x_prime.w[1] == 0
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&& (sig_x_prime.w[0] < 1000000000000000ull)) {
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res =
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((x & MASK_SIGN) ==
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MASK_SIGN) ? negativeSubnormal : positiveSubnormal;
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BID_RETURN (res);
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}
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}
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// otherwise, normal number, determine the sign
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res =
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((x & MASK_SIGN) == MASK_SIGN) ? negativeNormal : positiveNormal;
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BID_RETURN (res);
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}
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// true if the exponents of x and y are the same, false otherwise.
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// The special cases of sameQuantum (NaN, NaN) and sameQuantum (Inf, Inf) are
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// true.
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// If exactly one operand is infinite or exactly one operand is NaN, then false
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#if DECIMAL_CALL_BY_REFERENCE
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void
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bid64_sameQuantum (int *pres, UINT64 * px,
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UINT64 * py _EXC_MASKS_PARAM _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_sameQuantum (UINT64 x, UINT64 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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#endif
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int res;
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unsigned int exp_x, exp_y;
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// if both operands are NaN, return true; if just one is NaN, return false
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if ((x & MASK_NAN) == MASK_NAN || ((y & MASK_NAN) == MASK_NAN)) {
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res = ((x & MASK_NAN) == MASK_NAN && (y & MASK_NAN) == MASK_NAN);
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BID_RETURN (res);
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}
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// if both operands are INF, return true; if just one is INF, return false
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if ((x & MASK_INF) == MASK_INF || (y & MASK_INF) == MASK_INF) {
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res = ((x & MASK_INF) == MASK_INF && (y & MASK_INF) == MASK_INF);
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BID_RETURN (res);
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}
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// decode exponents for both numbers, and return true if they match
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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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} else {
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exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
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}
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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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} else {
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exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
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}
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res = (exp_x == exp_y);
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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_totalOrder (int *pres, UINT64 * px,
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UINT64 * py _EXC_MASKS_PARAM _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_totalOrder (UINT64 x, UINT64 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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#endif
|
|
int res;
|
|
int exp_x, exp_y;
|
|
UINT64 sig_x, sig_y, pyld_y, pyld_x;
|
|
UINT128 sig_n_prime;
|
|
char x_is_zero = 0, y_is_zero = 0;
|
|
|
|
// NaN (CASE1)
|
|
// if x and y are unordered numerically because either operand is NaN
|
|
// (1) totalOrder(-NaN, number) is true
|
|
// (2) totalOrder(number, +NaN) is true
|
|
// (3) if x and y are both NaN:
|
|
// i) negative sign bit < positive sign bit
|
|
// ii) signaling < quiet for +NaN, reverse for -NaN
|
|
// iii) lesser payload < greater payload for +NaN (reverse for -NaN)
|
|
// iv) else if bitwise identical (in canonical form), return 1
|
|
if ((x & MASK_NAN) == MASK_NAN) {
|
|
// if x is -NaN
|
|
if ((x & MASK_SIGN) == MASK_SIGN) {
|
|
// return true, unless y is -NaN also
|
|
if ((y & MASK_NAN) != MASK_NAN || (y & MASK_SIGN) != MASK_SIGN) {
|
|
res = 1; // y is a number, return 1
|
|
BID_RETURN (res);
|
|
} else { // if y and x are both -NaN
|
|
// if x and y are both -sNaN or both -qNaN, we have to compare payloads
|
|
// this xnor statement evaluates to true if both are sNaN or qNaN
|
|
if (!
