blob: 669b425f0dd73dd048f98865ca519d5cd976c79b [file] [log] [blame]
/* Copyright (C) 2007-2021 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"
static const UINT64 mult_factor[16] = {
1ull, 10ull, 100ull, 1000ull,
10000ull, 100000ull, 1000000ull, 10000000ull,
100000000ull, 1000000000ull, 10000000000ull, 100000000000ull,
1000000000000ull, 10000000000000ull,
100000000000000ull, 1000000000000000ull
};
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_quiet_equal (int *pres, UINT64 * px,
UINT64 *
py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
UINT64 y = *py;
#else
int
bid64_quiet_equal (UINT64 x,
UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
#endif
int res;
int exp_x, exp_y, exp_t;
UINT64 sig_x, sig_y, sig_t;
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y, lcv;
// NaN (CASE1)
// if either number is NAN, the comparison is unordered,
// rather than equal : return 0
if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) {
*pfpsf |= INVALID_EXCEPTION; // set exception if sNaN
}
res = 0;
BID_RETURN (res);
}
// SIMPLE (CASE2)
// if all the bits are the same, these numbers are equivalent.
if (x == y) {
res = 1;
BID_RETURN (res);
}
// INFINITY (CASE3)
if (((x & MASK_INF) == MASK_INF) && ((y & MASK_INF) == MASK_INF)) {
res = (((x ^ y) & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// ONE INFINITY (CASE3')
if (((x & MASK_INF) == MASK_INF) || ((y & MASK_INF) == MASK_INF)) {
res = 0;
BID_RETURN (res);
}
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (sig_x > 9999999999999999ull) {
non_canon_x = 1;
} else {
non_canon_x = 0;
}
} else {
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
sig_x = (x & MASK_BINARY_SIG1);
non_canon_x = 0;
}
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (sig_y > 9999999999999999ull) {
non_canon_y = 1;
} else {
non_canon_y = 0;
}
} else {
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
sig_y = (y & MASK_BINARY_SIG1);
non_canon_y = 0;
}
// ZERO (CASE4)
// some properties:
// (+ZERO==-ZERO) => therefore ignore the sign
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B =>
// therefore ignore the exponent field
// (Any non-canonical # is considered 0)
if (non_canon_x || sig_x == 0) {
x_is_zero = 1;
}
if (non_canon_y || sig_y == 0) {
y_is_zero = 1;
}
if (x_is_zero && y_is_zero) {
res = 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 ^ y) & 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, sig_y, sig_t); // and the smaller exp in x
}
if (exp_y - exp_x > 15) {
res = 0; // difference cannot be greater than 10^15
BID_RETURN (res);
}
for (lcv = 0; lcv < (exp_y - exp_x); lcv++) {
// recalculate y's significand upwards
sig_y = sig_y * 10;
if (sig_y > 9999999999999999ull) {
res = 0;
BID_RETURN (res);
}
}
res = (sig_y == sig_x);
BID_RETURN (res);
}
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_quiet_greater (int *pres, UINT64 * px,
UINT64 *
py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
UINT64 y = *py;
#else
int
bid64_quiet_greater (UINT64 x,
UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
#endif
int res;
int exp_x, exp_y;
UINT64 sig_x, sig_y;
UINT128 sig_n_prime;
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y;
// NaN (CASE1)
// if either number is NAN, the comparison is unordered, rather than equal :
// return 0
if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) {
*pfpsf |= INVALID_EXCEPTION; // set exception if sNaN
}
res = 0;
BID_RETURN (res);
}
// SIMPLE (CASE2)
// if all the bits are the same, these numbers are equal (not Greater).
if (x == y) {
res = 0;
BID_RETURN (res);
}
// INFINITY (CASE3)
if ((x & MASK_INF) == MASK_INF) {
// if x is neg infinity, there is no way it is greater than y, return 0
if (((x & MASK_SIGN) == MASK_SIGN)) {
res = 0;
BID_RETURN (res);
} else {
// x is pos infinity, it is greater, unless y is positive
// infinity => return y!=pos_infinity
res = (((y & MASK_INF) != MASK_INF)
|| ((y & MASK_SIGN) == MASK_SIGN));
BID_RETURN (res);
}
} else if ((y & MASK_INF) == MASK_INF) {
// x is finite, so if y is positive infinity, then x is less, return 0
// if y is negative infinity, then x is greater, return 1
res = ((y & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (sig_x > 9999999999999999ull) {
non_canon_x = 1;
} else {
non_canon_x = 0;
}
} else {
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
sig_x = (x & MASK_BINARY_SIG1);
non_canon_x = 0;
}
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (sig_y > 9999999999999999ull) {
non_canon_y = 1;
} else {
non_canon_y = 0;
}
} else {
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
sig_y = (y & MASK_BINARY_SIG1);
non_canon_y = 0;
}
// ZERO (CASE4)
// some properties:
//(+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater
//(ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore ignore the
// exponent field
// (Any non-canonical # is considered 0)
if (non_canon_x || sig_x == 0) {
x_is_zero = 1;
}
if (non_canon_y || sig_y == 0) {
y_is_zero = 1;
}
// if both numbers are zero, neither is greater => return NOTGREATERTHAN
if (x_is_zero && y_is_zero) {
res = 0;
BID_RETURN (res);
} else if (x_is_zero) {
// is x is zero, it is greater if Y is negative
res = ((y & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
} else if (y_is_zero) {
// is y is zero, X is greater if it is positive
res = ((x & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// OPPOSITE SIGN (CASE5)
// now, if the sign bits differ, x is greater if y is negative
if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
res = ((y & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// REDUNDANT REPRESENTATIONS (CASE6)
// if both components are either bigger or smaller,
// it is clear what needs to be done
if (sig_x > sig_y && exp_x > exp_y) {
res = ((x & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
if (sig_x < sig_y && exp_x < exp_y) {
res = ((x & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// if exp_x is 15 greater than exp_y, no need for compensation
if (exp_x - exp_y > 15) { // difference cannot be greater than 10^15
if (x & MASK_SIGN) // if both are negative
res = 0;
else // if both are positive
res = 1;
BID_RETURN (res);
}
// if exp_x is 15 less than exp_y, no need for compensation
if (exp_y - exp_x > 15) {
if (x & MASK_SIGN) // if both are negative
res = 1;
else // if both are positive
res = 0;
BID_RETURN (res);
}
// if |exp_x - exp_y| < 15, it comes down to the compensated significand
if (exp_x > exp_y) { // to simplify the loop below,
// otherwise adjust the x significand upwards
__mul_64x64_to_128MACH (sig_n_prime, sig_x,
mult_factor[exp_x - exp_y]);
// if postitive, return whichever significand is larger (converse if neg.)
