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/* Copyright (C) 2007-2015 Free Software Foundation, Inc. |
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This file is part of GCC. |
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GCC is free software; you can redistribute it and/or modify it under |
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the terms of the GNU General Public License as published by the Free |
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Software Foundation; either version 3, or (at your option) any later |
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version. |
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GCC is distributed in the hope that it will be useful, but WITHOUT ANY |
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WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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for more details. |
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Under Section 7 of GPL version 3, you are granted additional |
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permissions described in the GCC Runtime Library Exception, version |
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3.1, as published by the Free Software Foundation. |
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You should have received a copy of the GNU General Public License and |
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a copy of the GCC Runtime Library Exception along with this program; |
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see the files COPYING3 and COPYING.RUNTIME respectively. If not, see |
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. */ |
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#include "bid_internal.h" |
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/***************************************************************************** |
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* BID64 minimum function - returns greater of two numbers |
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*****************************************************************************/ |
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static const UINT64 mult_factor[16] = { |
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1ull, 10ull, 100ull, 1000ull, |
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10000ull, 100000ull, 1000000ull, 10000000ull, |
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100000000ull, 1000000000ull, 10000000000ull, 100000000000ull, |
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1000000000000ull, 10000000000000ull, |
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100000000000000ull, 1000000000000000ull |
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}; |
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#if DECIMAL_CALL_BY_REFERENCE |
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void |
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bid64_minnum (UINT64 * pres, UINT64 * px, UINT64 * py _EXC_FLAGS_PARAM) { |
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UINT64 x = *px; |
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UINT64 y = *py; |
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#else |
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UINT64 |
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bid64_minnum (UINT64 x, UINT64 y _EXC_FLAGS_PARAM) { |
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#endif |
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UINT64 res; |
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int exp_x, exp_y; |
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UINT64 sig_x, sig_y; |
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UINT128 sig_n_prime; |
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char x_is_zero = 0, y_is_zero = 0; |
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// check for non-canonical x |
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if ((x & MASK_NAN) == MASK_NAN) { // x is NaN |
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x = x & 0xfe03ffffffffffffull; // clear G6-G12 |
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if ((x & 0x0003ffffffffffffull) > 999999999999999ull) { |
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x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits |
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} |
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} else if ((x & MASK_INF) == MASK_INF) { // check for Infinity |
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x = x & (MASK_SIGN | MASK_INF); |
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} else { // x is not special |
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// check for non-canonical values - treated as zero |
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if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { |
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// if the steering bits are 11, then the exponent is G[0:w+1] |
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if (((x & MASK_BINARY_SIG2) | MASK_BINARY_OR2) > |
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9999999999999999ull) { |
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// non-canonical |
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x = (x & MASK_SIGN) | ((x & MASK_BINARY_EXPONENT2) << 2); |
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} // else canonical |
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} // else canonical |
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} |
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// check for non-canonical y |
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if ((y & MASK_NAN) == MASK_NAN) { // y is NaN |
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y = y & 0xfe03ffffffffffffull; // clear G6-G12 |
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if ((y & 0x0003ffffffffffffull) > 999999999999999ull) { |
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y = y & 0xfe00000000000000ull; // clear G6-G12 and the payload bits |
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} |