|
|
(((y & MASK_SNAN) == MASK_SNAN) ^ ((x & MASK_SNAN) ==
|
|
MASK_SNAN))) {
|
|
// it comes down to the payload. we want to return true if x has a
|
|
// larger payload, or if the payloads are equal (canonical forms
|
|
// are bitwise identical)
|
|
pyld_y = y & 0x0003ffffffffffffull;
|
|
pyld_x = x & 0x0003ffffffffffffull;
|
|
if (pyld_y > 999999999999999ull || pyld_y == 0) {
|
|
// if y is zero, x must be less than or numerically equal
|
|
// y's payload is 0
|
|
res = 1;
|
|
BID_RETURN (res);
|
|
}
|
|
// if x is zero and y isn't, x has the smaller payload
|
|
// definitely (since we know y isn't 0 at this point)
|
|
if (pyld_x > 999999999999999ull || pyld_x == 0) {
|
|
// x's payload is 0
|
|
res = 0;
|
|
BID_RETURN (res);
|
|
}
|
|
res = (pyld_x >= pyld_y);
|
|
BID_RETURN (res);
|
|
} else {
|
|
// either x = -sNaN and y = -qNaN or x = -qNaN and y = -sNaN
|
|
res = (y & MASK_SNAN) == MASK_SNAN; // totalOrder(-qNaN, -sNaN) == 1
|
|
BID_RETURN (res);
|
|
}
|
|
}
|
|
} else { // x is +NaN
|
|
// return false, unless y is +NaN also
|
|
if ((y & MASK_NAN) != MASK_NAN || (y & MASK_SIGN) == MASK_SIGN) {
|
|
res = 0; // y is a number, return 1
|
|
BID_RETURN (res);
|
|
} else {
|
|
// x and y are both +NaN;
|
|
// must investigate payload if both quiet or both signaling
|
|
// this xnor statement will be true if both x and y are +qNaN or +sNaN
|
|
if (!
|
|
(((y & MASK_SNAN) == MASK_SNAN) ^ ((x & MASK_SNAN) ==
|
|
MASK_SNAN))) {
|
|
// it comes down to the payload. we want to return true if x has a
|
|
// smaller payload, or if the payloads are equal (canonical forms
|
|
// are bitwise identical)
|
|
pyld_y = y & 0x0003ffffffffffffull;
|
|
pyld_x = x & 0x0003ffffffffffffull;
|
|
// if x is zero and y isn't, x has the smaller
|
|
// payload definitely (since we know y isn't 0 at this point)
|
|
if (pyld_x > 999999999999999ull || pyld_x == 0) {
|
|
res = 1;
|
|
BID_RETURN (res);
|
|
}
|
|
if (pyld_y > 999999999999999ull || pyld_y == 0) {
|
|
// if y is zero, x must be less than or numerically equal
|
|
res = 0;
|
|
BID_RETURN (res);
|
|
}
|
|
res = (pyld_x <= pyld_y);
|
|
BID_RETURN (res);
|
|
} else {
|
|
// return true if y is +qNaN and x is +sNaN
|
|
// (we know they're different bc of xor if_stmt above)
|
|
res = ((x & MASK_SNAN) == MASK_SNAN);
|
|
BID_RETURN (res);
|
|
}
|
|
}
|
|
}
|
|
} else if ((y & MASK_NAN) == MASK_NAN) {
|
|
// x is certainly not NAN in this case.
|
|
// return true if y is positive
|
|
res = ((y & MASK_SIGN) != MASK_SIGN);
|
|
BID_RETURN (res);
|
|
}
|
|
// SIMPLE (CASE2)
|
|
// if all the bits are the same, these numbers are equal.
