/* Copyright (C) 2007, 2009 Free Software Foundation, Inc.
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/* Copyright (C) 2007, 2009 Free Software Foundation, Inc.
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This file is part of GCC.
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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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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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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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Software Foundation; either version 3, or (at your option) any later
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version.
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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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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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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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FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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for more details.
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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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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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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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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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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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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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see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
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<http://www.gnu.org/licenses/>. */
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<http://www.gnu.org/licenses/>. */
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#include "bid_internal.h"
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#include "bid_internal.h"
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/*****************************************************************************
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/*****************************************************************************
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* BID64 minimum function - returns greater of two numbers
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* BID64 minimum function - returns greater of two numbers
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*****************************************************************************/
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*****************************************************************************/
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static const UINT64 mult_factor[16] = {
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static const UINT64 mult_factor[16] = {
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1ull, 10ull, 100ull, 1000ull,
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1ull, 10ull, 100ull, 1000ull,
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10000ull, 100000ull, 1000000ull, 10000000ull,
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10000ull, 100000ull, 1000000ull, 10000000ull,
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100000000ull, 1000000000ull, 10000000000ull, 100000000000ull,
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100000000ull, 1000000000ull, 10000000000ull, 100000000000ull,
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1000000000000ull, 10000000000000ull,
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1000000000000ull, 10000000000000ull,
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100000000000000ull, 1000000000000000ull
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100000000000000ull, 1000000000000000ull
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};
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};
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#if DECIMAL_CALL_BY_REFERENCE
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#if DECIMAL_CALL_BY_REFERENCE
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void
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void
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bid64_minnum (UINT64 * pres, UINT64 * px, UINT64 * py _EXC_FLAGS_PARAM) {
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bid64_minnum (UINT64 * pres, UINT64 * px, UINT64 * py _EXC_FLAGS_PARAM) {
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UINT64 x = *px;
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UINT64 x = *px;
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UINT64 y = *py;
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UINT64 y = *py;
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#else
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#else
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UINT64
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UINT64
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bid64_minnum (UINT64 x, UINT64 y _EXC_FLAGS_PARAM) {
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bid64_minnum (UINT64 x, UINT64 y _EXC_FLAGS_PARAM) {
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#endif
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#endif
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UINT64 res;
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UINT64 res;
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int exp_x, exp_y;
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int exp_x, exp_y;
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UINT64 sig_x, sig_y;
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UINT64 sig_x, sig_y;
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UINT128 sig_n_prime;
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UINT128 sig_n_prime;
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char x_is_zero = 0, y_is_zero = 0;
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char x_is_zero = 0, y_is_zero = 0;
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// check for non-canonical x
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// check for non-canonical x
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if ((x & MASK_NAN) == MASK_NAN) { // x is NaN
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if ((x & MASK_NAN) == MASK_NAN) { // x is NaN
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x = x & 0xfe03ffffffffffffull; // clear G6-G12
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x = x & 0xfe03ffffffffffffull; // clear G6-G12
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if ((x & 0x0003ffffffffffffull) > 999999999999999ull) {
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if ((x & 0x0003ffffffffffffull) > 999999999999999ull) {
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x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits
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x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits
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}
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}
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} else if ((x & MASK_INF) == MASK_INF) { // check for Infinity
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} else if ((x & MASK_INF) == MASK_INF) { // check for Infinity
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x = x & (MASK_SIGN | MASK_INF);
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x = x & (MASK_SIGN | MASK_INF);
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} else { // x is not special
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} else { // x is not special
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// check for non-canonical values - treated as zero
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// check for non-canonical values - treated as zero
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if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
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if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
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// if the steering bits are 11, then the exponent is G[0:w+1]
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// if the steering bits are 11, then the exponent is G[0:w+1]
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if (((x & MASK_BINARY_SIG2) | MASK_BINARY_OR2) >
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if (((x & MASK_BINARY_SIG2) | MASK_BINARY_OR2) >
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9999999999999999ull) {
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9999999999999999ull) {
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// non-canonical
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// non-canonical
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x = (x & MASK_SIGN) | ((x & MASK_BINARY_EXPONENT2) << 2);
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x = (x & MASK_SIGN) | ((x & MASK_BINARY_EXPONENT2) << 2);
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} // else canonical
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} // else canonical
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} // else canonical
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} // else canonical
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}
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}
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// check for non-canonical y
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// check for non-canonical y
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if ((y & MASK_NAN) == MASK_NAN) { // y is NaN
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if ((y & MASK_NAN) == MASK_NAN) { // y is NaN
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y = y & 0xfe03ffffffffffffull; // clear G6-G12
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y = y & 0xfe03ffffffffffffull; // clear G6-G12
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if ((y & 0x0003ffffffffffffull) > 999999999999999ull) {
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if ((y & 0x0003ffffffffffffull) > 999999999999999ull) {
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y = y & 0xfe00000000000000ull; // clear G6-G12 and the payload bits
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y = y & 0xfe00000000000000ull; // clear G6-G12 and the payload bits
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}
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}
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} else if ((y & MASK_INF) == MASK_INF) { // check for Infinity