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} else if ((y & MASK_INF) == MASK_INF) { // check for Infinity |
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y = y & (MASK_SIGN | MASK_INF); |
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} else { // y is not special |
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// check for non-canonical values - treated as zero |
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if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { |
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// if the steering bits are 11, then the exponent is G[0:w+1] |
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if (((y & MASK_BINARY_SIG2) | MASK_BINARY_OR2) > |
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9999999999999999ull) { |
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// non-canonical |
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y = (y & MASK_SIGN) | ((y & MASK_BINARY_EXPONENT2) << 2); |
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} // else canonical |
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} // else canonical |
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} |
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// NaN (CASE1) |
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if ((x & MASK_NAN) == MASK_NAN) { // x is NAN |
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if ((x & MASK_SNAN) == MASK_SNAN) { // x is SNaN |
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// if x is SNAN, then return quiet (x) |
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*pfpsf |= INVALID_EXCEPTION; // set exception if SNaN |
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x = x & 0xfdffffffffffffffull; // quietize x |
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res = x; |
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} else { // x is QNaN |
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if ((y & MASK_NAN) == MASK_NAN) { // y is NAN |
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if ((y & MASK_SNAN) == MASK_SNAN) { // y is SNAN |
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*pfpsf |= INVALID_EXCEPTION; // set invalid flag |
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} |
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res = x; |
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} else { |
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res = y; |
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} |
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} |
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BID_RETURN (res); |
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} else if ((y & MASK_NAN) == MASK_NAN) { // y is NaN, but x is not |
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if ((y & MASK_SNAN) == MASK_SNAN) { |
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*pfpsf |= INVALID_EXCEPTION; // set exception if SNaN |
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y = y & 0xfdffffffffffffffull; // quietize y |
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res = y; |
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} else { |
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// will return x (which is not NaN) |
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res = x; |
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} |
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BID_RETURN (res); |
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} |
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// SIMPLE (CASE2) |
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// if all the bits are the same, these numbers are equal, return either number |
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if (x == y) { |
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res = x; |
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BID_RETURN (res); |
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} |
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// INFINITY (CASE3) |
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if ((x & MASK_INF) == MASK_INF) { |
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// if x is neg infinity, there is no way it is greater than y, return x |
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if (((x & MASK_SIGN) == MASK_SIGN)) { |
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res = x; |
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BID_RETURN (res); |
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} |
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// x is pos infinity, return y |
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else { |
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res = y; |
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BID_RETURN (res); |
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} |
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} else if ((y & MASK_INF) == MASK_INF) { |
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// x is finite, so if y is positive infinity, then x is less, return y |
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// if y is negative infinity, then x is greater, return x |
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res = ((y & MASK_SIGN) == MASK_SIGN) ? y : x; |
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BID_RETURN (res); |
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} |
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// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => |
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if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { |
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exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; |
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sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; |
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} else { |
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exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; |
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sig_x = (x & MASK_BINARY_SIG1); |