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
res = 0;
BID_RETURN (res);
}
res = (((sig_n_prime.w[1] > 0)
|| sig_n_prime.w[0] > sig_y) ^ ((x & MASK_SIGN) ==
MASK_SIGN));
BID_RETURN (res);
}
// adjust the y significand upwards
__mul_64x64_to_128MACH (sig_n_prime, sig_y,
mult_factor[exp_y - exp_x]);
// if postitive, return whichever significand is larger
// (converse if negative)
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
res = 0;
BID_RETURN (res);
}
res = (((sig_n_prime.w[1] == 0)
&& (sig_x > sig_n_prime.w[0])) ^ ((x & MASK_SIGN) ==
MASK_SIGN));
BID_RETURN (res);
}
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_quiet_greater_equal (int *pres, UINT64 * px,
UINT64 *
py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
UINT64 y = *py;
#else
int
bid64_quiet_greater_equal (UINT64 x,
UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
#endif
int res;
int exp_x, exp_y;
UINT64 sig_x, sig_y;
UINT128 sig_n_prime;
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y;
// NaN (CASE1)
// if either number is NAN, the comparison is unordered : return 1
if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) {
*pfpsf |= INVALID_EXCEPTION; // set exception if sNaN
}
res = 0;
BID_RETURN (res);
}
// SIMPLE (CASE2)
// if all the bits are the same, these numbers are equal.
if (x == y) {
res = 1;
BID_RETURN (res);
}
// INFINITY (CASE3)
if ((x & MASK_INF) == MASK_INF) {
// if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) }
if ((x & MASK_SIGN) == MASK_SIGN) {
// x is -inf, so it is less than y unless y is -inf
res = (((y & MASK_INF) == MASK_INF)
&& (y & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
} else { // x is pos_inf, no way for it to be less than y
res = 1;
BID_RETURN (res);
}
} else if ((y & MASK_INF) == MASK_INF) {
// x is finite, so:
// if y is +inf, x<y
// if y is -inf, x>y
res = ((y & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (sig_x > 9999999999999999ull) {
non_canon_x = 1;
} else {
non_canon_x = 0;
}
} else {
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
sig_x = (x & MASK_BINARY_SIG1);
non_canon_x = 0;
}
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (sig_y > 9999999999999999ull) {
non_canon_y = 1;
} else {
non_canon_y = 0;
}
} else {
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
sig_y = (y & MASK_BINARY_SIG1);
non_canon_y = 0;
}
// ZERO (CASE4)
// some properties:
// (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B =>
// therefore ignore the exponent field
// (Any non-canonical # is considered 0)
if (non_canon_x || sig_x == 0) {
x_is_zero = 1;
}
if (non_canon_y || sig_y == 0) {
y_is_zero = 1;
}
if (x_is_zero && y_is_zero) {
// if both numbers are zero, they are equal
res = 1;
BID_RETURN (res);
} else if (x_is_zero) {
// if x is zero, it is lessthan if Y is positive
res = ((y & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
} else if (y_is_zero) {
// if y is zero, X is less if it is negative
res = ((x & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// OPPOSITE SIGN (CASE5)
// now, if the sign bits differ, x is less than if y is positive
if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
res = ((y & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// REDUNDANT REPRESENTATIONS (CASE6)
// if both components are either bigger or smaller
if (sig_x > sig_y && exp_x >= exp_y) {
res = ((x & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
if (sig_x < sig_y && exp_x <= exp_y) {
res = ((x & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// if exp_x is 15 greater than exp_y, no need for compensation
if (exp_x - exp_y > 15) {
res = ((x & MASK_SIGN) != MASK_SIGN);
// difference cannot be greater than 10^15
BID_RETURN (res);
}
// if exp_x is 15 less than exp_y, no need for compensation
if (exp_y - exp_x > 15) {
res = ((x & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// if |exp_x - exp_y| < 15, it comes down to the compensated significand
if (exp_x > exp_y) { // to simplify the loop below,
// otherwise adjust the x significand upwards
__mul_64x64_to_128MACH (sig_n_prime, sig_x,
mult_factor[exp_x - exp_y]);
// return 1 if values are equal
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
res = 1;
BID_RETURN (res);
}
// if postitive, return whichever significand abs is smaller
// (converse if negative)
res = (((sig_n_prime.w[1] == 0)
&& sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) !=
MASK_SIGN));
BID_RETURN (res);
}
// adjust the y significand upwards
__mul_64x64_to_128MACH (sig_n_prime, sig_y,
mult_factor[exp_y - exp_x]);
// return 0 if values are equal
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
res = 1;
BID_RETURN (res);
}
// if positive, return whichever significand abs is smaller
// (converse if negative)
res = (((sig_n_prime.w[1] > 0)
|| (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) !=
MASK_SIGN));
BID_RETURN (res);
}
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_quiet_greater_unordered (int *pres, UINT64 * px,
UINT64 *
py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
UINT64 y = *py;
#else
int
bid64_quiet_greater_unordered (UINT64 x,
UINT64 y _EXC_FLAGS_PARAM
_EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
int res;
int exp_x, exp_y;
UINT64 sig_x, sig_y;
UINT128 sig_n_prime;
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y;
// NaN (CASE1)
// if either number is NAN, the comparison is unordered, rather than equal :
// return 0
if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) {
*pfpsf |= INVALID_EXCEPTION; // set exception if sNaN
}
res = 1;
BID_RETURN (res);
}
// SIMPLE (CASE2)
// if all the bits are the same, these numbers are equal (not Greater).
if (x == y) {
res = 0;
BID_RETURN (res);
}
// INFINITY (CASE3)
if ((x & MASK_INF) == MASK_INF) {
// if x is neg infinity, there is no way it is greater than y, return 0
if (((x & MASK_SIGN) == MASK_SIGN)) {
res = 0;
BID_RETURN (res);
} else {
// x is pos infinity, it is greater, unless y is positive infinity =>
// return y!=pos_infinity
res = (((y & MASK_INF) != MASK_INF)
|| ((y & MASK_SIGN) == MASK_SIGN));
BID_RETURN (res);
}
} else if ((y & MASK_INF) == MASK_INF) {
// x is finite, so if y is positive infinity, then x is less, return 0
// if y is negative infinity, then x is greater, return 1
res = ((y & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (sig_x > 9999999999999999ull) {
non_canon_x = 1;
} else {
non_canon_x = 0;
}
} else {
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
sig_x = (x & MASK_BINARY_SIG1);
non_canon_x = 0;
}
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (sig_y > 9999999999999999ull) {
non_canon_y = 1;
} else {
non_canon_y = 0;
}
} else {
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
sig_y = (y & MASK_BINARY_SIG1);
non_canon_y = 0;
}
// ZERO (CASE4)
// some properties:
// (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B =>
// therefore ignore the exponent field
// (Any non-canonical # is considered 0)
if (non_canon_x || sig_x == 0) {
x_is_zero = 1;
}
if (non_canon_y || sig_y == 0) {
y_is_zero = 1;
}
// if both numbers are zero, neither is greater => return NOTGREATERTHAN
if (x_is_zero && y_is_zero) {
res = 0;
BID_RETURN (res);
} else if (x_is_zero) {
// is x is zero, it is greater if Y is negative
res = ((y & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
} else if (y_is_zero) {
// is y is zero, X is greater if it is positive
res = ((x & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// OPPOSITE SIGN (CASE5)
// now, if the sign bits differ, x is greater if y is negative
if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
res = ((y & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// REDUNDANT REPRESENTATIONS (CASE6)
// if both components are either bigger or smaller
if (sig_x > sig_y && exp_x >= exp_y) {
res = ((x & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
if (sig_x < sig_y && exp_x <= exp_y) {
res = ((x & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// if exp_x is 15 greater than exp_y, no need for compensation
if (exp_x - exp_y > 15) {
// difference cannot be greater than 10^15
res = ((x & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// if exp_x is 15 less than exp_y, no need for compensation
if (exp_y - exp_x > 15) {
res = ((x & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// if |exp_x - exp_y| < 15, it comes down to the compensated significand
if (exp_x > exp_y) { // to simplify the loop below,
// otherwise adjust the x significand upwards
__mul_64x64_to_128MACH (sig_n_prime, sig_x,
mult_factor[exp_x - exp_y]);
// if postitive, return whichever significand is larger
// (converse if negative)
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
res = 0;
BID_RETURN (res);
}
res = (((sig_n_prime.w[1] > 0)
|| sig_n_prime.w[0] > sig_y) ^ ((x & MASK_SIGN) ==
MASK_SIGN));
BID_RETURN (res);
}
// adjust the y significand upwards
__mul_64x64_to_128MACH (sig_n_prime, sig_y,
mult_factor[exp_y - exp_x]);
// if postitive, return whichever significand is larger (converse if negative)
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
res = 0;
BID_RETURN (res);
}
res = (((sig_n_prime.w[1] == 0)
&& (sig_x > sig_n_prime.w[0])) ^ ((x & MASK_SIGN) ==
MASK_SIGN));
BID_RETURN (res);
}
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_quiet_less (int *pres, UINT64 * px,
UINT64 *
py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM)
{
UINT64 x = *px;
UINT64 y = *py;
#else
int
bid64_quiet_less (UINT64 x,
UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
#endif
int res;
int exp_x, exp_y;
UINT64 sig_x, sig_y;
UINT128 sig_n_prime;
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y;
// NaN (CASE1)
// if either number is NAN, the comparison is unordered : return 0
if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) {
*pfpsf |= INVALID_EXCEPTION; // set exception if sNaN
}
res = 0;
BID_RETURN (res);
}
// SIMPLE (CASE2)
// if all the bits are the same, these numbers are equal.
