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[/] [openrisc/] [tags/] [gnu-src/] [gcc-4.5.1/] [gcc-4.5.1-or32-1.0rc1/] [libgcc/] [config/] [libbid/] [bid64_noncomp.c] - Rev 540
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/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. This file is part of GCC. GCC is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3, or (at your option) any later version. GCC is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. Under Section 7 of GPL version 3, you are granted additional permissions described in the GCC Runtime Library Exception, version 3.1, as published by the Free Software Foundation. You should have received a copy of the GNU General Public License and a copy of the GCC Runtime Library Exception along with this program; see the files COPYING3 and COPYING.RUNTIME respectively. If not, see <http://www.gnu.org/licenses/>. */ #include "bid_internal.h" static const UINT64 mult_factor[16] = { 1ull, 10ull, 100ull, 1000ull, 10000ull, 100000ull, 1000000ull, 10000000ull, 100000000ull, 1000000000ull, 10000000000ull, 100000000000ull, 1000000000000ull, 10000000000000ull, 100000000000000ull, 1000000000000000ull }; /***************************************************************************** * BID64 non-computational functions: * - bid64_isSigned * - bid64_isNormal * - bid64_isSubnormal * - bid64_isFinite * - bid64_isZero * - bid64_isInf * - bid64_isSignaling * - bid64_isCanonical * - bid64_isNaN * - bid64_copy * - bid64_negate * - bid64_abs * - bid64_copySign * - bid64_class * - bid64_sameQuantum * - bid64_totalOrder * - bid64_totalOrderMag * - bid64_radix ****************************************************************************/ #if DECIMAL_CALL_BY_REFERENCE void bid64_isSigned (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; #else int bid64_isSigned (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; res = ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // return 1 iff x is not zero, nor NaN nor subnormal nor infinity #if DECIMAL_CALL_BY_REFERENCE void bid64_isNormal (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; #else int bid64_isNormal (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; UINT128 sig_x_prime; UINT64 sig_x; unsigned int exp_x; if ((x & MASK_INF) == MASK_INF) { // x is either INF or NaN res = 0; } else { // decode number into exponent and significand if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; // check for zero or non-canonical if (sig_x > 9999999999999999ull || sig_x == 0) { res = 0; // zero or non-canonical BID_RETURN (res); } exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; } else { sig_x = (x & MASK_BINARY_SIG1); if (sig_x == 0) { res = 0; // zero BID_RETURN (res); } exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; } // if exponent is less than -383, the number may be subnormal // if (exp_x - 398 = -383) the number may be subnormal if (exp_x < 15) { __mul_64x64_to_128MACH (sig_x_prime, sig_x, mult_factor[exp_x]); if (sig_x_prime.w[1] == 0 && sig_x_prime.w[0] < 1000000000000000ull) { res = 0; // subnormal } else { res = 1; // normal } } else { res = 1; // normal } } BID_RETURN (res); } // return 1 iff x is not zero, nor NaN nor normal nor infinity #if DECIMAL_CALL_BY_REFERENCE void bid64_isSubnormal (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; #else int bid64_isSubnormal (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; UINT128 sig_x_prime; UINT64 sig_x; unsigned int exp_x; if ((x & MASK_INF) == MASK_INF) { // x is either INF or NaN res = 0; } else { // decode number into exponent and significand if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; // check for zero or non-canonical if (sig_x > 9999999999999999ull || sig_x == 0) { res = 0; // zero or non-canonical BID_RETURN (res); } exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; } else { sig_x = (x & MASK_BINARY_SIG1); if (sig_x == 0) { res = 0; // zero BID_RETURN (res); } exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; } // if exponent is less than -383, the number may be subnormal // if (exp_x - 398 = -383) the number may be subnormal if (exp_x < 15) { __mul_64x64_to_128MACH (sig_x_prime, sig_x, mult_factor[exp_x]); if (sig_x_prime.w[1] == 0 && sig_x_prime.w[0] < 1000000000000000ull) { res = 1; // subnormal } else { res = 0; // normal } } else { res = 0; // normal } } BID_RETURN (res); } //iff x is zero, subnormal or normal (not infinity or NaN) #if DECIMAL_CALL_BY_REFERENCE void bid64_isFinite (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; #else int bid64_isFinite (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; res = ((x & MASK_INF) != MASK_INF); BID_RETURN (res); } #if DECIMAL_CALL_BY_REFERENCE void bid64_isZero (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; #else int bid64_isZero (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; // if infinity or nan, return 0 if ((x & MASK_INF) == MASK_INF) { res = 0; } else if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] // => sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; // if(sig_x > 9999999999999999ull) {return 1;} res = (((x & MASK_BINARY_SIG2) | MASK_BINARY_OR2) > 9999999999999999ull); } else { res = ((x & MASK_BINARY_SIG1) == 0); } BID_RETURN (res); } #if DECIMAL_CALL_BY_REFERENCE void bid64_isInf (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; #else int bid64_isInf (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; res = ((x & MASK_INF) == MASK_INF) && ((x & MASK_NAN) != MASK_NAN); BID_RETURN (res); } #if DECIMAL_CALL_BY_REFERENCE void bid64_isSignaling (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; #else int bid64_isSignaling (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; res = ((x & MASK_SNAN) == MASK_SNAN); BID_RETURN (res); } #if DECIMAL_CALL_BY_REFERENCE void bid64_isCanonical (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; #else int bid64_isCanonical (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; if ((x & MASK_NAN) == MASK_NAN) { // NaN if (x & 0x01fc000000000000ull) { res = 0; } else if ((x & 0x0003ffffffffffffull) > 999999999999999ull) { // payload res = 0; } else { res = 1; } } else if ((x & MASK_INF) == MASK_INF) { if (x & 0x03ffffffffffffffull) { res = 0; } else { res = 1; } } else if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // 54-bit coeff. res = (((x & MASK_BINARY_SIG2) | MASK_BINARY_OR2) <= 9999999999999999ull); } else { // 53-bit coeff. res = 1; } BID_RETURN (res); } #if DECIMAL_CALL_BY_REFERENCE void bid64_isNaN (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; #else int bid64_isNaN (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; res = ((x & MASK_NAN) == MASK_NAN); BID_RETURN (res); } // copies a floating-point operand x to destination y, with no change #if DECIMAL_CALL_BY_REFERENCE void bid64_copy (UINT64 * pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; #else UINT64 bid64_copy (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif UINT64 res; res = x; BID_RETURN (res); } // copies a floating-point operand x to destination y, reversing the sign #if DECIMAL_CALL_BY_REFERENCE void bid64_negate (UINT64 * pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; #else UINT64 bid64_negate (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif UINT64 res; res = x ^ MASK_SIGN; BID_RETURN (res); } // copies a floating-point operand x to destination y, changing the sign to positive #if DECIMAL_CALL_BY_REFERENCE void bid64_abs (UINT64 * pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; #else UINT64 bid64_abs (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif UINT64 res; res = x & ~MASK_SIGN; BID_RETURN (res); } // copies operand x to destination in the same format as x, but // with the sign of y #if DECIMAL_CALL_BY_REFERENCE void bid64_copySign (UINT64 * pres, UINT64 * px, UINT64 * py _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; UINT64 y = *py; #else UINT64 bid64_copySign (UINT64 x, UINT64 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif UINT64 res; res = (x & ~MASK_SIGN) | (y & MASK_SIGN); BID_RETURN (res); } #if DECIMAL_CALL_BY_REFERENCE void bid64_class (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; #else int bid64_class (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; UINT128 sig_x_prime; UINT64 sig_x; int exp_x; if ((x & MASK_NAN) == MASK_NAN) { // is the NaN signaling? if ((x & MASK_SNAN) == MASK_SNAN) { res = signalingNaN; BID_RETURN (res); } // if NaN and not signaling, must be quietNaN res = quietNaN; BID_RETURN (res); } else if ((x & MASK_INF) == MASK_INF) { // is the Infinity negative? if ((x & MASK_SIGN) == MASK_SIGN) { res = negativeInfinity; } else { // otherwise, must be positive infinity res = positiveInfinity; } BID_RETURN (res); } else if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // decode number into exponent and significand sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; // check for zero or non-canonical if (sig_x > 9999999999999999ull || sig_x == 0) { if ((x & MASK_SIGN) == MASK_SIGN) { res = negativeZero; } else { res = positiveZero; } BID_RETURN (res); } exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; } else { sig_x = (x & MASK_BINARY_SIG1); if (sig_x == 0) { res = ((x & MASK_SIGN) == MASK_SIGN) ? negativeZero : positiveZero; BID_RETURN (res); } exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; } // if exponent is less than -383, number may be subnormal // if (exp_x - 398 < -383) if (exp_x < 15) { // sig_x *10^exp_x __mul_64x64_to_128MACH (sig_x_prime, sig_x, mult_factor[exp_x]); if (sig_x_prime.w[1] == 0 && (sig_x_prime.w[0] < 1000000000000000ull)) { res = ((x & MASK_SIGN) == MASK_SIGN) ? negativeSubnormal : positiveSubnormal; BID_RETURN (res); } } // otherwise, normal number, determine the sign res = ((x & MASK_SIGN) == MASK_SIGN) ? negativeNormal : positiveNormal; BID_RETURN (res); } // true if the exponents of x and y are the same, false otherwise. // The special cases of sameQuantum (NaN, NaN) and sameQuantum (Inf, Inf) are // true. // If exactly one operand is infinite or exactly one operand is NaN, then false #if DECIMAL_CALL_BY_REFERENCE void bid64_sameQuantum (int *pres, UINT64 * px, UINT64 * py _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; UINT64 y = *py; #else int bid64_sameQuantum (UINT64 x, UINT64 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; unsigned int exp_x, exp_y; // if both operands are NaN, return true; if just one is NaN, return false if ((x & MASK_NAN) == MASK_NAN || ((y & MASK_NAN) == MASK_NAN)) { res = ((x & MASK_NAN) == MASK_NAN && (y & MASK_NAN) == MASK_NAN); BID_RETURN (res); } // if both operands are INF, return true; if just one is INF, return false if ((x & MASK_INF) == MASK_INF || (y & MASK_INF) == MASK_INF) { res = ((x & MASK_INF) == MASK_INF && (y & MASK_INF) == MASK_INF); BID_RETURN (res); } // decode exponents for both numbers, and return true if they match if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { exp_x = (x & MASK_BINARY_EXPONENT2) >> 51; } else { exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; } if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) { exp_y = (y & MASK_BINARY_EXPONENT2) >> 51; } else { exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; } res = (exp_x == exp_y); BID_RETURN (res); } #if DECIMAL_CALL_BY_REFERENCE void bid64_totalOrder (int *pres, UINT64 * px, UINT64 * py _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; UINT64 y = *py; #else int bid64_totalOrder (UINT64 x, UINT64 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; int exp_x, exp_y; UINT64 sig_x, sig_y, pyld_y, pyld_x; UINT128 sig_n_prime; char x_is_zero = 0, y_is_zero = 0; // NaN (CASE1) // if x and y are unordered numerically because either operand is NaN // (1) totalOrder(-NaN, number) is true // (2) totalOrder(number, +NaN) is true // (3) if x and y are both NaN: // i) negative sign bit < positive sign bit // ii) signaling < quiet for +NaN, reverse for -NaN // iii) lesser payload < greater payload for +NaN (reverse for -NaN) // iv) else if bitwise identical (in canonical form), return 1 if ((x & MASK_NAN) == MASK_NAN) { // if