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[/] [openrisc/] [trunk/] [gnu-src/] [gcc-4.5.1/] [libgcc/] [config/] [libbid/] [bid64_compare.c] - Rev 280
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/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. This file is part of GCC. GCC is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3, or (at your option) any later version. GCC is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. Under Section 7 of GPL version 3, you are granted additional permissions described in the GCC Runtime Library Exception, version 3.1, as published by the Free Software Foundation. You should have received a copy of the GNU General Public License and a copy of the GCC Runtime Library Exception along with this program; see the files COPYING3 and COPYING.RUNTIME respectively. If not, see <http://www.gnu.org/licenses/>. */ #include "bid_internal.h" static const UINT64 mult_factor[16] = { 1ull, 10ull, 100ull, 1000ull, 10000ull, 100000ull, 1000000ull, 10000000ull, 100000000ull, 1000000000ull, 10000000000ull, 100000000000ull, 1000000000000ull, 10000000000000ull, 100000000000000ull, 1000000000000000ull }; #if DECIMAL_CALL_BY_REFERENCE void bid64_quiet_equal (int *pres, UINT64 * px, UINT64 * py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; UINT64 y = *py; #else int bid64_quiet_equal (UINT64 x, UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; int exp_x, exp_y, exp_t; UINT64 sig_x, sig_y, sig_t; char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y, lcv; // NaN (CASE1) // if either number is NAN, the comparison is unordered, // rather than equal : return 0 if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) { if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) { *pfpsf |= INVALID_EXCEPTION; // set exception if sNaN } res = 0; BID_RETURN (res); } // SIMPLE (CASE2) // if all the bits are the same, these numbers are equivalent. if (x == y) { res = 1; BID_RETURN (res); } // INFINITY (CASE3) if (((x & MASK_INF) == MASK_INF) && ((y & MASK_INF) == MASK_INF)) { res = (((x ^ y) & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // ONE INFINITY (CASE3') if (((x & MASK_INF) == MASK_INF) || ((y & MASK_INF) == MASK_INF)) { res = 0; BID_RETURN (res); } // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; if (sig_x > 9999999999999999ull) { non_canon_x = 1; } else { non_canon_x = 0; } } else { exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; sig_x = (x & MASK_BINARY_SIG1); non_canon_x = 0; } // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; if (sig_y > 9999999999999999ull) { non_canon_y = 1; } else { non_canon_y = 0; } } else { exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; sig_y = (y & MASK_BINARY_SIG1); non_canon_y = 0; } // ZERO (CASE4) // some properties: // (+ZERO==-ZERO) => therefore ignore the sign // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => // therefore ignore the exponent field // (Any non-canonical # is considered 0) if (non_canon_x || sig_x == 0) { x_is_zero = 1; } if (non_canon_y || sig_y == 0) { y_is_zero = 1; } if (x_is_zero && y_is_zero) { res = 1; BID_RETURN (res); } else if ((x_is_zero && !y_is_zero) || (!x_is_zero && y_is_zero)) { res = 0; BID_RETURN (res); } // OPPOSITE SIGN (CASE5) // now, if the sign bits differ => not equal : return 0 if ((x ^ y) & MASK_SIGN) { res = 0; BID_RETURN (res); } // REDUNDANT REPRESENTATIONS (CASE6) if (exp_x > exp_y) { // to simplify the loop below, SWAP (exp_x, exp_y, exp_t); // put the larger exp in y, SWAP (sig_x, sig_y, sig_t); // and the smaller exp in x } if (exp_y - exp_x > 15) { res = 0; // difference cannot be greater than 10^15 BID_RETURN (res); } for (lcv = 0; lcv < (exp_y - exp_x); lcv++) { // recalculate y's significand upwards sig_y = sig_y * 10; if (sig_y > 9999999999999999ull) { res = 0; BID_RETURN (res); } } res = (sig_y == sig_x); BID_RETURN (res); } #if DECIMAL_CALL_BY_REFERENCE void bid64_quiet_greater (int *pres, UINT64 * px, UINT64 * py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; UINT64 y = *py; #else int bid64_quiet_greater (UINT64 x, UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; int exp_x, exp_y; UINT64 sig_x, sig_y; UINT128 sig_n_prime; char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; // NaN (CASE1) // if either number is NAN, the comparison is unordered, rather than equal : // return 0 if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) { if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) { *pfpsf |= INVALID_EXCEPTION; // set exception if sNaN } res = 0; BID_RETURN (res); } // SIMPLE (CASE2) // if all the bits are the same, these numbers are equal (not Greater). if (x == y) { res = 0; BID_RETURN (res); } // INFINITY (CASE3) if ((x & MASK_INF) == MASK_INF) { // if x is neg infinity, there is no way it is greater than y, return 0 if (((x & MASK_SIGN) == MASK_SIGN)) { res = 0; BID_RETURN (res); } else { // x is pos infinity, it is greater, unless y is positive // infinity => return y!=pos_infinity res = (((y & MASK_INF) != MASK_INF) || ((y & MASK_SIGN) == MASK_SIGN)); BID_RETURN (res); } } else if ((y & MASK_INF) == MASK_INF) { // x is finite, so if y is positive infinity, then x is less, return 0 // if y is negative infinity, then x is greater, return 1 res = ((y & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; if (sig_x > 9999999999999999ull) { non_canon_x = 1; } else { non_canon_x = 0; } } else { exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; sig_x = (x & MASK_BINARY_SIG1); non_canon_x = 0; } // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; if (sig_y > 9999999999999999ull) { non_canon_y = 1; } else { non_canon_y = 0; } } else { exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; sig_y = (y & MASK_BINARY_SIG1); non_canon_y = 0; } // ZERO (CASE4) // some properties: //(+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater //(ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore ignore the // exponent field // (Any non-canonical # is considered 0) if (non_canon_x || sig_x == 0) { x_is_zero = 1; } if (non_canon_y || sig_y == 0) { y_is_zero = 1; } // if both numbers are zero, neither is greater => return NOTGREATERTHAN if (x_is_zero && y_is_zero) { res = 0; BID_RETURN (res); } else if (x_is_zero) { // is x is zero, it is greater if Y is negative res = ((y & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } else if (y_is_zero) { // is y is zero, X is greater if it is positive res = ((x & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // OPPOSITE SIGN (CASE5) // now, if the sign bits differ, x is greater if y is negative if (((x ^ y) & MASK_SIGN) == MASK_SIGN) { res = ((y & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // REDUNDANT REPRESENTATIONS (CASE6) // if both components are either bigger or smaller, // it is clear what needs to be done if (sig_x > sig_y && exp_x > exp_y) { res = ((x & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } if (sig_x < sig_y && exp_x < exp_y) { res = ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // if exp_x is 15 greater than exp_y, no need for compensation if (exp_x - exp_y > 15) { // difference cannot be greater than 10^15 if (x & MASK_SIGN) // if both are negative res = 0; else // if both are positive res = 1; BID_RETURN (res); } // if exp_x is 15 less than exp_y, no need for compensation if (exp_y - exp_x > 15) { if (x & MASK_SIGN) // if both are negative res = 1; else // if both are positive res = 0; BID_RETURN (res); } // if |exp_x - exp_y| < 15, it comes down to the compensated significand if (exp_x > exp_y) { // to simplify the loop below, // otherwise adjust the x significand upwards __mul_64x64_to_128MACH (sig_n_prime, sig_x, mult_factor[exp_x - exp_y]); // if postitive, return whichever significand is larger (converse if neg.) if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { res = 0; BID_RETURN (res); } res = (((sig_n_prime.w[1] > 0) || sig_n_prime.w[0] > sig_y) ^ ((x & MASK_SIGN) == MASK_SIGN)); BID_RETURN (res); } // adjust the y significand upwards __mul_64x64_to_128MACH (sig_n_prime, sig_y, mult_factor[exp_y - exp_x]); // if postitive, return whichever significand is larger // (converse if negative) if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { res = 0; BID_RETURN (res); } res = (((sig_n_prime.w[1] == 0) && (sig_x > sig_n_prime.w[0])) ^ ((x & MASK_SIGN) == MASK_SIGN)); BID_RETURN (res); } #if DECIMAL_CALL_BY_REFERENCE void bid64_quiet_greater_equal (int *pres, UINT64 * px, UINT64 * py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; UINT64 y = *py; #else int bid64_quiet_greater_equal (UINT64 x, UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; int exp_x, exp_y; UINT64 sig_x, sig_y; UINT128 sig_n_prime; char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; // NaN (CASE1) // if either number is NAN, the comparison is unordered : return 1 if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) { if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) { *pfpsf |= INVALID_EXCEPTION; // set exception if sNaN } res = 0; BID_RETURN (res); } // SIMPLE (CASE2) // if all the bits are the same, these numbers are equal. if (x == y) { res = 1; BID_RETURN (res); } // INFINITY (CASE3) if ((x & MASK_INF) == MASK_INF) { // if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) } if ((x & MASK_SIGN) == MASK_SIGN) { // x is -inf, so it is less than y unless y is -inf res = (((y & MASK_INF) == MASK_INF) && (y & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } else { // x is pos_inf, no way for it to be less than y res = 1; BID_RETURN (res); } } else if ((y & MASK_INF) == MASK_INF) { // x is finite, so: // if y is +inf, x<y // if y is -inf, x>y res = ((y & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; if (sig_x > 9999999999999999ull) { non_canon_x = 1; } else { non_canon_x = 0; } } else { exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; sig_x = (x & MASK_BINARY_SIG1); non_canon_x = 0; } // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; if (sig_y > 9999999999999999ull) { non_canon_y = 1; } else { non_canon_y = 0; } } else { exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; sig_y = (y & MASK_BINARY_SIG1); non_canon_y = 0; } // ZERO (CASE4) // some properties: // (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => // therefore ignore the exponent field // (Any non-canonical # is considered 0) if (non_canon_x || sig_x == 0) { x_is_zero = 1; } if (non_canon_y || sig_y == 0) { y_is_zero = 1; } if (x_is_zero && y_is_zero) { // if both numbers are zero, they are equal res = 1; BID_RETURN (res); } else if (x_is_zero) { // if x is zero, it is lessthan if Y is positive res = ((y & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } else if (y_is_zero) { // if y is zero, X is less if it is negative res = ((x & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // OPPOSITE SIGN (CASE5) // now, if the sign bits differ, x is less than if y is positive if (((x ^ y) & MASK_SIGN) == MASK_SIGN) { res = ((y & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // REDUNDANT REPRESENTATIONS (CASE6) // if both components are either bigger or smaller if (sig_x > sig_y && exp_x >= exp_y) { res = ((x & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } if (sig_x < sig_y && exp_x <= exp_y) { res = ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // if exp_x is 15 greater than exp_y, no need for compensation if (exp_x - exp_y > 15) { res = ((x & MASK_SIGN) != MASK_SIGN); // difference cannot be greater than 10^15 BID_RETURN (res); } // if exp_x is 15 less than exp_y, no need for compensation if (exp_y - exp_x > 15) { res = ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // if |exp_x - exp_y| < 15, it comes down to the compensated significand if (exp_x > exp_y) { // to simplify the loop below, // otherwise adjust the x significand upwards __mul_64x64_to_128MACH (sig_n_prime, sig_x, mult_factor[exp_x - exp_y]); // return 1 if values are equal if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { res = 1; BID_RETURN (res); } // if postitive, return whichever significand abs is smaller // (converse if negative) res = (((sig_n_prime.w[1] == 0) && sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) != MASK_SIGN)); BID_RETURN (res); } // adjust the y significand upwards __mul_64x64_to_128MACH (sig_n_prime, sig_y, mult_factor[exp_y - exp_x]); // return 0 if values are equal if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { res = 1; BID_RETURN (res); } // if positive, return whichever significand abs is smaller // (converse if negative) res = (((sig_n_prime.w[1] > 0) || (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) != MASK_SIGN)); BID_RETURN (res); } #if DECIMAL_CALL_BY_REFERENCE void bid64_quiet_greater_unordered (int *pres, UINT64 * px, UINT64 * py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; UINT64 y = *py; #else int bid64_quiet_greater_unordered (UINT64 x, UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; int exp_x, exp_y; UINT64 sig_x, sig_y; UINT128 sig_n_prime; char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; // NaN (CASE1) // if either number is NAN, the comparison is unordered, rather than equal : // return 0 if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) { if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) { *pfpsf |= INVALID_EXCEPTION; // set exception if sNaN } res = 1; BID_RETURN (res); } // SIMPLE (CASE2) // if all the bits are the same, these numbers are equal (not Greater). if (x == y) { res = 0; BID_RETURN (res); } // INFINITY (CASE3) if ((x & MASK_INF) == MASK_INF) { // if x is neg infinity, there is no way it is greater than y, return 0 if (((x & MASK_SIGN) == MASK_SIGN)) { res = 0; BID_RETURN (res); } else { // x is pos infinity, it is greater, unless y is positive infinity => // return y!=pos_infinity res = (((y & MASK_INF) != MASK_INF) || ((y & MASK_SIGN) == MASK_SIGN)); BID_RETURN (res); } } else if ((y & MASK_INF) == MASK_INF) { // x is finite, so if y is positive infinity, then x is less, return 0 // if y is negative infinity, then x is greater, return 1 res = ((y & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; if (sig_x > 9999999999999999ull) { non_canon_x = 1; } else { non_canon_x = 0; } } else { exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; sig_x = (x & MASK_BINARY_SIG1); non_canon_x = 0; } // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; if (sig_y > 9999999999999999ull) { non_canon_y = 1; } else { non_canon_y = 0; } } else { exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; sig_y = (y & MASK_BINARY_SIG1); non_canon_y = 0; } // ZERO (CASE4) // some properties: // (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => // therefore ignore the exponent field // (Any non-canonical # is considered 0) if (non_canon_x || sig_x == 0) { x_is_zero = 1; } if (non_canon_y || sig_y == 0) { y_is_zero = 1; } // if both numbers are zero, neither is greater => return NOTGREATERTHAN if (x_is_zero && y_is_zero) { res = 0; BID_RETURN (res); } else if (x_is_zero) { // is x is zero, it is greater if Y is negative res = ((y & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } else if (y_is_zero) { // is y is zero, X is greater if it is positive res = ((x & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // OPPOSITE SIGN (CASE5) // now, if the sign bits differ, x is greater if y is negative if (((x ^ y) & MASK_SIGN) == MASK_SIGN) { res = ((y & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // REDUNDANT REPRESENTATIONS (CASE6) // if both components are either bigger or smaller if (sig_x > sig_y && exp_x >= exp_y) { res = ((x & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } if (sig_x < sig_y && exp_x <= exp_y) { res = ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // if exp_x is 15 greater than exp_y, no need for compensation if (exp_x - exp_y > 15) { // difference cannot be greater than 10^15 res = ((x & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // if exp_x is 15 less than exp_y, no need for compensation if (exp_y - exp_x > 15) { res = ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // if |exp_x - exp_y| < 15, it comes down to the compensated significand if (exp_x > exp_y) { // to simplify the loop below, // otherwise adjust the x significand upwards __mul_64x64_to_128MACH (sig_n_prime, sig_x, mult_factor[exp_x - exp_y]); // if postitive, return whichever significand is larger // (converse if negative) if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { res = 0; BID_RETURN (res); } res = (((sig_n_prime.w[1] > 0) || sig_n_prime.w[0] > sig_y) ^ ((x & MASK_SIGN) == MASK_SIGN)); BID_RETURN (res); } // adjust the y significand upwards __mul_64x64_to_128MACH (sig_n_prime, sig_y, mult_factor[exp_y - exp_x]); // if postitive, return whichever significand is larger (converse if negative) if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { res = 0; BID_RETURN (res); } res = (((sig_n_prime.w[1] == 0) && (sig_x > sig_n_prime.w[0])) ^ ((x & MASK_SIGN) == MASK_SIGN)); BID_RETURN (res); } #if DECIMAL_CALL_BY_REFERENCE void bid64_quiet_less (int *pres, UINT64 * px, UINT64 * py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; UINT64 y = *py; #else int bid64_quiet_less (UINT64 x, UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; int exp_x, exp_y; UINT64 sig_x, sig_y; UINT128 sig_n_prime; char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; // NaN (CASE1) // if either number is NAN, the comparison is unordered : return 0 if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) { if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) { *pfpsf |= INVALID_EXCEPTION; // set exception if sNaN } res = 0; BID_RETURN (res); } // SIMPLE (CASE2) // if all the bits are the same, these numbers are equal. if (x == y) { res = 0; BID_RETURN (res); } // INFINITY (CASE3) if ((x & MASK_INF) == MASK_INF) { // if x==neg_inf, { res = (y == neg_inf)?0:1; BID_RETURN (res) } if ((x & MASK_SIGN) == MASK_SIGN) { // x is -inf, so it is less than y unless y is -inf res = (((y & MASK_INF) != MASK_INF) || (y & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } else { // x is pos_inf, no way for it to be less than y res = 0; BID_RETURN (res); } } else if ((y & MASK_INF) == MASK_INF) { // x is finite, so: // if y is +inf, x<y // if y is -inf, x>y res = ((y & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; if (sig_x > 9999999999999999ull) { non_canon_x = 1; } else { non_canon_x = 0; } } else { exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; sig_x = (x & MASK_BINARY_SIG1); non_canon_x = 0; } // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; if (sig_y > 9999999999999999ull) { non_canon_y = 1; } else { non_canon_y = 0; } } else { exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; sig_y = (y & MASK_BINARY_SIG1); non_canon_y = 0; } // ZERO (CASE4) // some properties: // (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => // therefore ignore the exponent field // (Any non-canonical # is considered 0) if (non_canon_x || sig_x == 0) { x_is_zero = 1; } if (non_canon_y || sig_y == 0) { y_is_zero = 1; } if (x_is_zero && y_is_zero) { // if both numbers are zero, they are equal res = 0; BID_RETURN (res); } else if (x_is_zero) { // if x is zero, it is lessthan if Y is positive res = ((y & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } else if (y_is_zero) { // if y is zero, X is less if it is negative res = ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // OPPOSITE