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} else if ((y & MASK_INF) == MASK_INF) { // check for Infinity
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y = y & (MASK_SIGN | MASK_INF);
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y = y & (MASK_SIGN | MASK_INF);
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} else { // y is not special
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} else { // y is not special
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// check for non-canonical values - treated as zero
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// check for non-canonical values - treated as zero
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if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
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if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
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// if the steering bits are 11, then the exponent is G[0:w+1]
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// if the steering bits are 11, then the exponent is G[0:w+1]
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if (((y & MASK_BINARY_SIG2) | MASK_BINARY_OR2) >
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if (((y & MASK_BINARY_SIG2) | MASK_BINARY_OR2) >
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9999999999999999ull) {
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9999999999999999ull) {
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// non-canonical
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// non-canonical
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y = (y & MASK_SIGN) | ((y & MASK_BINARY_EXPONENT2) << 2);
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y = (y & MASK_SIGN) | ((y & MASK_BINARY_EXPONENT2) << 2);
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} // else canonical
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} // else canonical
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} // else canonical
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} // else canonical
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}
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}
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// NaN (CASE1)
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// NaN (CASE1)
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if ((x & MASK_NAN) == MASK_NAN) { // x is NAN
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if ((x & MASK_NAN) == MASK_NAN) { // x is NAN
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if ((x & MASK_SNAN) == MASK_SNAN) { // x is SNaN
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if ((x & MASK_SNAN) == MASK_SNAN) { // x is SNaN
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// if x is SNAN, then return quiet (x)
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// if x is SNAN, then return quiet (x)
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*pfpsf |= INVALID_EXCEPTION; // set exception if SNaN
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*pfpsf |= INVALID_EXCEPTION; // set exception if SNaN
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x = x & 0xfdffffffffffffffull; // quietize x
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x = x & 0xfdffffffffffffffull; // quietize x
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res = x;
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res = x;
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} else { // x is QNaN
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} else { // x is QNaN
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if ((y & MASK_NAN) == MASK_NAN) { // y is NAN
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if ((y & MASK_NAN) == MASK_NAN) { // y is NAN
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if ((y & MASK_SNAN) == MASK_SNAN) { // y is SNAN
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if ((y & MASK_SNAN) == MASK_SNAN) { // y is SNAN
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*pfpsf |= INVALID_EXCEPTION; // set invalid flag
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*pfpsf |= INVALID_EXCEPTION; // set invalid flag
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}
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}
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res = x;
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res = x;
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} else {
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} else {
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res = y;
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res = y;
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}
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}
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}
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}
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BID_RETURN (res);
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BID_RETURN (res);
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} else if ((y & MASK_NAN) == MASK_NAN) { // y is NaN, but x is not
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} else if ((y & MASK_NAN) == MASK_NAN) { // y is NaN, but x is not
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if ((y & MASK_SNAN) == MASK_SNAN) {
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if ((y & MASK_SNAN) == MASK_SNAN) {
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*pfpsf |= INVALID_EXCEPTION; // set exception if SNaN
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*pfpsf |= INVALID_EXCEPTION; // set exception if SNaN
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y = y & 0xfdffffffffffffffull; // quietize y
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y = y & 0xfdffffffffffffffull; // quietize y
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res = y;
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res = y;
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} else {
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} else {
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// will return x (which is not NaN)
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// will return x (which is not NaN)
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res = x;
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res = x;
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}
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}
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BID_RETURN (res);
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BID_RETURN (res);
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}
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}
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// SIMPLE (CASE2)
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// SIMPLE (CASE2)
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// if all the bits are the same, these numbers are equal, return either number
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// if all the bits are the same, these numbers are equal, return either number
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if (x == y) {
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if (x == y) {
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res = x;
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res = x;
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BID_RETURN (res);
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BID_RETURN (res);
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}
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}
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// INFINITY (CASE3)
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// INFINITY (CASE3)
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if ((x & MASK_INF) == MASK_INF) {
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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 x
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// if x is neg infinity, there is no way it is greater than y, return x
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if (((x & MASK_SIGN) == MASK_SIGN)) {
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if (((x & MASK_SIGN) == MASK_SIGN)) {
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res = x;
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res = x;
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BID_RETURN (res);
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BID_RETURN (res);
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}
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}
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// x is pos infinity, return y
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// x is pos infinity, return y
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else {
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else {
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res = y;
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res = y;
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BID_RETURN (res);
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BID_RETURN (res);
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}
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}
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} else if ((y & MASK_INF) == MASK_INF) {
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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 y
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// x is finite, so if y is positive infinity, then x is less, return y
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// if y is negative infinity, then x is greater, return x
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// if y is negative infinity, then x is greater, return x
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res = ((y & MASK_SIGN) == MASK_SIGN) ? y : x;
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res = ((y & MASK_SIGN) == MASK_SIGN) ? y : x;
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BID_RETURN (res);
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BID_RETURN (res);
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}
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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 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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if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
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exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
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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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sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
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} else {
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} else {
