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/* Copyright (C) 2007-2022 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/>. */
#include "bid_internal.h"
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_equal, x, y)
int res;
int exp_x, exp_y, exp_t;
UINT128 sig_x, sig_y, sig_t;
UINT192 sig_n_prime192;
UINT256 sig_n_prime256;
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y;
// NaN (CASE1)
// if either number is NAN, the comparison is unordered,
// rather than equal : return 0
if (((x.w[1] & MASK_NAN) == MASK_NAN)
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) {
if ((x.w[1] & MASK_SNAN) == MASK_SNAN
|| (y.w[1] & MASK_SNAN) == MASK_SNAN) {
*pfpsf |= INVALID_EXCEPTION;
}
{
res = 0;
BID_RETURN (res);
}
}
// SIMPLE (CASE2)
// if all the bits are the same, these numbers are equivalent.
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
res = 1;
BID_RETURN (res);
}
// INFINITY (CASE3)
if ((x.w[1] & MASK_INF) == MASK_INF) {
if ((y.w[1] & MASK_INF) == MASK_INF) {
res = (((x.w[1] ^ y.w[1]) & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
} else {
res = 0;
BID_RETURN (res);
}
}
if ((y.w[1] & MASK_INF) == MASK_INF) {
res = 0;
BID_RETURN (res);
}
// CONVERT X
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
sig_x.w[0] = x.w[0];
exp_x = (x.w[1] >> 49) & 0x000000000003fffull;
// CHECK IF X IS CANONICAL
// 9999999999999999999999999999999999(decimal) =
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
// [0, 10^34) is the 754r supported canonical range.
// If the value exceeds that, it is interpreted as 0.
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull)
&& (sig_x.w[0] > 0x378d8e63ffffffffull))
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
non_canon_x = 1;
else
non_canon_x = 0;
// CONVERT Y
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
sig_y.w[0] = y.w[0];
// CHECK IF Y IS CANONICAL
// 9999999999999999999999999999999999(decimal) =
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
// [0, 10^34) is the 754r supported canonical range.
// If the value exceeds that, it is interpreted as 0.
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull)
&& (sig_y.w[0] > 0x378d8e63ffffffffull))
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
non_canon_y = 1;
else
non_canon_y = 0;
// some properties:
// (+ZERO == -ZERO) => therefore ignore the sign
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore
// ignore the exponent field
// (Any non-canonical # is considered 0)
if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) {
x_is_zero = 1;
}
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) {
y_is_zero = 1;
}
if (x_is_zero && y_is_zero) {
res = 1;
BID_RETURN (res);
} else if ((x_is_zero && !y_is_zero) || (!x_is_zero && y_is_zero)) {
res = 0;
BID_RETURN (res);
}
// OPPOSITE SIGN (CASE5)
// now, if the sign bits differ => not equal : return 0
if ((x.w[1] ^ y.w[1]) & MASK_SIGN) {
res = 0;
BID_RETURN (res);
}
// REDUNDANT REPRESENTATIONS (CASE6)
if (exp_x > exp_y) { // to simplify the loop below,
SWAP (exp_x, exp_y, exp_t); // put the larger exp in y,
SWAP (sig_x.w[1], sig_y.w[1], sig_t.w[1]); // and the smaller exp in x
SWAP (sig_x.w[0], sig_y.w[0], sig_t.w[0]); // and the smaller exp in x
}
if (exp_y - exp_x > 33) {
res = 0;
BID_RETURN (res);
} // difference cannot be greater than 10^33
if (exp_y - exp_x > 19) {
// recalculate y's significand upwards
__mul_128x128_to_256 (sig_n_prime256, sig_y,
ten2k128[exp_y - exp_x - 20]);
{
res = ((sig_n_prime256.w[3] == 0) && (sig_n_prime256.w[2] == 0)
&& (sig_n_prime256.w[1] == sig_x.w[1])
&& (sig_n_prime256.w[0] == sig_x.w[0]));
BID_RETURN (res);
}
}
//else{
// recalculate y's significand upwards
__mul_64x128_to_192 (sig_n_prime192, ten2k64[exp_y - exp_x], sig_y);
{
res = ((sig_n_prime192.w[2] == 0)
&& (sig_n_prime192.w[1] == sig_x.w[1])
&& (sig_n_prime192.w[0] == sig_x.w[0]));
BID_RETURN (res);
}
}
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_greater, x,
y)
int res;
int exp_x, exp_y;
int diff;
UINT128 sig_x, sig_y;
UINT192 sig_n_prime192;
UINT256 sig_n_prime256;
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y;
// NaN (CASE1)
// if either number is NAN, the comparison is unordered, rather than
// equal : return 0
if (((x.w[1] & MASK_NAN) == MASK_NAN)
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) {
if ((x.w[1] & MASK_SNAN) == MASK_SNAN
|| (y.w[1] & MASK_SNAN) == MASK_SNAN) {
*pfpsf |= INVALID_EXCEPTION;
}
{
res = 0;
BID_RETURN (res);
}
}
// SIMPLE (CASE2)
// if all the bits are the same, these numbers are equal (not Greater).
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
res = 0;
BID_RETURN (res);
}
// INFINITY (CASE3)
if ((x.w[1] & MASK_INF) == MASK_INF) {
// if x is neg infinity, there is no way it is greater than y, return 0
if (((x.w[1] & MASK_SIGN) == MASK_SIGN)) {
res = 0;
BID_RETURN (res);
}
// x is pos infinity, it is greater, unless y is positive infinity =>
// return y!=pos_infinity
else {
res = (((y.w[1] & MASK_INF) != MASK_INF)
|| ((y.w[1] & MASK_SIGN) == MASK_SIGN));
BID_RETURN (res);
}
} else if ((y.w[1] & MASK_INF) == MASK_INF) {
// x is finite, so if y is positive infinity, then x is less, return 0
// if y is negative infinity, then x is greater, return 1
{
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
}
// CONVERT X
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
sig_x.w[0] = x.w[0];
exp_x = (x.w[1] >> 49) & 0x000000000003fffull;
// CHECK IF X IS CANONICAL
// 9999999999999999999999999999999999(decimal) =
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
// [0, 10^34) is the 754r supported canonical range.
// If the value exceeds that, it is interpreted as 0.
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull)
&& (sig_x.w[0] > 0x378d8e63ffffffffull))
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
non_canon_x = 1;
else
non_canon_x = 0;
// CONVERT Y
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
sig_y.w[0] = y.w[0];
// CHECK IF Y IS CANONICAL
// 9999999999999999999999999999999999(decimal) =
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
// [0, 10^34) is the 754r supported canonical range.
// If the value exceeds that, it is interpreted as 0.