if (x == y) {
res = 0;
BID_RETURN (res);
}
// INFINITY (CASE3)
if ((x & MASK_INF) == MASK_INF) {
// if x==neg_inf, { res = (y == neg_inf)?0:1; BID_RETURN (res) }
if ((x & MASK_SIGN) == MASK_SIGN) {
// x is -inf, so it is less than y unless y is -inf
res = (((y & MASK_INF) != MASK_INF)
|| (y & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
} else {
// x is pos_inf, no way for it to be less than y
res = 0;
BID_RETURN (res);
}
} else if ((y & MASK_INF) == MASK_INF) {
// x is finite, so:
// if y is +inf, x<y
// if y is -inf, x>y
res = ((y & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (sig_x > 9999999999999999ull) {
non_canon_x = 1;
} else {
non_canon_x = 0;
}
} else {
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
sig_x = (x & MASK_BINARY_SIG1);
non_canon_x = 0;
}
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (sig_y > 9999999999999999ull) {
non_canon_y = 1;
} else {
non_canon_y = 0;
}
} else {
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
sig_y = (y & MASK_BINARY_SIG1);
non_canon_y = 0;
}
// ZERO (CASE4)
// some properties:
// (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B =>
// therefore ignore the exponent field
// (Any non-canonical # is considered 0)
if (non_canon_x || sig_x == 0) {
x_is_zero = 1;
}
if (non_canon_y || sig_y == 0) {
y_is_zero = 1;
}
if (x_is_zero && y_is_zero) {
// if both numbers are zero, they are equal
res = 0;
BID_RETURN (res);
} else if (x_is_zero) {
// if x is zero, it is lessthan if Y is positive
res = ((y & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
} else if (y_is_zero) {
// if y is zero, X is less if it is negative
res = ((x & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// OPPOSITE SIGN (CASE5)
// now, if the sign bits differ, x is less than if y is positive
if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
res = ((y & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// REDUNDANT REPRESENTATIONS (CASE6)
// if both components are either bigger or smaller,
// it is clear what needs to be done
if (sig_x > sig_y && exp_x >= exp_y) {
res = ((x & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
if (sig_x < sig_y && exp_x <= exp_y) {
res = ((x & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// if exp_x is 15 greater than exp_y, no need for compensation
if (exp_x - exp_y > 15) {
res = ((x & MASK_SIGN) == MASK_SIGN);
// difference cannot be greater than 10^15
BID_RETURN (res);
}
// if exp_x is 15 less than exp_y, no need for compensation
if (exp_y - exp_x > 15) {
res = ((x & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// if |exp_x - exp_y| < 15, it comes down to the compensated significand
if (exp_x > exp_y) { // to simplify the loop below,
// otherwise adjust the x significand upwards
__mul_64x64_to_128MACH (sig_n_prime, sig_x,
mult_factor[exp_x - exp_y]);
// return 0 if values are equal
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
res = 0;
BID_RETURN (res);
}
// if postitive, return whichever significand abs is smaller
// (converse if negative)
res = (((sig_n_prime.w[1] == 0)
&& sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) ==
MASK_SIGN));
BID_RETURN (res);
}
// adjust the y significand upwards
__mul_64x64_to_128MACH (sig_n_prime, sig_y,
mult_factor[exp_y - exp_x]);
// return 0 if values are equal
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
res = 0;
BID_RETURN (res);
}
// if positive, return whichever significand abs is smaller
// (converse if negative)
res = (((sig_n_prime.w[1] > 0)
|| (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) ==
MASK_SIGN));
BID_RETURN (res);
}
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_quiet_less_equal (int *pres, UINT64 * px,
UINT64 *
py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
UINT64 y = *py;
#else
int
bid64_quiet_less_equal (UINT64 x,
UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
#endif
int res;
int exp_x, exp_y;
UINT64 sig_x, sig_y;
UINT128 sig_n_prime;
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y;
// NaN (CASE1)
// if either number is NAN, the comparison is unordered, rather than equal :
// return 0
if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) {
*pfpsf |= INVALID_EXCEPTION; // set exception if sNaN
}
res = 0;
BID_RETURN (res);
}
// SIMPLE (CASE2)
// if all the bits are the same, these numbers are equal (LESSEQUAL).
if (x == y) {
res = 1;
BID_RETURN (res);
}
// INFINITY (CASE3)
if ((x & MASK_INF) == MASK_INF) {
if (((x & MASK_SIGN) == MASK_SIGN)) {
// if x is neg infinity, it must be lessthan or equal to y return 1
res = 1;
BID_RETURN (res);
} else {
// x is pos infinity, it is greater, unless y is positive infinity =>
// return y==pos_infinity
res = !(((y & MASK_INF) != MASK_INF)
|| ((y & MASK_SIGN) == MASK_SIGN));
BID_RETURN (res);
}
} else if ((y & MASK_INF) == MASK_INF) {
// x is finite, so if y is positive infinity, then x is less, return 1
// if y is negative infinity, then x is greater, return 0
res = ((y & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (sig_x > 9999999999999999ull) {
non_canon_x = 1;
} else {
non_canon_x = 0;
}
} else {
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
sig_x = (x & MASK_BINARY_SIG1);
non_canon_x = 0;
}
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (sig_y > 9999999999999999ull) {
non_canon_y = 1;
} else {
non_canon_y = 0;
}
} else {
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
sig_y = (y & MASK_BINARY_SIG1);
non_canon_y = 0;
}
// ZERO (CASE4)
// some properties:
// (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B =>
// therefore ignore the exponent field
// (Any non-canonical # is considered 0)
if (non_canon_x || sig_x == 0) {
x_is_zero = 1;
}
if (non_canon_y || sig_y == 0) {
y_is_zero = 1;
}
if (x_is_zero && y_is_zero) {
// if both numbers are zero, they are equal -> return 1
res = 1;
BID_RETURN (res);
} else if (x_is_zero) {
// if x is zero, it is lessthan if Y is positive
res = ((y & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
} else if (y_is_zero) {
// if y is zero, X is less if it is negative
res = ((x & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// OPPOSITE SIGN (CASE5)
// now, if the sign bits differ, x is less than if y is positive
if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
res = ((y & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// REDUNDANT REPRESENTATIONS (CASE6)
// if both components are either bigger or smaller
if (sig_x > sig_y && exp_x >= exp_y) {
res = ((x & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
if (sig_x < sig_y && exp_x <= exp_y) {
res = ((x & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// if exp_x is 15 greater than exp_y, no need for compensation
if (exp_x - exp_y > 15) {
res = ((x & MASK_SIGN) == MASK_SIGN);
// difference cannot be greater than 10^15
BID_RETURN (res);
}
// if exp_x is 15 less than exp_y, no need for compensation
if (exp_y - exp_x > 15) {
res = ((x & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// if |exp_x - exp_y| < 15, it comes down to the compensated significand
if (exp_x > exp_y) { // to simplify the loop below,
// otherwise adjust the x significand upwards
__mul_64x64_to_128MACH (sig_n_prime, sig_x,
mult_factor[exp_x - exp_y]);
// return 1 if values are equal
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
res = 1;
BID_RETURN (res);
}
// if postitive, return whichever significand abs is smaller
// (converse if negative)
res = (((sig_n_prime.w[1] == 0)
&& sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) ==
MASK_SIGN));
BID_RETURN (res);
}
// adjust the y significand upwards
__mul_64x64_to_128MACH (sig_n_prime, sig_y,
mult_factor[exp_y - exp_x]);
// return 1 if values are equal
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
res = 1;
BID_RETURN (res);
}
// if positive, return whichever significand abs is smaller
// (converse if negative)
res = (((sig_n_prime.w[1] > 0)
|| (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) ==
MASK_SIGN));
BID_RETURN (res);
}
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_quiet_less_unordered (int *pres, UINT64 * px,
UINT64 *
py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
UINT64 y = *py;
#else
int
bid64_quiet_less_unordered (UINT64 x,
UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
#endif
int res;
int exp_x, exp_y;
UINT64 sig_x, sig_y;
UINT128 sig_n_prime;
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y;
// NaN (CASE1)
// if either number is NAN, the comparison is unordered : return 0
if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) {
*pfpsf |= INVALID_EXCEPTION; // set exception if sNaN
}
res = 1;
BID_RETURN (res);
}
// SIMPLE (CASE2)
// if all the bits are the same, these numbers are equal.
