0,0 → 1,854 |
/* Copyright (C) 2007-2015 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); |
} |