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exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
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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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sig_x = (x & MASK_BINARY_SIG1);
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}
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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 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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if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
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exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
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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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sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
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} else {
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} else {
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exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
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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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sig_y = (y & MASK_BINARY_SIG1);
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}
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}
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// ZERO (CASE4)
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// ZERO (CASE4)
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// some properties:
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// some properties:
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// (+ZERO == -ZERO) => therefore
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// (+ZERO == -ZERO) => therefore
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// ignore the sign, and neither number is greater
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// 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 =>
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// (ZERO x 10^A == ZERO x 10^B) for any valid A, B =>
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// ignore the exponent field
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// ignore the exponent field
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// (Any non-canonical # is considered 0)
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// (Any non-canonical # is considered 0)
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if (sig_x == 0) {
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if (sig_x == 0) {
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x_is_zero = 1;
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x_is_zero = 1;
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}
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}
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if (sig_y == 0) {
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if (sig_y == 0) {
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y_is_zero = 1;
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y_is_zero = 1;
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}
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}
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if (x_is_zero && y_is_zero) {
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if (x_is_zero && y_is_zero) {
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// if both numbers are zero, neither is greater => return either
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// if both numbers are zero, neither is greater => return either
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res = y;
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res = y;
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BID_RETURN (res);
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BID_RETURN (res);
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} else if (x_is_zero) {
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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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// is x is zero, it is greater if Y is negative
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res = ((y & MASK_SIGN) == MASK_SIGN) ? y : x;
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res = ((y & MASK_SIGN) == MASK_SIGN) ? y : x;
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BID_RETURN (res);
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BID_RETURN (res);
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} else if (y_is_zero) {
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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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// is y is zero, X is greater if it is positive
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res = ((x & MASK_SIGN) != MASK_SIGN) ? y : x;;
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res = ((x & MASK_SIGN) != MASK_SIGN) ? y : x;;
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BID_RETURN (res);
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BID_RETURN (res);
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}
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}
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// OPPOSITE SIGN (CASE5)
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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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// 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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if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
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res = ((y & MASK_SIGN) == MASK_SIGN) ? y : x;
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res = ((y & MASK_SIGN) == MASK_SIGN) ? y : x;
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BID_RETURN (res);
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BID_RETURN (res);
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}
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}
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// REDUNDANT REPRESENTATIONS (CASE6)
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// REDUNDANT REPRESENTATIONS (CASE6)
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// if both components are either bigger or smaller,
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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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// 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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if (sig_x > sig_y && exp_x >= exp_y) {
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res = ((x & MASK_SIGN) != MASK_SIGN) ? y : x;
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res = ((x & MASK_SIGN) != MASK_SIGN) ? y : x;
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BID_RETURN (res);
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BID_RETURN (res);
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}
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}
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if (sig_x < sig_y && exp_x <= exp_y) {
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if (sig_x < sig_y && exp_x <= exp_y) {
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res = ((x & MASK_SIGN) == MASK_SIGN) ? y : x;
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res = ((x & MASK_SIGN) == MASK_SIGN) ? y : x;
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BID_RETURN (res);
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BID_RETURN (res);
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}
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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 is 15 greater than exp_y, no need for compensation
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if (exp_x - exp_y > 15) {
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if (exp_x - exp_y > 15) {
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res = ((x & MASK_SIGN) != MASK_SIGN) ? y : x; // difference cannot be >10^15
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res = ((x & MASK_SIGN) != MASK_SIGN) ? y : x; // difference cannot be >10^15
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BID_RETURN (res);
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BID_RETURN (res);
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}
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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_x is 15 less than exp_y, no need for compensation
|
if (exp_y - exp_x > 15) {
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if (exp_y - exp_x > 15) {
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res = ((x & MASK_SIGN) == MASK_SIGN) ? y : x;
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res = ((x & MASK_SIGN) == MASK_SIGN) ? y : x;
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BID_RETURN (res);
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BID_RETURN (res);
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}
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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| < 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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if (exp_x > exp_y) { // to simplify the loop below,
|
|
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// otherwise adjust the x significand upwards
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// otherwise adjust the x significand upwards
|
__mul_64x64_to_128MACH (sig_n_prime, sig_x,
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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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mult_factor[exp_x - exp_y]);
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// if postitive, return whichever significand is larger
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// if postitive, return whichever significand is larger
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// (converse if negative)
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// (converse if negative)
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
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if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
|
res = y;
|
res = y;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
|
|
res = (((sig_n_prime.w[1] > 0)
|
res = (((sig_n_prime.w[1] > 0)
|
|| sig_n_prime.w[0] > sig_y) ^ ((x & MASK_SIGN) ==
|
|| sig_n_prime.w[0] > sig_y) ^ ((x & MASK_SIGN) ==
|
MASK_SIGN)) ? y : x;
|
MASK_SIGN)) ? y : x;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
// adjust the y significand upwards
|
// adjust the y significand upwards
|
__mul_64x64_to_128MACH (sig_n_prime, sig_y,
|
__mul_64x64_to_128MACH (sig_n_prime, sig_y,
|
mult_factor[exp_y - exp_x]);