if (x == y) {
res = 0;
BID_RETURN (res);
}
// INFINITY (CASE3)
if ((x & MASK_INF) == MASK_INF) {
// if x==neg_inf, { res = (y == neg_inf)?0:1; BID_RETURN (res) }
if ((x & MASK_SIGN) == MASK_SIGN) {
// x is -inf, so it is less than y unless y is -inf
res = (((y & MASK_INF) != MASK_INF)
|| (y & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
} else {
// x is pos_inf, no way for it to be less than y
res = 0;
BID_RETURN (res);
}
} else if ((y & MASK_INF) == MASK_INF) {
// x is finite, so:
// if y is +inf, x<y
// if y is -inf, x>y
res = ((y & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (sig_x > 9999999999999999ull) {
non_canon_x = 1;
} else {
non_canon_x = 0;
}
} else {
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
sig_x = (x & MASK_BINARY_SIG1);
non_canon_x = 0;
}
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (sig_y > 9999999999999999ull) {
non_canon_y = 1;
} else {
non_canon_y = 0;
}
} else {
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
sig_y = (y & MASK_BINARY_SIG1);
non_canon_y = 0;
}
// ZERO (CASE4)
// some properties:
// (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B =>
// therefore ignore the exponent field
// (Any non-canonical # is considered 0)
if (non_canon_x || sig_x == 0) {
x_is_zero = 1;
}
if (non_canon_y || sig_y == 0) {
y_is_zero = 1;
}
if (x_is_zero && y_is_zero) {
// if both numbers are zero, they are equal
res = 0;
BID_RETURN (res);
} else if (x_is_zero) {
// if x is zero, it is lessthan if Y is positive
res = ((y & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
} else if (y_is_zero) {
// if y is zero, X is less if it is negative
res = ((x & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// OPPOSITE SIGN (CASE5)
// now, if the sign bits differ, x is less than if y is positive
if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
res = ((y & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// REDUNDANT REPRESENTATIONS (CASE6)
// if both components are either bigger or smaller
if (sig_x > sig_y && exp_x >= exp_y) {
res = ((x & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
if (sig_x < sig_y && exp_x <= exp_y) {
res = ((x & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// if exp_x is 15 greater than exp_y, no need for compensation
if (exp_x - exp_y > 15) {
res = ((x & MASK_SIGN) == MASK_SIGN);
// difference cannot be greater than 10^15
BID_RETURN (res);
}
// if exp_x is 15 less than exp_y, no need for compensation
if (exp_y - exp_x > 15) {
res = ((x & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// if |exp_x - exp_y| < 15, it comes down to the compensated significand
if (exp_x > exp_y) { // to simplify the loop below,
// otherwise adjust the x significand upwards
__mul_64x64_to_128MACH (sig_n_prime, sig_x,
mult_factor[exp_x - exp_y]);
// return 0 if values are equal
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
res = 0;
BID_RETURN (res);
}
// if postitive, return whichever significand abs is smaller
// (converse if negative)
res = (((sig_n_prime.w[1] == 0)
&& sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) ==
MASK_SIGN));
BID_RETURN (res);
}
// adjust the y significand upwards
__mul_64x64_to_128MACH (sig_n_prime, sig_y,
mult_factor[exp_y - exp_x]);
// return 0 if values are equal
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
res = 0;
BID_RETURN (res);
}
// if positive, return whichever significand abs is smaller
// (converse if negative)
res = (((sig_n_prime.w[1] > 0)
|| (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) ==
MASK_SIGN));
BID_RETURN (res);
}
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_quiet_not_equal (int *pres, UINT64 * px,
UINT64 *
py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
UINT64 y = *py;
#else
int
bid64_quiet_not_equal (UINT64 x,
UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
#endif
int res;
int exp_x, exp_y, exp_t;
UINT64 sig_x, sig_y, sig_t;
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y, lcv;
// NaN (CASE1)
// if either number is NAN, the comparison is unordered,
// rather than equal : return 1
if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) {
*pfpsf |= INVALID_EXCEPTION; // set exception if sNaN
}
res = 1;
BID_RETURN (res);
}
// SIMPLE (CASE2)
// if all the bits are the same, these numbers are equivalent.