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull)
&& (sig_y.w[0] > 0x378d8e63ffffffffull))
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
non_canon_y = 1;
else
non_canon_y = 0;
// ZERO (CASE4)
// some properties:
// (+ZERO == -ZERO) => therefore ignore the sign
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore
// ignore the exponent field
// (Any non-canonical # is considered 0)
if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) {
x_is_zero = 1;
}
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) {
y_is_zero = 1;
}
// if both numbers are zero, neither is greater => return NOTGREATERTHAN
if (x_is_zero && y_is_zero) {
res = 0;
BID_RETURN (res);
}
// is x is zero, it is greater if Y is negative
else if (x_is_zero) {
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// is y is zero, X is greater if it is positive
else if (y_is_zero) {
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// OPPOSITE SIGN (CASE5)
// now, if the sign bits differ, x is greater if y is negative
if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) {
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// REDUNDANT REPRESENTATIONS (CASE6)
// if exponents are the same, then we have a simple comparison
// of the significands
if (exp_y == exp_x) {
res = (((sig_x.w[1] > sig_y.w[1])
|| (sig_x.w[1] == sig_y.w[1]
&& sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) ==
MASK_SIGN));
BID_RETURN (res);
}
// if both components are either bigger or smaller,
// it is clear what needs to be done
if ((sig_x.w[1] > sig_y.w[1]
|| (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0]))
&& exp_x >= exp_y) {
{
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
}
if ((sig_x.w[1] < sig_y.w[1]
|| (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0]))
&& exp_x <= exp_y) {
{
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
}
diff = exp_x - exp_y;
// if |exp_x - exp_y| < 33, it comes down to the compensated significand
if (diff > 0) { // to simplify the loop below,
// if exp_x is 33 greater than exp_y, no need for compensation
if (diff > 33) {
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
} // difference cannot be greater than 10^33
if (diff > 19) { //128 by 128 bit multiply -> 256 bits
__mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]);
// if postitive, return whichever significand is larger
// (converse if negative)
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
&& sig_n_prime256.w[1] == sig_y.w[1]
&& (sig_n_prime256.w[0] == sig_y.w[0])) {
res = 0;
BID_RETURN (res);
} // if equal, return 0
{
res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0)
|| (sig_n_prime256.w[1] > sig_y.w[1])
|| (sig_n_prime256.w[1] == sig_y.w[1]
&& sig_n_prime256.w[0] >
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN));
BID_RETURN (res);
}
}
//else { //128 by 64 bit multiply -> 192 bits
__mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_x);
// if postitive, return whichever significand is larger
// (converse if negative)
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1]
&& (sig_n_prime192.w[0] == sig_y.w[0])) {
res = 0;
BID_RETURN (res);
} // if equal, return 0
{
res = (((sig_n_prime192.w[2] > 0) ||
(sig_n_prime192.w[1] > sig_y.w[1]) ||
(sig_n_prime192.w[1] == sig_y.w[1] &&
sig_n_prime192.w[0] > sig_y.w[0])) ^
((y.w[1] & MASK_SIGN) == MASK_SIGN));
BID_RETURN (res);
}
}
diff = exp_y - exp_x;
// if exp_x is 33 less than exp_y, no need for compensation
if (diff > 33) {
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
if (diff > 19) { //128 by 128 bit multiply -> 256 bits
// adjust the y significand upwards
__mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]);
// if postitive, return whichever significand is larger
// (converse if negative)
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
&& sig_n_prime256.w[1] == sig_x.w[1]
&& (sig_n_prime256.w[0] == sig_x.w[0])) {
res = 0;
BID_RETURN (res);
} // if equal, return 0
{
res = ((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0 ||
(sig_n_prime256.w[1] > sig_x.w[1] ||
(sig_n_prime256.w[1] == sig_x.w[1] &&
sig_n_prime256.w[0] > sig_x.w[0]))) ^
((x.w[1] & MASK_SIGN) != MASK_SIGN));
BID_RETURN (res);
}
}
//else { //128 by 64 bit multiply -> 192 bits
// adjust the y significand upwards
__mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_y);
// if postitive, return whichever significand is larger
// (converse if negative)
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1]
&& (sig_n_prime192.w[0] == sig_x.w[0])) {
res = 0;
BID_RETURN (res);
} // if equal, return 0
{
res = (sig_n_prime192.w[2] != 0
|| (sig_n_prime192.w[1] > sig_x.w[1]
|| (sig_n_prime192.w[1] == sig_x.w[1]
&& sig_n_prime192.w[0] >
sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
}
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int,
bid128_quiet_greater_equal, x,
y)
int res;
int exp_x, exp_y;
int diff;
UINT128 sig_x, sig_y;
UINT192 sig_n_prime192;
UINT256 sig_n_prime256;
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y;
// NaN (CASE1)
// if either number is NAN, the comparison is unordered,
// rather than equal : return 1
if (((x.w[1] & MASK_NAN) == MASK_NAN)
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) {
if ((x.w[1] & MASK_SNAN) == MASK_SNAN
|| (y.w[1] & MASK_SNAN) == MASK_SNAN) {
*pfpsf |= INVALID_EXCEPTION;
}
{
res = 0;
BID_RETURN (res);
}
}
// SIMPLE (CASE2)
// if all the bits are the same, these numbers are equal (not Greater).
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
res = 1;
BID_RETURN (res);
}
// INFINITY (CASE3)
if ((x.w[1] & MASK_INF) == MASK_INF) {
// if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) }
if ((x.w[1] & MASK_SIGN) == MASK_SIGN)
// x is -inf, so it is less than y unless y is -inf
{
res = (((y.w[1] & MASK_INF) == MASK_INF)
&& (y.w[1] & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
} else
// x is pos_inf, no way for it to be less than y
{
res = 1;
BID_RETURN (res);
}
} else if ((y.w[1] & MASK_INF) == MASK_INF) {
// x is finite, so if y is positive infinity, then x is less, return 0
// if y is negative infinity, then x is greater, return 1
{
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
}
// CONVERT X
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
sig_x.w[0] = x.w[0];
exp_x = (x.w[1] >> 49) & 0x000000000003fffull;
// CHECK IF X IS CANONICAL
// 9999999999999999999999999999999999(decimal) =
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
// [0, 10^34) is the 754r supported canonical range.
// If the value exceeds that, it is interpreted as 0.
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull)
&& (sig_x.w[0] > 0x378d8e63ffffffffull))
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
non_canon_x = 1;
else
non_canon_x = 0;
// CONVERT Y
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
sig_y.w[0] = y.w[0];
// CHECK IF Y IS CANONICAL
// 9999999999999999999999999999999999(decimal) =
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
// [0, 10^34) is the 754r supported canonical range.
// If the value exceeds that, it is interpreted as 0.