|
mult_factor[exp_y - exp_x]);
|
|
|
// if postitive, return whichever significand is larger (converse if negative)
|
// if postitive, return whichever significand is larger (converse if negative)
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
|
res = y;
|
res = y;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
res = (((sig_n_prime.w[1] == 0)
|
res = (((sig_n_prime.w[1] == 0)
|
&& (sig_x > sig_n_prime.w[0])) ^ ((x & MASK_SIGN) ==
|
&& (sig_x > sig_n_prime.w[0])) ^ ((x & MASK_SIGN) ==
|
MASK_SIGN)) ? y : x;
|
MASK_SIGN)) ? y : x;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
|
|
/*****************************************************************************
|
/*****************************************************************************
|
* BID64 minimum magnitude function - returns greater of two numbers
|
* BID64 minimum magnitude function - returns greater of two numbers
|
*****************************************************************************/
|
*****************************************************************************/
|
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
#if DECIMAL_CALL_BY_REFERENCE
|
void
|
void
|
bid64_minnum_mag (UINT64 * pres, UINT64 * px,
|
bid64_minnum_mag (UINT64 * pres, UINT64 * px,
|
UINT64 * py _EXC_FLAGS_PARAM) {
|
UINT64 * py _EXC_FLAGS_PARAM) {
|
UINT64 x = *px;
|
UINT64 x = *px;
|
UINT64 y = *py;
|
UINT64 y = *py;
|
#else
|
#else
|
UINT64
|
UINT64
|
bid64_minnum_mag (UINT64 x, UINT64 y _EXC_FLAGS_PARAM) {
|
bid64_minnum_mag (UINT64 x, UINT64 y _EXC_FLAGS_PARAM) {
|
#endif
|
#endif
|
|
|
UINT64 res;
|
UINT64 res;
|
int exp_x, exp_y;
|
int exp_x, exp_y;
|
UINT64 sig_x, sig_y;
|
UINT64 sig_x, sig_y;
|
UINT128 sig_n_prime;
|
UINT128 sig_n_prime;
|
|
|
// check for non-canonical x
|
// check for non-canonical x
|
if ((x & MASK_NAN) == MASK_NAN) { // x is NaN
|
if ((x & MASK_NAN) == MASK_NAN) { // x is NaN
|
x = x & 0xfe03ffffffffffffull; // clear G6-G12
|
x = x & 0xfe03ffffffffffffull; // clear G6-G12
|
if ((x & 0x0003ffffffffffffull) > 999999999999999ull) {
|
if ((x & 0x0003ffffffffffffull) > 999999999999999ull) {
|
x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits
|
x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits
|
}
|
}
|
} else if ((x & MASK_INF) == MASK_INF) { // check for Infinity
|
} else if ((x & MASK_INF) == MASK_INF) { // check for Infinity
|
x = x & (MASK_SIGN | MASK_INF);
|
x = x & (MASK_SIGN | MASK_INF);
|
} else { // x is not special
|
} else { // x is not special
|
// check for non-canonical values - treated as zero
|
// check for non-canonical values - treated as zero
|
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
// if the steering bits are 11, then the exponent is G[0:w+1]
|
// if the steering bits are 11, then the exponent is G[0:w+1]
|
if (((x & MASK_BINARY_SIG2) | MASK_BINARY_OR2) >
|
if (((x & MASK_BINARY_SIG2) | MASK_BINARY_OR2) >
|
9999999999999999ull) {
|
9999999999999999ull) {
|
// non-canonical
|
// non-canonical
|
x = (x & MASK_SIGN) | ((x & MASK_BINARY_EXPONENT2) << 2);
|
x = (x & MASK_SIGN) | ((x & MASK_BINARY_EXPONENT2) << 2);
|
} // else canonical
|
} // else canonical
|
} // else canonical
|
} // else canonical
|
}
|
}
|
|
|
// check for non-canonical y
|
// check for non-canonical y
|
if ((y & MASK_NAN) == MASK_NAN) { // y is NaN
|
if ((y & MASK_NAN) == MASK_NAN) { // y is NaN
|
y = y & 0xfe03ffffffffffffull; // clear G6-G12
|
y = y & 0xfe03ffffffffffffull; // clear G6-G12
|
if ((y & 0x0003ffffffffffffull) > 999999999999999ull) {
|
if ((y & 0x0003ffffffffffffull) > 999999999999999ull) {
|
y = y & 0xfe00000000000000ull; // clear G6-G12 and the payload bits
|
y = y & 0xfe00000000000000ull; // clear G6-G12 and the payload bits
|
}
|
}
|
} else if ((y & MASK_INF) == MASK_INF) { // check for Infinity
|
} else if ((y & MASK_INF) == MASK_INF) { // check for Infinity
|
y = y & (MASK_SIGN | MASK_INF);
|
y = y & (MASK_SIGN | MASK_INF);
|
} else { // y is not special
|
} else { // y is not special
|
// check for non-canonical values - treated as zero
|
// check for non-canonical values - treated as zero
|
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
// if the steering bits are 11, then the exponent is G[0:w+1]
|
// if the steering bits are 11, then the exponent is G[0:w+1]
|
if (((y & MASK_BINARY_SIG2) | MASK_BINARY_OR2) >
|
if (((y & MASK_BINARY_SIG2) | MASK_BINARY_OR2) >
|
9999999999999999ull) {
|
9999999999999999ull) {
|
// non-canonical
|
// non-canonical
|
y = (y & MASK_SIGN) | ((y & MASK_BINARY_EXPONENT2) << 2);
|
y = (y & MASK_SIGN) | ((y & MASK_BINARY_EXPONENT2) << 2);
|
} // else canonical
|
} // else canonical
|
} // else canonical
|
} // else canonical
|
}
|
}
|
|
|
// NaN (CASE1)
|
// NaN (CASE1)
|
if ((x & MASK_NAN) == MASK_NAN) { // x is NAN
|
if ((x & MASK_NAN) == MASK_NAN) { // x is NAN
|
if ((x & MASK_SNAN) == MASK_SNAN) { // x is SNaN
|
if ((x & MASK_SNAN) == MASK_SNAN) { // x is SNaN
|
// if x is SNAN, then return quiet (x)
|
// if x is SNAN, then return quiet (x)
|
*pfpsf |= INVALID_EXCEPTION; // set exception if SNaN
|
*pfpsf |= INVALID_EXCEPTION; // set exception if SNaN
|
x = x & 0xfdffffffffffffffull; // quietize x
|
x = x & 0xfdffffffffffffffull; // quietize x
|
res = x;
|
res = x;
|
} else { // x is QNaN
|
} else { // x is QNaN
|
if ((y & MASK_NAN) == MASK_NAN) { // y is NAN
|
if ((y & MASK_NAN) == MASK_NAN) { // y is NAN
|
if ((y & MASK_SNAN) == MASK_SNAN) { // y is SNAN
|
if ((y & MASK_SNAN) == MASK_SNAN) { // y is SNAN
|
*pfpsf |= INVALID_EXCEPTION; // set invalid flag
|
*pfpsf |= INVALID_EXCEPTION; // set invalid flag
|
}
|
}
|
res = x;
|
res = x;
|
} else {
|
} else {
|
res = y;
|
res = y;
|
}
|
}
|
}
|
}
|
BID_RETURN (res);
|
BID_RETURN (res);
|
} else if ((y & MASK_NAN) == MASK_NAN) { // y is NaN, but x is not
|
} else if ((y & MASK_NAN) == MASK_NAN) { // y is NaN, but x is not
|
if ((y & MASK_SNAN) == MASK_SNAN) {
|
if ((y & MASK_SNAN) == MASK_SNAN) {
|
*pfpsf |= INVALID_EXCEPTION; // set exception if SNaN
|
*pfpsf |= INVALID_EXCEPTION; // set exception if SNaN
|
y = y & 0xfdffffffffffffffull; // quietize y
|
y = y & 0xfdffffffffffffffull; // quietize y
|
res = y;
|
res = y;
|
} else {
|
} else {
|
// will return x (which is not NaN)
|
// will return x (which is not NaN)
|
res = x;
|
res = x;
|
}
|
}
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
// SIMPLE (CASE2)
|
// SIMPLE (CASE2)
|
// if all the bits are the same, these numbers are equal, return either number
|
// if all the bits are the same, these numbers are equal, return either number
|
if (x == y) {
|
if (x == y) {
|
res = x;
|
res = x;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
// INFINITY (CASE3)
|
// INFINITY (CASE3)
|
if ((x & MASK_INF) == MASK_INF) {
|
if ((x & MASK_INF) == MASK_INF) {
|
// x is infinity, its magnitude is greater than or equal to y
|
// x is infinity, its magnitude is greater than or equal to y
|
// return x only if y is infinity and x is negative
|
// return x only if y is infinity and x is negative
|
res = ((x & MASK_SIGN) == MASK_SIGN
|
res = ((x & MASK_SIGN) == MASK_SIGN
|
&& (y & MASK_INF) == MASK_INF) ? x : y;
|
&& (y & MASK_INF) == MASK_INF) ? x : y;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
} else if ((y & MASK_INF) == MASK_INF) {
|
} else if ((y & MASK_INF) == MASK_INF) {
|
// y is infinity, then it must be greater in magnitude, return x
|
// y is infinity, then it must be greater in magnitude, return x
|
res = x;
|
res = x;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
|
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
|
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
} else {
|
} else {
|
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
|
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
|
sig_x = (x & MASK_BINARY_SIG1);
|
sig_x = (x & MASK_BINARY_SIG1);
|
}
|
}
|
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+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) {
|
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
|
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
|
sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
} else {
|
} else {
|
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
|
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
|
sig_y = (y & MASK_BINARY_SIG1);
|
sig_y = (y & MASK_BINARY_SIG1);
|
}
|
}
|
|
|
// ZERO (CASE4)
|
// ZERO (CASE4)
|
// some properties:
|
// some properties:
|
// (+ZERO == -ZERO) => therefore
|
// (+ZERO == -ZERO) => therefore
|
// ignore the sign, and neither number is greater
|
// ignore the sign, and neither number is greater
|
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B =>
|
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B =>
|
// ignore the exponent field
|
// ignore the exponent field
|
// (Any non-canonical # is considered 0)
|
// (Any non-canonical # is considered 0)
|
if (sig_x == 0) {
|
if (sig_x == 0) {
|
res = x; // x_is_zero, its magnitude must be smaller than y
|
res = x; // x_is_zero, its magnitude must be smaller than y
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
if (sig_y == 0) {
|
if (sig_y == 0) {
|
res = y; // y_is_zero, its magnitude must be smaller than x
|
res = y; // y_is_zero, its magnitude must be smaller than x
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
// REDUNDANT REPRESENTATIONS (CASE6)
|
// REDUNDANT REPRESENTATIONS (CASE6)
|
// if both components are either bigger or smaller,
|
// if both components are either bigger or smaller,
|
// it is clear what needs to be done
|
// it is clear what needs to be done
|
if (sig_x > sig_y && exp_x >= exp_y) {
|
if (sig_x > sig_y && exp_x >= exp_y) {
|
res = y;
|
res = y;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
if (sig_x < sig_y && exp_x <= exp_y) {
|
if (sig_x < sig_y && exp_x <= exp_y) {
|
res = x;
|
res = x;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
// if exp_x is 15 greater than exp_y, no need for compensation
|
// if exp_x is 15 greater than exp_y, no need for compensation
|
if (exp_x - exp_y > 15) {
|
if (exp_x - exp_y > 15) {
|
res = y; // difference cannot be greater than 10^15
|
res = y; // difference cannot be greater than 10^15
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
// if exp_x is 15 less than exp_y, no need for compensation
|
// if exp_x is 15 less than exp_y, no need for compensation
|
if (exp_y - exp_x > 15) {
|
if (exp_y - exp_x > 15) {
|
res = x;
|
res = x;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
// if |exp_x - exp_y| < 15, it comes down to the compensated significand
|
// if |exp_x - exp_y| < 15, it comes down to the compensated significand
|
if (exp_x > exp_y) { // to simplify the loop below,
|
if (exp_x > exp_y) { // to simplify the loop below,
|
// otherwise adjust the x significand upwards
|
// otherwise adjust the x significand upwards
|
__mul_64x64_to_128MACH (sig_n_prime, sig_x,
|
__mul_64x64_to_128MACH (sig_n_prime, sig_x,
|
mult_factor[exp_x - exp_y]);
|
mult_factor[exp_x - exp_y]);
|
// now, sig_n_prime has: sig_x * 10^(exp_x-exp_y), this is
|
// now, sig_n_prime has: sig_x * 10^(exp_x-exp_y), this is
|
// the compensated signif.
|
// the compensated signif.