|
|
if (x == y) {
|
|
res = 1;
|
|
BID_RETURN (res);
|
|
}
|
|
// OPPOSITE SIGNS (CASE 3)
|
|
// if signs are opposite, return 1 if x is negative
|
|
// (if x<y, totalOrder is true)
|
|
if (((x & MASK_SIGN) == MASK_SIGN) ^ ((y & MASK_SIGN) == MASK_SIGN)) {
|
|
res = (x & MASK_SIGN) == MASK_SIGN;
|
|
BID_RETURN (res);
|
|
}
|
|
// INFINITY (CASE4)
|
|
if ((x & MASK_INF) == MASK_INF) {
|
|
// if x==neg_inf, return (y == neg_inf)?1:0;
|
|
if ((x & MASK_SIGN) == MASK_SIGN) {
|
|
res = 1;
|
|
BID_RETURN (res);
|
|
} else {
|
|
// x is positive infinity, only return1 if y
|
|
// is positive infinity as well
|
|
// (we know y has same sign as x)
|
|
res = ((y & MASK_INF) == MASK_INF);
|
|
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 || sig_x == 0) {
|
|
x_is_zero = 1;
|
|
}
|
|
} else {
|
|
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
|
|
sig_x = (x & MASK_BINARY_SIG1);
|
|
if (sig_x == 0) {
|
|
x_is_zero = 1;
|
|
}
|
|
}
|
|
|
|
// 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 || sig_y == 0) {
|
|
y_is_zero = 1;
|
|
}
|
|
} else {
|
|
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
|
|
sig_y = (y & MASK_BINARY_SIG1);
|
|
if (sig_y == 0) {
|
|
y_is_zero = 1;
|
|
}
|
|
}
|
|
|
|
// ZERO (CASE 5)
|
|
// if x and y represent the same entities, and
|
|
// both are negative , return true iff exp_x <= exp_y
|
|
if (x_is_zero && y_is_zero) {
|
|
if (!((x & MASK_SIGN) == MASK_SIGN) ^
|
|
((y & MASK_SIGN) == MASK_SIGN)) {
|
|
// if signs are the same:
|
|
// totalOrder(x,y) iff exp_x >= exp_y for negative numbers
|
|
// totalOrder(x,y) iff exp_x <= exp_y for positive numbers
|
|
if (exp_x == exp_y) {
|
|
res = 1;
|
|
BID_RETURN (res);
|
|
}
|
|
res = (exp_x <= exp_y) ^ ((x & MASK_SIGN) == MASK_SIGN);
|
|
BID_RETURN (res);
|
|
} else {
|
|
// signs are different.
|
|
// totalOrder(-0, +0) is true
|
|
// totalOrder(+0, -0) is false
|
|
res = ((x & MASK_SIGN) == MASK_SIGN);
|
|
BID_RETURN (res);
|
|
}
|
|
}
|
|
// if x is zero and y isn't, clearly x has the smaller payload.
|
|
if (x_is_zero) {
|
|
res = ((y & MASK_SIGN) != MASK_SIGN);
|
|
BID_RETURN (res);
|
|
}
|
|
// if y is zero, and x isn't, clearly y has the smaller payload.
|
|
if (y_is_zero) {
|
|
res = ((x & 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, it is
|
|
// definitely larger, so 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, it is
|
|
// definitely smaller, 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) {
|
|
// otherwise adjust the x significand upwards
|
|
__mul_64x64_to_128MACH (sig_n_prime, sig_x,
|
|
mult_factor[exp_x - exp_y]);
|
|
// if x and y represent the same entities,
|
|
// and both are negative, return true iff exp_x <= exp_y
|
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
|
|
// case cannot occure, because all bits must
|
|
// be the same - would have been caught if (x==y)
|
|
res = (exp_x <= exp_y) ^ ((x & MASK_SIGN) == MASK_SIGN);
|
|
BID_RETURN (res);
|
|
}
|
|
// if positive, return 1 if adjusted x is smaller than y
|
|
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 x and y represent the same entities,
|
|
// and both are negative, return true iff exp_x <= exp_y
|
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
|
|
// Cannot occur, because all bits must be the same.
