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Retro68/gcc/libgcc/config/libbid/bid128_minmax.c
Wolfgang Thaller aaf905ce07 add gcc 4.70
2012-03-28 01:13:14 +02:00

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/* Copyright (C) 2007, 2009 Free Software Foundation, Inc.
This file is part of GCC.
GCC is free software; you can redistribute it and/or modify it under
the terms of the GNU General Public License as published by the Free
Software Foundation; either version 3, or (at your option) any later
version.
GCC is distributed in the hope that it will be useful, but WITHOUT ANY
WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
for more details.
Under Section 7 of GPL version 3, you are granted additional
permissions described in the GCC Runtime Library Exception, version
3.1, as published by the Free Software Foundation.
You should have received a copy of the GNU General Public License and
a copy of the GCC Runtime Library Exception along with this program;
see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
<http://www.gnu.org/licenses/>. */
#define BID_128RES
#include "bid_internal.h"
/*****************************************************************************
* BID128 minimum number
*****************************************************************************/
#if DECIMAL_CALL_BY_REFERENCE
void
bid128_minnum (UINT128 * pres, UINT128 * px,
UINT128 * py _EXC_FLAGS_PARAM) {
UINT128 x = *px;
UINT128 y = *py;
#else
UINT128
bid128_minnum (UINT128 x, UINT128 y _EXC_FLAGS_PARAM) {
#endif
UINT128 res;
int exp_x, exp_y;
int diff;
UINT128 sig_x, sig_y;
UINT192 sig_n_prime192;
UINT256 sig_n_prime256;
char x_is_zero = 0, y_is_zero = 0;
BID_SWAP128 (x);
BID_SWAP128 (y);
// check for non-canonical x
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
x.w[1] = x.w[1] & 0xfe003fffffffffffull; // clear out G[6]-G[16]
// check for non-canonical NaN payload
if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
(((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
(x.w[0] > 0x38c15b09ffffffffull))) {
x.w[1] = x.w[1] & 0xffffc00000000000ull;
x.w[0] = 0x0ull;
}
} else if ((x.w[1] & MASK_ANY_INF) == MASK_INF) { // x = inf
x.w[1] = x.w[1] & (MASK_SIGN | MASK_INF);
x.w[0] = 0x0ull;
} else { // x is not special
// check for non-canonical values - treated as zero
if ((x.w[1] & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // G0_G1=11
// non-canonical
x.w[1] = (x.w[1] & MASK_SIGN) | ((x.w[1] << 2) & MASK_EXP);
x.w[0] = 0x0ull;
} else { // G0_G1 != 11
if ((x.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull ||
((x.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull
&& x.w[0] > 0x378d8e63ffffffffull)) {
// x is non-canonical if coefficient is larger than 10^34 -1
x.w[1] = (x.w[1] & MASK_SIGN) | (x.w[1] & MASK_EXP);
x.w[0] = 0x0ull;
} else { // canonical
;
}
}
}
// check for non-canonical y
if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NAN
y.w[1] = y.w[1] & 0xfe003fffffffffffull; // clear out G[6]-G[16]
// check for non-canonical NaN payload
if (((y.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
(((y.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
(y.w[0] > 0x38c15b09ffffffffull))) {
y.w[1] = y.w[1] & 0xffffc00000000000ull;
y.w[0] = 0x0ull;
}
} else if ((y.w[1] & MASK_ANY_INF) == MASK_INF) { // y = inf
y.w[1] = y.w[1] & (MASK_SIGN | MASK_INF);
y.w[0] = 0x0ull;
} else { // y is not special
// check for non-canonical values - treated as zero
if ((y.w[1] & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // G0_G1=11
// non-canonical
y.w[1] = (y.w[1] & MASK_SIGN) | ((y.w[1] << 2) & MASK_EXP);
y.w[0] = 0x0ull;
} else { // G0_G1 != 11
if ((y.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull ||
((y.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull
&& y.w[0] > 0x378d8e63ffffffffull)) {
// y is non-canonical if coefficient is larger than 10^34 -1
y.w[1] = (y.w[1] & MASK_SIGN) | (y.w[1] & MASK_EXP);
y.w[0] = 0x0ull;
} else { // canonical
;
}
}
}
// NaN (CASE1)
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNaN
// if x is SNAN, then return quiet (x)
*pfpsf |= INVALID_EXCEPTION; // set exception if SNaN
x.w[1] = x.w[1] & 0xfdffffffffffffffull; // quietize x
res = x;
} else { // x is QNaN
if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NAN
if ((y.w[1] & MASK_SNAN) == MASK_SNAN) { // y is SNAN
*pfpsf |= INVALID_EXCEPTION; // set invalid flag
}
res = x;
} else {
res = y;
}
}
BID_RETURN (res);
} else if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NaN, but x is not
if ((y.w[1] & MASK_SNAN) == MASK_SNAN) {
*pfpsf |= INVALID_EXCEPTION; // set exception if SNaN
y.w[1] = y.w[1] & 0xfdffffffffffffffull; // quietize y
res = y;
} else {
// will return x (which is not NaN)
res = x;
}
BID_RETURN (res);
}
// SIMPLE (CASE2)
// if all the bits are the same, these numbers are equal (not Greater).