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
|
// two numbers are equal, return minNum(x,y)
|
// two numbers are equal, return minNum(x,y)
|
res = ((y & MASK_SIGN) == MASK_SIGN) ? y : x;
|
res = ((y & MASK_SIGN) == MASK_SIGN) ? y : x;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
// now, if compensated_x (sig_n_prime) is greater than y, return y,
|
// now, if compensated_x (sig_n_prime) is greater than y, return y,
|
// otherwise return x
|
// otherwise return x
|
res = ((sig_n_prime.w[1] != 0) || sig_n_prime.w[0] > sig_y) ? y : x;
|
res = ((sig_n_prime.w[1] != 0) || sig_n_prime.w[0] > sig_y) ? y : x;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
// exp_y must be greater than exp_x, thus adjust the y significand upwards
|
// exp_y must be greater than exp_x, thus adjust the y significand upwards
|
__mul_64x64_to_128MACH (sig_n_prime, sig_y,
|
__mul_64x64_to_128MACH (sig_n_prime, sig_y,
|
mult_factor[exp_y - exp_x]);
|
mult_factor[exp_y - exp_x]);
|
|
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
|
res = ((y & MASK_SIGN) == MASK_SIGN) ? y : x;
|
res = ((y & MASK_SIGN) == MASK_SIGN) ? y : x;
|
// two numbers are equal, return either
|
// two numbers are equal, return either
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
|
|
res = ((sig_n_prime.w[1] == 0) && (sig_x > sig_n_prime.w[0])) ? y : x;
|
res = ((sig_n_prime.w[1] == 0) && (sig_x > sig_n_prime.w[0])) ? y : x;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
|
|
/*****************************************************************************
|
/*****************************************************************************
|
* BID64 maximum function - returns greater of two numbers
|
* BID64 maximum function - returns greater of two numbers
|
*****************************************************************************/
|
*****************************************************************************/
|
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
#if DECIMAL_CALL_BY_REFERENCE
|
void
|
void
|
bid64_maxnum (UINT64 * pres, UINT64 * px, UINT64 * py _EXC_FLAGS_PARAM) {
|
bid64_maxnum (UINT64 * pres, UINT64 * px, UINT64 * py _EXC_FLAGS_PARAM) {
|
UINT64 x = *px;
|
UINT64 x = *px;
|
UINT64 y = *py;
|
UINT64 y = *py;
|
#else
|
#else
|
UINT64
|
UINT64
|
bid64_maxnum (UINT64 x, UINT64 y _EXC_FLAGS_PARAM) {
|
bid64_maxnum (UINT64 x, UINT64 y _EXC_FLAGS_PARAM) {
|
#endif
|
#endif
|
|
|
UINT64 res;
|
UINT64 res;
|
int exp_x, exp_y;
|
int exp_x, exp_y;
|
UINT64 sig_x, sig_y;
|
UINT64 sig_x, sig_y;
|
UINT128 sig_n_prime;
|
UINT128 sig_n_prime;
|
char x_is_zero = 0, y_is_zero = 0;
|
char x_is_zero = 0, y_is_zero = 0;
|
|
|
// check for non-canonical x
|
// check for non-canonical x
|
if ((x & MASK_NAN) == MASK_NAN) { // x is NaN
|
if ((x & MASK_NAN) == MASK_NAN) { // x is NaN
|
x = x & 0xfe03ffffffffffffull; // clear G6-G12
|
x = x & 0xfe03ffffffffffffull; // clear G6-G12
|
if ((x & 0x0003ffffffffffffull) > 999999999999999ull) {
|
if ((x & 0x0003ffffffffffffull) > 999999999999999ull) {
|
x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits
|
x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits
|
}
|
}
|
} else if ((x & MASK_INF) == MASK_INF) { // check for Infinity
|
} else if ((x & MASK_INF) == MASK_INF) { // check for Infinity
|
x = x & (MASK_SIGN | MASK_INF);
|
x = x & (MASK_SIGN | MASK_INF);
|
} else { // x is not special
|
} else { // x is not special
|
// check for non-canonical values - treated as zero
|
// check for non-canonical values - treated as zero
|
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
// if the steering bits are 11, then the exponent is G[0:w+1]
|
// if the steering bits are 11, then the exponent is G[0:w+1]
|
if (((x & MASK_BINARY_SIG2) | MASK_BINARY_OR2) >
|
if (((x & MASK_BINARY_SIG2) | MASK_BINARY_OR2) >
|
9999999999999999ull) {
|
9999999999999999ull) {
|
// non-canonical
|
// non-canonical
|
x = (x & MASK_SIGN) | ((x & MASK_BINARY_EXPONENT2) << 2);
|
x = (x & MASK_SIGN) | ((x & MASK_BINARY_EXPONENT2) << 2);
|
} // else canonical
|
} // else canonical
|
} // else canonical
|
} // else canonical
|
}
|
}
|
|
|
// check for non-canonical y
|
// check for non-canonical y
|
if ((y & MASK_NAN) == MASK_NAN) { // y is NaN
|
if ((y & MASK_NAN) == MASK_NAN) { // y is NaN
|
y = y & 0xfe03ffffffffffffull; // clear G6-G12
|
y = y & 0xfe03ffffffffffffull; // clear G6-G12
|
if ((y & 0x0003ffffffffffffull) > 999999999999999ull) {
|
if ((y & 0x0003ffffffffffffull) > 999999999999999ull) {
|
y = y & 0xfe00000000000000ull; // clear G6-G12 and the payload bits
|
y = y & 0xfe00000000000000ull; // clear G6-G12 and the payload bits
|
}
|
}
|
} else if ((y & MASK_INF) == MASK_INF) { // check for Infinity
|
} else if ((y & MASK_INF) == MASK_INF) { // check for Infinity
|
y = y & (MASK_SIGN | MASK_INF);
|
y = y & (MASK_SIGN | MASK_INF);
|
} else { // y is not special
|
} else { // y is not special
|
// check for non-canonical values - treated as zero
|
// check for non-canonical values - treated as zero
|
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
// if the steering bits are 11, then the exponent is G[0:w+1]
|
// if the steering bits are 11, then the exponent is G[0:w+1]
|
if (((y & MASK_BINARY_SIG2) | MASK_BINARY_OR2) >
|
if (((y & MASK_BINARY_SIG2) | MASK_BINARY_OR2) >
|
9999999999999999ull) {
|
9999999999999999ull) {
|
// non-canonical
|
// non-canonical
|
y = (y & MASK_SIGN) | ((y & MASK_BINARY_EXPONENT2) << 2);
|
y = (y & MASK_SIGN) | ((y & MASK_BINARY_EXPONENT2) << 2);
|
} // else canonical
|
} // else canonical
|
} // else canonical
|
} // else canonical
|
}
|
}
|
|
|
// NaN (CASE1)
|
// NaN (CASE1)
|
if ((x & MASK_NAN) == MASK_NAN) { // x is NAN
|
if ((x & MASK_NAN) == MASK_NAN) { // x is NAN
|
if ((x & MASK_SNAN) == MASK_SNAN) { // x is SNaN
|
if ((x & MASK_SNAN) == MASK_SNAN) { // x is SNaN
|
// if x is SNAN, then return quiet (x)
|
// if x is SNAN, then return quiet (x)
|
*pfpsf |= INVALID_EXCEPTION; // set exception if SNaN
|
*pfpsf |= INVALID_EXCEPTION; // set exception if SNaN
|
x = x & 0xfdffffffffffffffull; // quietize x
|
x = x & 0xfdffffffffffffffull; // quietize x
|
res = x;
|
res = x;
|
} else { // x is QNaN
|
} else { // x is QNaN
|
if ((y & MASK_NAN) == MASK_NAN) { // y is NAN
|
if ((y & MASK_NAN) == MASK_NAN) { // y is NAN
|
if ((y & MASK_SNAN) == MASK_SNAN) { // y is SNAN
|
if ((y & MASK_SNAN) == MASK_SNAN) { // y is SNAN
|
*pfpsf |= INVALID_EXCEPTION; // set invalid flag
|
*pfpsf |= INVALID_EXCEPTION; // set invalid flag
|
}
|
}
|
res = x;
|
res = x;
|
} else {
|
} else {
|
res = y;
|
res = y;
|
}
|
}
|
}
|
}
|
BID_RETURN (res);
|
BID_RETURN (res);
|
} else if ((y & MASK_NAN) == MASK_NAN) { // y is NaN, but x is not
|
} else if ((y & MASK_NAN) == MASK_NAN) { // y is NaN, but x is not
|
if ((y & MASK_SNAN) == MASK_SNAN) {
|
if ((y & MASK_SNAN) == MASK_SNAN) {
|
*pfpsf |= INVALID_EXCEPTION; // set exception if SNaN
|
*pfpsf |= INVALID_EXCEPTION; // set exception if SNaN
|
y = y & 0xfdffffffffffffffull; // quietize y
|
y = y & 0xfdffffffffffffffull; // quietize y
|
res = y;
|
res = y;
|
} else {
|
} else {
|
// will return x (which is not NaN)
|
// will return x (which is not NaN)
|
res = x;
|
res = x;
|
}
|
}
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
// SIMPLE (CASE2)
|
// SIMPLE (CASE2)
|
// if all the bits are the same, these numbers are equal (not Greater).