if (x == y) {
res = 0;
BID_RETURN (res);
}
// INFINITY (CASE3)
if (((x & MASK_INF) == MASK_INF) && ((y & MASK_INF) == MASK_INF)) {
res = (((x ^ y) & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// ONE INFINITY (CASE3')
if (((x & MASK_INF) == MASK_INF) || ((y & MASK_INF) == MASK_INF)) {
res = 1;
BID_RETURN (res);
}
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (sig_x > 9999999999999999ull) {
non_canon_x = 1;
} else {
non_canon_x = 0;
}
} else {
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
sig_x = (x & MASK_BINARY_SIG1);
non_canon_x = 0;
}
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (sig_y > 9999999999999999ull) {
non_canon_y = 1;
} else {
non_canon_y = 0;
}
} else {
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
sig_y = (y & MASK_BINARY_SIG1);
non_canon_y = 0;
}
// ZERO (CASE4)
// some properties:
// (+ZERO==-ZERO) => therefore ignore the sign
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B =>
// therefore ignore the exponent field
// (Any non-canonical # is considered 0)
if (non_canon_x || sig_x == 0) {
x_is_zero = 1;
}
if (non_canon_y || sig_y == 0) {
y_is_zero = 1;
}
if (x_is_zero && y_is_zero) {
res = 0;
BID_RETURN (res);
} else if ((x_is_zero && !y_is_zero) || (!x_is_zero && y_is_zero)) {
res = 1;
BID_RETURN (res);
}
// OPPOSITE SIGN (CASE5)
// now, if the sign bits differ => not equal : return 1
if ((x ^ y) & MASK_SIGN) {
res = 1;
BID_RETURN (res);
}
// REDUNDANT REPRESENTATIONS (CASE6)
if (exp_x > exp_y) { // to simplify the loop below,
SWAP (exp_x, exp_y, exp_t); // put the larger exp in y,
SWAP (sig_x, sig_y, sig_t); // and the smaller exp in x
}
if (exp_y - exp_x > 15) {
res = 1;
BID_RETURN (res);
}
// difference cannot be greater than 10^16
for (lcv = 0; lcv < (exp_y - exp_x); lcv++) {
// recalculate y's significand upwards
sig_y = sig_y * 10;
if (sig_y > 9999999999999999ull) {
res = 1;
BID_RETURN (res);
}
}
{
res = sig_y != sig_x;
BID_RETURN (res);
}
}
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_quiet_not_greater (int *pres, UINT64 * px,
UINT64 *
py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
UINT64 y = *py;
#else
int
bid64_quiet_not_greater (UINT64 x,
UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
#endif
int res;
int exp_x, exp_y;
UINT64 sig_x, sig_y;
UINT128 sig_n_prime;
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y;
// NaN (CASE1)
// if either number is NAN, the comparison is unordered,
// rather than equal : return 0
if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) {
*pfpsf |= INVALID_EXCEPTION; // set exception if sNaN
}
res = 1;
BID_RETURN (res);
}
// SIMPLE (CASE2)
// if all the bits are the same, these numbers are equal (LESSEQUAL).
if (x == y) {
res = 1;
BID_RETURN (res);
}
// INFINITY (CASE3)
if ((x & MASK_INF) == MASK_INF) {
// if x is neg infinity, it must be lessthan or equal to y return 1
if (((x & MASK_SIGN) == MASK_SIGN)) {
res = 1;
BID_RETURN (res);
}
// x is pos infinity, it is greater, unless y is positive
// infinity => return y==pos_infinity
else {
res = !(((y & MASK_INF) != MASK_INF)
|| ((y & MASK_SIGN) == MASK_SIGN));
BID_RETURN (res);
}
} else if ((y & MASK_INF) == MASK_INF) {
// x is finite, so if y is positive infinity, then x is less, return 1
// if y is negative infinity, then x is greater, return 0
{
res = ((y & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
}
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (sig_x > 9999999999999999ull) {
non_canon_x = 1;
} else {
non_canon_x = 0;
}
} else {
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
sig_x = (x & MASK_BINARY_SIG1);
non_canon_x = 0;
}
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (sig_y > 9999999999999999ull) {
non_canon_y = 1;
} else {
non_canon_y = 0;
}
} else {
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
sig_y = (y & MASK_BINARY_SIG1);
non_canon_y = 0;
}
// ZERO (CASE4)
// some properties:
// (+ZERO==-ZERO) => therefore ignore the sign, and neither
// number is greater
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B =>
// therefore ignore the exponent field
// (Any non-canonical # is considered 0)
if (non_canon_x || sig_x == 0) {
x_is_zero = 1;
}
if (non_canon_y || sig_y == 0) {
y_is_zero = 1;
}
// if both numbers are zero, they are equal -> return 1
if (x_is_zero && y_is_zero) {
res = 1;
BID_RETURN (res);
}
// if x is zero, it is lessthan if Y is positive
else if (x_is_zero) {
res = ((y & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// if y is zero, X is less if it is negative
else if (y_is_zero) {
res = ((x & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// OPPOSITE SIGN (CASE5)
// now, if the sign bits differ, x is less than if y is positive
if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
res = ((y & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// REDUNDANT REPRESENTATIONS (CASE6)
// if both components are either bigger or smaller
if (sig_x > sig_y && exp_x >= exp_y) {
res = ((x & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
if (sig_x < sig_y && exp_x <= exp_y) {
res = ((x & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// if exp_x is 15 greater than exp_y, no need for compensation
if (exp_x - exp_y > 15) {
res = ((x & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// difference cannot be greater than 10^15
// if exp_x is 15 less than exp_y, no need for compensation
if (exp_y - exp_x > 15) {
res = ((x & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// if |exp_x - exp_y| < 15, it comes down to the compensated significand
if (exp_x > exp_y) { // to simplify the loop below,
// otherwise adjust the x significand upwards
__mul_64x64_to_128MACH (sig_n_prime, sig_x,
mult_factor[exp_x - exp_y]);
// return 1 if values are equal
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
res = 1;
BID_RETURN (res);
}
// if postitive, return whichever significand abs is smaller
// (converse if negative)
{
res = (((sig_n_prime.w[1] == 0)
&& sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) ==
MASK_SIGN));
BID_RETURN (res);
}
}
// adjust the y significand upwards
__mul_64x64_to_128MACH (sig_n_prime, sig_y,
mult_factor[exp_y - exp_x]);
// return 1 if values are equal
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
res = 1;
BID_RETURN (res);
}
// if positive, return whichever significand abs is smaller
// (converse if negative)
{
res = (((sig_n_prime.w[1] > 0)
|| (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) ==
MASK_SIGN));
BID_RETURN (res);
}
}
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_quiet_not_less (int *pres, UINT64 * px,
UINT64 *
py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
UINT64 y = *py;
#else
int
bid64_quiet_not_less (UINT64 x,
UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
#endif
int res;
int exp_x, exp_y;
UINT64 sig_x, sig_y;
UINT128 sig_n_prime;
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y;
// NaN (CASE1)
// if either number is NAN, the comparison is unordered : return 1
if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) {
*pfpsf |= INVALID_EXCEPTION; // set exception if sNaN
}
res = 1;
BID_RETURN (res);
}
// SIMPLE (CASE2)
// if all the bits are the same, these numbers are equal.