x is -NaN if ((x & MASK_SIGN) == MASK_SIGN) { // return true, unless y is -NaN also if ((y & MASK_NAN) != MASK_NAN || (y & MASK_SIGN) != MASK_SIGN) { res = 1; // y is a number, return 1 BID_RETURN (res); } else { // if y and x are both -NaN // if x and y are both -sNaN or both -qNaN, we have to compare payloads // this xnor statement evaluates to true if both are sNaN or qNaN if (! (((y & MASK_SNAN) == MASK_SNAN) ^ ((x & MASK_SNAN) == MASK_SNAN))) { // it comes down to the payload. we want to return true if x has a // larger payload, or if the payloads are equal (canonical forms // are bitwise identical) pyld_y = y & 0x0003ffffffffffffull; pyld_x = x & 0x0003ffffffffffffull; if (pyld_y > 999999999999999ull || pyld_y == 0) { // if y is zero, x must be less than or numerically equal // y's payload is 0 res = 1; BID_RETURN (res); } // if x is zero and y isn't, x has the smaller payload // definitely (since we know y isn't 0 at this point) if (pyld_x > 999999999999999ull || pyld_x == 0) { // x's payload is 0 res = 0; BID_RETURN (res); } res = (pyld_x >= pyld_y); BID_RETURN (res); } else { // either x = -sNaN and y = -qNaN or x = -qNaN and y = -sNaN res = (y & MASK_SNAN) == MASK_SNAN; // totalOrder(-qNaN, -sNaN) == 1 BID_RETURN (res); } } } else { // x is +NaN // return false, unless y is +NaN also if ((y & MASK_NAN) != MASK_NAN || (y & MASK_SIGN) == MASK_SIGN) { res = 0; // y is a number, return 1 BID_RETURN (res); } else { // x and y are both +NaN; // must investigate payload if both quiet or both signaling // this xnor statement will be true if both x and y are +qNaN or +sNaN if (! (((y & MASK_SNAN) == MASK_SNAN) ^ ((x & MASK_SNAN) == MASK_SNAN))) { // it comes down to the payload. we want to return true if x has a // smaller payload, or if the payloads are equal (canonical forms // are bitwise identical) pyld_y = y & 0x0003ffffffffffffull; pyld_x = x & 0x0003ffffffffffffull; // if x is zero and y isn't, x has the smaller // payload definitely (since we know y isn't 0 at this point) if (pyld_x > 999999999999999ull || pyld_x == 0) { res = 1; BID_RETURN (res); } if (pyld_y > 999999999999999ull || pyld_y == 0) { // if y is zero, x must be less than or numerically equal res = 0; BID_RETURN (res); } res = (pyld_x <= pyld_y); BID_RETURN (res); } else { // return true if y is +qNaN and x is +sNaN // (we know they're different bc of xor if_stmt above) res = ((x & MASK_SNAN) == MASK_SNAN); BID_RETURN (res); } } } } else if ((y & MASK_NAN) == MASK_NAN) { // x is certainly not NAN in this case. // return true if y is positive res = ((y & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // SIMPLE (CASE2) // if all the bits are the same, these numbers are equal. if (x == y) { res = 1; BID_RETURN (res); } // OPPOSITE SIGNS (CASE 3) // if signs are opposite, return 1 if x is negative // (if x<y, totalOrder is true) if (((x & MASK_SIGN) == MASK_SIGN) ^ ((y & MASK_SIGN) == MASK_SIGN)) { res = (x & MASK_SIGN) == MASK_SIGN; BID_RETURN (res); } // INFINITY (CASE4) if ((x & MASK_INF) == MASK_INF) { // if x==neg_inf, return (y == neg_inf)?1:0; if ((x & MASK_SIGN) == MASK_SIGN) { res = 1; BID_RETURN (res); } else { // x is positive infinity, only return1 if y // is positive infinity as well // (we know y has same sign as x) res = ((y & MASK_INF) == MASK_INF); BID_RETURN (res); } } else if ((y & MASK_INF) == MASK_INF) { // x is finite, so: // if y is +inf, x<y // if y is -inf, x>y res = ((y & MASK_SIGN) != MASK_SIGN); 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; if (sig_x > 9999999999999999ull || sig_x == 0) { x_is_zero = 1; } } else { exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; sig_x = (x & MASK_BINARY_SIG1); if (sig_x == 0) { x_is_zero = 1; } } // 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; if (sig_y > 9999999999999999ull || sig_y == 0) { y_is_zero = 1; } } else { exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; sig_y = (y & MASK_BINARY_SIG1); if (sig_y == 0) { y_is_zero = 1; } } // ZERO (CASE 5) // if x and y represent the same entities, and // both are negative , return true iff exp_x <= exp_y if (x_is_zero && y_is_zero) { if (!