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} |
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// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => |
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if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { |
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exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; |
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sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; |
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} else { |
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exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; |
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sig_y = (y & MASK_BINARY_SIG1); |
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} |
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// ZERO (CASE4) |
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// some properties: |
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// (+ZERO == -ZERO) => therefore |
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// ignore the sign, and neither number is greater |
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// (ZERO x 10^A == ZERO x 10^B) for any valid A, B => |
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// ignore the exponent field |
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// (Any non-canonical # is considered 0) |
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if (sig_x == 0) { |
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x_is_zero = 1; |
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} |
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if (sig_y == 0) { |
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y_is_zero = 1; |
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} |
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if (x_is_zero && y_is_zero) { |
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// if both numbers are zero, neither is greater => return either |
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res = y; |
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BID_RETURN (res); |
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} else if (x_is_zero) { |
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// is x is zero, it is greater if Y is negative |
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res = ((y & MASK_SIGN) == MASK_SIGN) ? y : x; |
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BID_RETURN (res); |
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} else if (y_is_zero) { |
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// is y is zero, X is greater if it is positive |
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res = ((x & MASK_SIGN) != MASK_SIGN) ? y : x;; |
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BID_RETURN (res); |
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} |
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// OPPOSITE SIGN (CASE5) |
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// now, if the sign bits differ, x is greater if y is negative |
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if (((x ^ y) & MASK_SIGN) == MASK_SIGN) { |
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res = ((y & MASK_SIGN) == MASK_SIGN) ? y : x; |
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BID_RETURN (res); |
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} |
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// REDUNDANT REPRESENTATIONS (CASE6) |
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// if both components are either bigger or smaller, |
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// it is clear what needs to be done |
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if (sig_x > sig_y && exp_x >= exp_y) { |
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res = ((x & MASK_SIGN) != MASK_SIGN) ? y : x; |
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BID_RETURN (res); |
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} |
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if (sig_x < sig_y && exp_x <= exp_y) { |
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res = ((x & MASK_SIGN) == MASK_SIGN) ? y : x; |
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BID_RETURN (res); |
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} |
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// if exp_x is 15 greater than exp_y, no need for compensation |
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if (exp_x - exp_y > 15) { |
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res = ((x & MASK_SIGN) != MASK_SIGN) ? y : x; // difference cannot be >10^15 |
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BID_RETURN (res); |
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} |
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// if exp_x is 15 less than exp_y, no need for compensation |
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if (exp_y - exp_x > 15) { |
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res = ((x & MASK_SIGN) == MASK_SIGN) ? y : x; |
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BID_RETURN (res); |
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} |
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// if |exp_x - exp_y| < 15, it comes down to the compensated significand |
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if (exp_x > exp_y) { // to simplify the loop below, |
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// otherwise adjust the x significand upwards |
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__mul_64x64_to_128MACH (sig_n_prime, sig_x, |
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mult_factor[exp_x - exp_y]); |
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// if postitive, return whichever significand is larger |
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// (converse if negative) |
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if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { |
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res = y; |