|
// if all the bits are the same, these numbers are equal (not Greater).
|
if (x == y) {
|
if (x == y) {
|
res = x;
|
res = x;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
// INFINITY (CASE3)
|
// INFINITY (CASE3)
|
if ((x & MASK_INF) == MASK_INF) {
|
if ((x & MASK_INF) == MASK_INF) {
|
// if x is neg infinity, there is no way it is greater than y, return y
|
// if x is neg infinity, there is no way it is greater than y, return y
|
// x is pos infinity, it is greater, unless y is positive infinity =>
|
// x is pos infinity, it is greater, unless y is positive infinity =>
|
// return y!=pos_infinity
|
// return y!=pos_infinity
|
if (((x & MASK_SIGN) == MASK_SIGN)) {
|
if (((x & MASK_SIGN) == MASK_SIGN)) {
|
res = y;
|
res = y;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
} else {
|
} else {
|
res = (((y & MASK_INF) != MASK_INF)
|
res = (((y & MASK_INF) != MASK_INF)
|
|| ((y & MASK_SIGN) == MASK_SIGN)) ? x : y;
|
|| ((y & MASK_SIGN) == MASK_SIGN)) ? x : y;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
} else if ((y & MASK_INF) == MASK_INF) {
|
} else if ((y & MASK_INF) == MASK_INF) {
|
// x is finite, so if y is positive infinity, then x is less, return y
|
// x is finite, so if y is positive infinity, then x is less, return y
|
// if y is negative infinity, then x is greater, return x
|
// if y is negative infinity, then x is greater, return x
|
res = ((y & MASK_SIGN) == MASK_SIGN) ? x : y;
|
res = ((y & MASK_SIGN) == MASK_SIGN) ? x : y;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
|
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
|
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
} else {
|
} else {
|
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
|
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
|
sig_x = (x & MASK_BINARY_SIG1);
|
sig_x = (x & MASK_BINARY_SIG1);
|
}
|
}
|
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+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) {
|
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
|
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
|
sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
} else {
|
} else {
|
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
|
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
|
sig_y = (y & MASK_BINARY_SIG1);
|
sig_y = (y & MASK_BINARY_SIG1);
|
}
|
}
|
|
|
// ZERO (CASE4)
|
// ZERO (CASE4)
|
// some properties:
|
// some properties:
|
// (+ZERO == -ZERO) => therefore
|
// (+ZERO == -ZERO) => therefore
|
// ignore the sign, and neither number is greater
|
// ignore the sign, and neither number is greater
|
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B =>
|
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B =>
|
// ignore the exponent field
|
// ignore the exponent field
|
// (Any non-canonical # is considered 0)
|
// (Any non-canonical # is considered 0)
|
if (sig_x == 0) {
|
if (sig_x == 0) {
|
x_is_zero = 1;
|
x_is_zero = 1;
|
}
|
}
|
if (sig_y == 0) {
|
if (sig_y == 0) {
|
y_is_zero = 1;
|
y_is_zero = 1;
|
}
|
}
|
|
|
if (x_is_zero && y_is_zero) {
|
if (x_is_zero && y_is_zero) {
|
// if both numbers are zero, neither is greater => return NOTGREATERTHAN
|
// if both numbers are zero, neither is greater => return NOTGREATERTHAN
|
res = y;
|
res = y;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
} else if (x_is_zero) {
|
} else if (x_is_zero) {
|
// is x is zero, it is greater if Y is negative
|
// is x is zero, it is greater if Y is negative
|
res = ((y & MASK_SIGN) == MASK_SIGN) ? x : y;
|
res = ((y & MASK_SIGN) == MASK_SIGN) ? x : y;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
} else if (y_is_zero) {
|
} else if (y_is_zero) {
|
// is y is zero, X is greater if it is positive
|
// is y is zero, X is greater if it is positive
|
res = ((x & MASK_SIGN) != MASK_SIGN) ? x : y;;
|
res = ((x & MASK_SIGN) != MASK_SIGN) ? x : y;;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
// OPPOSITE SIGN (CASE5)
|
// OPPOSITE SIGN (CASE5)
|
// now, if the sign bits differ, x is greater if y is negative
|
// now, if the sign bits differ, x is greater if y is negative
|
if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
|
if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
|
res = ((y & MASK_SIGN) == MASK_SIGN) ? x : y;
|
res = ((y & MASK_SIGN) == MASK_SIGN) ? x : y;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
// REDUNDANT REPRESENTATIONS (CASE6)
|
// REDUNDANT REPRESENTATIONS (CASE6)
|
|
|
// if both components are either bigger or smaller,
|
// if both components are either bigger or smaller,
|
// it is clear what needs to be done
|
// it is clear what needs to be done
|
if (sig_x > sig_y && exp_x >= exp_y) {
|
if (sig_x > sig_y && exp_x >= exp_y) {
|
res = ((x & MASK_SIGN) != MASK_SIGN) ? x : y;
|
res = ((x & MASK_SIGN) != MASK_SIGN) ? x : y;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
if (sig_x < sig_y && exp_x <= exp_y) {
|
if (sig_x < sig_y && exp_x <= exp_y) {
|
res = ((x & MASK_SIGN) == MASK_SIGN) ? x : y;
|
res = ((x & MASK_SIGN) == MASK_SIGN) ? x : y;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
// if exp_x is 15 greater than exp_y, no need for compensation
|
// if exp_x is 15 greater than exp_y, no need for compensation
|
if (exp_x - exp_y > 15) {
|
if (exp_x - exp_y > 15) {
|
res = ((x & MASK_SIGN) != MASK_SIGN) ? x : y;
|
res = ((x & MASK_SIGN) != MASK_SIGN) ? x : y;
|
// difference cannot be > 10^15
|
// difference cannot be > 10^15
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
// if exp_x is 15 less than exp_y, no need for compensation
|
// if exp_x is 15 less than exp_y, no need for compensation
|
if (exp_y - exp_x > 15) {
|
if (exp_y - exp_x > 15) {
|
res = ((x & MASK_SIGN) == MASK_SIGN) ? x : y;
|
res = ((x & MASK_SIGN) == MASK_SIGN) ? x : y;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
// if |exp_x - exp_y| < 15, it comes down to the compensated significand
|
// if |exp_x - exp_y| < 15, it comes down to the compensated significand
|
if (exp_x > exp_y) { // to simplify the loop below,
|
if (exp_x > exp_y) { // to simplify the loop below,
|
// otherwise adjust the x significand upwards
|
// otherwise adjust the x significand upwards
|
__mul_64x64_to_128MACH (sig_n_prime, sig_x,
|
__mul_64x64_to_128MACH (sig_n_prime, sig_x,
|
mult_factor[exp_x - exp_y]);
|
mult_factor[exp_x - exp_y]);
|
// if postitive, return whichever significand is larger
|
// if postitive, return whichever significand is larger
|
// (converse if negative)
|
// (converse if negative)
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
|
res = y;