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull)
&& (sig_y.w[0] > 0x378d8e63ffffffffull))
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
non_canon_y = 1;
else
non_canon_y = 0;
// ZERO (CASE4)
// some properties:
// (+ZERO == -ZERO) => therefore ignore the sign
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore
// ignore the exponent field
// (Any non-canonical # is considered 0)
if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) {
x_is_zero = 1;
}
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) {
y_is_zero = 1;
}
// if both numbers are zero, neither is greater => return NOTGREATERTHAN
if (x_is_zero && y_is_zero) {
res = 1;
BID_RETURN (res);
}
// is x is zero, it is greater if Y is negative
else if (x_is_zero) {
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// is y is zero, X is greater if it is positive
else if (y_is_zero) {
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// OPPOSITE SIGN (CASE5)
// now, if the sign bits differ, x is greater if y is negative
if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) {
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// REDUNDANT REPRESENTATIONS (CASE6)
// if exponents are the same, then we have a simple comparison of the
// significands
if (exp_y == exp_x) {
res = (((sig_x.w[1] > sig_y.w[1])
|| (sig_x.w[1] == sig_y.w[1]
&& sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) ==
MASK_SIGN));
BID_RETURN (res);
}
// if both components are either bigger or smaller,
// it is clear what needs to be done
if (sig_x.w[1] >= sig_y.w[1] && sig_x.w[0] >= sig_y.w[0]
&& exp_x > exp_y) {
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
if (sig_x.w[1] <= sig_y.w[1] && sig_x.w[0] <= sig_y.w[0]
&& exp_x < exp_y) {
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
diff = exp_x - exp_y;
// if |exp_x - exp_y| < 33, it comes down to the compensated significand
if (diff > 0) { // to simplify the loop below,
// if exp_x is 33 greater than exp_y, no need for compensation
if (diff > 33) {
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
} // difference cannot be greater than 10^33
if (diff > 19) { //128 by 128 bit multiply -> 256 bits
__mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]);
// if postitive, return whichever significand is larger
// (converse if negative)
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
&& sig_n_prime256.w[1] == sig_y.w[1]
&& (sig_n_prime256.w[0] == sig_y.w[0])) {
res = 1;
BID_RETURN (res);
} // if equal, return 1
{
res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0)
|| (sig_n_prime256.w[1] > sig_y.w[1])
|| (sig_n_prime256.w[1] == sig_y.w[1]
&& sig_n_prime256.w[0] >
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN));
BID_RETURN (res);
}
}
//else { //128 by 64 bit multiply -> 192 bits
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x);
// if postitive, return whichever significand is larger
// (converse if negative)
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1]
&& (sig_n_prime192.w[0] == sig_y.w[0])) {
res = 1;
BID_RETURN (res);
} // if equal, return 1
{
res = (((sig_n_prime192.w[2] > 0)
|| (sig_n_prime192.w[1] > sig_y.w[1])
|| (sig_n_prime192.w[1] == sig_y.w[1]
&& sig_n_prime192.w[0] >
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN));
BID_RETURN (res);
}
}
diff = exp_y - exp_x;
// if exp_x is 33 less than exp_y, no need for compensation
if (diff > 33) {
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
if (diff > 19) { //128 by 128 bit multiply -> 256 bits
// adjust the y significand upwards
__mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]);
// if postitive, return whichever significand is larger
// (converse if negative)
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
&& sig_n_prime256.w[1] == sig_x.w[1]
&& (sig_n_prime256.w[0] == sig_x.w[0])) {
res = 1;
BID_RETURN (res);
} // if equal, return 1
{
res = ((sig_n_prime256.w[3] == 0 && sig_n_prime256.w[2] == 0
&& (sig_n_prime256.w[1] < sig_x.w[1]
|| (sig_n_prime256.w[1] == sig_x.w[1]
&& sig_n_prime256.w[0] <
sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) ==
MASK_SIGN));
BID_RETURN (res);
}
}
//else { //128 by 64 bit multiply -> 192 bits
// adjust the y significand upwards
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y);
// if postitive, return whichever significand is larger
// (converse if negative)
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1]
&& (sig_n_prime192.w[0] == sig_x.w[0])) {
res = 1;
BID_RETURN (res);
} // if equal, return 1
{
res = (sig_n_prime192.w[2] == 0
&& (sig_n_prime192.w[1] < sig_x.w[1]
|| (sig_n_prime192.w[1] == sig_x.w[1]
&& sig_n_prime192.w[0] <
sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
}
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int,
bid128_quiet_greater_unordered,
x, y)
int res;
int exp_x, exp_y;
int diff;
UINT128 sig_x, sig_y;
UINT192 sig_n_prime192;
UINT256 sig_n_prime256;
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y;
// NaN (CASE1)
// if either number is NAN, the comparison is unordered,
// rather than
// equal : return 1
if (((x.w[1] & MASK_NAN) == MASK_NAN)
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) {
if ((x.w[1] & MASK_SNAN) == MASK_SNAN
|| (y.w[1] & MASK_SNAN) == MASK_SNAN) {
*pfpsf |= INVALID_EXCEPTION;
}
{
res = 1;
BID_RETURN (res);
}
}
// SIMPLE (CASE2)
// if all the bits are the same, these numbers are equal (not Greater).
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
res = 0;
BID_RETURN (res);
}
// INFINITY (CASE3)
if ((x.w[1] & MASK_INF) == MASK_INF) {
// if x is neg infinity, there is no way it is greater than y, return 0
if (((x.w[1] & MASK_SIGN) == MASK_SIGN)) {
res = 0;
BID_RETURN (res);
}
// x is pos infinity, it is greater, unless y is positive infinity =>
// return y!=pos_infinity
else {
res = (((y.w[1] & MASK_INF) != MASK_INF)
|| ((y.w[1] & MASK_SIGN) == MASK_SIGN));
BID_RETURN (res);
}
} else if ((y.w[1] & MASK_INF) == MASK_INF) {
// x is finite, so if y is positive infinity, then x is less, return 0
// if y is negative infinity, then x is greater, return 1
{
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
}
// CONVERT X
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
sig_x.w[0] = x.w[0];
exp_x = (x.w[1] >> 49) & 0x000000000003fffull;
// CHECK IF X IS CANONICAL
// 9999999999999999999999999999999999(decimal) =
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
// [0, 10^34) is the 754r supported canonical range.
// If the value exceeds that, it is interpreted as 0.
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull)
&& (sig_x.w[0] > 0x378d8e63ffffffffull))
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
non_canon_x = 1;
else
non_canon_x = 0;
// CONVERT Y
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
sig_y.w[0] = y.w[0];
// CHECK IF Y IS CANONICAL
// 9999999999999999999999999999999999(decimal) =
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
// [0, 10^34) is the 754r supported canonical range.
// If the value exceeds that, it is interpreted as 0.
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull)
&& (sig_y.w[0] > 0x378d8e63ffffffffull))
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
non_canon_y = 1;
else
non_canon_y = 0;
// ZERO (CASE4)
// some properties:
// (+ZERO == -ZERO) => therefore ignore the sign
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore
// ignore the exponent field
// (Any non-canonical # is considered 0)
if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) {
x_is_zero = 1;
}
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) {
y_is_zero = 1;
}
// if both numbers are zero, neither is greater => return NOTGREATERTHAN
if (x_is_zero && y_is_zero) {
res = 0;
BID_RETURN (res);
}
// is x is zero, it is greater if Y is negative
else if (x_is_zero) {
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// is y is zero, X is greater if it is positive
else if (y_is_zero) {
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// OPPOSITE SIGN (CASE5)
// now, if the sign bits differ, x is greater if y is negative
if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) {
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// REDUNDANT REPRESENTATIONS (CASE6)
// if exponents are the same, then we have a simple comparison of the
// significands
if (exp_y == exp_x) {
res = (((sig_x.w[1] > sig_y.w[1])
|| (sig_x.w[1] == sig_y.w[1]
&& sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) ==
MASK_SIGN));
BID_RETURN (res);
}
// if both components are either bigger or smaller,
// it is clear what needs to be done
if (sig_x.w[1] >= sig_y.w[1] && sig_x.w[0] >= sig_y.w[0]
&& exp_x > exp_y) {
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
if (sig_x.w[1] <= sig_y.w[1] && sig_x.w[0] <= sig_y.w[0]
&& exp_x < exp_y) {
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
diff = exp_x - exp_y;
// if |exp_x - exp_y| < 33, it comes down to the compensated significand
if (diff > 0) { // to simplify the loop below,
// if exp_x is 33 greater than exp_y, no need for compensation
if (diff > 33) {
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
} // difference cannot be greater than 10^33
if (diff > 19) { //128 by 128 bit multiply -> 256 bits
__mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]);
// if postitive, return whichever significand is larger
// (converse if negative)
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
&& sig_n_prime256.w[1] == sig_y.w[1]
&& (sig_n_prime256.w[0] == sig_y.w[0])) {
res = 0;
BID_RETURN (res);
} // if equal, return 0
{
res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0)
|| (sig_n_prime256.w[1] > sig_y.w[1])
|| (sig_n_prime256.w[1] == sig_y.w[1]
&& sig_n_prime256.w[0] >
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN));
BID_RETURN (res);
}
}
//else { //128 by 64 bit multiply -> 192 bits
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x);
// if postitive, return whichever significand is larger
// (converse if negative)
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1]
&& (sig_n_prime192.w[0] == sig_y.w[0])) {
res = 0;
BID_RETURN (res);
} // if equal, return 0
{
res = (((sig_n_prime192.w[2] > 0)
|| (sig_n_prime192.w[1] > sig_y.w[1])
|| (sig_n_prime192.w[1] == sig_y.w[1]
&& sig_n_prime192.w[0] >
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN));
BID_RETURN (res);
}
}
diff = exp_y - exp_x;
// if exp_x is 33 less than exp_y, no need for compensation
if (diff > 33) {
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
if (diff > 19) { //128 by 128 bit multiply -> 256 bits
// adjust the y significand upwards
__mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]);
// if postitive, return whichever significand is larger
// (converse if negative)
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
&& sig_n_prime256.w[1] == sig_x.w[1]
&& (sig_n_prime256.w[0] == sig_x.w[0])) {
res = 0;
BID_RETURN (res);
} // if equal, return 0
{
res = ((sig_n_prime256.w[3] == 0 && sig_n_prime256.w[2] == 0
&& (sig_n_prime256.w[1] < sig_x.w[1]
|| (sig_n_prime256.w[1] == sig_x.w[1]
&& sig_n_prime256.w[0] <
sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) ==
MASK_SIGN));
BID_RETURN (res);
}
}
//else { //128 by 64 bit multiply -> 192 bits
// adjust the y significand upwards
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y);
// if postitive, return whichever significand is larger
// (converse if negative)
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1]
&& (sig_n_prime192.w[0] == sig_x.w[0])) {
res = 0;
BID_RETURN (res);
} // if equal, return 0
{
res = (sig_n_prime192.w[2] == 0
&& (sig_n_prime192.w[1] < sig_x.w[1]
|| (sig_n_prime192.w[1] == sig_x.w[1]
&& sig_n_prime192.w[0] <
sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
}
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_less, x, y)
int res;
int exp_x, exp_y;
int diff;
UINT128 sig_x, sig_y;
UINT192 sig_n_prime192;
UINT256 sig_n_prime256;
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y;
// NaN (CASE1)
// if either number is NAN, the comparison is unordered,
// rather than equal : return 0
if (((x.w[1] & MASK_NAN) == MASK_NAN)
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) {
if ((x.w[1] & MASK_SNAN) == MASK_SNAN
|| (y.w[1] & MASK_SNAN) == MASK_SNAN) {
*pfpsf |= INVALID_EXCEPTION;
}
{
res = 0;
BID_RETURN (res);
}
}
// SIMPLE (CASE2)
// if all the bits are the same, these numbers are equal.