SIGN (CASE5) // now, if the sign bits differ, x is less than if y is positive if (((x ^ y) & MASK_SIGN) == MASK_SIGN) { res = ((y & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // REDUNDANT REPRESENTATIONS (CASE6) // if both components are either bigger or smaller, // it is clear what needs to be done if (sig_x > sig_y && exp_x >= exp_y) { res = ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } if (sig_x < sig_y && exp_x <= exp_y) { res = ((x & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // if exp_x is 15 greater than exp_y, no need for compensation if (exp_x - exp_y > 15) { res = ((x & MASK_SIGN) == MASK_SIGN); // difference cannot be greater than 10^15 BID_RETURN (res); } // if exp_x is 15 less than exp_y, no need for compensation if (exp_y - exp_x > 15) { res = ((x & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // if |exp_x - exp_y| < 15, it comes down to the compensated significand if (exp_x > exp_y) { // to simplify the loop below, // otherwise adjust the x significand upwards __mul_64x64_to_128MACH (sig_n_prime, sig_x, mult_factor[exp_x - exp_y]); // return 0 if values are equal if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { res = 0; BID_RETURN (res); } // if postitive, return whichever significand abs is smaller // (converse if negative) res = (((sig_n_prime.w[1] == 0) && sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) == MASK_SIGN)); BID_RETURN (res); } // adjust the y significand upwards __mul_64x64_to_128MACH (sig_n_prime, sig_y, mult_factor[exp_y - exp_x]); // return 0 if values are equal if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { res = 0; BID_RETURN (res); } // if positive, return whichever significand abs is smaller // (converse if negative) res = (((sig_n_prime.w[1] > 0) || (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) == MASK_SIGN)); BID_RETURN (res); } #if DECIMAL_CALL_BY_REFERENCE void bid64_quiet_less_equal (int *pres, UINT64 * px, UINT64 * py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; UINT64 y = *py; #else int bid64_quiet_less_equal (UINT64 x, UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; int exp_x, exp_y; UINT64 sig_x, sig_y; UINT128 sig_n_prime; char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; // NaN (CASE1) // if either number is NAN, the comparison is unordered, rather than equal : // return 0 if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) { if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) { *pfpsf |= INVALID_EXCEPTION; // set exception if sNaN } res = 0; BID_RETURN (res); } // SIMPLE (CASE2) // if all the bits are the same, these numbers are equal (LESSEQUAL). if (x == y) { res = 1; BID_RETURN (res); } // INFINITY (CASE3) if ((x & MASK_INF) == MASK_INF) { if (((x & MASK_SIGN) == MASK_SIGN)) { // if x is neg infinity, it must be lessthan or equal to y return 1 res = 1; BID_RETURN (res); } else { // x is pos infinity, it is greater, unless y is positive infinity => // return y==pos_infinity res = !(((y & MASK_INF) != MASK_INF) || ((y & MASK_SIGN) == MASK_SIGN)); BID_RETURN (res); } } else if ((y & MASK_INF) == MASK_INF) { // x is finite, so if y is positive infinity, then x is less, return 1 // if y is negative infinity, then x is greater, return 0 res = ((y & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; if (sig_x > 9999999999999999ull) { non_canon_x = 1; } else { non_canon_x = 0; } } else { exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; sig_x = (x & MASK_BINARY_SIG1); non_canon_x = 0; } // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; if (sig_y > 9999999999999999ull) { non_canon_y = 1; } else { non_canon_y = 0; } } else { exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; sig_y = (y & MASK_BINARY_SIG1); non_canon_y = 0; } // ZERO (CASE4) // some properties: // (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => // therefore ignore the exponent field // (Any non-canonical # is considered 0) if (non_canon_x || sig_x == 0) { x_is_zero = 1; } if (non_canon_y || sig_y == 0) { y_is_zero = 1; } if (x_is_zero && y_is_zero) { // if both numbers are zero, they are equal -> return 1 res = 1; BID_RETURN (res); } else if (x_is_zero) { // if x is zero, it is lessthan if Y is positive res = ((y & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } else if (y_is_zero) { // if y is zero, X is less if it is negative res = ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // OPPOSITE SIGN (CASE5) // now, if the sign bits differ, x is less than if y is positive if (((x ^ y) & MASK_SIGN) == MASK_SIGN) { res = ((y & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // REDUNDANT REPRESENTATIONS (CASE6) // if both components are either bigger or smaller if (sig_x > sig_y && exp_x >= exp_y) { res = ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } if (sig_x < sig_y && exp_x <= exp_y) { res = ((x & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // if exp_x is 15 greater than exp_y, no need for compensation if (exp_x - exp_y > 15) { res = ((x & MASK_SIGN) == MASK_SIGN); // difference cannot be greater than 10^15 BID_RETURN (res); } // if exp_x is 15 less than exp_y, no need for compensation if (exp_y - exp_x > 15) { res = ((x & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // if |exp_x - exp_y| < 15, it comes down to the compensated significand if (exp_x > exp_y) { // to simplify the loop below, // otherwise adjust the x significand upwards __mul_64x64_to_128MACH (sig_n_prime, sig_x, mult_factor[exp_x - exp_y]); // return 1 if values are equal if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { res = 1; BID_RETURN (res); } // if postitive, return whichever significand abs is smaller // (converse if negative) res = (((sig_n_prime.w[1] == 0) && sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) == MASK_SIGN)); BID_RETURN (res); } // adjust the y significand upwards __mul_64x64_to_128MACH (sig_n_prime, sig_y, mult_factor[exp_y - exp_x]); // return 1 if values are equal if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { res = 1; BID_RETURN (res); } // if positive, return whichever significand abs is smaller // (converse if negative) res = (((sig_n_prime.w[1] > 0) || (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) == MASK_SIGN)); BID_RETURN (res); } #if DECIMAL_CALL_BY_REFERENCE void bid64_quiet_less_unordered (int *pres, UINT64 * px, UINT64 * py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; UINT64 y = *py; #else int bid64_quiet_less_unordered (UINT64 x, UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; int exp_x, exp_y; UINT64 sig_x, sig_y; UINT128 sig_n_prime; char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; // NaN (CASE1) // if either number is NAN, the comparison is unordered : return 0 if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) { if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) { *pfpsf |= INVALID_EXCEPTION; // set exception if sNaN } res = 1; BID_RETURN (res); } // SIMPLE (CASE2) // if all the bits are the same, these numbers are equal. if (x == y) { res = 0; BID_RETURN (res); } // INFINITY (CASE3) if ((x & MASK_INF) == MASK_INF) { // if x==neg_inf, { res = (y == neg_inf)?0:1; BID_RETURN (res) } if ((x & MASK_SIGN) == MASK_SIGN) { // x is -inf, so it is less than y unless y is -inf res = (((y & MASK_INF) != MASK_INF) || (y & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } else { // x is pos_inf, no way for it to be less than y res = 0; BID_RETURN (res); } } else if ((y & MASK_INF) == MASK_INF) { // x is finite, so: // if y is +inf, x<y // if y is -inf, x>y res = ((y & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; if (sig_x > 9999999999999999ull) { non_canon_x = 1; } else { non_canon_x = 0; } } else { exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; sig_x = (x & MASK_BINARY_SIG1); non_canon_x = 0; } // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; if (sig_y > 9999999999999999ull) { non_canon_y = 1; } else { non_canon_y = 0; } } else { exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; sig_y = (y & MASK_BINARY_SIG1); non_canon_y = 0; } // ZERO (CASE4) // some properties: // (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => // therefore ignore the exponent field // (Any non-canonical # is considered 0) if (non_canon_x || sig_x == 0) { x_is_zero = 1; } if (non_canon_y || sig_y == 0) { y_is_zero = 1; } if (x_is_zero && y_is_zero) { // if both numbers are zero, they are equal res = 0; BID_RETURN (res); } else if (x_is_zero) { // if x is zero, it is lessthan if Y is positive res = ((y & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } else if (y_is_zero) { // if y is zero, X is less if it is negative res = ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // OPPOSITE SIGN (CASE5) // now, if the sign bits differ, x is less than if y is positive if (((x ^ y) & MASK_SIGN) == MASK_SIGN) { res = ((y & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // REDUNDANT REPRESENTATIONS (CASE6) // if both components are either bigger or smaller if (sig_x > sig_y && exp_x >= exp_y) { res = ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } if (sig_x < sig_y && exp_x <= exp_y) { res = ((x & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // if exp_x is 15 greater than exp_y, no need for compensation if (exp_x - exp_y > 15) { res = ((x & MASK_SIGN) == MASK_SIGN); // difference cannot be greater than 10^15 BID_RETURN (res); } // if exp_x is 15 less than exp_y, no need for compensation if (exp_y - exp_x > 15) { res = ((x & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // if |exp_x - exp_y| < 15, it comes down to the compensated significand if (exp_x > exp_y) { // to simplify the loop below, // otherwise adjust the x significand