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BID_RETURN (res); |
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} |
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res = (((sig_n_prime.w[1] > 0) |
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|| sig_n_prime.w[0] > sig_y) ^ ((x & MASK_SIGN) == |
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MASK_SIGN)) ? y : x; |
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BID_RETURN (res); |
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} |
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// adjust the y significand upwards |
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__mul_64x64_to_128MACH (sig_n_prime, sig_y, |
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mult_factor[exp_y - exp_x]); |
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// if postitive, return whichever significand is larger (converse if negative) |
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if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { |
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res = y; |
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BID_RETURN (res); |
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} |
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res = (((sig_n_prime.w[1] == 0) |
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&& (sig_x > sig_n_prime.w[0])) ^ ((x & MASK_SIGN) == |
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MASK_SIGN)) ? y : x; |
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BID_RETURN (res); |
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} |
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/***************************************************************************** |
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* BID64 minimum magnitude function - returns greater of two numbers |
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*****************************************************************************/ |
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#if DECIMAL_CALL_BY_REFERENCE |
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void |
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bid64_minnum_mag (UINT64 * pres, UINT64 * px, |
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UINT64 * py _EXC_FLAGS_PARAM) { |
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UINT64 x = *px; |
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UINT64 y = *py; |
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#else |
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UINT64 |
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bid64_minnum_mag (UINT64 x, UINT64 y _EXC_FLAGS_PARAM) { |
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#endif |
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UINT64 res; |
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int exp_x, exp_y; |
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UINT64 sig_x, sig_y; |
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UINT128 sig_n_prime; |
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// check for non-canonical x |
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if ((x & MASK_NAN) == MASK_NAN) { // x is NaN |
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x = x & 0xfe03ffffffffffffull; // clear G6-G12 |
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if ((x & 0x0003ffffffffffffull) > 999999999999999ull) { |
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x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits |
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} |
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} else if ((x & MASK_INF) == MASK_INF) { // check for Infinity |
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x = x & (MASK_SIGN | MASK_INF); |
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} else { // x is not special |
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// check for non-canonical values - treated as zero |
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if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { |
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// if the steering bits are 11, then the exponent is G[0:w+1] |
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if (((x & MASK_BINARY_SIG2) | MASK_BINARY_OR2) > |
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9999999999999999ull) { |
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// non-canonical |
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x = (x & MASK_SIGN) | ((x & MASK_BINARY_EXPONENT2) << 2); |
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} // else canonical |
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} // else canonical |
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} |
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// check for non-canonical y |
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if ((y & MASK_NAN) == MASK_NAN) { // y is NaN |
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y = y & 0xfe03ffffffffffffull; // clear G6-G12 |
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if ((y & 0x0003ffffffffffffull) > 999999999999999ull) { |
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y = y & 0xfe00000000000000ull; // clear G6-G12 and the payload bits |
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} |
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} else if ((y & MASK_INF) == MASK_INF) { // check for Infinity |
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y = y & (MASK_SIGN | MASK_INF); |
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} else { // y is not special |
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// check for non-canonical values - treated as zero |
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if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { |
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// if the steering bits are 11, then the exponent is G[0:w+1] |
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if (((y & MASK_BINARY_SIG2) | MASK_BINARY_OR2) > |
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9999999999999999ull) { |