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
res = 0;
BID_RETURN (res);
}
// INFINITY (CASE3)
if ((x.w[1] & MASK_INF) == MASK_INF) {
// if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) }
if ((x.w[1] & MASK_SIGN) == MASK_SIGN)
// x is -inf, so it is less than y unless y is -inf
{
res = (((y.w[1] & MASK_INF) != MASK_INF)
|| (y.w[1] & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
} else
// x is pos_inf, no way for it to be less than y
{
res = 0;
BID_RETURN (res);
}
} else if ((y.w[1] & MASK_INF) == MASK_INF) {
// x is finite, so if y is positive infinity, then x is less, return 0
// if y is negative infinity, then x is greater, return 1
{
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
}
// CONVERT X
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
sig_x.w[0] = x.w[0];
exp_x = (x.w[1] >> 49) & 0x000000000003fffull;
// CHECK IF X IS CANONICAL
// 9999999999999999999999999999999999(decimal) =
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
// [0, 10^34) is the 754r supported canonical range.
// If the value exceeds that, it is interpreted as 0.
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull)
&& (sig_x.w[0] > 0x378d8e63ffffffffull))
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
non_canon_x = 1;
else
non_canon_x = 0;
// CONVERT Y
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
sig_y.w[0] = y.w[0];
// CHECK IF Y IS CANONICAL
// 9999999999999999999999999999999999(decimal) =
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
// [0, 10^34) is the 754r supported canonical range.
// If the value exceeds that, it is interpreted as 0.
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull)
&& (sig_y.w[0] > 0x378d8e63ffffffffull))
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
non_canon_y = 1;
else
non_canon_y = 0;
// ZERO (CASE4)
// some properties:
// (+ZERO == -ZERO) => therefore ignore the sign
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore
// ignore the exponent field
// (Any non-canonical # is considered 0)
if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) {
x_is_zero = 1;
}
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) {
y_is_zero = 1;
}
// if both numbers are zero, neither is greater => return NOTGREATERTHAN
if (x_is_zero && y_is_zero) {
res = 0;
BID_RETURN (res);
}
// is x is zero, it is greater if Y is negative
else if (x_is_zero) {
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// is y is zero, X is greater if it is positive
else if (y_is_zero) {
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// OPPOSITE SIGN (CASE5)
// now, if the sign bits differ, x is greater if y is negative
if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) {
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// REDUNDANT REPRESENTATIONS (CASE6)
// if exponents are the same, then we have a simple comparison of the
// significands
if (exp_y == exp_x) {
res = (((sig_x.w[1] > sig_y.w[1])
|| (sig_x.w[1] == sig_y.w[1]
&& sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) !=
MASK_SIGN));
BID_RETURN (res);
}
// if both components are either bigger or smaller,
// it is clear what needs to be done
if ((sig_x.w[1] > sig_y.w[1]
|| (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0]))
&& exp_x >= exp_y) {
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
if ((sig_x.w[1] < sig_y.w[1]
|| (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0]))
&& exp_x <= exp_y) {
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
diff = exp_x - exp_y;
// if |exp_x - exp_y| < 33, it comes down to the compensated significand
if (diff > 0) { // to simplify the loop below,
// if exp_x is 33 greater than exp_y, no need for compensation
if (diff > 33) {
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
} // difference cannot be greater than 10^33
if (diff > 19) { //128 by 128 bit multiply -> 256 bits
__mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]);
// if postitive, return whichever significand is larger
// (converse if negative)
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
&& sig_n_prime256.w[1] == sig_y.w[1]
&& (sig_n_prime256.w[0] == sig_y.w[0])) {
res = 0;
BID_RETURN (res);
} // if equal, return 0
{
res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0)
|| (sig_n_prime256.w[1] > sig_y.w[1])
|| (sig_n_prime256.w[1] == sig_y.w[1]
&& sig_n_prime256.w[0] >
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN));
BID_RETURN (res);
}
}
//else { //128 by 64 bit multiply -> 192 bits
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x);
// if postitive, return whichever significand is larger
// (converse if negative)
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1]
&& (sig_n_prime192.w[0] == sig_y.w[0])) {
res = 0;
BID_RETURN (res);
} // if equal, return 0
{
res = (((sig_n_prime192.w[2] > 0)
|| (sig_n_prime192.w[1] > sig_y.w[1])
|| (sig_n_prime192.w[1] == sig_y.w[1]
&& sig_n_prime192.w[0] >
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN));
BID_RETURN (res);
}
}
diff = exp_y - exp_x;
// if exp_x is 33 less than exp_y, no need for compensation
if (diff > 33) {
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
if (diff > 19) { //128 by 128 bit multiply -> 256 bits
// adjust the y significand upwards
__mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]);
// if postitive, return whichever significand is larger
// (converse if negative)
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
&& sig_n_prime256.w[1] == sig_x.w[1]
&& (sig_n_prime256.w[0] == sig_x.w[0])) {
res = 0;
BID_RETURN (res);
} // if equal, return 1
{
res = ((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0
|| (sig_n_prime256.w[1] > sig_x.w[1]
|| (sig_n_prime256.w[1] == sig_x.w[1]
&& sig_n_prime256.w[0] >
sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) ==
MASK_SIGN));
BID_RETURN (res);
}
}
//else { //128 by 64 bit multiply -> 192 bits
// adjust the y significand upwards
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y);
// if postitive, return whichever significand is larger
// (converse if negative)
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1]
&& (sig_n_prime192.w[0] == sig_x.w[0])) {
res = 0;
BID_RETURN (res);
} // if equal, return 0
{
res = (sig_n_prime192.w[2] != 0
|| (sig_n_prime192.w[1] > sig_x.w[1]
|| (sig_n_prime192.w[1] == sig_x.w[1]
&& sig_n_prime192.w[0] >
sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
}
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_less_equal,
x, y)
int res;
int exp_x, exp_y;
int diff;
UINT128 sig_x, sig_y;
UINT192 sig_n_prime192;
UINT256 sig_n_prime256;
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y;
// NaN (CASE1)
// if either number is NAN, the comparison is unordered,
// rather than equal : return 0
if (((x.w[1] & MASK_NAN) == MASK_NAN)
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) {
if ((x.w[1] & MASK_SNAN) == MASK_SNAN
|| (y.w[1] & MASK_SNAN) == MASK_SNAN) {
*pfpsf |= INVALID_EXCEPTION;
}
{
res = 0;
BID_RETURN (res);
}
}
// SIMPLE (CASE2)
// if all the bits are the same, these numbers are equal (not Greater).