if (x == y) {
res = 1;
BID_RETURN (res);
}
// INFINITY (CASE3)
if ((x & MASK_INF) == MASK_INF) {
// if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) }
if ((x & MASK_SIGN) == MASK_SIGN)
// x is -inf, so it is less than y unless y is -inf
{
res = (((y & MASK_INF) == MASK_INF)
&& (y & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
} else
// x is pos_inf, no way for it to be less than y
{
res = 1;
BID_RETURN (res);
}
} else if ((y & MASK_INF) == MASK_INF) {
// x is finite, so:
// if y is +inf, x<y
// if y is -inf, x>y
{
res = ((y & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
}
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (sig_x > 9999999999999999ull) {
non_canon_x = 1;
} else {
non_canon_x = 0;
}
} else {
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
sig_x = (x & MASK_BINARY_SIG1);
non_canon_x = 0;
}
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (sig_y > 9999999999999999ull) {
non_canon_y = 1;
} else {
non_canon_y = 0;
}
} else {
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
sig_y = (y & MASK_BINARY_SIG1);
non_canon_y = 0;
}
// ZERO (CASE4)
// some properties:
// (+ZERO==-ZERO) => therefore ignore the sign, and neither
// number is greater
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B =>
// therefore ignore the exponent field
// (Any non-canonical # is considered 0)
if (non_canon_x || sig_x == 0) {
x_is_zero = 1;
}
if (non_canon_y || sig_y == 0) {
y_is_zero = 1;
}
// if both numbers are zero, they are equal
if (x_is_zero && y_is_zero) {
res = 1;
BID_RETURN (res);
}
// if x is zero, it is lessthan if Y is positive
else if (x_is_zero) {
res = ((y & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// if y is zero, X is less if it is negative
else if (y_is_zero) {
res = ((x & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// OPPOSITE SIGN (CASE5)
// now, if the sign bits differ, x is less than if y is positive
if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
res = ((y & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// REDUNDANT REPRESENTATIONS (CASE6)
// if both components are either bigger or smaller
if (sig_x > sig_y && exp_x >= exp_y) {
res = ((x & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
if (sig_x < sig_y && exp_x <= exp_y) {
res = ((x & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// if exp_x is 15 greater than exp_y, no need for compensation
if (exp_x - exp_y > 15) {
res = ((x & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// difference cannot be greater than 10^15
// if exp_x is 15 less than exp_y, no need for compensation
if (exp_y - exp_x > 15) {
res = ((x & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// if |exp_x - exp_y| < 15, it comes down to the compensated significand
if (exp_x > exp_y) { // to simplify the loop below,
// otherwise adjust the x significand upwards
__mul_64x64_to_128MACH (sig_n_prime, sig_x,
mult_factor[exp_x - exp_y]);
// return 0 if values are equal
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
res = 1;
BID_RETURN (res);
}
// if postitive, return whichever significand abs is smaller
// (converse if negative)
{
res = (((sig_n_prime.w[1] == 0)
&& sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) !=
MASK_SIGN));
BID_RETURN (res);
}
}
// adjust the y significand upwards
__mul_64x64_to_128MACH (sig_n_prime, sig_y,
mult_factor[exp_y - exp_x]);
// return 0 if values are equal
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
res = 1;
BID_RETURN (res);
}
// if positive, return whichever significand abs is smaller
// (converse if negative)
{
res = (((sig_n_prime.w[1] > 0)
|| (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) !=
MASK_SIGN));
BID_RETURN (res);
}
}
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_quiet_ordered (int *pres, UINT64 * px,
UINT64 *
py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
UINT64 y = *py;
#else
int
bid64_quiet_ordered (UINT64 x,
UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
#endif
int res;
// NaN (CASE1)
// if either number is NAN, the comparison is ordered, rather than equal : return 0
if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) {
*pfpsf |= INVALID_EXCEPTION; // set exception if sNaN
}
res = 0;
BID_RETURN (res);
} else {
res = 1;
BID_RETURN (res);
}
}
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_quiet_unordered (int *pres, UINT64 * px,
UINT64 *
py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
UINT64 y = *py;
#else
int
bid64_quiet_unordered (UINT64 x,
UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
#endif
int res;
// NaN (CASE1)
// if either number is NAN, the comparison is unordered,
// rather than equal : return 0
if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) {
*pfpsf |= INVALID_EXCEPTION; // set exception if sNaN
}
res = 1;
BID_RETURN (res);
} else {
res = 0;
BID_RETURN (res);
}
}
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_signaling_greater (int *pres, UINT64 * px,
UINT64 *
py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
UINT64 y = *py;
#else
int
bid64_signaling_greater (UINT64 x,
UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
#endif
int res;
int exp_x, exp_y;
UINT64 sig_x, sig_y;
UINT128 sig_n_prime;
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y;
// NaN (CASE1)
// if either number is NAN, the comparison is unordered,
// rather than equal : return 0
if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
*pfpsf |= INVALID_EXCEPTION; // set invalid exception if NaN
res = 0;
BID_RETURN (res);
}
// SIMPLE (CASE2)
// if all the bits are the same, these numbers are equal (not Greater).
if (x == y) {
res = 0;
BID_RETURN (res);
}
// INFINITY (CASE3)
if ((x & MASK_INF) == MASK_INF) {
// if x is neg infinity, there is no way it is greater than y, return 0
if (((x & MASK_SIGN) == MASK_SIGN)) {
res = 0;
BID_RETURN (res);
}
// x is pos infinity, it is greater,
// unless y is positive infinity => return y!=pos_infinity
else {
res = (((y & MASK_INF) != MASK_INF)
|| ((y & MASK_SIGN) == MASK_SIGN));
BID_RETURN (res);
}
} else if ((y & MASK_INF) == MASK_INF) {
// x is finite, so if y is positive infinity, then x is less, return 0
// if y is negative infinity, then x is greater, return 1
{
res = ((y & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
}
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (sig_x > 9999999999999999ull) {
non_canon_x = 1;
} else {
non_canon_x = 0;
}
} else {
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
sig_x = (x & MASK_BINARY_SIG1);
non_canon_x = 0;
}
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (sig_y > 9999999999999999ull) {
non_canon_y = 1;
} else {
non_canon_y = 0;
}
} else {
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
sig_y = (y & MASK_BINARY_SIG1);
non_canon_y = 0;
}
// ZERO (CASE4)
// some properties:
// (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B =>
// therefore ignore the exponent field
// (Any non-canonical # is considered 0)
if (non_canon_x || sig_x == 0) {
x_is_zero = 1;
}
if (non_canon_y || sig_y == 0) {
y_is_zero = 1;
}
// if both numbers are zero, neither is greater => return NOTGREATERTHAN
if (x_is_zero && y_is_zero) {
res = 0;
BID_RETURN (res);
}
// is x is zero, it is greater if Y is negative
else if (x_is_zero) {
res = ((y & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// is y is zero, X is greater if it is positive
else if (y_is_zero) {
res = ((x & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// OPPOSITE SIGN (CASE5)
// now, if the sign bits differ, x is greater if y is negative
if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
res = ((y & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// REDUNDANT REPRESENTATIONS (CASE6)
// if both components are either bigger or smaller
if (sig_x > sig_y && exp_x >= exp_y) {
res = ((x & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
if (sig_x < sig_y && exp_x <= exp_y) {
res = ((x & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// if exp_x is 15 greater than exp_y, no need for compensation
if (exp_x - exp_y > 15) {
res = ((x & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// difference cannot be greater than 10^15
// if exp_x is 15 less than exp_y, no need for compensation
if (exp_y - exp_x > 15) {
res = ((x & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// if |exp_x - exp_y| < 15, it comes down to the compensated significand
if (exp_x > exp_y) { // to simplify the loop below,
// otherwise adjust the x significand upwards
__mul_64x64_to_128MACH (sig_n_prime, sig_x,
mult_factor[exp_x - exp_y]);
// if postitive, return whichever significand is larger
// (converse if negative)
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
res = 0;
BID_RETURN (res);
}
{
res = (((sig_n_prime.w[1] > 0)
|| sig_n_prime.w[0] > sig_y) ^ ((x & MASK_SIGN) ==
MASK_SIGN));
BID_RETURN (res);
}
}
// adjust the y significand upwards
__mul_64x64_to_128MACH (sig_n_prime, sig_y,
mult_factor[exp_y - exp_x]);
// if postitive, return whichever significand is larger
// (converse if negative)
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
res = 0;
BID_RETURN (res);
}
{
res = (((sig_n_prime.w[1] == 0)
&& (sig_x > sig_n_prime.w[0])) ^ ((x & MASK_SIGN) ==
MASK_SIGN));
BID_RETURN (res);
}
}
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_signaling_greater_equal (int *pres, UINT64 * px,
UINT64 *
py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
UINT64 y = *py;
#else
int
bid64_signaling_greater_equal (UINT64 x,
UINT64 y _EXC_FLAGS_PARAM
_EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
int res;
int exp_x, exp_y;
UINT64 sig_x, sig_y;
UINT128 sig_n_prime;
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y;
// NaN (CASE1)
// if either number is NAN, the comparison is unordered : return 1
if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
*pfpsf |= INVALID_EXCEPTION; // set invalid exception if NaN
res = 0;
BID_RETURN (res);
}
// SIMPLE (CASE2)
// if all the bits are the same, these numbers are equal.