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
res = x;
BID_RETURN (res);
}
// INFINITY (CASE3)
if ((x.w[1] & MASK_INF) == MASK_INF) {
// if x is neg infinity, there is no way it is greater than y, return 0
res = (((x.w[1] & MASK_SIGN) == MASK_SIGN)) ? x : y;
BID_RETURN (res);
} else if ((y.w[1] & MASK_INF) == MASK_INF) {
// x is finite, so if y is positive infinity, then x is less, return 0
// if y is negative infinity, then x is greater, return 1
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x;
BID_RETURN (res);
}
// CONVERT X
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
sig_x.w[0] = x.w[0];
exp_x = (x.w[1] >> 49) & 0x000000000003fffull;
// CONVERT Y
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
sig_y.w[0] = y.w[0];
// ZERO (CASE4)
// some properties:
// (+ZERO == -ZERO) => therefore ignore the sign
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B => ignore the exponent
// field
// (Any non-canonical # is considered 0)
if ((sig_x.w[1] == 0) && (sig_x.w[0] == 0)) {
x_is_zero = 1;
}
if ((sig_y.w[1] == 0) && (sig_y.w[0] == 0)) {
y_is_zero = 1;
}
if (x_is_zero && y_is_zero) {
// if both numbers are zero, neither is greater => return either number
res = x;
BID_RETURN (res);
} else if (x_is_zero) {
// is x is zero, it is greater if Y is negative
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x;
BID_RETURN (res);
} else if (y_is_zero) {
// is y is zero, X is greater if it is positive
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN) ? y : x;
BID_RETURN (res);
}
// OPPOSITE SIGN (CASE5)
// now, if the sign bits differ, x is greater if y is negative
if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) {
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x;
BID_RETURN (res);
}
// REDUNDANT REPRESENTATIONS (CASE6)
// if exponents are the same, then we have a simple comparison of
// the significands
if (exp_y == exp_x) {
res = (((sig_x.w[1] > sig_y.w[1])
|| (sig_x.w[1] == sig_y.w[1]
&& sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) ==
MASK_SIGN)) ? y : x;
BID_RETURN (res);
}
// if both components are either bigger or smaller, it is clear what
// needs to be done
if (sig_x.w[1] >= sig_y.w[1] && sig_x.w[0] >= sig_y.w[0]
&& exp_x > exp_y) {
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN) ? y : x;
BID_RETURN (res);
}
if (sig_x.w[1] <= sig_y.w[1] && sig_x.w[0] <= sig_y.w[0]
&& exp_x < exp_y) {
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x;
BID_RETURN (res);
}
diff = exp_x - exp_y;
// if |exp_x - exp_y| < 33, it comes down to the compensated significand
if (diff > 0) { // to simplify the loop below,
// if exp_x is 33 greater than exp_y, no need for compensation
if (diff > 33) {
// difference cannot be greater than 10^33
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN) ? y : x;
BID_RETURN (res);
}
if (diff > 19) { //128 by 128 bit multiply -> 256 bits
__mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]);
// if postitive, return whichever significand is larger
// (converse if negative)
res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0)
|| (sig_n_prime256.w[1] > sig_y.w[1])
|| (sig_n_prime256.w[1] == sig_y.w[1]
&& sig_n_prime256.w[0] >
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) ==
MASK_SIGN)) ? y : x;
BID_RETURN (res);
}
__mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_x);
// if postitive, return whichever significand is larger
// (converse if negative)
res =
(((sig_n_prime192.w[2] > 0) || (sig_n_prime192.w[1] > sig_y.w[1])
|| (sig_n_prime192.w[1] == sig_y.w[1]
&& sig_n_prime192.w[0] >
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)) ? y : x;
BID_RETURN (res);
}
diff = exp_y - exp_x;
// if exp_x is 33 less than exp_y, no need for compensation
if (diff > 33) {
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x;
BID_RETURN (res);
}
if (diff > 19) { //128 by 128 bit multiply -> 256 bits
// adjust the y significand upwards
__mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]);
// if postitive, return whichever significand is larger
// (converse if negative)
res =
((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0
|| (sig_n_prime256.w[1] > sig_x.w[1]
|| (sig_n_prime256.w[1] == sig_x.w[1]
&& sig_n_prime256.w[0] >
sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) ==
MASK_SIGN)) ? x : y;
BID_RETURN (res);
}
// adjust the y significand upwards
__mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_y);
// if postitive, return whichever significand is larger (converse if negative)
res =
((sig_n_prime192.w[2] != 0
|| (sig_n_prime192.w[1] > sig_x.w[1]
|| (sig_n_prime192.w[1] == sig_x.w[1]
&& sig_n_prime192.w[0] > sig_x.w[0])))
^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)) ? x : y;
BID_RETURN (res);
}
/*****************************************************************************
* BID128 minimum magnitude function - returns greater of two numbers
*****************************************************************************/
#if DECIMAL_CALL_BY_REFERENCE
void
bid128_minnum_mag (UINT128 * pres, UINT128 * px,
UINT128 * py _EXC_FLAGS_PARAM) {
UINT128 x = *px;
UINT128 y = *py;
#else
UINT128
bid128_minnum_mag (UINT128 x, UINT128 y _EXC_FLAGS_PARAM) {
#endif
UINT128 res;
int exp_x, exp_y;
int diff;
UINT128 sig_x, sig_y;
UINT192 sig_n_prime192;
UINT256 sig_n_prime256;
BID_SWAP128 (x);
BID_SWAP128 (y);
// check for non-canonical x
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
x.w[1] = x.w[1] & 0xfe003fffffffffffull; // clear out G[6]-G[16]
// check for non-canonical NaN payload
if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
(((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
(x.w[0] > 0x38c15b09ffffffffull))) {
x.w[1] = x.w[1] & 0xffffc00000000000ull;
x.w[0] = 0x0ull;
}
} else if ((x.w[1] & MASK_ANY_INF) == MASK_INF) { // x = inf
x.w[1] = x.w[1] & (MASK_SIGN | MASK_INF);
x.w[0] = 0x0ull;
} else { // x is not special
// check for non-canonical values - treated as zero
if ((x.w[1] & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // G0_G1=11
// non-canonical
x.w[1] = (x.w[1] & MASK_SIGN) | ((x.w[1] << 2) & MASK_EXP);
x.w[0] = 0x0ull;
} else { // G0_G1 != 11
if ((x.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull ||
((x.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull
&& x.w[0] > 0x378d8e63ffffffffull)) {
// x is non-canonical if coefficient is larger than 10^34 -1
x.w[1] = (x.w[1] & MASK_SIGN) | (x.w[1] & MASK_EXP);
x.w[0] = 0x0ull;
} else { // canonical
;
}
}
}
// check for non-canonical y
if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NAN
y.w[1] = y.w[1] & 0xfe003fffffffffffull; // clear out G[6]-G[16]
// check for non-canonical NaN payload
if (((y.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
(((y.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
(y.w[0] > 0x38c15b09ffffffffull))) {
y.w[1] = y.w[1] & 0xffffc00000000000ull;
y.w[0] = 0x0ull;
}
} else if ((y.w[1] & MASK_ANY_INF) == MASK_INF) { // y = inf
y.w[1] = y.w[1] & (MASK_SIGN | MASK_INF);
y.w[0] = 0x0ull;
} else { // y is not special
// check for non-canonical values - treated as zero
if ((y.w[1] & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // G0_G1=11
// non-canonical
y.w[1] = (y.w[1] & MASK_SIGN) | ((y.w[1] << 2) & MASK_EXP);
y.w[0] = 0x0ull;
} else { // G0_G1 != 11
if ((y.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull ||
((y.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull
&& y.w[0] > 0x378d8e63ffffffffull)) {
// y is non-canonical if coefficient is larger than 10^34 -1
y.w[1] = (y.w[1] & MASK_SIGN) | (y.w[1] & MASK_EXP);
y.w[0] = 0x0ull;
} else { // canonical
;
}
}
}
// NaN (CASE1)
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNaN
// if x is SNAN, then return quiet (x)
*pfpsf |= INVALID_EXCEPTION; // set exception if SNaN
x.w[1] = x.w[1] & 0xfdffffffffffffffull; // quietize x
res = x;
} else { // x is QNaN
if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NAN
if ((y.w[1] & MASK_SNAN) == MASK_SNAN) { // y is SNAN
*pfpsf |= INVALID_EXCEPTION; // set invalid flag
}
res = x;
} else {
res = y;
}
}
BID_RETURN (res);
} else if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NaN, but x is not
if ((y.w[1] & MASK_SNAN) == MASK_SNAN) {
*pfpsf |= INVALID_EXCEPTION; // set exception if SNaN
y.w[1] = y.w[1] & 0xfdffffffffffffffull; // quietize y
res = y;
} else {
// will return x (which is not NaN)
res = x;
}
BID_RETURN (res);
}
// SIMPLE (CASE2)
// if all the bits are the same, these numbers are equal (not Greater).
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
res = y;
BID_RETURN (res);
}
// INFINITY (CASE3)
if ((x.w[1] & MASK_INF) == MASK_INF) {
// if x infinity, it has maximum magnitude.
// Check if magnitudes are equal. If x is negative, return it.