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
res = 1;
BID_RETURN (res);
}
// INFINITY (CASE3)
if ((x.w[1] & MASK_INF) == MASK_INF) {
// if x is neg infinity, there is no way it is greater than y, return 1
if (((x.w[1] & MASK_SIGN) == MASK_SIGN)) {
res = 1;
BID_RETURN (res);
}
// x is pos infinity, it is greater, unless y is positive infinity =>
// return y!=pos_infinity
else {
res = (((y.w[1] & MASK_INF) == MASK_INF)
&& ((y.w[1] & MASK_SIGN) != MASK_SIGN));
BID_RETURN (res);
}
} else if ((y.w[1] & MASK_INF) == MASK_INF) {
// x is finite, so if y is positive infinity, then x is less, return 0
// if y is negative infinity, then x is greater, return 1
{
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
}
// CONVERT X
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
sig_x.w[0] = x.w[0];
exp_x = (x.w[1] >> 49) & 0x000000000003fffull;
// CHECK IF X IS CANONICAL
// 9999999999999999999999999999999999(decimal) =
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
// [0, 10^34) is the 754r supported canonical range.
// If the value exceeds that, it is interpreted as 0.
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull)
&& (sig_x.w[0] > 0x378d8e63ffffffffull))
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
non_canon_x = 1;
else
non_canon_x = 0;
// CONVERT Y
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
sig_y.w[0] = y.w[0];
// CHECK IF Y IS CANONICAL
// 9999999999999999999999999999999999(decimal) =
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
// [0, 10^34) is the 754r supported canonical range.
// If the value exceeds that, it is interpreted as 0.
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull)
&& (sig_y.w[0] > 0x378d8e63ffffffffull))
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
non_canon_y = 1;
else
non_canon_y = 0;
// ZERO (CASE4)
// some properties:
// (+ZERO == -ZERO) => therefore ignore the sign
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore
// ignore the exponent field
// (Any non-canonical # is considered 0)
if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) {
x_is_zero = 1;
}
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) {
y_is_zero = 1;
}
// if both numbers are zero, neither is greater => return NOTGREATERTHAN
if (x_is_zero && y_is_zero) {
res = 1;
BID_RETURN (res);
}
// is x is zero, it is greater if Y is negative
else if (x_is_zero) {
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// is y is zero, X is greater if it is positive
else if (y_is_zero) {
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// OPPOSITE SIGN (CASE5)
// now, if the sign bits differ, x is greater if y is negative
if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) {
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// REDUNDANT REPRESENTATIONS (CASE6)
// if exponents are the same, then we have a simple comparison of the
// significands
if (exp_y == exp_x) {
res = (((sig_x.w[1] > sig_y.w[1]) || (sig_x.w[1] == sig_y.w[1] &&
sig_x.w[0] >=
sig_y.w[0])) ^ ((x.
w[1] &
MASK_SIGN) !=
MASK_SIGN));
BID_RETURN (res);
}
// if both components are either bigger or smaller,
// it is clear what needs to be done
if ((sig_x.w[1] > sig_y.w[1]
|| (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0]))
&& exp_x >= exp_y) {
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
if ((sig_x.w[1] < sig_y.w[1]
|| (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0]))
&& exp_x <= exp_y) {
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
diff = exp_x - exp_y;
// if |exp_x - exp_y| < 33, it comes down to the compensated significand
if (diff > 0) { // to simplify the loop below,
// if exp_x is 33 greater than exp_y, no need for compensation
if (diff > 33) {
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
} // difference cannot be greater than 10^33
if (diff > 19) { //128 by 128 bit multiply -> 256 bits
__mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]);
// if postitive, return whichever significand is larger
// (converse if negative)
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
&& sig_n_prime256.w[1] == sig_y.w[1]
&& (sig_n_prime256.w[0] == sig_y.w[0])) {
res = 1;
BID_RETURN (res);
} // if equal, return 0
{
res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0)
|| (sig_n_prime256.w[1] > sig_y.w[1])
|| (sig_n_prime256.w[1] == sig_y.w[1]
&& sig_n_prime256.w[0] >
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN));
BID_RETURN (res);
}
}
//else { //128 by 64 bit multiply -> 192 bits
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x);
// if postitive, return whichever significand is larger
// (converse if negative)
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1]
&& (sig_n_prime192.w[0] == sig_y.w[0])) {
res = 1;
BID_RETURN (res);
} // if equal, return 0
{
res = (((sig_n_prime192.w[2] > 0)
|| (sig_n_prime192.w[1] > sig_y.w[1])
|| (sig_n_prime192.w[1] == sig_y.w[1]
&& sig_n_prime192.w[0] >
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN));
BID_RETURN (res);
}
}
diff = exp_y - exp_x;
// if exp_x is 33 less than exp_y, no need for compensation
if (diff > 33) {
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
if (diff > 19) { //128 by 128 bit multiply -> 256 bits
// adjust the y significand upwards
__mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]);
// if postitive, return whichever significand is larger
// (converse if negative)
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
&& sig_n_prime256.w[1] == sig_x.w[1]
&& (sig_n_prime256.w[0] == sig_x.w[0])) {
res = 1;
BID_RETURN (res);
} // if equal, return 0
{
res =
((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0
|| (sig_n_prime256.w[1] > sig_x.w[1]
|| (sig_n_prime256.w[1] == sig_x.w[1]
&& sig_n_prime256.w[0] >
sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN));
BID_RETURN (res);
}
}
//else { //128 by 64 bit multiply -> 192 bits
// adjust the y significand upwards
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y);
// if postitive, return whichever significand is larger
// (converse if negative)
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1]
&& (sig_n_prime192.w[0] == sig_x.w[0])) {
res = 1;
BID_RETURN (res);
} // if equal, return 0
{
res = (sig_n_prime192.w[2] != 0
|| (sig_n_prime192.w[1] > sig_x.w[1]
|| (sig_n_prime192.w[1] == sig_x.w[1]
&& sig_n_prime192.w[0] >
sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
}
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int,
bid128_quiet_less_unordered,
x, y)
int res;
int exp_x, exp_y;
int diff;
UINT128 sig_x, sig_y;
UINT192 sig_n_prime192;
UINT256 sig_n_prime256;
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y;
// NaN (CASE1)
// if either number is NAN, the comparison is unordered
if (((x.w[1] & MASK_NAN) == MASK_NAN)
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) {
if ((x.w[1] & MASK_SNAN) == MASK_SNAN
|| (y.w[1] & MASK_SNAN) == MASK_SNAN) {
*pfpsf |= INVALID_EXCEPTION;
}
{
res = 1;
BID_RETURN (res);
}
}
// SIMPLE (CASE2)
// if all the bits are the same, these numbers are equal.
