--- /dev/null
+/* Copyright (C) 2007, 2009 Free Software Foundation, Inc.
+
+This file is part of GCC.
+
+GCC is free software; you can redistribute it and/or modify it under
+the terms of the GNU General Public License as published by the Free
+Software Foundation; either version 3, or (at your option) any later
+version.
+
+GCC is distributed in the hope that it will be useful, but WITHOUT ANY
+WARRANTY; without even the implied warranty of MERCHANTABILITY or
+FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
+for more details.
+
+Under Section 7 of GPL version 3, you are granted additional
+permissions described in the GCC Runtime Library Exception, version
+3.1, as published by the Free Software Foundation.
+
+You should have received a copy of the GNU General Public License and
+a copy of the GCC Runtime Library Exception along with this program;
+see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
+<http://www.gnu.org/licenses/>. */
+
+#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.w[0] <
+ sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN);
+ BID_RETURN (res);
+}
+}
+
+BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_ordered, x,
+ y)
+
+ int res;
+
+ // NaN (CASE1)
+ // if either number is NAN, the comparison is ordered : 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);
+}
+}
+{
+ res = 1;
+ BID_RETURN (res);
+}
+}
+
+BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_unordered,
+ x, y)
+
+ int res;
+
+ // NaN (CASE1)
+ // if either number is NAN, the comparison is unordered : 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);
+}
+}
+{
+ res = 0;
+ BID_RETURN (res);
+}
+}
+
+BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_signaling_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)) {
+*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_signaling_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)) {
+*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_signaling_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)) {
+*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_signaling_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)) {
+*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, |x| < |y|, return 1 if positive
+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_signaling_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)) {
+*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_signaling_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)) {
+*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_signaling_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)) {
+*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_signaling_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)) {
+*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.w[0] <
+ sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN);
+ BID_RETURN (res);
+}
+}
projects / msp430-gcc.git / blobdiff