upwards __mul_64x64_to_128MACH (sig_n_prime, sig_x, mult_factor[exp_x - exp_y]); // return 0 if values are equal if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { res = 0; BID_RETURN (res); } // if postitive, return whichever significand abs is smaller // (converse if negative) res = (((sig_n_prime.w[1] == 0) && sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) == MASK_SIGN)); BID_RETURN (res); } // adjust the y significand upwards __mul_64x64_to_128MACH (sig_n_prime, sig_y, mult_factor[exp_y - exp_x]); // return 0 if values are equal if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { res = 0; BID_RETURN (res); } // if positive, return whichever significand abs is smaller // (converse if negative) res = (((sig_n_prime.w[1] > 0) || (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) == MASK_SIGN)); BID_RETURN (res); } #if DECIMAL_CALL_BY_REFERENCE void bid64_quiet_not_equal (int *pres, UINT64 * px, UINT64 * py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; UINT64 y = *py; #else int bid64_quiet_not_equal (UINT64 x, UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; int exp_x, exp_y, exp_t; UINT64 sig_x, sig_y, sig_t; char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y, lcv; // NaN (CASE1) // if either number is NAN, the comparison is unordered, // rather than equal : return 1 if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) { if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) { *pfpsf |= INVALID_EXCEPTION; // set exception if sNaN } res = 1; BID_RETURN (res); } // SIMPLE (CASE2) // if all the bits are the same, these numbers are equivalent. if (x == y) { res = 0; BID_RETURN (res); } // INFINITY (CASE3) if (((x & MASK_INF) == MASK_INF) && ((y & MASK_INF) == MASK_INF)) { res = (((x ^ y) & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // ONE INFINITY (CASE3') if (((x & MASK_INF) == MASK_INF) || ((y & MASK_INF) == MASK_INF)) { res = 1; BID_RETURN (res); } // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; if (sig_x > 9999999999999999ull) { non_canon_x = 1; } else { non_canon_x = 0; } } else { exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; sig_x = (x & MASK_BINARY_SIG1); non_canon_x = 0; } // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; if (sig_y > 9999999999999999ull) { non_canon_y = 1; } else { non_canon_y = 0; } } else { exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; sig_y = (y & MASK_BINARY_SIG1); non_canon_y = 0; } // ZERO (CASE4) // some properties: // (+ZERO==-ZERO) => therefore ignore the sign // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => // therefore ignore the exponent field // (Any non-canonical # is considered 0) if (non_canon_x || sig_x == 0) { x_is_zero = 1; } if (non_canon_y || sig_y == 0) { y_is_zero = 1; } if (x_is_zero && y_is_zero) { res = 0; BID_RETURN (res); } else if ((x_is_zero && !y_is_zero) || (!x_is_zero && y_is_zero)) { res = 1; BID_RETURN (res); } // OPPOSITE SIGN (CASE5) // now, if the sign bits differ => not equal : return 1 if ((x ^ y) & MASK_SIGN) { res = 1; BID_RETURN (res); } // REDUNDANT REPRESENTATIONS (CASE6) if (exp_x > exp_y) { // to simplify the loop below, SWAP (exp_x, exp_y, exp_t); // put the larger exp in y, SWAP (sig_x, sig_y, sig_t); // and the smaller exp in x } if (exp_y - exp_x > 15) { res = 1; BID_RETURN (res); } // difference cannot be greater than 10^16 for (lcv = 0; lcv < (exp_y - exp_x); lcv++) { // recalculate y's significand upwards sig_y = sig_y * 10; if (sig_y > 9999999999999999ull) { res = 1; BID_RETURN (res); } } { res = sig_y != sig_x; BID_RETURN (res); } } #if DECIMAL_CALL_BY_REFERENCE void bid64_quiet_not_greater (int *pres, UINT64 * px, UINT64 * py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; UINT64 y = *py; #else int bid64_quiet_not_greater (UINT64 x, UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; int exp_x, exp_y; UINT64 sig_x, sig_y; UINT128 sig_n_prime; char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; // NaN (CASE1) // if either number is NAN, the comparison is unordered, // rather than equal : return 0 if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) { if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) { *pfpsf |= INVALID_EXCEPTION; // set exception if sNaN } res = 1; BID_RETURN (res); } // SIMPLE (CASE2) // if all the bits are the same, these numbers are equal (LESSEQUAL). if (x == y) { res = 1; BID_RETURN (res); } // INFINITY (CASE3) if ((x & MASK_INF) == MASK_INF) { // if x is neg infinity, it must be lessthan or equal to y return 1 if (((x & MASK_SIGN) == MASK_SIGN)) { res = 1; BID_RETURN (res); } // x is pos infinity, it is greater, unless y is positive // infinity => return y==pos_infinity else { res = !(((y & MASK_INF) != MASK_INF) || ((y & MASK_SIGN) == MASK_SIGN)); BID_RETURN (res); } } else if ((y & MASK_INF) == MASK_INF) { // x is finite, so if y is positive infinity, then x is less, return 1 // if y is negative infinity, then x is greater, return 0 { res = ((y & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } } // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; if (sig_x > 9999999999999999ull) { non_canon_x = 1; } else { non_canon_x = 0; } } else { exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; sig_x = (x & MASK_BINARY_SIG1); non_canon_x = 0; } // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; if (sig_y > 9999999999999999ull) { non_canon_y = 1; } else { non_canon_y = 0; } } else { exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; sig_y = (y & MASK_BINARY_SIG1); non_canon_y = 0; } // ZERO (CASE4) // some properties: // (+ZERO==-ZERO) => therefore ignore the sign, and neither // number is greater // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => // therefore ignore the exponent field // (Any non-canonical # is considered 0) if (non_canon_x || sig_x == 0) { x_is_zero = 1; } if (non_canon_y || sig_y == 0) { y_is_zero = 1; } // if both numbers are zero, they are equal -> return 1 if (x_is_zero && y_is_zero) { res = 1; BID_RETURN (res); } // if x is zero, it is lessthan if Y is positive else if (x_is_zero) { res = ((y & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // if y is zero, X is less if it is negative else if (y_is_zero) { res = ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // OPPOSITE SIGN (CASE5) // now, if the sign bits differ, x is less than if y is positive if (((x ^ y) & MASK_SIGN) == MASK_SIGN) { res = ((y & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // REDUNDANT REPRESENTATIONS (CASE6) // if both components are either bigger or smaller if (sig_x > sig_y && exp_x >= exp_y) { res = ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } if (sig_x < sig_y && exp_x <= exp_y) { res = ((x & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // if exp_x is 15 greater than exp_y, no need for compensation if (exp_x - exp_y > 15) { res = ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // difference cannot be greater than 10^15 // if exp_x is 15 less than exp_y, no need for compensation if (exp_y - exp_x > 15) { res = ((x & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // if |exp_x - exp_y| < 15, it comes down to the compensated significand if (exp_x > exp_y) { // to simplify the loop below, // otherwise adjust the x significand upwards __mul_64x64_to_128MACH (sig_n_prime, sig_x, mult_factor[exp_x - exp_y]); // return 1 if values are equal if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { res = 1; BID_RETURN (res); } // if postitive, return whichever significand abs is smaller // (converse if negative) { res = (((sig_n_prime.w[1] == 0) && sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) == MASK_SIGN)); BID_RETURN (res); } } // adjust the y significand upwards __mul_64x64_to_128MACH (sig_n_prime, sig_y, mult_factor[exp_y - exp_x]); // return 1 if values are equal if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { res = 1; BID_RETURN (res); } // if positive, return whichever significand abs is smaller // (converse if negative) { res = (((sig_n_prime.w[1] > 0) || (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) == MASK_SIGN)); BID_RETURN (res); } } #if DECIMAL_CALL_BY_REFERENCE void bid64_quiet_not_less (int *pres, UINT64 * px, UINT64 * py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; UINT64 y = *py; #else int bid64_quiet_not_less (UINT64 x, UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; int exp_x, exp_y; UINT64 sig_x, sig_y; UINT128 sig_n_prime; char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; // NaN (CASE1) // if either number is NAN, the comparison is unordered : return 1 if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) { if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) { *pfpsf |= INVALID_EXCEPTION; // set exception if sNaN } res = 1; BID_RETURN (res); } // SIMPLE (CASE2) // if all the bits are the same, these numbers are equal. if (x == y) { res = 1; BID_RETURN (res); } // INFINITY (CASE3) if ((x & MASK_INF) == MASK_INF) { // if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) } if ((x & MASK_SIGN) == MASK_SIGN) // x is -inf, so it is less than y unless y is -inf { res = (((y & MASK_INF) == MASK_INF) && (y & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } else // x is pos_inf, no way for it to be less than y { res = 1; BID_RETURN (res); } } else if ((y & MASK_INF) == MASK_INF) { // x is finite, so: // if y is +inf, x<y // if y is -inf, x>y { res = ((y & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } } // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; if (sig_x > 9999999999999999ull) { non_canon_x = 1; } else { non_canon_x = 0; } } else { exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; sig_x = (x & MASK_BINARY_SIG1); non_canon_x = 0; } // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; if (sig_y > 9999999999999999ull) { non_canon_y = 1; } else { non_canon_y = 0; } } else { exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; sig_y = (y & MASK_BINARY_SIG1); non_canon_y = 0; } // ZERO (CASE4) // some properties: // (+ZERO==-ZERO) => therefore ignore the sign, and neither // number is greater // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => // therefore ignore the exponent field // (Any non-canonical # is considered 0) if (non_canon_x || sig_x == 0) { x_is_zero = 1; } if (non_canon_y || sig_y == 0) { y_is_zero = 1; } // if both numbers are zero, they are equal if (x_is_zero && y_is_zero) { res = 1; BID_RETURN (res); } // if x is zero, it is lessthan if Y is positive else if (x_is_zero) { res = ((y & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // if y is zero, X is less if it is negative else if (y_is_zero) { res = ((x & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // OPPOSITE SIGN (CASE5) // now, if the sign bits differ, x is less than if y is positive if (((x ^ y) & MASK_SIGN) == MASK_SIGN) { res = ((y & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // REDUNDANT REPRESENTATIONS (CASE6) // if both components are either bigger or smaller if (sig_x > sig_y && exp_x >= exp_y) { res = ((x & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } if (sig_x < sig_y && exp_x <= exp_y) { res = ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // if exp_x is 15 greater than exp_y, no need for compensation if (exp_x - exp_y > 15) { res = ((x & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // difference cannot be greater than 10^15 // if exp_x is 15 less than exp_y, no need for compensation if (exp_y - exp_x > 15) { res = ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // if |exp_x - exp_y| < 15, it comes down to the compensated significand if (exp_x > exp_y) { // to simplify the loop below, // otherwise adjust the x significand upwards __mul_64x64_to_128MACH (sig_n_prime, sig_x, mult_factor[exp_x - exp_y]); // return 0 if values are equal if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { res = 1; BID_RETURN (res); } // if postitive, return whichever significand abs is smaller // (converse if negative) { res = (((sig_n_prime.w[1] == 0) && sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) != MASK_SIGN)); BID_RETURN (res); } } // adjust the y significand upwards __mul_64x64_to_128MACH (sig_n_prime, sig_y, mult_factor[exp_y - exp_x]); // return 0 if values are equal if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { res = 1; BID_RETURN (res); } // if positive, return whichever significand abs is smaller // (converse if negative) { res = (((sig_n_prime.w[1] > 0) || (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) != MASK_SIGN)); BID_RETURN (res); } } #if DECIMAL_CALL_BY_REFERENCE void bid64_quiet_ordered (int *pres, UINT64 * px, UINT64 * py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; UINT64 y = *py; #else int bid64_quiet_ordered (UINT64 x, UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; // NaN (CASE1) // if either number is NAN, the comparison is ordered, rather than equal : return 0 if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) { if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) { *pfpsf |= INVALID_EXCEPTION; // set exception if sNaN } res = 0; BID_RETURN (res); } else { res = 1; BID_RETURN (res); } } #if DECIMAL_CALL_BY_REFERENCE void bid64_quiet_unordered (int *pres, UINT64 * px, UINT64 * py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; UINT64 y = *py; #else int bid64_quiet_unordered (UINT64 x, UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; // NaN (CASE1) // if either number is NAN, the comparison is unordered, // rather than equal : return 0 if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) { if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) { *pfpsf |= INVALID_EXCEPTION; // set exception if sNaN } res = 1; BID_RETURN (res); } else { res = 0; BID_RETURN (res); } } #if DECIMAL_CALL_BY_REFERENCE void bid64_signaling_greater (int *pres, UINT64 * px, UINT64 * py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; UINT64 y = *py; #else int bid64_signaling_greater (UINT64 x, UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; int exp_x, exp_y; UINT64 sig_x, sig_y; UINT128 sig_n_prime; char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; // NaN (CASE1) // if either number is NAN, the comparison is unordered, // rather than equal : return 0 if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) { *pfpsf |= INVALID_EXCEPTION; // set invalid exception if NaN res = 0; BID_RETURN (res); } // SIMPLE (CASE2) // if all the bits are the same, these numbers are equal (not Greater). if (x == y) { res = 0; BID_RETURN (res); } // INFINITY (CASE3) if ((x & MASK_INF) == MASK_INF) { // if x is neg infinity, there is no way it is greater than y, return 0 if (((x & MASK_SIGN) == MASK_SIGN)) { res = 0; BID_RETURN (res); } // x is pos infinity, it is greater, // unless y is positive infinity => return y!=pos_infinity else { res = (((y & MASK_INF) != MASK_INF) || ((y & MASK_SIGN) == MASK_SIGN)); BID_RETURN (res); } } else if ((y & MASK_INF) == MASK_INF) { // x is finite, so if y is positive infinity, then x is less, return 0 // if y is negative infinity, then x is greater, return 1 { res = ((y & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } } // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; if (sig_x > 9999999999999999ull) { non_canon_x = 1; } else { non_canon_x = 0; } } else { exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; sig_x = (x & MASK_BINARY_SIG1); non_canon_x = 0; } // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; if (sig_y > 9999999999999999ull) { non_canon_y = 1; } else { non_canon_y = 0; } } else { exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; sig_y = (y & MASK_BINARY_SIG1); non_canon_y = 0; } // ZERO (CASE4) // some properties: // (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => // therefore ignore the exponent field // (Any non-canonical # is considered 0) if (non_canon_x || sig_x == 0) { x_is_zero = 1; } if (non_canon_y || sig_y == 0) { y_is_zero = 1; } // if both numbers are zero, neither is greater => return NOTGREATERTHAN if (x_is_zero && y_is_zero) { res = 0; BID_RETURN (res); } // is x is zero, it is greater if Y is negative else if (x_is_zero) { res = ((y & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // is y is zero, X is greater if it is positive else if (y_is_zero) { res = ((x & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // OPPOSITE SIGN (CASE5) // now, if the sign bits differ, x is greater if y is negative if (((x ^ y) & MASK_SIGN) == MASK_SIGN) { res = ((y & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // REDUNDANT REPRESENTATIONS (CASE6) // if both components are either bigger or smaller if (sig_x > sig_y && exp_x >= exp_y) { res = ((x & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } if (sig_x < sig_y && exp_x <= exp_y) { res = ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // if exp_x is 15 greater than exp_y, no need for compensation if (exp_x - exp_y > 15) { res = ((x & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // difference cannot be greater than 10^15 // if exp_x is 15 less than exp_y, no need for compensation if (exp_y - exp_x > 15) { res = ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // if |exp_x - exp_y| < 15, it comes down to the compensated significand if (exp_x > exp_y) { // to simplify the loop below, // otherwise adjust the x significand upwards __mul_64x64_to_128MACH (sig_n_prime, sig_x, mult_factor[exp_x - exp_y]); // if postitive, return whichever significand is larger // (converse if negative) if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { res = 0; BID_RETURN (res); } { res = (((sig_n_prime.w[1] > 0) || sig_n_prime.w[0] > sig_y) ^ ((x & MASK_SIGN) == MASK_SIGN)); BID_RETURN (res); } } // adjust the y significand upwards __mul_64x64_to_128MACH (sig_n_prime, sig_y, mult_factor[exp_y - exp_x]); // if postitive, return whichever significand is larger // (converse if negative) if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { res = 0; BID_RETURN (res); } { res = (((sig_n_prime.w[1] == 0) && (sig_x > sig_n_prime.w[0])) ^ ((x & MASK_SIGN) == MASK_SIGN)); BID_RETURN (res); } } #if DECIMAL_CALL_BY_REFERENCE void bid64_signaling_greater_equal (int *pres, UINT64 * px, UINT64 * py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; UINT64 y = *py; #else int bid64_signaling_greater_equal (UINT64 x, UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; int exp_x, exp_y; UINT64 sig_x, sig_y; UINT128 sig_n_prime; char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; // NaN (CASE1) // if either number is NAN, the comparison is unordered : return 1 if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) { *pfpsf |= INVALID_EXCEPTION; // set invalid exception if NaN res = 0; BID_RETURN (res); } // SIMPLE (CASE2) // if all the bits are the same, these numbers are equal. if (x == y) { res = 1; BID_RETURN (res); } // INFINITY (CASE3) if ((x & MASK_INF) == MASK_INF) { // if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) } if ((x & MASK_SIGN) == MASK_SIGN) // x is -inf, so it is less than y unless y is -inf { res = (((y & MASK_INF) == MASK_INF) && (y & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } else // x is pos_inf, no way for it to be less than y { res = 1; BID_RETURN (res); } } else if ((y & MASK_INF) == MASK_INF) { // x is finite, so: // if y is +inf, x<y // if y is -inf, x>y { res = ((y & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } } // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; if (sig_x > 9999999999999999ull) { non_canon_x = 1; } else { non_canon_x = 0; } } else { exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; sig_x = (x & MASK_BINARY_SIG1); non_canon_x = 0; } // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; if (sig_y > 9999999999999999ull) { non_canon_y = 1; } else { non_canon_y = 0; } } else { exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; sig_y = (y & MASK_BINARY_SIG1); non_canon_y = 0; } // ZERO (CASE4) // some properties: // (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => // therefore ignore the exponent field // (Any non-canonical # is considered 0) if (non_canon_x || sig_x == 0) { x_is_zero = 1; } if (non_canon_y || sig_y == 0) { y_is_zero = 1; } // if both numbers are zero, they are equal if (x_is_zero && y_is_zero) { res = 1; BID_RETURN (res); } // if x is zero, it is lessthan if Y is positive else if (x_is_zero) { res = ((y & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // if y is zero, X is less if it is negative else if (y_is_zero) { res = ((x & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // OPPOSITE SIGN (CASE5) // now, if the sign bits differ, x is less than if y is positive if (((x ^ y) & MASK_SIGN) == MASK_SIGN) { res = ((y & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // REDUNDANT REPRESENTATIONS (CASE6) // if both components are either bigger or smaller if (sig_x > sig_y && exp_x >= exp_y) { res = ((x & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } if (sig_x < sig_y && exp_x <= exp_y) { res = ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // if exp_x is 15 greater than exp_y, no need for compensation if (exp_x - exp_y > 15) { res = ((x & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // difference cannot be greater than 10^15 // if exp_x is 15 less than exp_y, no need for compensation if (exp_y - exp_x > 15) { res = ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // if |exp_x - exp_y| < 15, it comes down to the compensated significand if (exp_x > exp_y) { // to simplify the loop below, // otherwise adjust the x significand upwards __mul_64x64_to_128MACH (sig_n_prime, sig_x, mult_factor[exp_x - exp_y]); // return 1 if values are equal if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { res = 1; BID_RETURN (res); } // if postitive, return whichever significand abs is smaller // (converse if negative) { res = (((sig_n_prime.w[1] == 0) && sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) != MASK_SIGN)); BID_RETURN (res); } } // adjust the y significand upwards __mul_64x64_to_128MACH (sig_n_prime, sig_y, mult_factor[exp_y - exp_x]); // return 0 if values are equal if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { res = 1; BID_RETURN (res); } // if positive, return whichever significand abs is smaller // (converse if negative) { res = (((sig_n_prime.w[1] > 0) || (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) != MASK_SIGN)); BID_RETURN (res); } } #if DECIMAL_CALL_BY_REFERENCE void bid64_signaling_greater_unordered (int *pres, UINT64 * px, UINT64 * py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; UINT64 y = *py; #else int bid64_signaling_greater_unordered (UINT64 x, UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; int exp_x, exp_y; UINT64 sig_x, sig_y; UINT128 sig_n_prime; char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; // NaN (CASE1) // if either number is NAN, the comparison is unordered, // rather than equal : return 0 if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) { *pfpsf |= INVALID_EXCEPTION; // set invalid exception if NaN res = 1; BID_RETURN (res); } // SIMPLE (CASE2) // if all the bits are the same, these numbers are equal (not Greater). if (x == y) { res = 0; BID_RETURN (res); } // INFINITY (CASE3) if ((x & MASK_INF) == MASK_INF) { // if x is neg infinity, there is no way it is greater than y, return 0 if (((x & MASK_SIGN) == MASK_SIGN)) { res = 0; BID_RETURN (res); } // x is pos infinity, it is greater, // unless y is positive infinity => return y!=pos_infinity else { res = (((y & MASK_INF) != MASK_INF) || ((y & MASK_SIGN) == MASK_SIGN)); BID_RETURN (res); } } else if ((y & MASK_INF) == MASK_INF) { // x is finite, so if y is positive infinity, then x is less, return 0 // if y is negative infinity, then x is greater, return 1 { res = ((y & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } } // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; if (sig_x > 9999999999999999ull) { non_canon_x = 1; } else { non_canon_x = 0; } } else { exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; sig_x = (x & MASK_BINARY_SIG1); non_canon_x = 0; } // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; if (sig_y > 9999999999999999ull) { non_canon_y = 1; } else { non_canon_y = 0; } } else { exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; sig_y = (y & MASK_BINARY_SIG1); non_canon_y = 0; } // ZERO (CASE4) // some properties: // (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => // therefore ignore the exponent field // (Any non-canonical # is considered 0) if (non_canon_x || sig_x == 0) { x_is_zero = 1; } if (non_canon_y || sig_y == 0) { y_is_zero = 1; } // if both numbers are zero, neither is greater => return NOTGREATERTHAN if (x_is_zero && y_is_zero) { res = 0; BID_RETURN (res); } // is x is zero, it is greater if Y is negative else if (x_is_zero) { res = ((y & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // is y is zero, X is greater if it is positive else if (y_is_zero) { res = ((x & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // OPPOSITE SIGN (CASE5) // now, if the sign bits differ, x is greater if y is negative if (((x ^ y) & MASK_SIGN) == MASK_SIGN) { res = ((y & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // REDUNDANT REPRESENTATIONS (CASE6) // if both components are either bigger or smaller if (sig_x > sig_y && exp_x >= exp_y) { res = ((x & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } if (sig_x < sig_y && exp_x <= exp_y) { res = ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // if exp_x is 15 greater than exp_y, no need for compensation if (exp_x - exp_y > 15) { res = ((x & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // difference cannot be greater than 10^15 // if exp_x is 15 less than exp_y, no need for compensation if (exp_y - exp_x > 15) { res = ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // if |exp_x - exp_y| < 15, it comes down to the compensated significand if (exp_x > exp_y) { // to simplify the loop below, // otherwise adjust the x significand upwards __mul_64x64_to_128MACH (sig_n_prime, sig_x, mult_factor[exp_x - exp_y]); // if postitive, return whichever significand is larger // (converse if negative) if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { res = 0; BID_RETURN (res); } { res = (((sig_n_prime.w[1] > 0) || sig_n_prime.w[0] > sig_y) ^ ((x & MASK_SIGN) == MASK_SIGN)); BID_RETURN (res); } } // adjust the y significand upwards __mul_64x64_to_128MACH (sig_n_prime, sig_y, mult_factor[exp_y - exp_x]); // if postitive, return whichever significand is larger // (converse if negative) if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { res = 0; BID_RETURN (res); } { res = (((sig_n_prime.w[1] == 0) && (sig_x > sig_n_prime.w[0])) ^ ((x & MASK_SIGN) == MASK_SIGN)); BID_RETURN (res); } } #if DECIMAL_CALL_BY_REFERENCE void bid64_signaling_less (int *pres, UINT64 * px, UINT64 * py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; UINT64 y = *py; #else int bid64_signaling_less (UINT64 x, UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; int exp_x, exp_y; UINT64 sig_x, sig_y; UINT128 sig_n_prime; char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; // NaN (CASE1) // if either number is NAN, the comparison is unordered : return 0 if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) { *pfpsf |= INVALID_EXCEPTION; // set invalid exception if NaN res = 0; BID_RETURN (res); } // SIMPLE (CASE2) // if all the bits are the same, these numbers are equal. if (x == y) { res = 0; BID_RETURN (res); } // INFINITY (CASE3) if ((x & MASK_INF) == MASK_INF) { // if x==neg_inf, { res = (y == neg_inf)?0:1; BID_RETURN (res) } if ((x & MASK_SIGN) == MASK_SIGN) // x is -inf, so it is less than y unless y is -inf { res = (((y & MASK_INF) != MASK_INF) || (y & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } else // x is pos_inf, no way for it to be less than y { res = 0; BID_RETURN (res); } } else if ((y & MASK_INF) == MASK_INF) { // x is finite, so: // if y is +inf, x<y // if y is -inf, x>y { res = ((y & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } } // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; if (sig_x > 9999999999999999ull) { non_canon_x = 1; } else { non_canon_x = 0; } } else { exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; sig_x = (x & MASK_BINARY_SIG1); non_canon_x = 0; } // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; if (sig_y > 9999999999999999ull) { non_canon_y = 1; } else { non_canon_y = 0; } } else { exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; sig_y = (y & MASK_BINARY_SIG1); non_canon_y = 0; } // ZERO (CASE4) // some properties: // (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => // therefore ignore the exponent field // (Any non-canonical # is considered 0) if (non_canon_x || sig_x == 0) { x_is_zero = 1; } if (non_canon_y || sig_y == 0) { y_is_zero = 1; } // if both numbers are zero, they are equal if (x_is_zero && y_is_zero) { res = 0; BID_RETURN (res); } // if x is zero, it is lessthan if Y is positive else if (x_is_zero) { res = ((y & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // if y is zero, X is less if it is negative else