if (x == y) {
res = 1;
BID_RETURN (res);
}
// INFINITY (CASE3)
if ((x & MASK_INF) == MASK_INF) {
// if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) }
if ((x & MASK_SIGN) == MASK_SIGN)
// x is -inf, so it is less than y unless y is -inf
{
res = (((y & MASK_INF) == MASK_INF)
&& (y & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
} else
// x is pos_inf, no way for it to be less than y
{
res = 1;
BID_RETURN (res);
}
} else if ((y & MASK_INF) == MASK_INF) {
// x is finite, so:
// if y is +inf, x<y
// if y is -inf, x>y
{
res = ((y & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
}
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (sig_x > 9999999999999999ull) {
non_canon_x = 1;
} else {
non_canon_x = 0;
}
} else {
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
sig_x = (x & MASK_BINARY_SIG1);
non_canon_x = 0;
}
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (sig_y > 9999999999999999ull) {
non_canon_y = 1;
} else {
non_canon_y = 0;
}
} else {
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
sig_y = (y & MASK_BINARY_SIG1);
non_canon_y = 0;
}
// ZERO (CASE4)
// some properties:
// (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B =>
// therefore ignore the exponent field
// (Any non-canonical # is considered 0)
if (non_canon_x || sig_x == 0) {
x_is_zero = 1;
}
if (non_canon_y || sig_y == 0) {
y_is_zero = 1;
}
// if both numbers are zero, they are equal
if (x_is_zero && y_is_zero) {
res = 1;
BID_RETURN (res);
}
// if x is zero, it is lessthan if Y is positive
else if (x_is_zero) {
res = ((y & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// if y is zero, X is less if it is negative
else if (y_is_zero) {
res = ((x & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// OPPOSITE SIGN (CASE5)
// now, if the sign bits differ, x is less than if y is positive
if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
res = ((y & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// REDUNDANT REPRESENTATIONS (CASE6)
// if both components are either bigger or smaller
if (sig_x > sig_y && exp_x >= exp_y) {
res = ((x & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
if (sig_x < sig_y && exp_x <= exp_y) {
res = ((x & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// if exp_x is 15 greater than exp_y, no need for compensation
if (exp_x - exp_y > 15) {
res = ((x & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// difference cannot be greater than 10^15
// if exp_x is 15 less than exp_y, no need for compensation
if (exp_y - exp_x > 15) {
res = ((x & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// if |exp_x - exp_y| < 15, it comes down to the compensated significand
if (exp_x > exp_y) { // to simplify the loop below,
// otherwise adjust the x significand upwards
__mul_64x64_to_128MACH (sig_n_prime, sig_x,
mult_factor[exp_x - exp_y]);
// return 1 if values are equal
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
res = 1;
BID_RETURN (res);
}
// if postitive, return whichever significand abs is smaller
// (converse if negative)
{
res = (((sig_n_prime.w[1] == 0)
&& sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) !=
MASK_SIGN));
BID_RETURN (res);
}
}
// adjust the y significand upwards
__mul_64x64_to_128MACH (sig_n_prime, sig_y,
mult_factor[exp_y - exp_x]);
// return 0 if values are equal
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
res = 1;
BID_RETURN (res);
}
// if positive, return whichever significand abs is smaller
// (converse if negative)
{
res = (((sig_n_prime.w[1] > 0)
|| (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) !=
MASK_SIGN));
BID_RETURN (res);
}
}
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_signaling_greater_unordered (int *pres, UINT64 * px,
UINT64 *
py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
UINT64 y = *py;
#else
int
bid64_signaling_greater_unordered (UINT64 x,
UINT64 y _EXC_FLAGS_PARAM
_EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
int res;
int exp_x, exp_y;
UINT64 sig_x, sig_y;
UINT128 sig_n_prime;
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y;
// NaN (CASE1)
// if either number is NAN, the comparison is unordered,
// rather than equal : return 0
if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
*pfpsf |= INVALID_EXCEPTION; // set invalid exception if NaN
res = 1;
BID_RETURN (res);
}
// SIMPLE (CASE2)
// if all the bits are the same, these numbers are equal (not Greater).
if (x == y) {
res = 0;
BID_RETURN (res);
}
// INFINITY (CASE3)
if ((x & MASK_INF) == MASK_INF) {
// if x is neg infinity, there is no way it is greater than y, return 0
if (((x & MASK_SIGN) == MASK_SIGN)) {
res = 0;
BID_RETURN (res);
}
// x is pos infinity, it is greater,
// unless y is positive infinity => return y!=pos_infinity
else {
res = (((y & MASK_INF) != MASK_INF)
|| ((y & MASK_SIGN) == MASK_SIGN));
BID_RETURN (res);
}
} else if ((y & MASK_INF) == MASK_INF) {
// x is finite, so if y is positive infinity, then x is less, return 0
// if y is negative infinity, then x is greater, return 1
{
res = ((y & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
}
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (sig_x > 9999999999999999ull) {
non_canon_x = 1;
} else {
non_canon_x = 0;
}
} else {
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
sig_x = (x & MASK_BINARY_SIG1);
non_canon_x = 0;
}
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (sig_y > 9999999999999999ull) {
non_canon_y = 1;
} else {
non_canon_y = 0;
}
} else {
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
sig_y = (y & MASK_BINARY_SIG1);
non_canon_y = 0;
}
// ZERO (CASE4)
// some properties:
// (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B =>
// therefore ignore the exponent field
// (Any non-canonical # is considered 0)
if (non_canon_x || sig_x == 0) {
x_is_zero = 1;
}
if (non_canon_y || sig_y == 0) {
y_is_zero = 1;
}
// if both numbers are zero, neither is greater => return NOTGREATERTHAN
if (x_is_zero && y_is_zero) {
res = 0;
BID_RETURN (res);
}
// is x is zero, it is greater if Y is negative
else if (x_is_zero) {
res = ((y & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// is y is zero, X is greater if it is positive
else if (y_is_zero) {
res = ((x & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// OPPOSITE SIGN (CASE5)
// now, if the sign bits differ, x is greater if y is negative
if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
res = ((y & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// REDUNDANT REPRESENTATIONS (CASE6)
// if both components are either bigger or smaller
if (sig_x > sig_y && exp_x >= exp_y) {
res = ((x & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
if (sig_x < sig_y && exp_x <= exp_y) {
res = ((x & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// if exp_x is 15 greater than exp_y, no need for compensation
if (exp_x - exp_y > 15) {
res = ((x & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// difference cannot be greater than 10^15
// if exp_x is 15 less than exp_y, no need for compensation
if (exp_y - exp_x > 15) {
res = ((x & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// if |exp_x - exp_y| < 15, it comes down to the compensated significand
if (exp_x > exp_y) { // to simplify the loop below,
// otherwise adjust the x significand upwards
__mul_64x64_to_128MACH (sig_n_prime, sig_x,
mult_factor[exp_x - exp_y]);
// if postitive, return whichever significand is larger
// (converse if negative)
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
res = 0;
BID_RETURN (res);
}
{
res = (((sig_n_prime.w[1] > 0)
|| sig_n_prime.w[0] > sig_y) ^ ((x & MASK_SIGN) ==
MASK_SIGN));
BID_RETURN (res);
}
}
// adjust the y significand upwards
__mul_64x64_to_128MACH (sig_n_prime, sig_y,
mult_factor[exp_y - exp_x]);
// if postitive, return whichever significand is larger
// (converse if negative)
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
res = 0;
BID_RETURN (res);
}
{
res = (((sig_n_prime.w[1] == 0)
&& (sig_x > sig_n_prime.w[0])) ^ ((x & MASK_SIGN) ==
MASK_SIGN));
BID_RETURN (res);
}
}
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_signaling_less (int *pres, UINT64 * px,
UINT64 *
py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
UINT64 y = *py;
#else
int
bid64_signaling_less (UINT64 x,
UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
#endif
int res;
int exp_x, exp_y;
UINT64 sig_x, sig_y;
UINT128 sig_n_prime;
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y;
// NaN (CASE1)
// if either number is NAN, the comparison is unordered : return 0
if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
*pfpsf |= INVALID_EXCEPTION; // set invalid exception if NaN
res = 0;
BID_RETURN (res);
}
// SIMPLE (CASE2)
// if all the bits are the same, these numbers are equal.