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// non-canonical |
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y = (y & MASK_SIGN) | ((y & MASK_BINARY_EXPONENT2) << 2); |
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} // else canonical |
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} // else canonical |
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} |
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312 |
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// NaN (CASE1) |
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if ((x & MASK_NAN) == MASK_NAN) { // x is NAN |
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if ((x & MASK_SNAN) == MASK_SNAN) { // x is SNaN |
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// if x is SNAN, then return quiet (x) |
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*pfpsf |= INVALID_EXCEPTION; // set exception if SNaN |
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x = x & 0xfdffffffffffffffull; // quietize x |
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res = x; |
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} else { // x is QNaN |
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if ((y & MASK_NAN) == MASK_NAN) { // y is NAN |
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if ((y & MASK_SNAN) == MASK_SNAN) { // y is SNAN |
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*pfpsf |= INVALID_EXCEPTION; // set invalid flag |
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} |
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res = x; |
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} else { |
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res = y; |
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} |
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} |
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BID_RETURN (res); |
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} else if ((y & MASK_NAN) == MASK_NAN) { // y is NaN, but x is not |
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if ((y & MASK_SNAN) == MASK_SNAN) { |
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*pfpsf |= INVALID_EXCEPTION; // set exception if SNaN |
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y = y & 0xfdffffffffffffffull; // quietize y |
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res = y; |
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} else { |
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// will return x (which is not NaN) |
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res = x; |
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} |
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BID_RETURN (res); |
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} |
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// SIMPLE (CASE2) |
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343 |
// if all the bits are the same, these numbers are equal, return either number |
|
|
344 |
if (x == y) { |
|
|
345 |
res = x; |
|
|
346 |
BID_RETURN (res); |
|
|
347 |
} |
|
|
348 |
// INFINITY (CASE3) |
|
|
349 |
if ((x & MASK_INF) == MASK_INF) { |
|
|
350 |
// x is infinity, its magnitude is greater than or equal to y |
|
|
351 |
// return x only if y is infinity and x is negative |
|
|
352 |
res = ((x & MASK_SIGN) == MASK_SIGN |
|
|
353 |
&& (y & MASK_INF) == MASK_INF) ? x : y; |
|
|
354 |
BID_RETURN (res); |
|
|
355 |
} else if ((y & MASK_INF) == MASK_INF) { |
|
|
356 |
// y is infinity, then it must be greater in magnitude, return x |
|
|
357 |
res = x; |
|
|
358 |
BID_RETURN (res); |
|
|
359 |
} |
|
|
360 |
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => |
|
|
361 |
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { |
|
|
362 |
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; |
|
|
363 |
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; |
|
|
364 |
} else { |
|
|
365 |
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; |
|
|
366 |
sig_x = (x & MASK_BINARY_SIG1); |
|
|
367 |
} |
|
|
368 |
|
|
|
369 |
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => |
|
|
370 |
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { |
|
|
371 |
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; |
|
|
372 |
sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; |
|
|
373 |
} else { |
|
|
374 |
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; |
|
|
375 |
sig_y = (y & MASK_BINARY_SIG1); |
|
|
376 |
} |
|
|
377 |
|
|
|
378 |
// ZERO (CASE4) |
|
|
379 |
// some properties: |
|
|
380 |
// (+ZERO == -ZERO) => therefore |
|
|
381 |
// ignore the sign, and neither number is greater |
|
|
382 |
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B => |
|
|
383 |
// ignore the exponent field |
|
|
384 |
// (Any non-canonical # is considered 0) |
|
|
385 |
if (sig_x == 0) { |
|
|
386 |
res = x; // x_is_zero, its magnitude must be smaller than y |
|
|
387 |
BID_RETURN (res); |
|
|
388 |
} |
|
|
389 |
if (sig_y == 0) { |
|
|
390 |
res = y; // y_is_zero, its magnitude must be smaller than x |
|
|
391 |
BID_RETURN (res); |
|
|
392 |
} |
|
|
393 |
// REDUNDANT REPRESENTATIONS (CASE6) |
|
|
394 |
// if both components are either bigger or smaller, |
|
|
395 |
// it is clear what needs to be done |
|
|
396 |
if (sig_x > sig_y && exp_x >= exp_y) { |
|
|
397 |
res = y; |
|
|
398 |
BID_RETURN (res); |
|
|
399 |
} |
|
|
400 |
if (sig_x < sig_y && exp_x <= exp_y) { |
|
|
401 |
res = x; |
|
|
402 |
BID_RETURN (res); |
|
|
403 |
} |
|
|
404 |
// if exp_x is 15 greater than exp_y, no need for compensation |
|
|
405 |
if (exp_x - exp_y > 15) { |
|
|
406 |
res = y; // difference cannot be greater than 10^15 |
|
|
407 |
BID_RETURN (res); |
|
|
408 |
} |
|
|
409 |
// if exp_x is 15 less than exp_y, no need for compensation |
|
|
410 |
if (exp_y - exp_x > 15) { |
|
|
411 |
res = x; |
|
|
412 |
BID_RETURN (res); |
|
|
413 |
} |
|
|
414 |
// if |exp_x - exp_y| < 15, it comes down to the compensated significand |
|
|
415 |
if (exp_x > exp_y) { // to simplify the loop below, |
|
|
416 |
// otherwise adjust the x significand upwards |
|
|
417 |
__mul_64x64_to_128MACH (sig_n_prime, sig_x, |
|
|
418 |
mult_factor[exp_x - exp_y]); |