if (y_is_zero) { res = ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // OPPOSITE SIGN (CASE5) // now, if the sign bits differ, x is less than if y is positive if (((x ^ y) & MASK_SIGN) == MASK_SIGN) { res = ((y & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // REDUNDANT REPRESENTATIONS (CASE6) // if both components are either bigger or smaller if (sig_x > sig_y && exp_x >= exp_y) { res = ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } if (sig_x < sig_y && exp_x <= exp_y) { res = ((x & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // if exp_x is 15 greater than exp_y, no need for compensation if (exp_x - exp_y > 15) { res = ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // difference cannot be greater than 10^15 // if exp_x is 15 less than exp_y, no need for compensation if (exp_y - exp_x > 15) { res = ((x & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // if |exp_x - exp_y| < 15, it comes down to the compensated significand if (exp_x > exp_y) { // to simplify the loop below, // otherwise adjust the x significand upwards __mul_64x64_to_128MACH (sig_n_prime, sig_x, mult_factor[exp_x - exp_y]); // return 0 if values are equal if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { res = 0; BID_RETURN (res); } // if postitive, return whichever significand abs is smaller // (converse if negative) { res = (((sig_n_prime.w[1] == 0) && sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) == MASK_SIGN)); BID_RETURN (res); } } // adjust the y significand upwards __mul_64x64_to_128MACH (sig_n_prime, sig_y, mult_factor[exp_y - exp_x]); // return 0 if values are equal if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { res = 0; BID_RETURN (res); } // if positive, return whichever significand abs is smaller // (converse if negative) { res = (((sig_n_prime.w[1] > 0) || (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) == MASK_SIGN)); BID_RETURN (res); } } #if DECIMAL_CALL_BY_REFERENCE void bid64_signaling_less_equal (int *pres, UINT64 * px, UINT64 * py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; UINT64 y = *py; #else int bid64_signaling_less_equal (UINT64 x, UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; int exp_x, exp_y; UINT64 sig_x, sig_y; UINT128 sig_n_prime; char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; // NaN (CASE1) // if either number is NAN, the comparison is unordered, // rather than equal : return 0 if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) { *pfpsf |= INVALID_EXCEPTION; // set invalid exception if NaN res = 0; BID_RETURN (res); } // SIMPLE (CASE2) // if all the bits are the same, these numbers are equal (LESSEQUAL). if (x == y) { res = 1; BID_RETURN (res); } // INFINITY (CASE3) if ((x & MASK_INF) == MASK_INF) { // if x is neg infinity, it must be lessthan or equal to y return 1 if (((x & MASK_SIGN) == MASK_SIGN)) { res = 1; BID_RETURN (res); } // x is pos infinity, it is greater, // unless y is positive infinity => return y==pos_infinity else { res = !(((y & MASK_INF) != MASK_INF) || ((y & MASK_SIGN) == MASK_SIGN)); BID_RETURN (res); } } else if ((y & MASK_INF) == MASK_INF) { // x is finite, so if y is positive infinity, then x is less, return 1 // if y is negative infinity, then x is greater, return 0 { res = ((y & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } } // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; if (sig_x > 9999999999999999ull) { non_canon_x = 1; } else { non_canon_x = 0; } } else { exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; sig_x = (x & MASK_BINARY_SIG1); non_canon_x = 0; } // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; if (sig_y > 9999999999999999ull) { non_canon_y = 1; } else { non_canon_y = 0; } } else { exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; sig_y = (y & MASK_BINARY_SIG1); non_canon_y = 0; } // ZERO (CASE4) // some properties: // (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => // therefore ignore the exponent field // (Any non-canonical # is considered 0) if (non_canon_x || sig_x == 0) { x_is_zero = 1; } if (non_canon_y || sig_y == 0) { y_is_zero = 1; } // if both numbers are zero, they are equal -> return 1 if (x_is_zero && y_is_zero) { res = 1; BID_RETURN (res); } // if x is zero, it is lessthan if Y is positive else if (x_is_zero) { res = ((y & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // if y is zero, X is less if it is negative else if (y_is_zero) { res = ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // OPPOSITE SIGN (CASE5) // now, if the sign bits differ, x is less than if y is positive if (((x ^ y) & MASK_SIGN) == MASK_SIGN) { res = ((y & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // REDUNDANT REPRESENTATIONS (CASE6) // if both components are either bigger or smaller if (sig_x > sig_y && exp_x >= exp_y) { res = ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } if (sig_x < sig_y && exp_x <= exp_y) { res = ((x & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // if exp_x is 15 greater than exp_y, no need for compensation if (exp_x - exp_y > 15) { res = ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // difference cannot be greater than 10^15 // if exp_x is 15 less than exp_y, no need for compensation if (exp_y - exp_x > 15) { res = ((x & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // if |exp_x - exp_y| < 15, it comes down to the compensated significand if (exp_x > exp_y) { // to simplify the loop below, // otherwise adjust the x significand upwards __mul_64x64_to_128MACH (sig_n_prime, sig_x, mult_factor[exp_x - exp_y]); // return 1 if values are equal if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { res = 1; BID_RETURN (res); } // if postitive, return whichever significand abs is smaller // (converse if negative) { res = (((sig_n_prime.w[1] == 0) && sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) == MASK_SIGN)); BID_RETURN (res); } } // adjust the y significand upwards __mul_64x64_to_128MACH (sig_n_prime, sig_y, mult_factor[exp_y - exp_x]); // return 1 if values are equal if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { res = 1; BID_RETURN (res); } // if positive, return whichever significand abs is smaller // (converse if negative) { res = (((sig_n_prime.w[1] > 0) || (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) == MASK_SIGN)); BID_RETURN (res); } } #if DECIMAL_CALL_BY_REFERENCE void bid64_signaling_less_unordered (int *pres, UINT64 * px, UINT64 * py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; UINT64 y = *py; #else int bid64_signaling_less_unordered (UINT64 x, UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; int exp_x, exp_y; UINT64 sig_x, sig_y; UINT128 sig_n_prime; char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; // NaN (CASE1) // if either number is NAN, the comparison is unordered : return 0 if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) { *pfpsf |= INVALID_EXCEPTION; // set invalid exception if NaN res = 1; BID_RETURN (res); } // SIMPLE (CASE2) // if all the bits are the same, these numbers are equal. if (x == y) { res = 0; BID_RETURN (res); } // INFINITY (CASE3) if ((x & MASK_INF) == MASK_INF) { // if x==neg_inf, { res = (y == neg_inf)?0:1; BID_RETURN (res) } if ((x & MASK_SIGN) == MASK_SIGN) // x is -inf, so it is less than y unless y is -inf { res = (((y & MASK_INF) != MASK_INF) || (y & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } else // x is pos_inf, no way for it to be less than y { res = 0; BID_RETURN (res); } } else if ((y & MASK_INF) == MASK_INF) { // x is finite, so: // if y is +inf, x<y // if y is -inf, x>y { res = ((y & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } } // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; if (sig_x > 9999999999999999ull) { non_canon_x = 1; } else { non_canon_x = 0; } } else { exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; sig_x = (x & MASK_BINARY_SIG1); non_canon_x = 0; } // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; if (sig_y > 9999999999999999ull) { non_canon_y = 1; } else { non_canon_y = 0; } } else { exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; sig_y = (y & MASK_BINARY_SIG1); non_canon_y = 0; } // ZERO (CASE4) // some properties: // (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => // therefore ignore the exponent field // (Any non-canonical # is considered 0) if (non_canon_x || sig_x == 0) { x_is_zero = 1; } if (non_canon_y || sig_y == 0) { y_is_zero = 1; } // if both numbers are zero, they are equal if (x_is_zero && y_is_zero) { res = 0; BID_RETURN (res); } // if x is zero, it is lessthan if Y is positive else if (x_is_zero) { res = ((y & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // if y is zero, X is less if it is negative else if (y_is_zero) { res = ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // OPPOSITE SIGN (CASE5) // now, if the sign bits differ, x is less than if y is positive if (((x ^ y) & MASK_SIGN) == MASK_SIGN) { res = ((y & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // REDUNDANT REPRESENTATIONS (CASE6) // if both components are either bigger or smaller if (sig_x > sig_y && exp_x >= exp_y) { res = ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } if (sig_x < sig_y && exp_x <= exp_y) { res = ((x & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // if exp_x is 15 greater than exp_y, no need for compensation if (exp_x - exp_y > 15) { res = ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // difference cannot be greater than 10^15 // if exp_x is 15 less than exp_y, no need for compensation if (exp_y - exp_x > 15) { res = ((x & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // if |exp_x - exp_y| < 15, it comes down to the compensated significand if (exp_x > exp_y) { // to simplify the loop below, // otherwise adjust the x significand upwards __mul_64x64_to_128MACH (sig_n_prime, sig_x, mult_factor[exp_x - exp_y]); // return 0 if values are equal if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { res = 0; BID_RETURN (res); } // if postitive, return whichever significand abs is smaller // (converse if negative) { res = (((sig_n_prime.w[1] == 0) && sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) == MASK_SIGN)); BID_RETURN (res); } } // adjust the y significand upwards __mul_64x64_to_128MACH (sig_n_prime, sig_y, mult_factor[exp_y - exp_x]); // return 0 if values are equal if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { res = 0; BID_RETURN (res); } // if positive, return whichever significand abs is smaller // (converse if negative) { res = (((sig_n_prime.w[1] > 0) || (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) == MASK_SIGN)); BID_RETURN (res); } } #if DECIMAL_CALL_BY_REFERENCE void bid64_signaling_not_greater (int *pres, UINT64 * px, UINT64 * py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; UINT64 y = *py; #else int bid64_signaling_not_greater (UINT64 x, UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; int exp_x, exp_y; UINT64 sig_x, sig_y; UINT128 sig_n_prime; char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; // NaN (CASE1) // if either number is NAN, the comparison is unordered, // rather than equal : return 0 if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) { *pfpsf |= INVALID_EXCEPTION; // set invalid exception if NaN res = 1; BID_RETURN (res); } // SIMPLE (CASE2) // if all the bits are the same, these numbers are equal (LESSEQUAL). if (x == y) { res = 1; BID_RETURN (res); } // INFINITY (CASE3) if ((x & MASK_INF) == MASK_INF) { // if x is neg infinity, it must be lessthan or equal to y return 1 if (((x & MASK_SIGN) == MASK_SIGN)) { res = 1; BID_RETURN (res); } // x is pos infinity, it is greater, // unless y is positive infinity => return y==pos_infinity else { res = !(((y & MASK_INF) != MASK_INF) || ((y & MASK_SIGN) == MASK_SIGN)); BID_RETURN (res); } } else if ((y & MASK_INF) == MASK_INF) { // x is finite, so if y is positive infinity, then x is less, return 1 // if y is negative infinity, then x is greater, return 0 { res = ((y & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } } // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; if (sig_x > 9999999999999999ull) { non_canon_x = 1; } else { non_canon_x = 0; } } else { exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; sig_x = (x & MASK_BINARY_SIG1); non_canon_x = 0; } // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; if (sig_y > 9999999999999999ull) { non_canon_y = 1; } else { non_canon_y = 0; } } else { exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; sig_y = (y & MASK_BINARY_SIG1); non_canon_y = 0; } // ZERO (CASE4) // some properties: // (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => // therefore ignore the exponent field // (Any non-canonical # is considered 0) if (non_canon_x || sig_x == 0) { x_is_zero = 1; } if (non_canon_y || sig_y == 0) { y_is_zero = 1; } // if both numbers are zero, they are equal -> return 1 if (x_is_zero && y_is_zero) { res = 1; BID_RETURN (res); } // if x is zero, it is lessthan if Y is positive else if (x_is_zero) { res = ((y & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // if y is zero, X is less if it is negative else if (y_is_zero) { res = ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // OPPOSITE SIGN (CASE5) // now, if the sign bits differ, x is less than if y is positive if (((x ^ y) & MASK_SIGN) == MASK_SIGN) { res = ((y & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // REDUNDANT REPRESENTATIONS (CASE6) // if both components are either bigger or smaller if (sig_x > sig_y && exp_x >= exp_y) { res = ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } if (sig_x < sig_y && exp_x <= exp_y) { res = ((x & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // if exp_x is 15 greater than exp_y, no need for compensation if (exp_x - exp_y > 15) { res = ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // difference cannot be greater than 10^15 // if exp_x is 15 less than exp_y, no need for compensation if (exp_y - exp_x > 15) { res = ((x & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // if |exp_x - exp_y| < 15, it comes down to the compensated significand if (exp_x > exp_y) { // to simplify the loop below, // otherwise adjust the x significand upwards __mul_64x64_to_128MACH (sig_n_prime, sig_x, mult_factor[exp_x - exp_y]); // return 1 if values are equal if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { res = 1; BID_RETURN (res); } // if postitive, return whichever significand abs is smaller // (converse if negative) { res = (((sig_n_prime.w[1] == 0) && sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) == MASK_SIGN)); BID_RETURN (res); } } // adjust the y significand upwards __mul_64x64_to_128MACH (sig_n_prime, sig_y, mult_factor[exp_y - exp_x]); // return 1 if values are equal if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { res = 1; BID_RETURN (res); } // if positive, return whichever significand abs is smaller // (converse if negative) { res = (((sig_n_prime.w[1] > 0) || (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) == MASK_SIGN)); BID_RETURN (res); } } #if DECIMAL_CALL_BY_REFERENCE void bid64_signaling_not_less (int *pres, UINT64 * px, UINT64 * py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; UINT64 y = *py; #else int bid64_signaling_not_less (UINT64 x, UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; int exp_x, exp_y; UINT64 sig_x, sig_y; UINT128 sig_n_prime; char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y; // NaN (CASE1) // if either number is NAN, the comparison is unordered : return 1 if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) { *pfpsf |= INVALID_EXCEPTION; // set invalid exception if NaN res = 1; BID_RETURN (res); } // SIMPLE (CASE2) // if all the bits are the same, these numbers are equal. if (x == y) { res = 1; BID_RETURN (res); } // INFINITY (CASE3) if ((x & MASK_INF) == MASK_INF) { // if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) } if ((x & MASK_SIGN) == MASK_SIGN) // x is -inf, so it is less than y unless y is -inf { res = (((y & MASK_INF) == MASK_INF) && (y & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } else // x is pos_inf, no way for it to be less than y { res = 1; BID_RETURN (res); } } else if ((y & MASK_INF) == MASK_INF) { // x is finite, so: // if y is +inf, x<y // if y is -inf, x>y { res = ((y & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } } // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; if (sig_x > 9999999999999999ull) { non_canon_x = 1; } else { non_canon_x = 0; } } else { exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; sig_x = (x & MASK_BINARY_SIG1); non_canon_x = 0; } // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; if (sig_y > 9999999999999999ull) { non_canon_y = 1; } else { non_canon_y = 0; } } else { exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; sig_y = (y & MASK_BINARY_SIG1); non_canon_y = 0; } // ZERO (CASE4) // some properties: // (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => // therefore ignore the exponent field // (Any non-canonical # is considered 0) if (non_canon_x || sig_x == 0) { x_is_zero = 1; } if (non_canon_y || sig_y == 0) { y_is_zero = 1; } // if both numbers are zero, they are equal if (x_is_zero && y_is_zero) { res = 1; BID_RETURN (res); } // if x is zero, it is lessthan if Y is positive else if (x_is_zero) { res = ((y & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // if y is zero, X is less if it is negative else if (y_is_zero) { res = ((x & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // OPPOSITE SIGN (CASE5) // now, if the sign bits differ, x is less than if y is positive if (((x ^ y) & MASK_SIGN) == MASK_SIGN) { res = ((y & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // REDUNDANT REPRESENTATIONS (CASE6) // if both components are either bigger or smaller if (sig_x > sig_y && exp_x >= exp_y) { res = ((x & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } if (sig_x < sig_y && exp_x <= exp_y) { res = ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // if exp_x is 15 greater than exp_y, no need for compensation if (exp_x - exp_y > 15) { res = ((x & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // difference cannot be greater than 10^15 // if exp_x is 15 less than exp_y, no need for compensation if (exp_y - exp_x > 15) { res = ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // if |exp_x - exp_y| < 15, it comes down to the compensated significand if (exp_x > exp_y) { // to simplify the loop below, // otherwise adjust the x significand upwards __mul_64x64_to_128MACH (sig_n_prime, sig_x, mult_factor[exp_x - exp_y]); // return 0 if values are equal if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { res = 1; BID_RETURN (res); } // if postitive, return whichever significand abs is smaller // (converse if negative) { res = (((sig_n_prime.w[1] == 0) && sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) != MASK_SIGN)); BID_RETURN (res); } } // adjust the y significand upwards __mul_64x64_to_128MACH (sig_n_prime, sig_y, mult_factor[exp_y - exp_x]); // return 0 if values are equal if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { res = 1; BID_RETURN (res); } // if positive, return whichever significand abs is smaller // (converse if negative) { res = (((sig_n_prime.w[1] > 0) || (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) != MASK_SIGN)); BID_RETURN (res); } }
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