diff options
Diffstat (limited to 'gcc-4.9/libgcc/config/libbid/bid64_minmax.c')
| -rw-r--r-- | gcc-4.9/libgcc/config/libbid/bid64_minmax.c | 854 |
1 files changed, 854 insertions, 0 deletions
diff --git a/gcc-4.9/libgcc/config/libbid/bid64_minmax.c b/gcc-4.9/libgcc/config/libbid/bid64_minmax.c new file mode 100644 index 000000000..e54946b18 --- /dev/null +++ b/gcc-4.9/libgcc/config/libbid/bid64_minmax.c @@ -0,0 +1,854 @@ +/* Copyright (C) 2007-2014 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); +} |