|
|
419 |
// now, sig_n_prime has: sig_x * 10^(exp_x-exp_y), this is |
|
|
420 |
// the compensated signif. |
|
|
421 |
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { |
|
|
422 |
// two numbers are equal, return minNum(x,y) |
|
|
423 |
res = ((y & MASK_SIGN) == MASK_SIGN) ? y : x; |
|
|
424 |
BID_RETURN (res); |
|
|
425 |
} |
|
|
426 |
// now, if compensated_x (sig_n_prime) is greater than y, return y, |
|
|
427 |
// otherwise return x |
|
|
428 |
res = ((sig_n_prime.w[1] != 0) || sig_n_prime.w[0] > sig_y) ? y : x; |
|
|
429 |
BID_RETURN (res); |
|
|
430 |
} |
|
|
431 |
// exp_y must be greater than exp_x, thus adjust the y significand upwards |
|
|
432 |
__mul_64x64_to_128MACH (sig_n_prime, sig_y, |
|
|
433 |
mult_factor[exp_y - exp_x]); |
|
|
434 |
|
|
|
435 |
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { |
|
|
436 |
res = ((y & MASK_SIGN) == MASK_SIGN) ? y : x; |
|
|
437 |
// two numbers are equal, return either |
|
|
438 |
BID_RETURN (res); |
|
|
439 |
} |
|
|
440 |
|
|
|
441 |
res = ((sig_n_prime.w[1] == 0) && (sig_x > sig_n_prime.w[0])) ? y : x; |
|
|
442 |
BID_RETURN (res); |
|
|
443 |
} |
|
|
444 |
|
|
|
445 |
/***************************************************************************** |
|
|
446 |
* BID64 maximum function - returns greater of two numbers |
|
|
447 |
*****************************************************************************/ |
|
|
448 |
|
|
|
449 |
#if DECIMAL_CALL_BY_REFERENCE |
|
|
450 |
void |
|
|
451 |
bid64_maxnum (UINT64 * pres, UINT64 * px, UINT64 * py _EXC_FLAGS_PARAM) { |
|
|
452 |
UINT64 x = *px; |
|
|
453 |
UINT64 y = *py; |
|
|
454 |
#else |
|
|
455 |
UINT64 |
|
|
456 |
bid64_maxnum (UINT64 x, UINT64 y _EXC_FLAGS_PARAM) { |
|
|
457 |
#endif |
|
|
458 |
|
|
|
459 |
UINT64 res; |
|
|
460 |
int exp_x, exp_y; |
|
|
461 |
UINT64 sig_x, sig_y; |
|
|
462 |
UINT128 sig_n_prime; |
|
|
463 |
char x_is_zero = 0, y_is_zero = 0; |
|
|
464 |
|
|
|
465 |
// check for non-canonical x |
|
|
466 |
if ((x & MASK_NAN) == MASK_NAN) { // x is NaN |
|
|
467 |
x = x & 0xfe03ffffffffffffull; // clear G6-G12 |
|
|
468 |
if ((x & 0x0003ffffffffffffull) > 999999999999999ull) { |
|
|
469 |
x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits |
|
|
470 |
} |
|
|
471 |
} else if ((x & MASK_INF) == MASK_INF) { // check for Infinity |
|
|
472 |
x = x & (MASK_SIGN | MASK_INF); |
|
|
473 |
} else { // x is not special |
|
|
474 |
// check for non-canonical values - treated as zero |
|
|
475 |
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { |
|
|
476 |
// if the steering bits are 11, then the exponent is G[0:w+1] |
|
|
477 |
if (((x & MASK_BINARY_SIG2) | MASK_BINARY_OR2) > |
|
|
478 |
9999999999999999ull) { |
|
|
479 |
// non-canonical |
|
|
480 |
x = (x & MASK_SIGN) | ((x & MASK_BINARY_EXPONENT2) << 2); |
|
|
481 |
} // else canonical |
|
|
482 |
} // else canonical |
|
|
483 |
} |
|
|
484 |
|
|
|
485 |
// check for non-canonical y |
|
|
486 |
if ((y & MASK_NAN) == MASK_NAN) { // y is NaN |
|
|
487 |
y = y & 0xfe03ffffffffffffull; // clear G6-G12 |
|
|
488 |
if ((y & 0x0003ffffffffffffull) > 999999999999999ull) { |
|
|
489 |
y = y & 0xfe00000000000000ull; // clear G6-G12 and the payload bits |
|
|
490 |
} |
|
|
491 |
} else if ((y & MASK_INF) == MASK_INF) { // check for Infinity |
|
|
492 |
y = y & (MASK_SIGN | MASK_INF); |
|
|
493 |
} else { // y is not special |
|
|
494 |
// check for non-canonical values - treated as zero |
|
|
495 |
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { |
|
|
496 |
// if the steering bits are 11, then the exponent is G[0:w+1] |
|
|
497 |
if (((y & MASK_BINARY_SIG2) | MASK_BINARY_OR2) > |
|
|
498 |
9999999999999999ull) { |
|
|
499 |
// non-canonical |
|
|
500 |
y = (y & MASK_SIGN) | ((y & MASK_BINARY_EXPONENT2) << 2); |
|
|
501 |
} // else canonical |
|
|
502 |
} // else canonical |
|
|
503 |
} |
|
|
504 |
|
|
|
505 |
// NaN (CASE1) |
|
|
506 |
if ((x & MASK_NAN) == MASK_NAN) { // x is NAN |
|
|
507 |
if ((x & MASK_SNAN) == MASK_SNAN) { // x is SNaN |
|
|
508 |
// if x is SNAN, then return quiet (x) |
|
|
509 |
*pfpsf |= INVALID_EXCEPTION; // set exception if SNaN |
|
|
510 |
x = x & 0xfdffffffffffffffull; // quietize x |
|
|
511 |
res = x; |
|
|
512 |
} else { // x is QNaN |
|
|
513 |
if ((y & MASK_NAN) == MASK_NAN) { // y is NAN |
|
|
514 |
if ((y & MASK_SNAN) == MASK_SNAN) { // y is SNAN |
|
|
515 |
*pfpsf |= INVALID_EXCEPTION; // set invalid flag |
|
|
516 |
} |
|
|
517 |
res = x; |
|
|
518 |
} else { |
|
|
519 |
res = y; |
|
|
520 |
} |
|
|
521 |
} |
|
|
522 |
BID_RETURN (res); |
|
|
523 |
} else if ((y & MASK_NAN) == MASK_NAN) { // y is NaN, but x is not |
|
|
524 |
if ((y & MASK_SNAN) == MASK_SNAN) { |
|
|
525 |
*pfpsf |= INVALID_EXCEPTION; // set exception if SNaN |
|
|
526 |
y = y & 0xfdffffffffffffffull; // quietize y |
|
|
527 |
res = y; |
|
|
528 |
} else { |
|
|
529 |
// will return x (which is not NaN) |
|
|
530 |
res = x; |
|
|
531 |
} |
|
|
532 |
BID_RETURN (res); |
|
|
533 |
} |
|
|
534 |
// SIMPLE (CASE2) |
|
|
535 |
// if all the bits are the same, these numbers are equal (not Greater). |
|
|
536 |
if (x == y) { |
|
|
537 |
res = x; |
|
|
538 |
BID_RETURN (res); |
|
|
539 |
} |
|
|
540 |
// INFINITY (CASE3) |
|
|
541 |
if ((x & MASK_INF) == MASK_INF) { |
|
|
542 |
// if x is neg infinity, there is no way it is greater than y, return y |
|
|
543 |
// x is pos infinity, it is greater, unless y is positive infinity => |
|
|
544 |
// return y!=pos_infinity |
|
|
545 |
if (((x & MASK_SIGN) == MASK_SIGN)) { |
|
|
546 |
res = y; |
|
|
547 |
BID_RETURN (res); |
|
|
548 |
} else { |
|
|
549 |
res = (((y & MASK_INF) != MASK_INF) |
|
|
550 |
|| ((y & MASK_SIGN) == MASK_SIGN)) ? x : y; |
|
|
551 |
BID_RETURN (res); |
|
|
552 |
} |
|
|
553 |
} else if ((y & MASK_INF) == MASK_INF) { |
|
|
554 |
// x is finite, so if y is positive infinity, then x is less, return y |
|
|
555 |
// if y is negative infinity, then x is greater, return x |
|
|
556 |
res = ((y & MASK_SIGN) == MASK_SIGN) ? x : y; |
|
|
557 |
BID_RETURN (res); |
|
|
558 |
} |
|
|
559 |
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => |
|
|
560 |
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { |
|
|
561 |
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; |