|
|
// Case would have been caught if (x==y)
|
|
res = (exp_x <= exp_y) ^ ((x & MASK_SIGN) == MASK_SIGN);
|
|
BID_RETURN (res);
|
|
}
|
|
// values are not equal, for positive numbers return 1
|
|
// if x is less than y. 0 otherwise
|
|
res = ((sig_n_prime.w[1] > 0)
|
|
|| (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) ==
|
|
MASK_SIGN);
|
|
BID_RETURN (res);
|
|
}
|
|
|
|
// totalOrderMag is TotalOrder(abs(x), abs(y))
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
|
void
|
|
bid64_totalOrderMag (int *pres, UINT64 * px,
|
|
UINT64 * py _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
|
|
UINT64 x = *px;
|
|
UINT64 y = *py;
|
|
#else
|
|
int
|
|
bid64_totalOrderMag (UINT64 x,
|
|
UINT64 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
|
|
#endif
|
|
int res;
|
|
int exp_x, exp_y;
|
|
UINT64 sig_x, sig_y, pyld_y, pyld_x;
|
|
UINT128 sig_n_prime;
|
|
char x_is_zero = 0, y_is_zero = 0;
|
|
|
|
// NaN (CASE 1)
|
|
// if x and y are unordered numerically because either operand is NaN
|
|
// (1) totalOrder(number, +NaN) is true
|
|
// (2) if x and y are both NaN:
|
|
// i) signaling < quiet for +NaN
|
|
// ii) lesser payload < greater payload for +NaN
|
|
// iii) else if bitwise identical (in canonical form), return 1
|
|
if ((x & MASK_NAN) == MASK_NAN) {
|
|
// x is +NaN
|
|
|
|
// return false, unless y is +NaN also
|
|
if ((y & MASK_NAN) != MASK_NAN) {
|
|
res = 0; // y is a number, return 1
|
|
BID_RETURN (res);
|
|
|
|
} else {
|
|
|
|
// x and y are both +NaN;
|
|
// must investigate payload if both quiet or both signaling
|
|
// this xnor statement will be true if both x and y are +qNaN or +sNaN
|
|
if (!
|
|
(((y & MASK_SNAN) == MASK_SNAN) ^ ((x & MASK_SNAN) ==
|
|
MASK_SNAN))) {
|
|
// it comes down to the payload. we want to return true if x has a
|
|
// smaller payload, or if the payloads are equal (canonical forms
|
|
// are bitwise identical)
|
|
pyld_y = y & 0x0003ffffffffffffull;
|
|
pyld_x = x & 0x0003ffffffffffffull;
|
|
// if x is zero and y isn't, x has the smaller
|
|
// payload definitely (since we know y isn't 0 at this point)
|
|
if (pyld_x > 999999999999999ull || pyld_x == 0) {
|
|
res = 1;
|
|
BID_RETURN (res);
|
|
}
|
|
|
|
if (pyld_y > 999999999999999ull || pyld_y == 0) {
|
|
// if y is zero, x must be less than or numerically equal
|
|
res = 0;
|
|
BID_RETURN (res);
|
|
}
|
|
res = (pyld_x <= pyld_y);
|
|
BID_RETURN (res);
|
|
|
|
} else {
|
|
// return true if y is +qNaN and x is +sNaN
|
|
// (we know they're different bc of xor if_stmt above)
|
|
res = ((x & MASK_SNAN) == MASK_SNAN);
|
|
BID_RETURN (res);
|
|
}
|
|
}
|
|
|
|
} else if ((y & MASK_NAN) == MASK_NAN) {
|
|
// x is certainly not NAN in this case.
|
|
// return true if y is positive
|
|
res = 1;
|
|
BID_RETURN (res);
|
|
}
|
|
// SIMPLE (CASE2)
|
|
// if all the bits (except sign bit) are the same,
|
|
// these numbers are equal.
|
|
if ((x & ~MASK_SIGN) == (y & ~MASK_SIGN)) {
|
|
res = 1;
|
|
BID_RETURN (res);
|
|
}
|
|
// INFINITY (CASE3)
|
|
if ((x & MASK_INF) == MASK_INF) {
|
|
// x is positive infinity, only return1
|
|
// if y is positive infinity as well
|
|
res = ((y & MASK_INF) == MASK_INF);
|
|
BID_RETURN (res);
|
|
} else if ((y & MASK_INF) == MASK_INF) {
|
|
// x is finite, so:
|
|
// if y is +inf, x<y
|
|
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 || sig_x == 0) {
|
|
x_is_zero = 1;
|
|
}
|
|
} else {
|
|
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
|
|
sig_x = (x & MASK_BINARY_SIG1);
|
|
if (sig_x == 0) {
|
|
x_is_zero = 1;
|
|
}
|
|
}
|
|
|
|
// 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 || sig_y == 0) {
|
|
y_is_zero = 1;
|
|
}
|
|
} else {
|
|
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
|
|
sig_y = (y & MASK_BINARY_SIG1);
|
|
if (sig_y == 0) {
|
|
y_is_zero = 1;
|
|
}
|
|
}
|
|
|
|
// ZERO (CASE 5)
|
|
// if x and y represent the same entities,
|
|
// and both are negative , return true iff exp_x <= exp_y
|
|
if (x_is_zero && y_is_zero) {
|
|
// totalOrder(x,y) iff exp_x <= exp_y for positive numbers
|
|
res = (exp_x <= exp_y);
|
|
BID_RETURN (res);
|
|
}
|
|
// if x is zero and y isn't, clearly x has the smaller payload.