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
res = 0;
BID_RETURN (res);
}
// INFINITY (CASE3)
if ((x.w[1] & MASK_INF) == MASK_INF) {
// if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) }
if ((x.w[1] & MASK_SIGN) == MASK_SIGN)
// x is -inf, so it is less than y unless y is -inf
{
res = (((y.w[1] & MASK_INF) != MASK_INF)
|| (y.w[1] & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
} else
// x is pos_inf, no way for it to be less than y
{
res = 0;
BID_RETURN (res);
}
} else if ((y.w[1] & MASK_INF) == MASK_INF) {
// x is finite, so if y is positive infinity, then x is less, return 0
// if y is negative infinity, then x is greater, return 1
{
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
}
// CONVERT X
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
sig_x.w[0] = x.w[0];
exp_x = (x.w[1] >> 49) & 0x000000000003fffull;
// CHECK IF X IS CANONICAL
// 9999999999999999999999999999999999(decimal) =
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
// [0, 10^34) is the 754r supported canonical range.
// If the value exceeds that, it is interpreted as 0.
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull)
&& (sig_x.w[0] > 0x378d8e63ffffffffull))
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
non_canon_x = 1;
else
non_canon_x = 0;
// CONVERT Y
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
sig_y.w[0] = y.w[0];
// CHECK IF Y IS CANONICAL
// 9999999999999999999999999999999999(decimal) =
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
// [0, 10^34) is the 754r supported canonical range.
// If the value exceeds that, it is interpreted as 0.
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull)
&& (sig_y.w[0] > 0x378d8e63ffffffffull))
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
non_canon_y = 1;
else
non_canon_y = 0;
// ZERO (CASE4)
// some properties:
// (+ZERO == -ZERO) => therefore ignore the sign
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore
// ignore the exponent field
// (Any non-canonical # is considered 0)
if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) {
x_is_zero = 1;
}
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) {
y_is_zero = 1;
}
// if both numbers are zero, neither is greater => return NOTGREATERTHAN
if (x_is_zero && y_is_zero) {
res = 0;
BID_RETURN (res);
}
// is x is zero, it is greater if Y is negative
else if (x_is_zero) {
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// is y is zero, X is greater if it is positive
else if (y_is_zero) {
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// OPPOSITE SIGN (CASE5)
// now, if the sign bits differ, x is greater if y is negative
if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) {
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// REDUNDANT REPRESENTATIONS (CASE6)
// if exponents are the same, then we have a simple comparison
// of the significands
if (exp_y == exp_x) {
res = (((sig_x.w[1] > sig_y.w[1])
|| (sig_x.w[1] == sig_y.w[1]
&& sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) !=
MASK_SIGN));
BID_RETURN (res);
}
// if both components are either bigger or smaller,
// it is clear what needs to be done
if ((sig_x.w[1] > sig_y.w[1]
|| (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0]))
&& exp_x >= exp_y) {
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
if ((sig_x.w[1] < sig_y.w[1]
|| (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0]))
&& exp_x <= exp_y) {
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
diff = exp_x - exp_y;
// if |exp_x - exp_y| < 33, it comes down to the compensated significand
if (diff > 0) { // to simplify the loop below,
// if exp_x is 33 greater than exp_y, no need for compensation
if (diff > 33) {
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
} // difference cannot be greater than 10^33
if (diff > 19) { //128 by 128 bit multiply -> 256 bits
__mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]);
// if postitive, return whichever significand is larger
// (converse if negative)
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
&& sig_n_prime256.w[1] == sig_y.w[1]
&& (sig_n_prime256.w[0] == sig_y.w[0])) {
res = 0;
BID_RETURN (res);
} // if equal, return 0
{
res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0)
|| (sig_n_prime256.w[1] > sig_y.w[1])
|| (sig_n_prime256.w[1] == sig_y.w[1]
&& sig_n_prime256.w[0] >
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN));
BID_RETURN (res);
}
}
//else { //128 by 64 bit multiply -> 192 bits
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x);
// if postitive, return whichever significand is larger
// (converse if negative)
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1]
&& (sig_n_prime192.w[0] == sig_y.w[0])) {
res = 0;
BID_RETURN (res);
} // if equal, return 0
{
res = (((sig_n_prime192.w[2] > 0)
|| (sig_n_prime192.w[1] > sig_y.w[1])
|| (sig_n_prime192.w[1] == sig_y.w[1]
&& sig_n_prime192.w[0] >
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN));
BID_RETURN (res);
}
}
diff = exp_y - exp_x;
// if exp_x is 33 less than exp_y, no need for compensation
if (diff > 33) {
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
if (diff > 19) { //128 by 128 bit multiply -> 256 bits
// adjust the y significand upwards
__mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]);
// if postitive, return whichever significand is larger
// (converse if negative)
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
&& sig_n_prime256.w[1] == sig_x.w[1]
&& (sig_n_prime256.w[0] == sig_x.w[0])) {
res = 0;
BID_RETURN (res);
} // if equal, return 1
{
res =
((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0
|| (sig_n_prime256.w[1] > sig_x.w[1]
|| (sig_n_prime256.w[1] == sig_x.w[1]
&& sig_n_prime256.w[0] >
sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN));
BID_RETURN (res);
}
}
//else { //128 by 64 bit multiply -> 192 bits
// adjust the y significand upwards
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y);
// if postitive, return whichever significand is larger
// (converse if negative)
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1]
&& (sig_n_prime192.w[0] == sig_x.w[0])) {
res = 0;
BID_RETURN (res);
} // if equal, return 0
{
res = (sig_n_prime192.w[2] != 0
|| (sig_n_prime192.w[1] > sig_x.w[1]
|| (sig_n_prime192.w[1] == sig_x.w[1]
&& sig_n_prime192.w[0] >
sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
}
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_not_equal,
x, y)
int res;
int exp_x, exp_y, exp_t;
UINT128 sig_x, sig_y, sig_t;
UINT192 sig_n_prime192;
UINT256 sig_n_prime256;
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y;
// NaN (CASE1)
// if either number is NAN, the comparison is unordered,
// rather than equal : return 0
if (((x.w[1] & MASK_NAN) == MASK_NAN)
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) {
if ((x.w[1] & MASK_SNAN) == MASK_SNAN
|| (y.w[1] & MASK_SNAN) == MASK_SNAN) {
*pfpsf |= INVALID_EXCEPTION;
}
{
res = 1;
BID_RETURN (res);
}
}
// SIMPLE (CASE2)
// if all the bits are the same, these numbers are equivalent.
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
res = 0;
BID_RETURN (res);
}
// INFINITY (CASE3)
if ((x.w[1] & MASK_INF) == MASK_INF) {
if ((y.w[1] & MASK_INF) == MASK_INF) {
res = (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
} else {
res = 1;
BID_RETURN (res);
}
}
if ((y.w[1] & MASK_INF) == MASK_INF) {
res = 1;
BID_RETURN (res);
}
// CONVERT X
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
sig_x.w[0] = x.w[0];
exp_x = (x.w[1] >> 49) & 0x000000000003fffull;
// CHECK IF X IS CANONICAL
// 9999999999999999999999999999999999(decimal) =
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
// [0, 10^34) is the 754r supported canonical range.
// If the value exceeds that, it is interpreted as 0.
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull)
&& (sig_x.w[0] > 0x378d8e63ffffffffull))
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
non_canon_x = 1;
else
non_canon_x = 0;
// CONVERT Y
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
sig_y.w[0] = y.w[0];
// CHECK IF Y IS CANONICAL
// 9999999999999999999999999999999999(decimal) =
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
// [0, 10^34) is the 754r supported canonical range.
// If the value exceeds that, it is interpreted as 0.
