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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" /***************************************************************************** * BID64 minimum function - returns greater of two numbers *****************************************************************************/ 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_minnum (UINT64 * pres, UINT64 * px, UINT64 * py _EXC_FLAGS_PARAM) { UINT64 x = *px; UINT64 y = *py; #else UINT64 bid64_minnum (UINT64 x, UINT64 y _EXC_FLAGS_PARAM) { #endif UINT64 res; int exp_x, exp_y; UINT64 sig_x, sig_y; UINT128 sig_n_prime; char x_is_zero = 0, y_is_zero = 0; // check for non-canonical x if ((x & MASK_NAN) == MASK_NAN) { // x is NaN x = x & 0xfe03ffffffffffffull; // clear G6-G12 if ((x & 0x0003ffffffffffffull) > 999999999999999ull) { x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits } } else if ((x & MASK_INF) == MASK_INF) { // check for Infinity x = x & (MASK_SIGN | MASK_INF); } else { // x is not special // check for non-canonical values - treated as zero if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // if the steering bits are 11, then the exponent is G[0:w+1] if (((x & MASK_BINARY_SIG2) | MASK_BINARY_OR2) > 9999999999999999ull) { // non-canonical x = (x & MASK_SIGN) | ((x & MASK_BINARY_EXPONENT2) << 2); } // else canonical } // else canonical } // check for non-canonical y if ((y & MASK_NAN) == MASK_NAN) { // y is NaN y = y & 0xfe03ffffffffffffull; // clear G6-G12 if ((y & 0x0003ffffffffffffull) > 999999999999999ull) { y = y & 0xfe00000000000000ull; // clear G6-G12 and the payload bits } } else if ((y & MASK_INF) == MASK_INF) { // check for Infinity y = y & (MASK_SIGN | MASK_INF); } else { // y is not special // check for non-canonical values - treated as zero if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // if the steering bits are 11, then the exponent is G[0:w+1] if (((y & MASK_BINARY_SIG2) | MASK_BINARY_OR2) > 9999999999999999ull) { // non-canonical y = (y & MASK_SIGN) | ((y & MASK_BINARY_EXPONENT2) << 2); } // else canonical } // else canonical } // NaN (CASE1) if ((x & MASK_NAN) == MASK_NAN) { // x is NAN if ((x & MASK_SNAN) == MASK_SNAN) { // x is SNaN // if x is SNAN, then return quiet (x) *pfpsf |= INVALID_EXCEPTION; // set exception if SNaN x = x & 0xfdffffffffffffffull; // quietize x res = x; } else { // x is QNaN if ((y & MASK_NAN) == MASK_NAN) { // y is NAN if ((y & MASK_SNAN) == MASK_SNAN) { // y is SNAN *pfpsf |= INVALID_EXCEPTION; // set invalid flag } res = x; } else { res = y; } } BID_RETURN (res); } else if ((y & MASK_NAN) == MASK_NAN) { // y is NaN, but x is not if ((y & MASK_SNAN) == MASK_SNAN) { *pfpsf |= INVALID_EXCEPTION; // set exception if SNaN y = y & 0xfdffffffffffffffull; // quietize y res = y; } else { // will return x (which is not NaN) res = x; } BID_RETURN (res); } // SIMPLE (CASE2) // if all the bits are the same, these numbers are equal, return either number if (x == y) { res = x; 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 x if (((x & MASK_SIGN) == MASK_SIGN)) { res = x; BID_RETURN (res); } // x is pos infinity, return y else { res = y; BID_RETURN (res); } } else if ((y & MASK_INF) == MASK_INF) { // x is finite, so if y is positive infinity, then x is less, return y // if y is negative infinity, then x is greater, return x res = ((y & MASK_SIGN) == MASK_SIGN) ? y : x; 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; } else { exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; sig_x = (x & MASK_BINARY_SIG1); } // 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; } else { exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; sig_y = (y & MASK_BINARY_SIG1); } // 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 => // ignore the exponent field // (Any non-canonical # is considered 0) if (sig_x == 0) { x_is_zero = 1; } if (sig_y == 0) { y_is_zero = 1; } if (x_is_zero && y_is_zero) { // if both numbers are zero, neither is greater => return either res = y; 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) ? y : x; 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) ? y : x;; 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) ? y : x; 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) ? y : x; BID_RETURN (res); } if (sig_x < sig_y && exp_x <= exp_y) { res = ((x & MASK_SIGN) == MASK_SIGN) ? y : x; 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) ? y : x; // difference cannot be >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) ? y : x; 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 = y; BID_RETURN (res); } res = (((sig_n_prime.w[1] > 0) || sig_n_prime.w[0] > sig_y) ^ ((x & MASK_SIGN) == MASK_SIGN)) ? y : x; 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 = y; BID_RETURN (res); } res = (((sig_n_prime.w[1] == 0) && (sig_x > sig_n_prime.w[0])) ^ ((x & MASK_SIGN) == MASK_SIGN)) ? y : x; BID_RETURN (res); } /***************************************************************************** * BID64 minimum magnitude function - returns greater of two numbers *****************************************************************************/ #if DECIMAL_CALL_BY_REFERENCE void bid64_minnum_mag (UINT64 * pres, UINT64 * px, UINT64 * py _EXC_FLAGS_PARAM) { UINT64 x = *px; UINT64 y = *py; #else UINT64 bid64_minnum_mag (UINT64 x, UINT64 y _EXC_FLAGS_PARAM) { #endif UINT64 res; int exp_x, exp_y; UINT64 sig_x, sig_y; UINT128 sig_n_prime; // check for non-canonical x if ((x & MASK_NAN) == MASK_NAN) { // x is NaN x = x & 0xfe03ffffffffffffull; // clear G6-G12 if ((x & 0x0003ffffffffffffull) > 999999999999999ull) { x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits } } else if ((x & MASK_INF) == MASK_INF) { // check for Infinity x = x & (MASK_SIGN | MASK_INF); } else { // x is not special // check for non-canonical values - treated as zero if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // if the steering bits are 11, then the exponent is G[0:w+1] if (((x & MASK_BINARY_SIG2) | MASK_BINARY_OR2) > 9999999999999999ull) { // non-canonical x = (x & MASK_SIGN) | ((x & MASK_BINARY_EXPONENT2) << 2); } // else canonical } // else canonical } // check for non-canonical y if ((y & MASK_NAN) == MASK_NAN) { // y is NaN y = y & 0xfe03ffffffffffffull; // clear G6-G12 if ((y & 0x0003ffffffffffffull) > 999999999999999ull) { y = y & 0xfe00000000000000ull; // clear G6-G12 and the payload bits } } else if ((y & MASK_INF) == MASK_INF) { // check for Infinity y = y & (MASK_SIGN | MASK_INF); } else { // y is not special // check for non-canonical values - treated as zero if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // if the steering bits are 11, then the exponent is G[0:w+1] if (((y & MASK_BINARY_SIG2) | MASK_BINARY_OR2) > 9999999999999999ull) { // non-canonical y = (y & MASK_SIGN) | ((y & MASK_BINARY_EXPONENT2) << 2); } // else canonical } // else canonical } // NaN (CASE1) if ((x & MASK_NAN) == MASK_NAN) { // x is NAN if ((x & MASK_SNAN) == MASK_SNAN) { // x is SNaN // if x is SNAN, then return quiet (x) *pfpsf |= INVALID_EXCEPTION; // set exception if SNaN x = x & 0xfdffffffffffffffull; // quietize x res = x; } else { // x is QNaN if ((y & MASK_NAN) == MASK_NAN) { // y is NAN if ((y & MASK_SNAN) == MASK_SNAN) { // y is SNAN *pfpsf |= INVALID_EXCEPTION; // set invalid flag } res = x; } else { res = y; } } BID_RETURN (res); } else if ((y & MASK_NAN) == MASK_NAN) { // y is NaN, but x is not if ((y & MASK_SNAN) == MASK_SNAN) { *pfpsf |= INVALID_EXCEPTION; // set exception if SNaN y = y & 0xfdffffffffffffffull; // quietize y res = y; } else { // will return x (which is not NaN) res = x; } BID_RETURN (res); } // SIMPLE (CASE2) // if all the bits are the same, these numbers are equal, return either number if (x == y) { res = x; BID_RETURN (res); } // INFINITY (CASE3) if ((x & MASK_INF) == MASK_INF) { // x is infinity, its magnitude is greater than or equal to y // return x only if y is infinity and x is negative res = ((x & MASK_SIGN) == MASK_SIGN && (y & MASK_INF) == MASK_INF) ? x : y; BID_RETURN (res); } else if ((y & MASK_INF) == MASK_INF) { // y is infinity, then it must be greater in magnitude, return x res = x; 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; } else { exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; sig_x = (x & MASK_BINARY_SIG1); } // 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; } else { exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; sig_y = (y & MASK_BINARY_SIG1); } // 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 => // ignore the exponent field // (Any non-canonical # is considered 0) if (sig_x == 0) { res = x; // x_is_zero, its magnitude must be smaller than y BID_RETURN (res); } if (sig_y == 0) { res = y; // y_is_zero, its magnitude must be smaller than x 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 = y; BID_RETURN (res); } if (sig_x < sig_y && exp_x <= exp_y) { res = x; BID_RETURN (res); } // if exp_x is 15 greater than exp_y, no need for compensation if (exp_x - exp_y > 15) { res = y; // 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; 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]); // now, sig_n_prime has: sig_x * 10^(exp_x-exp_y), this is // the compensated signif. if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { // two numbers are equal, return minNum(x,y) res = ((y & MASK_SIGN) == MASK_SIGN) ? y : x; BID_RETURN (res); } // now, if compensated_x (sig_n_prime) is greater than y, return y, // otherwise return x res = ((sig_n_prime.w[1] != 0) || sig_n_prime.w[0] > sig_y) ? y : x; BID_RETURN (res); } // exp_y must be greater than exp_x, thus adjust the y significand upwards __mul_64x64_to_128MACH (sig_n_prime, sig_y, mult_factor[exp_y - exp_x]); if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { res = ((y & MASK_SIGN) == MASK_SIGN) ? y : x; // two numbers are equal, return either BID_RETURN (res); } res = ((sig_n_prime.w[1] == 0) && (sig_x > sig_n_prime.w[0])) ? y : x; BID_RETURN (res); } /***************************************************************************** * BID64 maximum function - returns greater of two numbers *****************************************************************************/ #if DECIMAL_CALL_BY_REFERENCE void bid64_maxnum (UINT64 * pres, UINT64 * px, UINT64 * py _EXC_FLAGS_PARAM) { UINT64 x = *px; UINT64 y = *py; #else UINT64 bid64_maxnum (UINT64 x, UINT64 y _EXC_FLAGS_PARAM) { #endif UINT64 res; int exp_x, exp_y; UINT64 sig_x, sig_y; UINT128 sig_n_prime; char x_is_zero = 0, y_is_zero = 0; // check for non-canonical x if ((x & MASK_NAN) == MASK_NAN) { // x is NaN x = x & 0xfe03ffffffffffffull; // clear G6-G12 if ((x & 0x0003ffffffffffffull) > 999999999999999ull) { x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits } } else if ((x & MASK_INF) == MASK_INF) { // check for Infinity x = x & (MASK_SIGN | MASK_INF); } else { // x is not special // check for non-canonical values - treated as zero if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // if the steering bits are 11, then the exponent is G[0:w+1] if (((x & MASK_BINARY_SIG2) | MASK_BINARY_OR2) > 9999999999999999ull) { // non-canonical x = (x & MASK_SIGN) | ((x & MASK_BINARY_EXPONENT2) << 2); } // else canonical } // else canonical } // check for non-canonical y if ((y & MASK_NAN) == MASK_NAN) { // y is NaN y = y & 0xfe03ffffffffffffull; // clear G6-G12 if ((y & 0x0003ffffffffffffull) > 999999999999999ull) { y = y & 0xfe00000000000000ull; // clear G6-G12 and the payload bits } } else if ((y & MASK_INF) == MASK_INF) { // check for Infinity y = y & (MASK_SIGN | MASK_INF); } else { // y is not special // check for non-canonical values - treated as zero if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // if the steering bits are 11, then the exponent is G[0:w+1] if (((y & MASK_BINARY_SIG2) | MASK_BINARY_OR2) > 9999999999999999ull) { // non-canonical y = (y & MASK_SIGN) | ((y & MASK_BINARY_EXPONENT2) << 2); } // else canonical } // else canonical } // NaN (CASE1) if ((x & MASK_NAN) == MASK_NAN) { // x is NAN if ((x & MASK_SNAN) == MASK_SNAN) { // x is SNaN // if x is SNAN, then return quiet (x) *pfpsf |= INVALID_EXCEPTION; // set exception if SNaN x = x & 0xfdffffffffffffffull; // quietize x res = x; } else { // x is QNaN if ((y & MASK_NAN) == MASK_NAN) { // y is NAN if ((y & MASK_SNAN) == MASK_SNAN) { // y is SNAN *pfpsf |= INVALID_EXCEPTION; // set invalid flag } res = x; } else { res = y; } } BID_RETURN (res); } else if ((y & MASK_NAN) == MASK_NAN) { // y is NaN, but x is not if ((y & MASK_SNAN) == MASK_SNAN) { *pfpsf |= INVALID_EXCEPTION; // set exception if SNaN y = y & 0xfdffffffffffffffull; // quietize y res = y; } else { // will return x (which is not NaN) res = x; } BID_RETURN (res); } // SIMPLE (CASE2) // if all the bits are the same, these numbers are equal (not Greater). if (x == y) { res = x; 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 y // x is pos infinity, it is greater, unless y is positive infinity => // return y!=pos_infinity if (((x & MASK_SIGN) == MASK_SIGN)) { res = y; BID_RETURN (res); } else { res = (((y & MASK_INF) != MASK_INF) || ((y & MASK_SIGN) == MASK_SIGN)) ? x : y; BID_RETURN (res); } } else if ((y & MASK_INF) == MASK_INF) { // x is finite, so if y is positive infinity, then x is less, return y // if y is negative infinity, then x is greater, return x res = ((y & MASK_SIGN) == MASK_SIGN) ? x : y; 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; } else { exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; sig_x = (x & MASK_BINARY_SIG1); } // 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; } else { exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; sig_y = (y & MASK_BINARY_SIG1); } // 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 => // ignore the exponent field // (Any non-canonical # is considered 0) if (sig_x == 0) { x_is_zero = 1; } if (sig_y == 0) { y_is_zero = 1; } if (x_is_zero && y_is_zero) { // if both numbers are zero, neither is greater => return NOTGREATERTHAN res = y; 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) ? x : y; 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) ? x : y;; 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) ? x : y; 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) ? x : y; BID_RETURN (res); } if (sig_x < sig_y && exp_x <= exp_y) { res = ((x & MASK_SIGN) == MASK_SIGN) ? x : y; 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) ? x : y; // difference cannot be > 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) ? x : y; 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 = y; BID_RETURN (res); } res = (((sig_n_prime.w[1] > 0) || sig_n_prime.w[0] > sig_y) ^ ((x & MASK_SIGN) == MASK_SIGN)) ? x : y; 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 = y; BID_RETURN (res); } res = (((sig_n_prime.w[1] == 0) && (sig_x > sig_n_prime.w[0])) ^ ((x & MASK_SIGN) == MASK_SIGN)) ? x : y; BID_RETURN (res); } /***************************************************************************** * BID64 maximum magnitude function - returns greater of two numbers *****************************************************************************/ #if DECIMAL_CALL_BY_REFERENCE void bid64_maxnum_mag (UINT64 * pres, UINT64 * px, UINT64 * py _EXC_FLAGS_PARAM) { UINT64 x = *px; UINT64 y = *py; #else UINT64 bid64_maxnum_mag (UINT64 x, UINT64 y _EXC_FLAGS_PARAM) { #endif UINT64 res; int exp_x, exp_y; UINT64 sig_x, sig_y; UINT128 sig_n_prime; // check for non-canonical x if ((x & MASK_NAN) == MASK_NAN) { // x is NaN x = x & 0xfe03ffffffffffffull; // clear G6-G12 if ((x & 0x0003ffffffffffffull) > 999999999999999ull) { x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits } } else if ((x & MASK_INF) == MASK_INF) { // check for Infinity x = x & (MASK_SIGN | MASK_INF); } else { // x is not special // check for non-canonical values - treated as zero if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // if the steering bits are 11, then the exponent is G[0:w+1] if (((x & MASK_BINARY_SIG2) | MASK_BINARY_OR2) > 9999999999999999ull) { // non-canonical x = (x & MASK_SIGN) | ((x & MASK_BINARY_EXPONENT2) << 2); } // else canonical } // else canonical } // check for non-canonical y if ((y & MASK_NAN) == MASK_NAN) { // y is NaN y = y & 0xfe03ffffffffffffull; // clear G6-G12 if ((y & 0x0003ffffffffffffull) > 999999999999999ull) { y = y & 0xfe00000000000000ull; // clear G6-G12 and the payload bits } } else if ((y & MASK_INF) == MASK_INF) { // check for Infinity y = y & (MASK_SIGN | MASK_INF); } else { // y is not special // check for non-canonical values - treated as zero if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // if the steering bits are 11, then the exponent is G[0:w+1] if (((y & MASK_BINARY_SIG2) | MASK_BINARY_OR2) > 9999999999999999ull) { // non-canonical y = (y & MASK_SIGN) | ((y & MASK_BINARY_EXPONENT2) << 2); } // else canonical } // else canonical } // NaN (CASE1) if ((x & MASK_NAN) == MASK_NAN) { // x is NAN if ((x & MASK_SNAN) == MASK_SNAN) { // x is SNaN // if x is SNAN, then return quiet (x) *pfpsf |= INVALID_EXCEPTION; // set exception if SNaN x = x & 0xfdffffffffffffffull; // quietize x res = x; } else { // x is QNaN if ((y & MASK_NAN) == MASK_NAN) { // y is NAN if ((y & MASK_SNAN) == MASK_SNAN) { // y is SNAN *pfpsf |= INVALID_EXCEPTION; // set invalid flag } res = x; } else { res = y; } } BID_RETURN (res); } else if ((y & MASK_NAN) == MASK_NAN) { // y is NaN, but x is not if ((y & MASK_SNAN) == MASK_SNAN) { *pfpsf |= INVALID_EXCEPTION; // set exception if SNaN y = y & 0xfdffffffffffffffull; // quietize y res = y; } else { // will return x (which is not NaN) res = x; } BID_RETURN (res); } // SIMPLE (CASE2) // if all the bits are the same, these numbers are equal, return either number if (x == y) { res = x; BID_RETURN (res); } // INFINITY (CASE3) if ((x & MASK_INF) == MASK_INF) { // x is infinity, its magnitude is greater than or equal to y // return y as long as x isn't negative infinity res = ((x & MASK_SIGN) == MASK_SIGN && (y & MASK_INF) == MASK_INF) ? y : x; BID_RETURN (res); } else if ((y & MASK_INF) == MASK_INF) { // y is infinity, then it must be greater in magnitude res = y; 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; } else { exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; sig_x = (x & MASK_BINARY_SIG1); } // 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; } else { exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; sig_y = (y & MASK_BINARY_SIG1); } // 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 => // ignore the exponent field // (Any non-canonical # is considered 0) if (sig_x == 0) { res = y; // x_is_zero, its magnitude must be smaller than y BID_RETURN (res); } if (sig_y == 0) { res = x; // y_is_zero, its magnitude must be smaller than x 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; BID_RETURN (res); } if (sig_x < sig_y && exp_x <= exp_y) { res = y; BID_RETURN (res); } // if exp_x is 15 greater than exp_y, no need for compensation if (exp_x - exp_y > 15) { res = x; // 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 = y; 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]); // now, sig_n_prime has: sig_x * 10^(exp_x-exp_y), // this is the compensated signif. if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { // two numbers are equal, return maxNum(x,y) res = ((y & MASK_SIGN) == MASK_SIGN) ? x : y; BID_RETURN (res); } // now, if compensated_x (sig_n_prime) is greater than y return y, // otherwise return x res = ((sig_n_prime.w[1] != 0) || sig_n_prime.w[0] > sig_y) ? x : y; BID_RETURN (res); } // exp_y must be greater than exp_x, thus adjust the y significand upwards __mul_64x64_to_128MACH (sig_n_prime, sig_y, mult_factor[exp_y - exp_x]); if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { res = ((y & MASK_SIGN) == MASK_SIGN) ? x : y; // two numbers are equal, return either BID_RETURN (res); } res = ((sig_n_prime.w[1] == 0) && (sig_x > sig_n_prime.w[0])) ? x : y; BID_RETURN (res); }