|
|
562 |
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; |
|
|
563 |
} else { |
|
|
564 |
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; |
|
|
565 |
sig_x = (x & MASK_BINARY_SIG1); |
|
|
566 |
} |
|
|
567 |
|
|
|
568 |
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => |
|
|
569 |
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { |
|
|
570 |
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; |
|
|
571 |
sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; |
|
|
572 |
} else { |
|
|
573 |
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; |
|
|
574 |
sig_y = (y & MASK_BINARY_SIG1); |
|
|
575 |
} |
|
|
576 |
|
|
|
577 |
// ZERO (CASE4) |
|
|
578 |
// some properties: |
|
|
579 |
// (+ZERO == -ZERO) => therefore |
|
|
580 |
// ignore the sign, and neither number is greater |
|
|
581 |
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B => |
|
|
582 |
// ignore the exponent field |
|
|
583 |
// (Any non-canonical # is considered 0) |
|
|
584 |
if (sig_x == 0) { |
|
|
585 |
x_is_zero = 1; |
|
|
586 |
} |
|
|
587 |
if (sig_y == 0) { |
|
|
588 |
y_is_zero = 1; |
|
|
589 |
} |
|
|
590 |
|
|
|
591 |
if (x_is_zero && y_is_zero) { |
|
|
592 |
// if both numbers are zero, neither is greater => return NOTGREATERTHAN |
|
|
593 |
res = y; |
|
|
594 |
BID_RETURN (res); |
|
|
595 |
} else if (x_is_zero) { |
|
|
596 |
// is x is zero, it is greater if Y is negative |
|
|
597 |
res = ((y & MASK_SIGN) == MASK_SIGN) ? x : y; |
|
|
598 |
BID_RETURN (res); |
|
|
599 |
} else if (y_is_zero) { |
|
|
600 |
// is y is zero, X is greater if it is positive |
|
|
601 |
res = ((x & MASK_SIGN) != MASK_SIGN) ? x : y;; |
|
|
602 |
BID_RETURN (res); |
|
|
603 |
} |
|
|
604 |
// OPPOSITE SIGN (CASE5) |
|
|
605 |
// now, if the sign bits differ, x is greater if y is negative |
|
|
606 |
if (((x ^ y) & MASK_SIGN) == MASK_SIGN) { |
|
|
607 |
res = ((y & MASK_SIGN) == MASK_SIGN) ? x : y; |
|
|
608 |
BID_RETURN (res); |
|
|
609 |
} |
|
|
610 |
// REDUNDANT REPRESENTATIONS (CASE6) |
|
|
611 |
|
|
|
612 |
// if both components are either bigger or smaller, |
|
|
613 |
// it is clear what needs to be done |
|
|
614 |
if (sig_x > sig_y && exp_x >= exp_y) { |
|
|
615 |
res = ((x & MASK_SIGN) != MASK_SIGN) ? x : y; |
|
|
616 |
BID_RETURN (res); |
|
|
617 |
} |
|
|
618 |
if (sig_x < sig_y && exp_x <= exp_y) { |
|
|
619 |
res = ((x & MASK_SIGN) == MASK_SIGN) ? x : y; |
|
|
620 |
BID_RETURN (res); |
|
|
621 |
} |
|
|
622 |
// if exp_x is 15 greater than exp_y, no need for compensation |
|
|
623 |
if (exp_x - exp_y > 15) { |
|
|
624 |
res = ((x & MASK_SIGN) != MASK_SIGN) ? x : y; |
|
|
625 |
// difference cannot be > 10^15 |
|
|
626 |
BID_RETURN (res); |
|
|
627 |
} |
|
|
628 |
// if exp_x is 15 less than exp_y, no need for compensation |
|
|
629 |
if (exp_y - exp_x > 15) { |
|
|
630 |
res = ((x & MASK_SIGN) == MASK_SIGN) ? x : y; |
|
|
631 |
BID_RETURN (res); |
|
|
632 |
} |
|
|
633 |
// if |exp_x - exp_y| < 15, it comes down to the compensated significand |
|
|
634 |
if (exp_x > exp_y) { // to simplify the loop below, |
|
|
635 |
// otherwise adjust the x significand upwards |
|
|
636 |
__mul_64x64_to_128MACH (sig_n_prime, sig_x, |
|
|
637 |
mult_factor[exp_x - exp_y]); |
|
|
638 |
// if postitive, return whichever significand is larger |
|
|
639 |
// (converse if negative) |
|
|
640 |
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { |
|
|
641 |
res = y; |
|
|
642 |
BID_RETURN (res); |
|
|
643 |
} |
|
|
644 |
res = (((sig_n_prime.w[1] > 0) |
|
|
645 |
|| sig_n_prime.w[0] > sig_y) ^ ((x & MASK_SIGN) == |
|
|
646 |
MASK_SIGN)) ? x : y; |
|
|
647 |
BID_RETURN (res); |
|
|
648 |
} |
|
|
649 |
// adjust the y significand upwards |
|
|
650 |
__mul_64x64_to_128MACH (sig_n_prime, sig_y, |
|
|
651 |
mult_factor[exp_y - exp_x]); |
|
|
652 |
|
|
|
653 |
// if postitive, return whichever significand is larger (converse if negative) |
|
|
654 |
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { |
|
|
655 |
res = y; |
|
|
656 |
BID_RETURN (res); |
|
|
657 |
} |
|
|
658 |
res = (((sig_n_prime.w[1] == 0) |
|
|
659 |
&& (sig_x > sig_n_prime.w[0])) ^ ((x & MASK_SIGN) == |
|
|
660 |
MASK_SIGN)) ? x : y; |
|
|
661 |
BID_RETURN (res); |
|
|
662 |
} |
|
|
663 |
|
|
|
664 |
/***************************************************************************** |
|
|
665 |
* BID64 maximum magnitude function - returns greater of two numbers |
|
|
666 |
*****************************************************************************/ |
|
|
667 |
|
|
|
668 |
#if DECIMAL_CALL_BY_REFERENCE |
|
|
669 |
void |
|
|
670 |
bid64_maxnum_mag (UINT64 * pres, UINT64 * px, |
|
|
671 |
UINT64 * py _EXC_FLAGS_PARAM) { |
|
|
672 |
UINT64 x = *px; |
|
|
673 |
UINT64 y = *py; |
|
|
674 |
#else |
|
|
675 |
UINT64 |
|
|
676 |
bid64_maxnum_mag (UINT64 x, UINT64 y _EXC_FLAGS_PARAM) { |
|
|
677 |
#endif |
|
|
678 |
|
|
|
679 |
UINT64 res; |
|
|
680 |
int exp_x, exp_y; |
|
|
681 |
UINT64 sig_x, sig_y; |
|
|
682 |
UINT128 sig_n_prime; |
|
|
683 |
|
|
|
684 |
// check for non-canonical x |
|
|
685 |
if ((x & MASK_NAN) == MASK_NAN) { // x is NaN |
|
|
686 |
x = x & 0xfe03ffffffffffffull; // clear G6-G12 |
|
|
687 |
if ((x & 0x0003ffffffffffffull) > 999999999999999ull) { |
|
|
688 |
x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits |
|
|
689 |
} |
|
|
690 |
} else if ((x & MASK_INF) == MASK_INF) { // check for Infinity |
|
|
691 |
x = x & (MASK_SIGN | MASK_INF); |
|
|
692 |
} else { // x is not special |
|
|
693 |
// check for non-canonical values - treated as zero |
|
|
694 |
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { |
|
|
695 |
// if the steering bits are 11, then the exponent is G[0:w+1] |
|
|
696 |
if (((x & MASK_BINARY_SIG2) | MASK_BINARY_OR2) > |
|
|
697 |
9999999999999999ull) { |
|
|
698 |
// non-canonical |
|
|
699 |
x = (x & MASK_SIGN) | ((x & MASK_BINARY_EXPONENT2) << 2); |
|
|
700 |
} // else canonical |
|
|
701 |
} // else canonical |
|
|
702 |
} |
|
|
703 |
|
|
|
704 |
// check for non-canonical y |
|
|
705 |
if ((y & MASK_NAN) == MASK_NAN) { // y is NaN |
|
|
706 |
y = y & 0xfe03ffffffffffffull; // clear G6-G12 |
|
|
707 |
if ((y & 0x0003ffffffffffffull) > 999999999999999ull) { |
|
|
708 |
y = y & 0xfe00000000000000ull; // clear G6-G12 and the payload bits |