|
|
if (x_is_zero) {
|
|
res = 1;
|
|
BID_RETURN (res);
|
|
}
|
|
// if y is zero, and x isn't, clearly y has the smaller payload.
|
|
if (y_is_zero) {
|
|
res = 0;
|
|
BID_RETURN (res);
|
|
}
|
|
// REDUNDANT REPRESENTATIONS (CASE6)
|
|
// if both components are either bigger or smaller
|
|
if (sig_x > sig_y && exp_x >= exp_y) {
|
|
res = 0;
|
|
BID_RETURN (res);
|
|
}
|
|
if (sig_x < sig_y && exp_x <= exp_y) {
|
|
res = 1;
|
|
BID_RETURN (res);
|
|
}
|
|
// if exp_x is 15 greater than exp_y, it is definitely
|
|
// larger, so no need for compensation
|
|
if (exp_x - exp_y > 15) {
|
|
res = 0; // difference cannot be greater than 10^15
|
|
BID_RETURN (res);
|
|
}
|
|
// if exp_x is 15 less than exp_y, it is definitely
|
|
// smaller, no need for compensation
|
|
if (exp_y - exp_x > 15) {
|
|
res = 1;
|
|
BID_RETURN (res);
|
|
}
|
|
// if |exp_x - exp_y| < 15, it comes down
|
|
// to the compensated significand
|
|
if (exp_x > exp_y) {
|
|
|
|
// otherwise adjust the x significand upwards
|
|
__mul_64x64_to_128MACH (sig_n_prime, sig_x,
|
|
mult_factor[exp_x - exp_y]);
|
|
|
|
// if x and y represent the same entities,
|
|
// and both are negative, return true iff exp_x <= exp_y
|
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
|
|
// case cannot occur, because all bits
|
|
// must be the same - would have been caught if (x==y)
|
|
res = (exp_x <= exp_y);
|
|
BID_RETURN (res);
|
|
}
|
|
// if positive, return 1 if adjusted x is smaller than y
|
|
res = ((sig_n_prime.w[1] == 0) && sig_n_prime.w[0] < sig_y);
|
|
BID_RETURN (res);
|
|
}
|
|
// adjust the y significand upwards
|
|
__mul_64x64_to_128MACH (sig_n_prime, sig_y,
|
|
mult_factor[exp_y - exp_x]);
|
|
|
|
// if x and y represent the same entities,
|
|
// and both are negative, return true iff exp_x <= exp_y
|
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
|
|
res = (exp_x <= exp_y);
|
|
BID_RETURN (res);
|
|
}
|
|
// values are not equal, for positive numbers
|
|
// return 1 if x is less than y. 0 otherwise
|
|
res = ((sig_n_prime.w[1] > 0) || (sig_x < sig_n_prime.w[0]));
|
|
BID_RETURN (res);
|
|
|
|
}
|
|
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
|
void
|
|
bid64_radix (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
|
|
UINT64 x = *px;
|
|
#else
|
|
int
|
|
bid64_radix (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
|
|
#endif
|
|
int res;
|
|
if (x) // dummy test
|
|
res = 10;
|
|
else
|
|
res = 10;
|
|
BID_RETURN (res);
|
|
}
|