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[/] [openrisc/] [tags/] [gnu-src/] [gcc-4.5.1/] [gcc-4.5.1-or32-1.0rc4/] [libgcc/] [config/] [libbid/] [bid128_noncomp.c] - Rev 594
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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" /***************************************************************************** * * BID128 non-computational functions: * - bid128_isSigned * - bid128_isNormal * - bid128_isSubnormal * - bid128_isFinite * - bid128_isZero * - bid128_isInf * - bid128_isSignaling * - bid128_isCanonical * - bid128_isNaN * - bid128_copy * - bid128_negate * - bid128_abs * - bid128_copySign * - bid128_class * - bid128_totalOrder * - bid128_totalOrderMag * - bid128_sameQuantum * - bid128_radix ****************************************************************************/ #if DECIMAL_CALL_BY_REFERENCE void bid128_isSigned (int *pres, UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT128 x = *px; #else int bid128_isSigned (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; res = ((x.w[HIGH_128W] & 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 bid128_isNormal (int *pres, UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT128 x = *px; #else int bid128_isNormal (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; UINT64 x_exp, C1_hi, C1_lo; BID_UI64DOUBLE tmp1; int exp, q, x_nr_bits; BID_SWAP128 (x); // test for special values - infinity or NaN if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { // x is special res = 0; BID_RETURN (res); } // unpack x x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions C1_hi = x.w[1] & MASK_COEFF; C1_lo = x.w[0]; // test for zero if (C1_hi == 0 && C1_lo == 0) { res = 0; BID_RETURN (res); } // test for non-canonical values of the argument x if ((((C1_hi > 0x0001ed09bead87c0ull) || ((C1_hi == 0x0001ed09bead87c0ull) && (C1_lo > 0x378d8e63ffffffffull))) && ((x.w[1] & 0x6000000000000000ull) != 0x6000000000000000ull)) || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { res = 0; BID_RETURN (res); } // x is subnormal or normal // determine the number of digits q in the significand // q = nr. of decimal digits in x // determine first the nr. of bits in x if (C1_hi == 0) { if (C1_lo >= 0x0020000000000000ull) { // x >= 2^53 // split the 64-bit value in two 32-bit halves to avoid rounding errors if (C1_lo >= 0x0000000100000000ull) { // x >= 2^32 tmp1.d = (double) (C1_lo >> 32); // exact conversion x_nr_bits = 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); } else { // x < 2^32 tmp1.d = (double) (C1_lo); // exact conversion x_nr_bits = 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); } } else { // if x < 2^53 tmp1.d = (double) C1_lo; // exact conversion x_nr_bits = 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); } } else { // C1_hi != 0 => nr. bits = 64 + nr_bits (C1_hi) tmp1.d = (double) C1_hi; // exact conversion x_nr_bits = 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); } q = nr_digits[x_nr_bits - 1].digits; if (q == 0) { q = nr_digits[x_nr_bits - 1].digits1; if (C1_hi > nr_digits[x_nr_bits - 1].threshold_hi || (C1_hi == nr_digits[x_nr_bits - 1].threshold_hi && C1_lo >= nr_digits[x_nr_bits - 1].threshold_lo)) q++; } exp = (int) (x_exp >> 49) - 6176; // test for subnormal values of x if (exp + q <= -6143) { res = 0; BID_RETURN (res); } else { res = 1; BID_RETURN (res); } } // return 1 iff x is not zero, nor NaN nor normal nor infinity #if DECIMAL_CALL_BY_REFERENCE void bid128_isSubnormal (int *pres, UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT128 x = *px; #else int bid128_isSubnormal (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; UINT64 x_exp, C1_hi, C1_lo; BID_UI64DOUBLE tmp1; int exp, q, x_nr_bits; BID_SWAP128 (x); // test for special values - infinity or NaN if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { // x is special res = 0; BID_RETURN (res); } // unpack x x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions C1_hi = x.w[1] & MASK_COEFF; C1_lo = x.w[0]; // test for zero if (C1_hi == 0 && C1_lo == 0) { res = 0; BID_RETURN (res); } // test for non-canonical values of the argument x if ((((C1_hi > 0x0001ed09bead87c0ull) || ((C1_hi == 0x0001ed09bead87c0ull) && (C1_lo > 0x378d8e63ffffffffull))) && ((x.w[1] & 0x6000000000000000ull) != 0x6000000000000000ull)) || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { res = 0; BID_RETURN (res); } // x is subnormal or normal // determine the number of digits q in the significand // q = nr. of decimal digits in x // determine first the nr. of bits in x if (C1_hi == 0) { if (C1_lo >= 0x0020000000000000ull) { // x >= 2^53 // split the 64-bit value in two 32-bit halves to avoid rounding errors if (C1_lo >= 0x0000000100000000ull) { // x >= 2^32 tmp1.d = (double) (C1_lo >> 32); // exact conversion x_nr_bits = 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); } else { // x < 2^32 tmp1.d = (double) (C1_lo); // exact conversion x_nr_bits = 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); } } else { // if x < 2^53 tmp1.d = (double) C1_lo; // exact conversion x_nr_bits = 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); } } else { // C1_hi != 0 => nr. bits = 64 + nr_bits (C1_hi) tmp1.d = (double) C1_hi; // exact conversion x_nr_bits = 65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); } q = nr_digits[x_nr_bits - 1].digits; if (q == 0) { q = nr_digits[x_nr_bits - 1].digits1; if (C1_hi > nr_digits[x_nr_bits - 1].threshold_hi || (C1_hi == nr_digits[x_nr_bits - 1].threshold_hi && C1_lo >= nr_digits[x_nr_bits - 1].threshold_lo)) q++; } exp = (int) (x_exp >> 49) - 6176; // test for subnormal values of x if (exp + q <= -6143) { res = 1; } else { res = 0; } BID_RETURN (res); } #if DECIMAL_CALL_BY_REFERENCE void bid128_isFinite (int *pres, UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT128 x = *px; #else int bid128_isFinite (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; res = ((x.w[HIGH_128W] & MASK_INF) != MASK_INF); BID_RETURN (res); } #if DECIMAL_CALL_BY_REFERENCE void bid128_isZero (int *pres, UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT128 x = *px; #else int bid128_isZero (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; UINT128 sig_x; BID_SWAP128 (x); if ((x.w[1] & MASK_INF) == MASK_INF) { res = 0; BID_RETURN (res); } sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; sig_x.w[0] = x.w[0]; if ((sig_x.w[1] > 0x0001ed09bead87c0ull) || // significand is non-canonical ((sig_x.w[1] == 0x0001ed09bead87c0ull) && (sig_x.w[0] > 0x378d8e63ffffffffull)) || // significand is non-canonical ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull && (x.w[1] & MASK_INF) != MASK_INF) || // significand is non-canonical (sig_x.w[1] == 0 && sig_x.w[0] == 0)) { // significand is 0 res = 1; BID_RETURN (res); } res = 0; BID_RETURN (res); } #if DECIMAL_CALL_BY_REFERENCE void bid128_isInf (int *pres, UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT128 x = *px; #else int bid128_isInf (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; res = ((x.w[HIGH_128W] & MASK_INF) == MASK_INF) && ((x.w[HIGH_128W] & MASK_NAN) != MASK_NAN); BID_RETURN (res); } #if DECIMAL_CALL_BY_REFERENCE void bid128_isSignaling (int *pres, UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT128 x = *px; #else int bid128_isSignaling (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; res = ((x.w[HIGH_128W] & MASK_SNAN) == MASK_SNAN); BID_RETURN (res); } // return 1 iff x is a canonical number ,infinity, or NaN. #if DECIMAL_CALL_BY_REFERENCE void bid128_isCanonical (int *pres, UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT128 x = *px; #else int bid128_isCanonical (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; UINT128 sig_x; BID_SWAP128 (x); if ((x.w[1] & MASK_NAN) == MASK_NAN) { // NaN if (x.w[1] & 0x01ffc00000000000ull) { res = 0; BID_RETURN (res); } sig_x.w[1] = x.w[1] & 0x00003fffffffffffull; // 46 bits sig_x.w[0] = x.w[0]; // 64 bits // payload must be < 10^33 = 0x0000314dc6448d93_38c15b0a00000000 if (sig_x.w[1] < 0x0000314dc6448d93ull || (sig_x.w[1] == 0x0000314dc6448d93ull && sig_x.w[0] < 0x38c15b0a00000000ull)) { res = 1; } else { res = 0; } BID_RETURN (res); } else if ((x.w[1] & MASK_INF) == MASK_INF) { // infinity if ((x.w[1] & 0x03ffffffffffffffull) || x.w[0]) { res = 0; } else { res = 1; } BID_RETURN (res); } // not NaN or infinity; extract significand to ensure it is canonical sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; sig_x.w[0] = x.w[0]; // a canonical number has a coefficient < 10^34 // (0x0001ed09_bead87c0_378d8e64_00000000) if ((sig_x.w[1] > 0x0001ed09bead87c0ull) || // significand is non-canonical ((sig_x.w[1] == 0x0001ed09bead87c0ull) && (sig_x.w[0] > 0x378d8e63ffffffffull)) || // significand is non-canonical ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { res = 0; } else { res = 1; } BID_RETURN (res); } #if DECIMAL_CALL_BY_REFERENCE void bid128_isNaN (int *pres, UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT128 x = *px; #else int bid128_isNaN (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; res = ((x.w[HIGH_128W] & 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 bid128_copy (UINT128 * pres, UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT128 x = *px; #else UINT128 bid128_copy (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif UINT128 res; res = x; BID_RETURN (res); } // copies a floating-point operand x to destination y, reversing the sign #if DECIMAL_CALL_BY_REFERENCE void bid128_negate (UINT128 * pres, UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT128 x = *px; #else UINT128 bid128_negate (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif UINT128 res; x.w[HIGH_128W] ^= MASK_SIGN; res = x; BID_RETURN (res); } // copies a floating-point operand x to destination y, changing the sign to positive #if DECIMAL_CALL_BY_REFERENCE void bid128_abs (UINT128 * pres, UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT128 x = *px; #else UINT128 bid128_abs (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif UINT128 res; x.w[HIGH_128W] &= ~MASK_SIGN; res = x; 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 bid128_copySign (UINT128 * pres, UINT128 * px, UINT128 * py _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT128 x = *px; UINT128 y = *py; #else UINT128 bid128_copySign (UINT128 x, UINT128 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif UINT128 res; x.w[HIGH_128W] = (x.w[HIGH_128W] & ~MASK_SIGN) | (y.w[HIGH_128W] & MASK_SIGN); res = x; BID_RETURN (res); } #if DECIMAL_CALL_BY_REFERENCE void bid128_class (int *pres, UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT128 x = *px; #else int bid128_class (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; UINT256 sig_x_prime256; UINT192 sig_x_prime192; UINT128 sig_x; int exp_x; BID_SWAP128 (x); if ((x.w[1] & MASK_NAN) == MASK_NAN) { if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { res = signalingNaN; } else { res = quietNaN; } BID_RETURN (res); } if ((x.w[1] & MASK_INF) == MASK_INF) { if ((x.w[1] & MASK_SIGN) == MASK_SIGN) { res = negativeInfinity; } else { res = positiveInfinity; } BID_RETURN (res); } // decode number into exponent and significand sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; sig_x.w[0] = x.w[0]; // check for zero or non-canonical if ((sig_x.w[1] > 0x0001ed09bead87c0ull) || ((sig_x.w[1] == 