|
res = y;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
res = (((sig_n_prime.w[1] > 0)
|
res = (((sig_n_prime.w[1] > 0)
|
|| sig_n_prime.w[0] > sig_y) ^ ((x & MASK_SIGN) ==
|
|| sig_n_prime.w[0] > sig_y) ^ ((x & MASK_SIGN) ==
|
MASK_SIGN)) ? x : y;
|
MASK_SIGN)) ? x : y;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
// adjust the y significand upwards
|
// adjust the y significand upwards
|
__mul_64x64_to_128MACH (sig_n_prime, sig_y,
|
__mul_64x64_to_128MACH (sig_n_prime, sig_y,
|
mult_factor[exp_y - exp_x]);
|
mult_factor[exp_y - exp_x]);
|
|
|
// if postitive, return whichever significand is larger (converse if negative)
|
// if postitive, return whichever significand is larger (converse if negative)
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
|
res = y;
|
res = y;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
res = (((sig_n_prime.w[1] == 0)
|
res = (((sig_n_prime.w[1] == 0)
|
&& (sig_x > sig_n_prime.w[0])) ^ ((x & MASK_SIGN) ==
|
&& (sig_x > sig_n_prime.w[0])) ^ ((x & MASK_SIGN) ==
|
MASK_SIGN)) ? x : y;
|
MASK_SIGN)) ? x : y;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
|
|
/*****************************************************************************
|
/*****************************************************************************
|
* BID64 maximum magnitude function - returns greater of two numbers
|
* BID64 maximum magnitude function - returns greater of two numbers
|
*****************************************************************************/
|
*****************************************************************************/
|
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
#if DECIMAL_CALL_BY_REFERENCE
|
void
|
void
|
bid64_maxnum_mag (UINT64 * pres, UINT64 * px,
|
bid64_maxnum_mag (UINT64 * pres, UINT64 * px,
|
UINT64 * py _EXC_FLAGS_PARAM) {
|
UINT64 * py _EXC_FLAGS_PARAM) {
|
UINT64 x = *px;
|
UINT64 x = *px;
|
UINT64 y = *py;
|
UINT64 y = *py;
|
#else
|
#else
|
UINT64
|
UINT64
|
bid64_maxnum_mag (UINT64 x, UINT64 y _EXC_FLAGS_PARAM) {
|
bid64_maxnum_mag (UINT64 x, UINT64 y _EXC_FLAGS_PARAM) {
|
#endif
|
#endif
|
|
|
UINT64 res;
|
UINT64 res;
|
int exp_x, exp_y;
|
int exp_x, exp_y;
|
UINT64 sig_x, sig_y;
|
UINT64 sig_x, sig_y;
|
UINT128 sig_n_prime;
|
UINT128 sig_n_prime;
|
|
|
// check for non-canonical x
|
// check for non-canonical x
|
if ((x & MASK_NAN) == MASK_NAN) { // x is NaN
|
if ((x & MASK_NAN) == MASK_NAN) { // x is NaN
|
x = x & 0xfe03ffffffffffffull; // clear G6-G12
|
x = x & 0xfe03ffffffffffffull; // clear G6-G12
|
if ((x & 0x0003ffffffffffffull) > 999999999999999ull) {
|
if ((x & 0x0003ffffffffffffull) > 999999999999999ull) {
|
x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits
|
x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits
|
}
|
}
|
} else if ((x & MASK_INF) == MASK_INF) { // check for Infinity
|
} else if ((x & MASK_INF) == MASK_INF) { // check for Infinity
|
x = x & (MASK_SIGN | MASK_INF);
|
x = x & (MASK_SIGN | MASK_INF);
|
} else { // x is not special
|
} else { // x is not special
|
// check for non-canonical values - treated as zero
|
// check for non-canonical values - treated as zero
|
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
// if the steering bits are 11, then the exponent is G[0:w+1]
|
// if the steering bits are 11, then the exponent is G[0:w+1]
|
if (((x & MASK_BINARY_SIG2) | MASK_BINARY_OR2) >
|
if (((x & MASK_BINARY_SIG2) | MASK_BINARY_OR2) >
|
9999999999999999ull) {
|
9999999999999999ull) {
|
// non-canonical
|
// non-canonical
|
x = (x & MASK_SIGN) | ((x & MASK_BINARY_EXPONENT2) << 2);
|
x = (x & MASK_SIGN) | ((x & MASK_BINARY_EXPONENT2) << 2);
|
} // else canonical
|
} // else canonical
|
} // else canonical
|
} // else canonical
|
}
|
}
|
|
|
// check for non-canonical y
|
// check for non-canonical y
|
if ((y & MASK_NAN) == MASK_NAN) { // y is NaN
|
if ((y & MASK_NAN) == MASK_NAN) { // y is NaN
|
y = y & 0xfe03ffffffffffffull; // clear G6-G12
|
y = y & 0xfe03ffffffffffffull; // clear G6-G12
|
if ((y & 0x0003ffffffffffffull) > 999999999999999ull) {
|
if ((y & 0x0003ffffffffffffull) > 999999999999999ull) {
|
y = y & 0xfe00000000000000ull; // clear G6-G12 and the payload bits
|
y = y & 0xfe00000000000000ull; // clear G6-G12 and the payload bits
|
}
|
}
|
} else if ((y & MASK_INF) == MASK_INF) { // check for Infinity
|
} else if ((y & MASK_INF) == MASK_INF) { // check for Infinity
|
y = y & (MASK_SIGN | MASK_INF);
|
y = y & (MASK_SIGN | MASK_INF);
|
} else { // y is not special
|
} else { // y is not special
|
// check for non-canonical values - treated as zero
|
// check for non-canonical values - treated as zero
|
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
// if the steering bits are 11, then the exponent is G[0:w+1]
|
// if the steering bits are 11, then the exponent is G[0:w+1]
|
if (((y & MASK_BINARY_SIG2) | MASK_BINARY_OR2) >
|
if (((y & MASK_BINARY_SIG2) | MASK_BINARY_OR2) >
|
9999999999999999ull) {
|
9999999999999999ull) {
|
// non-canonical
|
// non-canonical
|
y = (y & MASK_SIGN) | ((y & MASK_BINARY_EXPONENT2) << 2);
|
y = (y & MASK_SIGN) | ((y & MASK_BINARY_EXPONENT2) << 2);
|
} // else canonical
|
} // else canonical
|
} // else canonical
|
} // else canonical
|
}
|
}
|
|
|
// NaN (CASE1)
|
// NaN (CASE1)
|
if ((x & MASK_NAN) == MASK_NAN) { // x is NAN
|
if ((x & MASK_NAN) == MASK_NAN) { // x is NAN
|
if ((x & MASK_SNAN) == MASK_SNAN) { // x is SNaN
|
if ((x & MASK_SNAN) == MASK_SNAN) { // x is SNaN
|
// if x is SNAN, then return quiet (x)
|
// if x is SNAN, then return quiet (x)
|
*pfpsf |= INVALID_EXCEPTION; // set exception if SNaN
|
*pfpsf |= INVALID_EXCEPTION; // set exception if SNaN
|
x = x & 0xfdffffffffffffffull; // quietize x
|
x = x & 0xfdffffffffffffffull; // quietize x
|
res = x;
|
res = x;
|
} else { // x is QNaN
|
} else { // x is QNaN
|
if ((y & MASK_NAN) == MASK_NAN) { // y is NAN
|
if ((y & MASK_NAN) == MASK_NAN) { // y is NAN
|
if ((y & MASK_SNAN) == MASK_SNAN) { // y is SNAN
|
if ((y & MASK_SNAN) == MASK_SNAN) { // y is SNAN
|
*pfpsf |= INVALID_EXCEPTION; // set invalid flag
|
*pfpsf |= INVALID_EXCEPTION; // set invalid flag
|
}
|
}
|
res = x;
|
res = x;
|
} else {
|
} else {
|
res = y;
|
res = y;
|
}
|
}
|
}
|
}
|
BID_RETURN (res);
|
BID_RETURN (res);
|
} else if ((y & MASK_NAN) == MASK_NAN) { // y is NaN, but x is not
|
} else if ((y & MASK_NAN) == MASK_NAN) { // y is NaN, but x is not
|
if ((y & MASK_SNAN) == MASK_SNAN) {
|
if ((y & MASK_SNAN) == MASK_SNAN) {
|
*pfpsf |= INVALID_EXCEPTION; // set exception if SNaN
|
*pfpsf |= INVALID_EXCEPTION; // set exception if SNaN
|
