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- /* Copyright (C) 2007-2022 Free Software Foundation, Inc.
- This file is part of GCC.
- GCC is free software; you can redistribute it and/or modify it under
- the terms of the GNU General Public License as published by the Free
- Software Foundation; either version 3, or (at your option) any later
- version.
- GCC is distributed in the hope that it will be useful, but WITHOUT ANY
- WARRANTY; without even the implied warranty of MERCHANTABILITY or
- FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
- for more details.
- Under Section 7 of GPL version 3, you are granted additional
- permissions described in the GCC Runtime Library Exception, version
- 3.1, as published by the Free Software Foundation.
- You should have received a copy of the GNU General Public License and
- a copy of the GCC Runtime Library Exception along with this program;
- see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
- <http://www.gnu.org/licenses/>. */
- #include "bid_internal.h"
- /*****************************************************************************
- * 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);
- }
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