|
|
709 |
} |
|
|
710 |
} else if ((y & MASK_INF) == MASK_INF) { // check for Infinity |
|
|
711 |
y = y & (MASK_SIGN | MASK_INF); |
|
|
712 |
} else { // y is not special |
|
|
713 |
// check for non-canonical values - treated as zero |
|
|
714 |
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { |
|
|
715 |
// if the steering bits are 11, then the exponent is G[0:w+1] |
|
|
716 |
if (((y & MASK_BINARY_SIG2) | MASK_BINARY_OR2) > |
|
|
717 |
9999999999999999ull) { |
|
|
718 |
// non-canonical |
|
|
719 |
y = (y & MASK_SIGN) | ((y & MASK_BINARY_EXPONENT2) << 2); |
|
|
720 |
} // else canonical |
|
|
721 |
} // else canonical |
|
|
722 |
} |
|
|
723 |
|
|
|
724 |
// NaN (CASE1) |
|
|
725 |
if ((x & MASK_NAN) == MASK_NAN) { // x is NAN |
|
|
726 |
if ((x & MASK_SNAN) == MASK_SNAN) { // x is SNaN |
|
|
727 |
// if x is SNAN, then return quiet (x) |
|
|
728 |
*pfpsf |= INVALID_EXCEPTION; // set exception if SNaN |
|
|
729 |
x = x & 0xfdffffffffffffffull; // quietize x |
|
|
730 |
res = x; |
|
|
731 |
} else { // x is QNaN |
|
|
732 |
if ((y & MASK_NAN) == MASK_NAN) { // y is NAN |
|
|
733 |
if ((y & MASK_SNAN) == MASK_SNAN) { // y is SNAN |
|
|
734 |
*pfpsf |= INVALID_EXCEPTION; // set invalid flag |
|
|
735 |
} |
|
|
736 |
res = x; |
|
|
737 |
} else { |
|
|
738 |
res = y; |
|
|
739 |
} |
|
|
740 |
} |
|
|
741 |
BID_RETURN (res); |
|
|
742 |
} else if ((y & MASK_NAN) == MASK_NAN) { // y is NaN, but x is not |
|
|
743 |
if ((y & MASK_SNAN) == MASK_SNAN) { |
|
|
744 |
*pfpsf |= INVALID_EXCEPTION; // set exception if SNaN |
|
|
745 |
y = y & 0xfdffffffffffffffull; // quietize y |
|
|
746 |
res = y; |
|
|
747 |
} else { |
|
|
748 |
// will return x (which is not NaN) |
|
|
749 |
res = x; |
|
|
750 |
} |
|
|
751 |
BID_RETURN (res); |
|
|
752 |
} |
|
|
753 |
// SIMPLE (CASE2) |
|
|
754 |
// if all the bits are the same, these numbers are equal, return either number |
|
|
755 |
if (x == y) { |
|
|
756 |
res = x; |
|
|
757 |
BID_RETURN (res); |
|
|
758 |
} |
|
|
759 |
// INFINITY (CASE3) |
|
|
760 |
if ((x & MASK_INF) == MASK_INF) { |
|
|
761 |
// x is infinity, its magnitude is greater than or equal to y |
|
|
762 |
// return y as long as x isn't negative infinity |
|
|
763 |
res = ((x & MASK_SIGN) == MASK_SIGN |
|
|
764 |
&& (y & MASK_INF) == MASK_INF) ? y : x; |
|
|
765 |
BID_RETURN (res); |
|
|
766 |
} else if ((y & MASK_INF) == MASK_INF) { |
|
|
767 |
// y is infinity, then it must be greater in magnitude |
|
|
768 |
res = y; |
|
|
769 |
BID_RETURN (res); |
|
|
770 |
} |
|
|
771 |
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => |
|
|
772 |
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { |
|
|
773 |
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; |
|
|
774 |
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; |
|
|
775 |
} else { |
|
|
776 |
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; |
|
|
777 |
sig_x = (x & MASK_BINARY_SIG1); |
|
|
778 |
} |
|
|
779 |
|
|
|
780 |
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => |
|
|
781 |
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { |
|
|
782 |
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; |
|
|
783 |
sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2; |
|
|
784 |
} else { |
|
|
785 |
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; |
|
|
786 |
sig_y = (y & MASK_BINARY_SIG1); |
|
|
787 |
} |
|
|
788 |
|
|
|
789 |
// ZERO (CASE4) |
|
|
790 |
// some properties: |
|
|
791 |
// (+ZERO == -ZERO) => therefore |
|
|
792 |
// ignore the sign, and neither number is greater |
|
|
793 |
// (ZERO x 10^A == ZERO x 10^B) for any valid A, B => |
|
|
794 |
// ignore the exponent field |
|
|
795 |
// (Any non-canonical # is considered 0) |
|
|
796 |
if (sig_x == 0) { |
|
|
797 |
res = y; // x_is_zero, its magnitude must be smaller than y |
|
|
798 |
BID_RETURN (res); |
|
|
799 |
} |
|
|
800 |
if (sig_y == 0) { |
|
|
801 |
res = x; // y_is_zero, its magnitude must be smaller than x |
|
|
802 |
BID_RETURN (res); |
|
|
803 |
} |
|
|
804 |
// REDUNDANT REPRESENTATIONS (CASE6) |
|
|
805 |
// if both components are either bigger or smaller, |
|
|
806 |
// it is clear what needs to be done |
|
|
807 |
if (sig_x > sig_y && exp_x >= exp_y) { |
|
|
808 |
res = x; |
|
|
809 |
BID_RETURN (res); |
|
|
810 |
} |
|
|
811 |
if (sig_x < sig_y && exp_x <= exp_y) { |
|
|
812 |
res = y; |
|
|
813 |
BID_RETURN (res); |
|
|
814 |
} |
|
|
815 |
// if exp_x is 15 greater than exp_y, no need for compensation |
|
|
816 |
if (exp_x - exp_y > 15) { |
|
|
817 |
res = x; // difference cannot be greater than 10^15 |
|
|
818 |
BID_RETURN (res); |
|
|
819 |
} |
|
|
820 |
// if exp_x is 15 less than exp_y, no need for compensation |
|
|
821 |
if (exp_y - exp_x > 15) { |
|
|
822 |
res = y; |
|
|
823 |
BID_RETURN (res); |
|
|
824 |
} |
|
|
825 |
// if |exp_x - exp_y| < 15, it comes down to the compensated significand |
|
|
826 |
if (exp_x > exp_y) { // to simplify the loop below, |
|
|
827 |
// otherwise adjust the x significand upwards |
|
|
828 |
__mul_64x64_to_128MACH (sig_n_prime, sig_x, |
|
|
829 |
mult_factor[exp_x - exp_y]); |
|
|
830 |
// now, sig_n_prime has: sig_x * 10^(exp_x-exp_y), |
|
|
831 |
// this is the compensated signif. |
|
|
832 |
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { |
|
|
833 |
// two numbers are equal, return maxNum(x,y) |
|
|
834 |
res = ((y & MASK_SIGN) == MASK_SIGN) ? x : y; |
|
|
835 |
BID_RETURN (res); |
|
|
836 |
} |
|
|
837 |
// now, if compensated_x (sig_n_prime) is greater than y return y, |
|
|
838 |
// otherwise return x |
|
|
839 |
res = ((sig_n_prime.w[1] != 0) || sig_n_prime.w[0] > sig_y) ? x : y; |
|
|
840 |
BID_RETURN (res); |
|
|
841 |
} |
|
|
842 |
// exp_y must be greater than exp_x, thus adjust the y significand upwards |
|
|
843 |
__mul_64x64_to_128MACH (sig_n_prime, sig_y, |
|
|
844 |
mult_factor[exp_y - exp_x]); |
|
|
845 |
|
|
|
846 |
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { |
|
|
847 |
res = ((y & MASK_SIGN) == MASK_SIGN) ? x : y; |
|
|
848 |
// two numbers are equal, return either |
|
|
849 |
BID_RETURN (res); |
|
|
850 |
} |
|
|
851 |
|
|
|
852 |
res = ((sig_n_prime.w[1] == 0) && (sig_x > sig_n_prime.w[0])) ? x : y; |
|
|
853 |
BID_RETURN (res); |
|
|
854 |
} |