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN
&& (y.w[1] & MASK_INF) == MASK_INF) ? x : y;
BID_RETURN (res);
} else if ((y.w[1] & MASK_INF) == MASK_INF) {
// x is finite, so if y is infinity, then x is less in magnitude
res = x;
BID_RETURN (res);
}
// CONVERT X
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
sig_x.w[0] = x.w[0];
exp_x = (x.w[1] >> 49) & 0x000000000003fffull;
// CONVERT Y
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
sig_y.w[0] = y.w[0];
// ZERO (CASE4)
// some properties:
// (+ZERO == -ZERO) => therefore ignore the sign
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B =>
// therefore ignore the exponent field
// (Any non-canonical # is considered 0)
if ((sig_x.w[1] == 0) && (sig_x.w[0] == 0)) {
res = x;
BID_RETURN (res);
}
if ((sig_y.w[1] == 0) && (sig_y.w[0] == 0)) {
res = y;
BID_RETURN (res);
}
// REDUNDANT REPRESENTATIONS (CASE6)
// check if exponents are the same and significands are the same
if (exp_y == exp_x && sig_x.w[1] == sig_y.w[1]
&& sig_x.w[0] == sig_y.w[0]) {
if (x.w[1] & 0x8000000000000000ull) { // x is negative
res = x;
BID_RETURN (res);
} else {
res = y;
BID_RETURN (res);
}
} else if (((sig_x.w[1] > sig_y.w[1] || (sig_x.w[1] == sig_y.w[1]
&& sig_x.w[0] > sig_y.w[0]))
&& exp_x == exp_y)
|| ((sig_x.w[1] > sig_y.w[1]
|| (sig_x.w[1] == sig_y.w[1]
&& sig_x.w[0] >= sig_y.w[0]))
&& exp_x > exp_y)) {
// if both components are either bigger or smaller, it is clear what
// needs to be done; also if the magnitudes are equal
res = y;
BID_RETURN (res);
} else if (((sig_y.w[1] > sig_x.w[1] || (sig_y.w[1] == sig_x.w[1]
&& sig_y.w[0] > sig_x.w[0]))
&& exp_y == exp_x)
|| ((sig_y.w[1] > sig_x.w[1]
|| (sig_y.w[1] == sig_x.w[1]
&& sig_y.w[0] >= sig_x.w[0]))
&& exp_y > exp_x)) {
res = x;
BID_RETURN (res);
} else {
; // continue
}
diff = exp_x - exp_y;
// if |exp_x - exp_y| < 33, it comes down to the compensated significand
if (diff > 0) { // to simplify the loop below,
// if exp_x is 33 greater than exp_y, no need for compensation
if (diff > 33) {
res = y; // difference cannot be greater than 10^33
BID_RETURN (res);
}
if (diff > 19) { //128 by 128 bit multiply -> 256 bits
__mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]);
// if positive, return whichever significand is larger
// (converse if negative)
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
&& sig_n_prime256.w[1] == sig_y.w[1]
&& (sig_n_prime256.w[0] == sig_y.w[0])) {
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x; // if equal
BID_RETURN (res);
}
res = (((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0)
|| (sig_n_prime256.w[1] > sig_y.w[1])
|| (sig_n_prime256.w[1] == sig_y.w[1]
&& sig_n_prime256.w[0] > sig_y.w[0])) ? y : x;
BID_RETURN (res);
}
__mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_x);
// if positive, return whichever significand is larger
// (converse if negative)
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1]
&& (sig_n_prime192.w[0] == sig_y.w[0])) {
// if = in magnitude, return +, (if possible)
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x;
BID_RETURN (res);
}
res = ((sig_n_prime192.w[2] > 0)
|| (sig_n_prime192.w[1] > sig_y.w[1])
|| (sig_n_prime192.w[1] == sig_y.w[1]
&& sig_n_prime192.w[0] > sig_y.w[0])) ? y : x;
BID_RETURN (res);
}
diff = exp_y - exp_x;
// if exp_x is 33 less than exp_y, no need for compensation
if (diff > 33) {
res = x;
BID_RETURN (res);
}
if (diff > 19) { //128 by 128 bit multiply -> 256 bits
// adjust the y significand upwards
__mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]);
// if positive, return whichever significand is larger
// (converse if negative)
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
&& sig_n_prime256.w[1] == sig_x.w[1]
&& (sig_n_prime256.w[0] == sig_x.w[0])) {
// if = in magnitude, return +, (if possible)
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x;
BID_RETURN (res);
}
res = (sig_n_prime256.w[3] == 0 && sig_n_prime256.w[2] == 0
&& (sig_n_prime256.w[1] < sig_x.w[1]
|| (sig_n_prime256.w[1] == sig_x.w[1]
&& sig_n_prime256.w[0] < sig_x.w[0]))) ? y : x;
BID_RETURN (res);
}
// adjust the y significand upwards
__mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_y);
// if positive, return whichever significand is larger (converse if negative)