((x & MASK_SIGN) == MASK_SIGN) ^ ((y & MASK_SIGN) == MASK_SIGN)) { // if signs are the same: // totalOrder(x,y) iff exp_x >= exp_y for negative numbers // totalOrder(x,y) iff exp_x <= exp_y for positive numbers if (exp_x == exp_y) { res = 1; BID_RETURN (res); } res = (exp_x <= exp_y) ^ ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } else { // signs are different. // totalOrder(-0, +0) is true // totalOrder(+0, -0) is false res = ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } } // if x is zero and y isn't, clearly x has the smaller payload. if (x_is_zero) { res = ((y & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // if y is zero, and x isn't, clearly y has the smaller payload. if (y_is_zero) { res = ((x & MASK_SIGN) == MASK_SIGN); 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); BID_RETURN (res); } if (sig_x < sig_y && exp_x <= exp_y) { res = ((x & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // if exp_x is 15 greater than exp_y, it is // definitely larger, so no need for compensation if (exp_x - exp_y > 15) { // difference cannot be greater than 10^15 res = ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // if exp_x is 15 less than exp_y, it is // definitely smaller, no need for compensation if (exp_y - exp_x > 15) { res = ((x & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // if |exp_x - exp_y| < 15, it comes down // to the compensated significand if (exp_x > exp_y) { // otherwise adjust the x significand upwards __mul_64x64_to_128MACH (sig_n_prime, sig_x, mult_factor[exp_x - exp_y]); // if x and y represent the same entities, // and both are negative, return true iff exp_x <= exp_y if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { // case cannot occure, because all bits must // be the same - would have been caught if (x==y) res = (exp_x <= exp_y) ^ ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // if positive, return 1 if adjusted x is smaller than y res = ((sig_n_prime.w[1] == 0) && sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // adjust the y significand upwards __mul_64x64_to_128MACH (sig_n_prime, sig_y, mult_factor[exp_y - exp_x]); // if x and y represent the same entities, // and both are negative, return true iff exp_x <= exp_y if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { // Cannot occur, because all bits must be the same. // Case would have been caught if (x==y) res = (exp_x <= exp_y) ^ ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // values are not equal, for positive numbers return 1 // if x is less than y. 0 otherwise res = ((sig_n_prime.w[1] > 0) || (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // totalOrderMag is TotalOrder(abs(x), abs(y)) #if DECIMAL_CALL_BY_REFERENCE void bid64_totalOrderMag (int *pres, UINT64 * px, UINT64 * py _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; UINT64 y = *py; #else int bid64_totalOrderMag (UINT64 x, UINT64 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; int exp_x, exp_y; UINT64 sig_x, sig_y, pyld_y, pyld_x; UINT128 sig_n_prime; char x_is_zero = 0, y_is_zero = 0; // NaN (CASE 1) // if x and y are unordered numerically because either operand is NaN // (1) totalOrder(number, +NaN) is true // (2) if x and y are both NaN: // i) signaling < quiet for +NaN // ii) lesser payload < greater payload for +NaN // iii) else if bitwise identical (in canonical form), return 1 if ((x & MASK_NAN) == MASK_NAN) { // x is +NaN // return false, unless y is +NaN also if ((y & MASK_NAN) != MASK_NAN) { res = 0; // y is a number, return 1 BID_RETURN (res); } else { // x and y are both +NaN; // must investigate payload if both quiet or both signaling // this xnor statement will be true if both x and y are +qNaN or +sNaN if (! (((y & MASK_SNAN) == MASK_SNAN) ^ ((x & MASK_SNAN) == MASK_SNAN))) { // it comes down to the payload. we want to return true if x has a // smaller payload, or if the payloads are equal (canonical forms // are bitwise identical) pyld_y = y & 