y = y & 0xfdffffffffffffffull; // quietize y
|
y = y & 0xfdffffffffffffffull; // quietize y
|
res = y;
|
res = y;
|
} else {
|
} else {
|
// will return x (which is not NaN)
|
// will return x (which is not NaN)
|
res = x;
|
res = x;
|
}
|
}
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
// SIMPLE (CASE2)
|
// SIMPLE (CASE2)
|
// if all the bits are the same, these numbers are equal, return either number
|
// if all the bits are the same, these numbers are equal, return either number
|
if (x == y) {
|
if (x == y) {
|
res = x;
|
res = x;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
// INFINITY (CASE3)
|
// INFINITY (CASE3)
|
if ((x & MASK_INF) == MASK_INF) {
|
if ((x & MASK_INF) == MASK_INF) {
|
// x is infinity, its magnitude is greater than or equal to y
|
// x is infinity, its magnitude is greater than or equal to y
|
// return y as long as x isn't negative infinity
|
// return y as long as x isn't negative infinity
|
res = ((x & MASK_SIGN) == MASK_SIGN
|
res = ((x & MASK_SIGN) == MASK_SIGN
|
&& (y & MASK_INF) == MASK_INF) ? y : x;
|
&& (y & MASK_INF) == MASK_INF) ? y : x;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
} else if ((y & MASK_INF) == MASK_INF) {
|
} else if ((y & MASK_INF) == MASK_INF) {
|
// y is infinity, then it must be greater in magnitude
|
// y is infinity, then it must be greater in magnitude
|
res = y;
|
res = y;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
|
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
|
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
} else {
|
} else {
|
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
|
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
|
sig_x = (x & MASK_BINARY_SIG1);
|
sig_x = (x & MASK_BINARY_SIG1);
|
}
|
}
|
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+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) {
|
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
|
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
|
sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
} else {
|
} else {
|
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
|
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
|
sig_y = (y & MASK_BINARY_SIG1);
|
sig_y = (y & MASK_BINARY_SIG1);
|
}
|
}
|
|
|
// ZERO (CASE4)
|
// ZERO (CASE4)
|
// some properties:
|
// some properties:
|
// (+ZERO == -ZERO) => therefore
|
// (+ZERO == -ZERO) => therefore
|
// ignore the sign, and neither number is greater
|
// ignore the sign, and neither number is greater
|
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B =>
|
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B =>
|
// ignore the exponent field
|
// ignore the exponent field
|
// (Any non-canonical # is considered 0)
|
// (Any non-canonical # is considered 0)
|
if (sig_x == 0) {
|
if (sig_x == 0) {
|
res = y; // x_is_zero, its magnitude must be smaller than y
|
res = y; // x_is_zero, its magnitude must be smaller than y
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
if (sig_y == 0) {
|
if (sig_y == 0) {
|
res = x; // y_is_zero, its magnitude must be smaller than x
|
res = x; // y_is_zero, its magnitude must be smaller than x
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
// REDUNDANT REPRESENTATIONS (CASE6)
|
// REDUNDANT REPRESENTATIONS (CASE6)
|
// if both components are either bigger or smaller,
|
// if both components are either bigger or smaller,
|
// it is clear what needs to be done
|
// it is clear what needs to be done
|
if (sig_x > sig_y && exp_x >= exp_y) {
|
if (sig_x > sig_y && exp_x >= exp_y) {
|
res = x;
|
res = x;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
if (sig_x < sig_y && exp_x <= exp_y) {
|
if (sig_x < sig_y && exp_x <= exp_y) {
|
res = y;
|
res = y;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
// if exp_x is 15 greater than exp_y, no need for compensation
|
// if exp_x is 15 greater than exp_y, no need for compensation
|
if (exp_x - exp_y > 15) {
|
if (exp_x - exp_y > 15) {
|
res = x; // difference cannot be greater than 10^15
|
res = x; // difference cannot be greater than 10^15
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
// if exp_x is 15 less than exp_y, no need for compensation
|
// if exp_x is 15 less than exp_y, no need for compensation
|
if (exp_y - exp_x > 15) {
|
if (exp_y - exp_x > 15) {
|
res = y;
|
res = y;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
// if |exp_x - exp_y| < 15, it comes down to the compensated significand
|
// if |exp_x - exp_y| < 15, it comes down to the compensated significand
|
if (exp_x > exp_y) { // to simplify the loop below,
|
if (exp_x > exp_y) { // to simplify the loop below,
|
// otherwise adjust the x significand upwards
|
// otherwise adjust the x significand upwards
|
__mul_64x64_to_128MACH (sig_n_prime, sig_x,
|
__mul_64x64_to_128MACH (sig_n_prime, sig_x,
|
mult_factor[exp_x - exp_y]);
|
mult_factor[exp_x - exp_y]);
|
// now, sig_n_prime has: sig_x * 10^(exp_x-exp_y),
|
// now, sig_n_prime has: sig_x * 10^(exp_x-exp_y),
|
// this is the compensated signif.
|
// this is the compensated signif.
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
|
// two numbers are equal, return maxNum(x,y)
|
// two numbers are equal, return maxNum(x,y)
|
res = ((y & MASK_SIGN) == MASK_SIGN) ? x : y;
|
res = ((y & MASK_SIGN) == MASK_SIGN) ? x : y;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
// now, if compensated_x (sig_n_prime) is greater than y return y,
|
// now, if compensated_x (sig_n_prime) is greater than y return y,
|
// otherwise return x
|
// otherwise return x
|
res = ((sig_n_prime.w[1] != 0) || sig_n_prime.w[0] > sig_y) ? x : y;
|
res = ((sig_n_prime.w[1] != 0) || sig_n_prime.w[0] > sig_y) ? x : y;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
// exp_y must be greater than exp_x, thus adjust the y significand upwards
|
// exp_y must be greater than exp_x, thus adjust the y significand upwards
|
__mul_64x64_to_128MACH (sig_n_prime, sig_y,
|
__mul_64x64_to_128MACH (sig_n_prime, sig_y,
|
mult_factor[exp_y - exp_x]);
|
mult_factor[exp_y - exp_x]);
|
|
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
|
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
|
res = ((y & MASK_SIGN) == MASK_SIGN) ? x : y;
|
res = ((y & MASK_SIGN) == MASK_SIGN) ? x : y;
|
// two numbers are equal, return either
|
// two numbers are equal, return either
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
|
|
res = ((sig_n_prime.w[1] == 0) && (sig_x > sig_n_prime.w[0])) ? x : y;
|
res = ((sig_n_prime.w[1] == 0) && (sig_x > sig_n_prime.w[0])) ? x : y;
|
BID_RETURN (res);
|
BID_RETURN (res);
|
}
|
}
|
|
|