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1]
&& (sig_n_prime192.w[0] == sig_x.w[0])) {
// if = in magnitude, return +, if possible)
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x;
BID_RETURN (res);
}
res = (sig_n_prime192.w[2] == 0
&& (sig_n_prime192.w[1] < sig_x.w[1]
|| (sig_n_prime192.w[1] == sig_x.w[1]
&& sig_n_prime192.w[0] < sig_x.w[0]))) ? y : x;
BID_RETURN (res);
}
/*****************************************************************************
* BID128 maximum function - returns greater of two numbers
*****************************************************************************/
#if DECIMAL_CALL_BY_REFERENCE
void
bid128_maxnum (UINT128 * pres, UINT128 * px,
UINT128 * py _EXC_FLAGS_PARAM) {
UINT128 x = *px;
UINT128 y = *py;
#else
UINT128
bid128_maxnum (UINT128 x, UINT128 y _EXC_FLAGS_PARAM) {
#endif
UINT128 res;
int exp_x, exp_y;
int diff;
UINT128 sig_x, sig_y;
UINT192 sig_n_prime192;
UINT256 sig_n_prime256;
char x_is_zero = 0, y_is_zero = 0;
BID_SWAP128 (x);
BID_SWAP128 (y);
// check for non-canonical x
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
x.w[1] = x.w[1] & 0xfe003fffffffffffull; // clear out G[6]-G[16]
// check for non-canonical NaN payload
if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
(((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
(x.w[0] > 0x38c15b09ffffffffull))) {
x.w[1] = x.w[1] & 0xffffc00000000000ull;
x.w[0] = 0x0ull;
}
} else if ((x.w[1] & MASK_ANY_INF) == MASK_INF) { // x = inf
x.w[1] = x.w[1] & (MASK_SIGN | MASK_INF);
x.w[0] = 0x0ull;
} else { // x is not special
// check for non-canonical values - treated as zero
if ((x.w[1] & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // G0_G1=11
// non-canonical
x.w[1] = (x.w[1] & MASK_SIGN) | ((x.w[1] << 2) & MASK_EXP);
x.w[0] = 0x0ull;
} else { // G0_G1 != 11
if ((x.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull ||
((x.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull
&& x.w[0] > 0x378d8e63ffffffffull)) {
// x is non-canonical if coefficient is larger than 10^34 -1
x.w[1] = (x.w[1] & MASK_SIGN) | (x.w[1] & MASK_EXP);
x.w[0] = 0x0ull;
} else { // canonical
;
}
}
}
// check for non-canonical y
if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NAN
y.w[1] = y.w[1] & 0xfe003fffffffffffull; // clear out G[6]-G[16]
// check for non-canonical NaN payload
if (((y.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
(((y.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
(y.w[0] > 0x38c15b09ffffffffull))) {
y.w[1] = y.w[1] & 0xffffc00000000000ull;
y.w[0] = 0x0ull;
}
} else if ((y.w[1] & MASK_ANY_INF) == MASK_INF) { // y = inf
y.w[1] = y.w[1] & (MASK_SIGN | MASK_INF);
y.w[0] = 0x0ull;
} else { // y is not special
// check for non-canonical values - treated as zero
if ((y.w[1] & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // G0_G1=11
// non-canonical
y.w[1] = (y.w[1] & MASK_SIGN) | ((y.w[1] << 2) & MASK_EXP);
y.w[0] = 0x0ull;
} else { // G0_G1 != 11
if ((y.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull ||
((y.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull
&& y.w[0] > 0x378d8e63ffffffffull)) {
// y is non-canonical if coefficient is larger than 10^34 -1
y.w[1] = (y.w[1] & MASK_SIGN) | (y.w[1] & MASK_EXP);
y.w[0] = 0x0ull;
} else { // canonical
;
}
}
}
// NaN (CASE1)
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNaN
// if x is SNAN, then return quiet (x)
*pfpsf |= INVALID_EXCEPTION; // set exception if SNaN
x.w[1] = x.w[1] & 0xfdffffffffffffffull; // quietize x
res = x;
} else { // x is QNaN
if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NAN
if ((y.w[1] & MASK_SNAN) == MASK_SNAN) { // y is SNAN
*pfpsf |= INVALID_EXCEPTION; // set invalid flag
}
res = x;
} else {
res = y;
}
}
BID_RETURN (res);
} else if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NaN, but x is not
if ((y.w[1] & MASK_SNAN) == MASK_SNAN) {
*pfpsf |= INVALID_EXCEPTION; // set exception if SNaN
y.w[1] = y.w[1] & 0xfdffffffffffffffull; // quietize y
res = y;
} else {
// will return x (which is not NaN)
res = x;
}
BID_RETURN (res);
}
// SIMPLE (CASE2)
// if all the bits are the same, these numbers are equal (not Greater).