if (x == y) {
res = 0;
BID_RETURN (res);
}
// INFINITY (CASE3)
if ((x & MASK_INF) == MASK_INF) {
// if x==neg_inf, { res = (y == neg_inf)?0:1; BID_RETURN (res) }
if ((x & MASK_SIGN) == MASK_SIGN)
// x is -inf, so it is less than y unless y is -inf
{
res = (((y & MASK_INF) != MASK_INF)
|| (y & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
} else
// x is pos_inf, no way for it to be less than y
{
res = 0;
BID_RETURN (res);
}
} else if ((y & MASK_INF) == MASK_INF) {
// x is finite, so:
// if y is +inf, x<y
// if y is -inf, x>y
{
res = ((y & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
}
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (sig_x > 9999999999999999ull) {
non_canon_x = 1;
} else {
non_canon_x = 0;
}
} else {
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
sig_x = (x & MASK_BINARY_SIG1);
non_canon_x = 0;
}
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (sig_y > 9999999999999999ull) {
non_canon_y = 1;
} else {
non_canon_y = 0;
}
} else {
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
sig_y = (y & MASK_BINARY_SIG1);
non_canon_y = 0;
}
// ZERO (CASE4)
// some properties:
// (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B =>
// therefore ignore the exponent field
// (Any non-canonical # is considered 0)
if (non_canon_x || sig_x == 0) {
x_is_zero = 1;
}
if (non_canon_y || sig_y == 0) {
y_is_zero = 1;
}
// if both numbers are zero, they are equal
if (x_is_zero && y_is_zero) {
res = 0;
BID_RETURN (res);
}
// if x is zero, it is lessthan if Y is positive
else if (x_is_zero) {
res = ((y & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// if y is zero, X is less if it is negative
else if (y_is_zero) {
res = ((x & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// OPPOSITE SIGN (CASE5)
// now, if the sign bits differ, x is less than if y is positive
if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
res = ((y & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// REDUNDANT REPRESENTATIONS (CASE6)
// if both components are either bigger or smaller
if (sig_x > sig_y && exp_x >= exp_y) {
res = ((x & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
if (sig_x < sig_y && exp_x <= exp_y) {
res = ((x & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// if exp_x is 15 greater than exp_y, no need for compensation
if (exp_x - exp_y > 15) {
res = ((x & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// difference cannot be greater than 10^15
// if exp_x is 15 less than exp_y, no need for compensation
if (exp_y - exp_x > 15) {
res = ((x & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// if |exp_x - exp_y| < 15, it comes down to the compensated significand
if (exp_x > exp_y) { // to simplify the loop below,
// otherwise adjust the x significand upwards
__mul_64x64_to_128MACH (sig_n_prime, sig_x,
mult_factor[exp_x - exp_y]);
// return 0 if values are equal
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
res = 0;
BID_RETURN (res);
}
// if postitive, return whichever significand abs is smaller
// (converse if negative)
{
res = (((sig_n_prime.w[1] == 0)
&& sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) ==
MASK_SIGN));
BID_RETURN (res);
}
}
// adjust the y significand upwards
__mul_64x64_to_128MACH (sig_n_prime, sig_y,
mult_factor[exp_y - exp_x]);
// return 0 if values are equal
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
res = 0;
BID_RETURN (res);
}
// if positive, return whichever significand abs is smaller
// (converse if negative)
{
res = (((sig_n_prime.w[1] > 0)
|| (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) ==
MASK_SIGN));
BID_RETURN (res);
}
}
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_signaling_less_equal (int *pres, UINT64 * px,
UINT64 *
py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
UINT64 y = *py;
#else
int
bid64_signaling_less_equal (UINT64 x,
UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
#endif
int res;
int exp_x, exp_y;
UINT64 sig_x, sig_y;
UINT128 sig_n_prime;
char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y;
// NaN (CASE1)
// if either number is NAN, the comparison is unordered,
// rather than equal : return 0
if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
*pfpsf |= INVALID_EXCEPTION; // set invalid exception if NaN
res = 0;
BID_RETURN (res);
}
// SIMPLE (CASE2)
// if all the bits are the same, these numbers are equal (LESSEQUAL).
if (x == y) {
res = 1;
BID_RETURN (res);
}
// INFINITY (CASE3)
if ((x & MASK_INF) == MASK_INF) {
// if x is neg infinity, it must be lessthan or equal to y return 1
if (((x & MASK_SIGN) == MASK_SIGN)) {
res = 1;
BID_RETURN (res);
}
// x is pos infinity, it is greater,
// unless y is positive infinity => return y==pos_infinity
else {
res = !(((y & MASK_INF) != MASK_INF)
|| ((y & MASK_SIGN) == MASK_SIGN));
BID_RETURN (res);
}
} else if ((y & MASK_INF) == MASK_INF) {
// x is finite, so if y is positive infinity, then x is less, return 1
// if y is negative infinity, then x is greater, return 0
{
res = ((y & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
}
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (sig_x > 9999999999999999ull) {
non_canon_x = 1;
} else {
non_canon_x = 0;
}
} else {
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
sig_x = (x & MASK_BINARY_SIG1);
non_canon_x = 0;
}
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (sig_y > 9999999999999999ull) {
non_canon_y = 1;
} else {
non_canon_y = 0;
}
} else {
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
sig_y = (y & MASK_BINARY_SIG1);
non_canon_y = 0;
}
// ZERO (CASE4)
// some properties:
// (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B =>
// therefore ignore the exponent field
// (Any non-canonical # is considered 0)
if (non_canon_x || sig_x == 0) {
x_is_zero = 1;
}
if (non_canon_y || sig_y == 0) {
y_is_zero = 1;
}
// if both numbers are zero, they are equal -> return 1
if (x_is_zero && y_is_zero) {
res = 1;
BID_RETURN (res);
}
// if x is zero, it is lessthan if Y is positive
else if (x_is_zero) {
res = ((y & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// if y is zero, X is less if it is negative
else if (y_is_zero) {
res = ((x & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// OPPOSITE SIGN (CASE5)
// now, if the sign bits differ, x is less than if y is positive
if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
res = ((y & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// REDUNDANT REPRESENTATIONS (CASE6)
// if both components are either bigger or smaller
if (sig_x > sig_y && exp_x >= exp_y) {
res = ((x & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
if (sig_x < sig_y && exp_x <= exp_y) {
res = ((x & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// if exp_x is 15 greater than exp_y, no need for compensation
if (exp_x - exp_y > 15) {
res = ((x & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// difference cannot be greater than 10^15
// if exp_x is 15 less than exp_y, no need for compensation
if (exp_y - exp_x > 15) {
res = ((x & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// if |exp_x - exp_y| < 15, it comes down to the compensated significand
if (exp_x > exp_y) { // to simplify the loop below,
// otherwise adjust the x significand upwards
__mul_64x64_to_128MACH