0x0001ed09bead87c0ull) && (sig_x.w[0] > 0x378d8e63ffffffffull)) || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) { if ((x.w[1] & MASK_SIGN) == MASK_SIGN) { res = negativeZero; } else { res = positiveZero; } BID_RETURN (res); } exp_x = (x.w[1] >> 49) & 0x000000000003fffull; // if exponent is less than -6176, the number may be subnormal // (less than the smallest normal value) // the smallest normal value is 1 x 10^-6143 = 10^33 x 10^-6176 // if (exp_x - 6176 < -6143) if (exp_x < 33) { // sig_x * 10^exp_x if (exp_x > 19) { __mul_128x128_to_256 (sig_x_prime256, sig_x, ten2k128[exp_x - 20]); // 10^33 = 0x0000314dc6448d93_38c15b0a00000000 if ((sig_x_prime256.w[3] == 0) && (sig_x_prime256.w[2] == 0) && ((sig_x_prime256.w[1] < 0x0000314dc6448d93ull) || ((sig_x_prime256.w[1] == 0x0000314dc6448d93ull) && (sig_x_prime256.w[0] < 0x38c15b0a00000000ull)))) { res = ((x.w[1] & MASK_SIGN) == MASK_SIGN) ? negativeSubnormal : positiveSubnormal; BID_RETURN (res); } } else { __mul_64x128_to_192 (sig_x_prime192, ten2k64[exp_x], sig_x); // 10^33 = 0x0000314dc6448d93_38c15b0a00000000 if ((sig_x_prime192.w[2] == 0) && ((sig_x_prime192.w[1] < 0x0000314dc6448d93ull) || ((sig_x_prime192.w[1] == 0x0000314dc6448d93ull) && (sig_x_prime192.w[0] < 0x38c15b0a00000000ull)))) { res = ((x.w[1] & MASK_SIGN) == MASK_SIGN) ? negativeSubnormal : positiveSubnormal; BID_RETURN (res); } } } // otherwise, normal number, determine the sign res = ((x.w[1] & 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 bid128_sameQuantum (int *pres, UINT128 * px, UINT128 * py _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT128 x = *px; UINT128 y = *py; #else int bid128_sameQuantum (UINT128 x, UINT128 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; UINT64 x_exp, y_exp; BID_SWAP128 (x); BID_SWAP128 (y); // if both operands are NaN, return true if ((x.w[1] & MASK_NAN) == MASK_NAN || ((y.w[1] & MASK_NAN) == MASK_NAN)) { res = ((x.w[1] & MASK_NAN) == MASK_NAN && (y.w[1] & MASK_NAN) == MASK_NAN); BID_RETURN (res); } // if both operands are INF, return true if ((x.w[1] & MASK_INF) == MASK_INF || (y.w[1] & MASK_INF) == MASK_INF) { res = ((x.w[1] & MASK_INF) == MASK_INF) && ((y.w[1] & MASK_INF) == MASK_INF); BID_RETURN (res); } // decode exponents for both numbers, and return true if they match if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { // G0_G1=11 x_exp = (x.w[1] << 2) & MASK_EXP; // biased and shifted left 49 bits } else { // G0_G1 != 11 x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bits } if ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { // G0_G1=11 y_exp = (y.w[1] << 2) & MASK_EXP; // biased and shifted left 49 bits } else { // G0_G1 != 11 y_exp = y.w[1] & MASK_EXP; // biased and shifted left 49 bits } res = (x_exp == y_exp); BID_RETURN (res); } #if DECIMAL_CALL_BY_REFERENCE void bid128_totalOrder (int *pres, UINT128 * px, UINT128 * py _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT128 x = *px; UINT128 y = *py; #else int bid128_totalOrder (UINT128 x, UINT128 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; int exp_x, exp_y; UINT128 sig_x, sig_y, pyld_y, pyld_x; UINT192 sig_n_prime192; UINT256 sig_n_prime256; char x_is_zero = 0, y_is_zero = 0; BID_SWAP128 (x); BID_SWAP128 (y); // NaN (CASE 1) // 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.w[1] & MASK_NAN) == MASK_NAN) { // if x is -NaN if ((x.w[1] & MASK_SIGN) == MASK_SIGN) { // return true, unless y is -NaN also if ((y.w[1] & MASK_NAN) != MASK_NAN || (y.w[1] & MASK_SIGN) != MASK_SIGN) { res = 1; // y is a number, return 1 BID_RETURN (res); } else { // if y and x are both -NaN pyld_x.w[1] = x.w[1] & 0x00003fffffffffffull; pyld_x.w[0] = x.w[0]; pyld_y.w[1] = y.w[1] & 0x00003fffffffffffull; pyld_y.w[0] = y.w[0]; if ((pyld_x.w[1] > 0x0000314dc6448d93ull) || ((pyld_x.w[1] == 