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
res = x;
BID_RETURN (res);
}
// INFINITY (CASE3)
if ((x.w[1] & MASK_INF) == MASK_INF) {
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x;
BID_RETURN (res);
} else if ((y.w[1] & MASK_INF) == MASK_INF) {
// x is finite, so if y is positive infinity, then x is less, return 0
// if y is negative infinity, then x is greater, return 1
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? x : y;
BID_RETURN (res);
}
// CONVERT X
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
sig_x.w[0] = x.w[0];
exp_x = (x.w[1] >> 49) & 0x000000000003fffull;
// CONVERT Y
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
sig_y.w[0] = y.w[0];
// ZERO (CASE4)
// some properties:
// (+ZERO == -ZERO) => therefore ignore the sign
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B =>
// therefore ignore the exponent field
// (Any non-canonical # is considered 0)
if ((sig_x.w[1] == 0) && (sig_x.w[0] == 0)) {
x_is_zero = 1;
}
if ((sig_y.w[1] == 0) && (sig_y.w[0] == 0)) {
y_is_zero = 1;
}
if (x_is_zero && y_is_zero) {
// if both numbers are zero, neither is greater => return either number
res = x;
BID_RETURN (res);
} else if (x_is_zero) {
// is x is zero, it is greater if Y is negative
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? x : y;
BID_RETURN (res);
} else if (y_is_zero) {
// is y is zero, X is greater if it is positive
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN) ? x : y;
BID_RETURN (res);
}
// OPPOSITE SIGN (CASE5)
// now, if the sign bits differ, x is greater if y is negative
if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) {
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? x : y;
BID_RETURN (res);
}
// REDUNDANT REPRESENTATIONS (CASE6)
// if exponents are the same, then we have a simple comparison of
// the significands
if (exp_y == exp_x) {
res = (((sig_x.w[1] > sig_y.w[1]) || (sig_x.w[1] == sig_y.w[1] &&
sig_x.w[0] >= sig_y.w[0])) ^
((x.w[1] & MASK_SIGN) == MASK_SIGN)) ? x : y;
BID_RETURN (res);
}
// if both components are either bigger or smaller, it is clear what
// needs to be done
if ((sig_x.w[1] > sig_y.w[1]
|| (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0]))
&& exp_x >= exp_y) {
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN) ? x : y;
BID_RETURN (res);
}
if ((sig_x.w[1] < sig_y.w[1]
|| (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0]))
&& exp_x <= exp_y) {
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN) ? x : y;
BID_RETURN (res);
}
diff = exp_x - exp_y;
// if |exp_x - exp_y| < 33, it comes down to the compensated significand
if (diff > 0) { // to simplify the loop below,
// if exp_x is 33 greater than exp_y, no need for compensation
if (diff > 33) {
// difference cannot be greater than 10^33
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN) ? x : y;
BID_RETURN (res);
}
if (diff > 19) { //128 by 128 bit multiply -> 256 bits
__mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]);
// if postitive, return whichever significand is larger
// (converse if negative)
res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0)
|| (sig_n_prime256.w[1] > sig_y.w[1])
|| (sig_n_prime256.w[1] == sig_y.w[1]
&& sig_n_prime256.w[0] >
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) ==
MASK_SIGN)) ? x : y;
BID_RETURN (res);
}
__mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_x);
// if postitive, return whichever significand is larger
// (converse if negative)
res =
(((sig_n_prime192.w[2] > 0) || (sig_n_prime192.w[1] > sig_y.w[1])
|| (sig_n_prime192.w[1] == sig_y.w[1]
&& sig_n_prime192.w[0] >
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)) ? x : y;
BID_RETURN (res);
}
diff = exp_y - exp_x;
// if exp_x is 33 less than exp_y, no need for compensation
if (diff > 33) {
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN) ? x : y;
BID_RETURN (res);
}
if (diff > 19) { //128 by 128 bit multiply -> 256 bits
// adjust the y significand upwards
__mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]);
// if postitive, return whichever significand is larger
// (converse if negative)
res =
((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0
|| (sig_n_prime256.w[1] > sig_x.w[1]
|| (sig_n_prime256.w[1] == sig_x.w[1]
&& sig_n_prime256.w[0] >
sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) !=
MASK_SIGN)) ? x : y;
BID_RETURN (res);
}
// adjust the y significand upwards
__mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_y);
// if postitive, return whichever significand is larger (converse if negative)
res =
((sig_n_prime192.w[2] != 0
|| (sig_n_prime192.w[1] > sig_x.w[1]
|| (sig_n_prime192.w[1] == sig_x.w[1]
&& sig_n_prime192.w[0] >
sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) !=
MASK_SIGN)) ? x : y;
BID_RETURN (res);
}
/*****************************************************************************
* BID128 maximum magnitude function - returns greater of two numbers
*****************************************************************************/
#if DECIMAL_CALL_BY_REFERENCE
void
bid128_maxnum_mag (UINT128 * pres, UINT128 * px,
UINT128 * py _EXC_FLAGS_PARAM) {
UINT128 x = *px;
UINT128 y = *py;
#else
UINT128
bid128_maxnum_mag (UINT128 x, UINT128 y _EXC_FLAGS_PARAM) {
#endif
UINT128 res;
int exp_x, exp_y;
int diff;
UINT128 sig_x, sig_y;
UINT192 sig_n_prime192;
UINT256 sig_n_prime256;
BID_SWAP128 (x);
BID_SWAP128 (y);
// check for non-canonical x
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
x.w[1] = x.w[1] & 0xfe003fffffffffffull; // clear out G[6]-G[16]
// check for non-canonical NaN payload
if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
(((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
(x.w[0] > 0x38c15b09ffffffffull))) {
x.w[1] = x.w[1] & 0xffffc00000000000ull;
x.w[0] = 0x0ull;
}
} else if ((x.w[1] & MASK_ANY_INF) == MASK_INF) { // x = inf
x.w[1] = x.w[1] & (MASK_SIGN | MASK_INF);
x.w[0] = 0x0ull;
} else { // x is not special
// check for non-canonical values - treated as zero
if ((x.w[1] & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // G0_G1=11
// non-canonical
x.w[1] = (x.w[1] & MASK_SIGN) | ((x.w[1] << 2) & MASK_EXP);
x.w[0] = 0x0ull;
} else { // G0_G1 != 11
if ((x.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull ||
((x.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull
&& x.w[0] > 0x378d8e63ffffffffull)) {
// x is non-canonical if coefficient is larger than 10^34 -1
x.w[1] = (x.w[1] & MASK_SIGN) | (x.w[1] & MASK_EXP);
x.w[0] = 0x0ull;
} else { // canonical
;
}
}
}
// check for non-canonical y
if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NAN
y.w[1] = y.w[1] & 0xfe003fffffffffffull; // clear out G[6]-G[16]
// check for non-canonical NaN payload
if (((y.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
(((y.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
(y.w[0] > 0x38c15b09ffffffffull))) {
y.w[1] = y.w[1] & 0xffffc00000000000ull;
y.w[0] = 0x0ull;
}
} else if ((y.w[1] & MASK_ANY_INF) == MASK_INF) { // y = inf
y.w[1] = y.w[1] & (MASK_SIGN | MASK_INF);
y.w[0] = 0x0ull;
} else { // y is not special
// check for non-canonical values - treated as zero
if ((y.w[1] & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // G0_G1=11
// non-canonical
y.w[1] = (y.w[1] & MASK_SIGN) | ((y.w[1] << 2) & MASK_EXP);
y.w[0] = 0x0ull;
} else { // G0_G1 != 11
if ((y.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull ||
((y.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull &&
y.w[0] > 0x378d8e63ffffffffull)) {
// y is non-canonical if coefficient is larger than 10^34 -1
y.w[1] = (y.w[1] & MASK_SIGN) | (y.w[1] & MASK_EXP);
y.w[0] = 0x0ull;
} else { // canonical
;
}
}
}
// NaN (CASE1)
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNaN
// if x is SNAN, then return quiet (x)
*pfpsf |= INVALID_EXCEPTION; // set exception if SNaN
x.w[1] = x.w[1] & 0xfdffffffffffffffull; // quietize x
res = x;
} else { // x is QNaN
if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NAN
if ((y.w[1] & MASK_SNAN) == MASK_SNAN) { // y is SNAN
*pfpsf |= INVALID_EXCEPTION; // set invalid flag
}
res = x;
} else {
res = y;
}
}
BID_RETURN (res);
} else if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NaN, but x is not
if ((y.w[1] & MASK_SNAN) == MASK_SNAN) {
*pfpsf |= INVALID_EXCEPTION; // set exception if SNaN
y.w[1] = y.w[1] & 0xfdffffffffffffffull; // quietize y
res = y;
} else {
// will return x (which is not NaN)
res = x;
}
BID_RETURN (res);
}
// SIMPLE (CASE2)
// if all the bits are the same, these numbers are equal (not Greater).