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull)
&& (sig_y.w[0] > 0x378d8e63ffffffffull))
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
non_canon_y = 1;
else
non_canon_y = 0;
// some properties:
// (+ZERO == -ZERO) => therefore ignore the sign
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore
// ignore the exponent field
// (Any non-canonical # is considered 0)
if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) {
x_is_zero = 1;
}
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) {
y_is_zero = 1;
}
if (x_is_zero && y_is_zero) {
res = 0;
BID_RETURN (res);
} else if ((x_is_zero && !y_is_zero) || (!x_is_zero && y_is_zero)) {
res = 1;
BID_RETURN (res);
}
// OPPOSITE SIGN (CASE5)
// now, if the sign bits differ => not equal : return 0
if ((x.w[1] ^ y.w[1]) & MASK_SIGN) {
res = 1;
BID_RETURN (res);
}
// REDUNDANT REPRESENTATIONS (CASE6)
if (exp_x > exp_y) { // to simplify the loop below,
SWAP (exp_x, exp_y, exp_t); // put the larger exp in y,
SWAP (sig_x.w[1], sig_y.w[1], sig_t.w[1]); // and the smaller exp in x
SWAP (sig_x.w[0], sig_y.w[0], sig_t.w[0]); // and the smaller exp in x
}
if (exp_y - exp_x > 33) {
res = 1;
BID_RETURN (res);
} // difference cannot be greater than 10^33
if (exp_y - exp_x > 19) {
// recalculate y's significand upwards
__mul_128x128_to_256 (sig_n_prime256, sig_y,
ten2k128[exp_y - exp_x - 20]);
{
res = ((sig_n_prime256.w[3] != 0) || (sig_n_prime256.w[2] != 0)
|| (sig_n_prime256.w[1] != sig_x.w[1])
|| (sig_n_prime256.w[0] != sig_x.w[0]));
BID_RETURN (res);
}
}
//else{
// recalculate y's significand upwards
__mul_64x128_to192 (sig_n_prime192, ten2k64[exp_y - exp_x], sig_y);
{
res = ((sig_n_prime192.w[2] != 0)
|| (sig_n_prime192.w[1] != sig_x.w[1])
|| (sig_n_prime192.w[0] != sig_x.w[0]));
BID_RETURN (res);
}
}
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_not_greater,
x, y)
int res;
int exp_x, exp_y;
int diff;
UINT128 sig_x, sig_y;
UINT192 sig_n_prime192;
UINT256 sig_n_prime256;
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y;
// NaN (CASE1)
// if either number is NAN, the comparison is unordered,
// rather than equal : return 0
if (((x.w[1] & MASK_NAN) == MASK_NAN)
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) {
if ((x.w[1] & MASK_SNAN) == MASK_SNAN
|| (y.w[1] & MASK_SNAN) == MASK_SNAN) {
*pfpsf |= INVALID_EXCEPTION;
}
{
res = 1;
BID_RETURN (res);
}
}
// SIMPLE (CASE2)
// if all the bits are the same, these numbers are equal (not Greater).
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
res = 1;
BID_RETURN (res);
}
// INFINITY (CASE3)
if ((x.w[1] & MASK_INF) == MASK_INF) {
// if x is neg infinity, there is no way it is greater than y, return 1
if (((x.w[1] & MASK_SIGN) == MASK_SIGN)) {
res = 1;
BID_RETURN (res);
}
// x is pos infinity, it is greater, unless y is positive infinity => return y!=pos_infinity
else {
res = (((y.w[1] & MASK_INF) == MASK_INF)
&& ((y.w[1] & MASK_SIGN) != MASK_SIGN));
BID_RETURN (res);
}
} else if ((y.w[1] & MASK_INF) == MASK_INF) {
// x is finite, so if y is positive infinity, then x is less, return 0
// if y is negative infinity, then x is greater, return 1
{
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
}
// CONVERT X
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
sig_x.w[0] = x.w[0];
exp_x = (x.w[1] >> 49) & 0x000000000003fffull;
// CHECK IF X IS CANONICAL
// 9999999999999999999999999999999999(decimal) =
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
// [0, 10^34) is the 754r supported canonical range.
// If the value exceeds that, it is interpreted as 0.
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull)
&& (sig_x.w[0] > 0x378d8e63ffffffffull))
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
non_canon_x = 1;
else
non_canon_x = 0;
// CONVERT Y
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
sig_y.w[0] = y.w[0];
// CHECK IF Y IS CANONICAL
// 9999999999999999999999999999999999(decimal) =
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
// [0, 10^34) is the 754r supported canonical range.
// If the value exceeds that, it is interpreted as 0.
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull)
&& (sig_y.w[0] > 0x378d8e63ffffffffull))
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
non_canon_y = 1;
else
non_canon_y = 0;
// ZERO (CASE4)
// some properties:
// (+ZERO == -ZERO) => therefore ignore the sign
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore
// ignore the exponent field
// (Any non-canonical # is considered 0)
if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) {
x_is_zero = 1;
}
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) {
y_is_zero = 1;
}
// if both numbers are zero, neither is greater => return NOTGREATERTHAN
if (x_is_zero && y_is_zero) {
res = 1;
BID_RETURN (res);
}
// is x is zero, it is greater if Y is negative
else if (x_is_zero) {
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// is y is zero, X is greater if it is positive
else if (y_is_zero) {
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// OPPOSITE SIGN (CASE5)
// now, if the sign bits differ, x is greater if y is negative
if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) {
res = ((y.w[1] & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// REDUNDANT REPRESENTATIONS (CASE6)
// if exponents are the same, then we have a simple comparison
// of the significands
if (exp_y == exp_x) {
res = (((sig_x.w[1] > sig_y.w[1])
|| (sig_x.w[1] == sig_y.w[1]
&& sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) !=
MASK_SIGN));
BID_RETURN (res);
}
// if both components are either bigger or smaller,
// it is clear what needs to be done
if ((sig_x.w[1] > sig_y.w[1]
|| (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0]))
&& exp_x >= exp_y) {
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
if ((sig_x.w[1] < sig_y.w[1]
|| (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0]))
&& exp_x <= exp_y) {
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
diff = exp_x - exp_y;
// if |exp_x - exp_y| < 33, it comes down to the compensated significand
if (diff > 0) { // to simplify the loop below,
// if exp_x is 33 greater than exp_y, no need for compensation
if (diff > 33) {
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
} // difference cannot be greater than 10^33
if (diff > 19) { //128 by 128 bit multiply -> 256 bits
__mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]);
// if postitive, return whichever significand is larger
// (converse if negative)
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
&& sig_n_prime256.w[1] == sig_y.w[1]
&& (sig_n_prime256.w[0] == sig_y.w[0])) {
res = 1;
BID_RETURN (res);
} // if equal, return 0
{
res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0)
|| (sig_n_prime256.w[1] > sig_y.w[1])
|| (sig_n_prime256.w[1] == sig_y.w[1]
&& sig_n_prime256.w[0] >
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN));
BID_RETURN (res);
}
}
//else { //128 by 64 bit multiply -> 192 bits
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x);
// if postitive, return whichever significand is larger
// (converse if negative)
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1]
&& (sig_n_prime192.w[0] == sig_y.w[0])) {
res = 1;
BID_RETURN (res);
} // if equal, return 0
{
res = (((sig_n_prime192.w[2] > 0)
|| (sig_n_prime192.w[1] > sig_y.w[1])
|| (sig_n_prime192.w[1] == sig_y.w[1]
&& sig_n_prime192.w[0] >
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN));
BID_RETURN (res);
}
}
diff = exp_y - exp_x;
// if exp_x is 33 less than exp_y, no need for compensation
if (diff > 33) {
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
if (diff > 19) { //128 by 128 bit multiply -> 256 bits
// adjust the y significand upwards
__mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]);
// if postitive, return whichever significand is larger
// (converse if negative)
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
&& sig_n_prime256.w[1] == sig_x.w[1]
&& (sig_n_prime256.w[0] == sig_x.w[0])) {
res = 1;
BID_RETURN (res);
} // if equal, return 0
{
res =
((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0
|| (sig_n_prime256.w[1] > sig_x.w[1]
|| (sig_n_prime256.w[1] == sig_x.w[1]
&& sig_n_prime256.w[0] >
sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN));
BID_RETURN (res);
}
}
//else { //128 by 64 bit multiply -> 192 bits
// adjust the y significand upwards
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y);
// if postitive, return whichever significand is larger
// (converse if negative)
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1]
&& (sig_n_prime192.w[0] == sig_x.w[0])) {
res = 1;
BID_RETURN (res);
} // if equal, return 0
{
res = (sig_n_prime192.w[2] != 0
|| (sig_n_prime192.w[1] > sig_x.w[1]
|| (sig_n_prime192.w[1] == sig_x.w[1]
&& sig_n_prime192.w[0] >
sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
}
BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_not_less, x,
y)
int res;
int exp_x, exp_y;
int diff;
UINT128 sig_x, sig_y;
UINT192 sig_n_prime192;
UINT256 sig_n_prime256;
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y;
// NaN (CASE1)
// if either number is NAN, the comparison is unordered,
// rather than equal : return 1
if (((x.w[1] & MASK_NAN) == MASK_NAN)
|| ((y.w[1] & MASK_NAN) == MASK_NAN)) {
if ((x.w[1] & MASK_SNAN) == MASK_SNAN
|| (y.w[1] & MASK_SNAN) == MASK_SNAN) {
*pfpsf |= INVALID_EXCEPTION;
}
{
res = 1;
BID_RETURN (res);
}
}
// SIMPLE (CASE2)
// if all the bits are the same, these numbers are equal (not Greater).