0x0000314dc6448d93ull) && (pyld_x.w[0] > 0x38c15b09ffffffffull))) { pyld_x.w[1] = 0; pyld_x.w[0] = 0; } if ((pyld_y.w[1] > 0x0000314dc6448d93ull) || ((pyld_y.w[1] == 0x0000314dc6448d93ull) && (pyld_y.w[0] > 0x38c15b09ffffffffull))) { pyld_y.w[1] = 0; pyld_y.w[0] = 0; } // if x and y are both -SNaN or both -QNaN, we have to compare payloads // this statement evaluates to true if both are SNaN or QNaN if (! (((y.w[1] & MASK_SNAN) == MASK_SNAN) ^ ((x.w[1] & 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) if ((pyld_x.w[1] > pyld_y.w[1]) || ((pyld_x.w[1] == pyld_y.w[1]) && (pyld_x.w[0] >= pyld_y.w[0]))) res = 1; else res = 0; BID_RETURN (res); } else { // either x = -SNaN and y = -QNaN or x = -QNaN and y = -SNaN res = ((y.w[1] & MASK_SNAN) == MASK_SNAN); // totalOrder (-QNaN, -SNaN) == 1 BID_RETURN (res); } } } else { // x is +NaN // return false, unless y is +NaN also if ((y.w[1] & MASK_NAN) != MASK_NAN || (y.w[1] & MASK_SIGN) == MASK_SIGN) { res = 0; // y is a number, return 1 BID_RETURN (res); } else { // x and y are both +NaN; pyld_x.w[1] = x.w[1] & 0x00003fffffffffffull; pyld_x.w[0] = x.w[0]; pyld_y.w[1] = y.w[1] & 0x00003fffffffffffull; pyld_y.w[0] = y.w[0]; if ((pyld_x.w[1] > 0x0000314dc6448d93ull) || ((pyld_x.w[1] == 0x0000314dc6448d93ull) && (pyld_x.w[0] > 0x38c15b09ffffffffull))) { pyld_x.w[1] = 0; pyld_x.w[0] = 0; } if ((pyld_y.w[1] > 0x0000314dc6448d93ull) || ((pyld_y.w[1] == 0x0000314dc6448d93ull) && (pyld_y.w[0] > 0x38c15b09ffffffffull))) { pyld_y.w[1] = 0; pyld_y.w[0] = 0; } // if x and y are both +SNaN or both +QNaN, we have to compare payloads // this statement evaluates to true if both are SNaN or QNaN if (! (((y.w[1] & MASK_SNAN) == MASK_SNAN) ^ ((x.w[1] & 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) if ((pyld_x.w[1] < pyld_y.w[1]) || ((pyld_x.w[1] == pyld_y.w[1]) && (pyld_x.w[0] <= pyld_y.w[0]))) res = 1; else res = 0; BID_RETURN (res); } else { // either x = SNaN and y = QNaN or x = QNaN and y = SNaN res = ((x.w[1] & MASK_SNAN) == MASK_SNAN); // totalOrder (-QNaN, -SNaN) == 1 BID_RETURN (res); } } } } else if ((y.w[1] & MASK_NAN) == MASK_NAN) { // x is certainly not NAN in this case. // return true if y is positive res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // SIMPLE (CASE 2) // if all the bits are the same, the numbers are equal. if ((x.w[1] == y.w[1]) && (x.w[0] == y.w[0])) { 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.w[1] & MASK_SIGN) == MASK_SIGN) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN)) { res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // INFINITY (CASE 4) if ((x.w[1] & MASK_INF) == MASK_INF) { // if x == neg_inf, return (y == neg_inf); if ((x.w[1] & MASK_SIGN) == MASK_SIGN) { res = 1; BID_RETURN (res); } else { // x is positive infinity, only return1 if y is positive infinity as well res = ((y.w[1] & MASK_INF) == MASK_INF); BID_RETURN (res); // && (y & MASK_SIGN) != MASK_SIGN); (we know y has same sign as x) } } else if ((y.w[1] & MASK_INF) == MASK_INF) { // x is finite, so: // if y is +inf, x<y // if y is -inf, x>y res = ((y.w[1] & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // CONVERT x sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; sig_x.w[0] = x.w[0]; exp_x = (x.w[1] >> 49) & 0x000000000003fffull; // CHECK IF x IS CANONICAL // 9999999999999999999999999999999999 (decimal) = // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) // [0, 10^34) is the 754r supported canonical range. // If the value exceeds that, it is interpreted as 0. if ((((sig_x.w[1] > 0x0001ed09bead87c0ull) || ((sig_x.w[1] == 0x0001ed09bead87c0ull) && (sig_x.w[0] > 0x378d8e63ffffffffull))) && ((x.w[1] & 0x6000000000000000ull) != 0x6000000000000000ull)) || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) { x_is_zero = 1; // check