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
res = y;
BID_RETURN (res);
}
// INFINITY (CASE3)
if ((x.w[1] & MASK_INF) == MASK_INF) {
// if x infinity, it has maximum magnitude
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN
&& (y.w[1] & MASK_INF) == MASK_INF) ? y : x;
BID_RETURN (res);
} else if ((y.w[1] & MASK_INF) == MASK_INF) {
// x is finite, so if y is positive infinity, then x is less, return 0
// if y is negative infinity, then x is greater, return 1
res = y;
BID_RETURN (res);
}
// CONVERT X
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
sig_x.w[0] = x.w[0];
exp_x = (x.w[1] >> 49) & 0x000000000003fffull;
// CONVERT Y
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
sig_y.w[0] = y.w[0];
// ZERO (CASE4)
// some properties:
// (+ZERO == -ZERO) => therefore ignore the sign
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B =>
// therefore ignore the exponent field
// (Any non-canonical # is considered 0)
if ((sig_x.w[1] == 0) && (sig_x.w[0] == 0)) {
res = y;
BID_RETURN (res);
}
if ((sig_y.w[1] == 0) && (sig_y.w[0] == 0)) {
res = x;
BID_RETURN (res);
}
// REDUNDANT REPRESENTATIONS (CASE6)
if (exp_y == exp_x && sig_x.w[1] == sig_y.w[1]
&& sig_x.w[0] == sig_y.w[0]) {
// check if exponents are the same and significands are the same
if (x.w[1] & 0x8000000000000000ull) { // x is negative
res = y;
BID_RETURN (res);
} else {
res = x;
BID_RETURN (res);
}
} else if (((sig_x.w[1] > sig_y.w[1] || (sig_x.w[1] == sig_y.w[1]
&& sig_x.w[0] > sig_y.w[0]))
&& exp_x == exp_y)
|| ((sig_x.w[1] > sig_y.w[1]
|| (sig_x.w[1] == sig_y.w[1]
&& sig_x.w[0] >= sig_y.w[0]))
&& exp_x > exp_y)) {
// if both components are either bigger or smaller, it is clear what
// needs to be done; also if the magnitudes are equal
res = x;
BID_RETURN (res);
} else if (((sig_y.w[1] > sig_x.w[1] || (sig_y.w[1] == sig_x.w[1]
&& sig_y.w[0] > sig_x.w[0]))
&& exp_y == exp_x)
|| ((sig_y.w[1] > sig_x.w[1]
|| (sig_y.w[1] == sig_x.w[1]
&& sig_y.w[0] >= sig_x.w[0]))
&& exp_y > exp_x)) {
res = y;
BID_RETURN (res);
} else {
; // continue
}
diff = exp_x - exp_y;
// if |exp_x - exp_y| < 33, it comes down to the compensated significand
if (diff > 0) { // to simplify the loop below,
// if exp_x is 33 greater than exp_y, no need for compensation
if (diff > 33) {
res = x; // difference cannot be greater than 10^33
BID_RETURN (res);
}
if (diff > 19) { //128 by 128 bit multiply -> 256 bits
__mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]);
// if postitive, return whichever significand is larger
// (converse if negative)
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
&& sig_n_prime256.w[1] == sig_y.w[1]
&& (sig_n_prime256.w[0] == sig_y.w[0])) {
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? x : y; // if equal
BID_RETURN (res);
}
res = (((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0)
|| (sig_n_prime256.w[1] > sig_y.w[1])
|| (sig_n_prime256.w[1] == sig_y.w[1]
&& sig_n_prime256.w[0] > sig_y.w[0])) ? x : y;
BID_RETURN (res);
}
__mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_x);
// if postitive, return whichever significand is larger (converse if negative)
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1]
&& (sig_n_prime192.w[0] == sig_y.w[0])) {
// if equal, return positive magnitude
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? x : y;
BID_RETURN (res);
}
res = ((sig_n_prime192.w[2] > 0)
|| (sig_n_prime192.w[1] > sig_y.w[1])
|| (sig_n_prime192.w[1] == sig_y.w[1]
&& sig_n_prime192.w[0] > sig_y.w[0])) ? x : y;
BID_RETURN (res);
}
diff = exp_y - exp_x;
// if exp_x is 33 less than exp_y, no need for compensation
if (diff > 33) {
res = y;
BID_RETURN (res);
}
if (diff > 19) { //128 by 128 bit multiply -> 256 bits
// adjust the y significand upwards
__mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]);
// if postitive, return whichever significand is larger
// (converse if negative)
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
&& sig_n_prime256.w[1] == sig_x.w[1]
&& (sig_n_prime256.w[0] == sig_x.w[0])) {
// if equal, return positive (if possible)
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? x : y;
BID_RETURN (res);
}
res = (sig_n_prime256.w[3] == 0 && sig_n_prime256.w[2] == 0
&& (sig_n_prime256.w[1] < sig_x.w[1]
|| (sig_n_prime256.w[1] == sig_x.w[1]
&& sig_n_prime256.w[0] < sig_x.w[0]))) ? x : y;
BID_RETURN (res);
}
// adjust the y significand upwards
__mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_y);
// if postitive, return whichever significand is larger (converse if negative)
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1]
&& (sig_n_prime192.w[0] == sig_x.w[0])) {
// if equal, return positive (if possible)
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? x : y;
BID_RETURN (res);
}
res = (sig_n_prime192.w[2] == 0
&& (sig_n_prime192.w[1] < sig_x.w[1]
|| (sig_n_prime192.w[1] == sig_x.w[1]
&& sig_n_prime192.w[0] < sig_x.w[0]))) ? x : y;
BID_RETURN (res);
}
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