0x0003ffffffffffffull; pyld_x = x & 0x0003ffffffffffffull; // if x is zero and y isn't, x has the smaller // payload definitely (since we know y isn't 0 at this point) if (pyld_x > 999999999999999ull || pyld_x == 0) { res = 1; BID_RETURN (res); } if (pyld_y > 999999999999999ull || pyld_y == 0) { // if y is zero, x must be less than or numerically equal res = 0; BID_RETURN (res); } res = (pyld_x <= pyld_y); BID_RETURN (res); } else { // return true if y is +qNaN and x is +sNaN // (we know they're different bc of xor if_stmt above) res = ((x & MASK_SNAN) == MASK_SNAN); BID_RETURN (res); } } } else if ((y & MASK_NAN) == MASK_NAN) { // x is certainly not NAN in this case. // return true if y is positive res = 1; BID_RETURN (res); } // SIMPLE (CASE2) // if all the bits (except sign bit) are the same, // these numbers are equal. if ((x & ~MASK_SIGN) == (y & ~MASK_SIGN)) { res = 1; BID_RETURN (res); } // INFINITY (CASE3) if ((x & MASK_INF) == MASK_INF) { // x is positive infinity, only return1 // if y is positive infinity as well res = ((y & MASK_INF) == MASK_INF); BID_RETURN (res); } else if ((y & MASK_INF) == MASK_INF) { // x is finite, so: // if y is +inf, x<y res = 1; 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; if (sig_x > 9999999999999999ull || sig_x == 0) { x_is_zero = 1; } } else { exp_x = (x & MASK_BINARY_EXPONENT1) >> 53; sig_x = (x & MASK_BINARY_SIG1); if (sig_x == 0) { x_is_zero = 1; } } // 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; if (sig_y > 9999999999999999ull || sig_y == 0) { y_is_zero = 1; } } else { exp_y = (y & MASK_BINARY_EXPONENT1) >> 53; sig_y = (y & MASK_BINARY_SIG1); if (sig_y == 0) { y_is_zero = 1; } } // ZERO (CASE 5) // if x and y represent the same entities, // and both are negative , return true iff exp_x <= exp_y if (x_is_zero && y_is_zero) { // totalOrder(x,y) iff exp_x <= exp_y for positive numbers res = (exp_x <= exp_y); BID_RETURN (res); } // if x is zero and y isn't, clearly x has the smaller payload. if (x_is_zero) { res = 1; BID_RETURN (res); } // if y is zero, and x isn't, clearly y has the smaller payload. if (y_is_zero) { res = 0; BID_RETURN (res); } // REDUNDANT REPRESENTATIONS (CASE6) // if both components are either bigger or smaller if (sig_x > sig_y && exp_x >= exp_y) { res = 0; BID_RETURN (res); } if (sig_x < sig_y && exp_x <= exp_y) { res = 1; BID_RETURN (res); } // if exp_x is 15 greater than exp_y, it is definitely // larger, so no need for compensation if (exp_x - exp_y > 15) { res = 0; // difference cannot be greater than 10^15 BID_RETURN (res); } // if exp_x is 15 less than exp_y, it is definitely // smaller, no need for compensation if (exp_y - exp_x > 15) { res = 1; BID_RETURN (res); } // if |exp_x - exp_y| < 15, it comes down // to the compensated significand if (exp_x > exp_y) { // otherwise adjust the x significand upwards __mul_64x64_to_128MACH (sig_n_prime, sig_x, mult_factor[exp_x - exp_y]); // if x and y represent the same entities, // and both are negative, return true iff exp_x <= exp_y if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) { // case cannot occur, because all bits // must be the same - would have been caught if (x==y) res = (exp_x <= exp_y); BID_RETURN (res); } // if positive, return 1 if adjusted x is smaller than y res = ((sig_n_prime.w[1] == 0) && sig_n_prime.w[0] < sig_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 x and y represent the same entities, // and both are negative, return true iff exp_x <= exp_y if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) { res = (exp_x <= exp_y); BID_RETURN (res); } // values are not equal, for positive numbers // return 1 if x is less than y. 0 otherwise res = ((sig_n_prime.w[1] > 0) || (sig_x < sig_n_prime.w[0])); BID_RETURN (res); } #if DECIMAL_CALL_BY_REFERENCE void bid64_radix (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; #else int bid64_radix (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; if (x) // dummy test res = 10; else res = 10; BID_RETURN (res); }
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