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
res = 1;
BID_RETURN (res);
}
// INFINITY (CASE3)
if ((x.w[1] & MASK_INF) == MASK_INF) {
// if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) }
if ((x.w[1] & MASK_SIGN) == MASK_SIGN)
// x is -inf, so it is less than y unless y is -inf
{
res = (((y.w[1] & MASK_INF) == MASK_INF)
&& (y.w[1] & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
} else
// x is pos_inf, no way for it to be less than y
{
res = 1;
BID_RETURN (res);
}
} else if ((y.w[1] & MASK_INF) == MASK_INF) {
// x is finite, so if y is positive infinity, then x is less, return 0
// if y is negative infinity, then x is greater, return 1
{
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
}
// CONVERT X
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
sig_x.w[0] = x.w[0];
exp_x = (x.w[1] >> 49) & 0x000000000003fffull;
// CHECK IF X IS CANONICAL
// 9999999999999999999999999999999999(decimal) =
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
// [0, 10^34) is the 754r supported canonical range.
// If the value exceeds that, it is interpreted as 0.
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
|| ((sig_x.w[1] == 0x0001ed09bead87c0ull)
&& (sig_x.w[0] > 0x378d8e63ffffffffull))
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
non_canon_x = 1;
else
non_canon_x = 0;
// CONVERT Y
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
sig_y.w[0] = y.w[0];
// CHECK IF Y IS CANONICAL
// 9999999999999999999999999999999999(decimal) =
// 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
// [0, 10^34) is the 754r supported canonical range.
// If the value exceeds that, it is interpreted as 0.
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
|| ((sig_y.w[1] == 0x0001ed09bead87c0ull)
&& (sig_y.w[0] > 0x378d8e63ffffffffull))
|| ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
non_canon_y = 1;
else
non_canon_y = 0;
// ZERO (CASE4)
// some properties:
// (+ZERO == -ZERO) => therefore ignore the sign
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore
// ignore the exponent field
// (Any non-canonical # is considered 0)
if (non_canon_x || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) {
x_is_zero = 1;
}
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) {
y_is_zero = 1;
}
// if both numbers are zero, neither is greater => return NOTGREATERTHAN
if (x_is_zero && y_is_zero) {
res = 1;
BID_RETURN (res);
}
// is x is zero, it is greater if Y is negative
else if (x_is_zero) {
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// is y is zero, X is greater if it is positive
else if (y_is_zero) {
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// OPPOSITE SIGN (CASE5)
// now, if the sign bits differ, x is greater if y is negative
if (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) {
res = ((y.w[1] & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// REDUNDANT REPRESENTATIONS (CASE6)
// if exponents are the same, then we have a simple comparison
// of the significands
if (exp_y == exp_x) {
res = (((sig_x.w[1] > sig_y.w[1])
|| (sig_x.w[1] == sig_y.w[1]
&& sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) ==
MASK_SIGN));
BID_RETURN (res);
}
// if both components are either bigger or smaller,
// it is clear what needs to be done
if (sig_x.w[1] >= sig_y.w[1] && sig_x.w[0] >= sig_y.w[0]
&& exp_x > exp_y) {
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
if (sig_x.w[1] <= sig_y.w[1] && sig_x.w[0] <= sig_y.w[0]
&& exp_x < exp_y) {
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
diff = exp_x - exp_y;
// if |exp_x - exp_y| < 33, it comes down to the compensated significand
if (diff > 0) { // to simplify the loop below,
// if exp_x is 33 greater than exp_y, no need for compensation
if (diff > 33) {
res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
} // difference cannot be greater than 10^33
if (diff > 19) { //128 by 128 bit multiply -> 256 bits
__mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]);
// if postitive, return whichever significand is larger
// (converse if negative)
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
&& sig_n_prime256.w[1] == sig_y.w[1]
&& (sig_n_prime256.w[0] == sig_y.w[0])) {
res = 1;
BID_RETURN (res);
} // if equal, return 1
{
res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0)
|| (sig_n_prime256.w[1] > sig_y.w[1])
|| (sig_n_prime256.w[1] == sig_y.w[1]
&& sig_n_prime256.w[0] >
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN));
BID_RETURN (res);
}
}
//else { //128 by 64 bit multiply -> 192 bits
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x);
// if postitive, return whichever significand is larger
// (converse if negative)
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1]
&& (sig_n_prime192.w[0] == sig_y.w[0])) {
res = 1;
BID_RETURN (res);
} // if equal, return 1
{
res = (((sig_n_prime192.w[2] > 0)
|| (sig_n_prime192.w[1] > sig_y.w[1])
|| (sig_n_prime192.w[1] == sig_y.w[1]
&& sig_n_prime192.w[0] >
sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN));
BID_RETURN (res);
}
}
diff = exp_y - exp_x;
// if exp_x is 33 less than exp_y, no need for compensation
if (diff > 33) {
res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
if (diff > 19) { //128 by 128 bit multiply -> 256 bits
// adjust the y significand upwards
__mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]);
// if postitive, return whichever significand is larger
// (converse if negative)
if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
&& sig_n_prime256.w[1] == sig_x.w[1]
&& (sig_n_prime256.w[0] == sig_x.w[0])) {
res = 1;
BID_RETURN (res);
} // if equal, return 1
{
res =
((sig_n_prime256.w[3] == 0 && sig_n_prime256.w[2] == 0
&& (sig_n_prime256.w[1] < sig_x.w[1]
|| (sig_n_prime256.w[1] == sig_x.w[1]
&& sig_n_prime256.w[0] <
sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN));
BID_RETURN (res);
}
}
//else { //128 by 64 bit multiply -> 192 bits
// adjust the y significand upwards
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y);
// if postitive, return whichever significand is larger
// (converse if negative)
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1]
&& (sig_n_prime192.w[0] == sig_x.w[0])) {
res = 1;
BID_RETURN (res);
} // if equal, return 1
{
res = (sig_n_prime192.w[2] == 0
&& (sig_n_prime192.w[1] < sig_x.w[1]
|| (sig_n_prime192.w[1] == sig_x.w[1]
&& sig_n_prime192.