for the case where the exponent is shifted right by 2 bits! if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { exp_x = (x.w[1] >> 47) & 0x000000000003fffull; } } // CONVERT y exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; sig_y.w[0] = y.w[0]; // CHECK IF y IS CANONICAL // 9999999999999999999999999999999999(decimal) = // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) // [0, 10^34) is the 754r supported canonical range. // If the value exceeds that, it is interpreted as 0. if ((((sig_y.w[1] > 0x0001ed09bead87c0ull) || ((sig_y.w[1] == 0x0001ed09bead87c0ull) && (sig_y.w[0] > 0x378d8e63ffffffffull))) && ((y.w[1] & 0x6000000000000000ull) != 0x6000000000000000ull)) || ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) { y_is_zero = 1; // check for the case where the exponent is shifted right by 2 bits! if ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { exp_y = (y.w[1] >> 47) & 0x000000000003fffull; } } // 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) { // we know that signs must be the same because we would have caught it // in case3 if signs were different // 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.w[1] & 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.w[1] & 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.w[1] & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // REDUNDANT REPRESENTATIONS (CASE 6) // if both components are either bigger or smaller if (((sig_x.w[1] > sig_y.w[1]) || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0])) && exp_x >= exp_y) { res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } if (((sig_x.w[1] < sig_y.w[1]) || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0])) && exp_x <= exp_y) { res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } // if |exp_x - exp_y| < 33, it comes down to the compensated significand if (exp_x > exp_y) { // if exp_x is 33 greater than exp_y, it is definitely larger, // so no need for compensation if (exp_x - exp_y > 33) { res = ((x.w[1] & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); // difference cannot be greater than 10^33 } // otherwise adjust the x significand upwards if (exp_x - exp_y > 19) { __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[exp_x - exp_y - 20]); // the compensated significands are equal (ie "x and y represent the same // entities") return 1 if (negative && expx > expy) || // (positive && expx < expy) if ((sig_n_prime256.w[3] == 0) && (sig_n_prime256.w[2] == 0) && (sig_n_prime256.w[1] == sig_y.w[1]) && (sig_n_prime256.w[0] == sig_y.w[0])) { // the case exp_x == exp_y cannot occur, because all bits must be // the same - would have been caught if (x == y) res = ((exp_x <= exp_y) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN)); BID_RETURN (res); } // if positive, return 1 if adjusted x is smaller than y res = (((sig_n_prime256.w[3] == 0) && (sig_n_prime256.w[2] == 0) && ((sig_n_prime256.w[1] < sig_y.w[1]) || (sig_n_prime256.w[1] == sig_y.w[1] && sig_n_prime256.w[0] < sig_y.w[0]))) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN)); BID_RETURN (res); } __mul_64x128_to_192 (sig_n_prime192, ten2k64[exp_x - exp_y], sig_x); // if positive, return whichever significand is larger // (converse if negative) if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1] && (sig_n_prime192.w[0] == sig_y.w[0])) { res = ((exp_x <= exp_y) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN)); BID_RETURN (res); } res = (((sig_n_prime192.w[2] == 0) && ((sig_n_prime192.w[1] < sig_y.w[1]) || (sig_n_prime192.w[1] == sig_y.w[1] && sig_n_prime192.w[0] < sig_y.w[0]))) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN)); BID_RETURN (res); } // if exp_x is 33 less than exp_y, it is definitely smaller, // no need for compensation if (exp_y - exp_x > 33) { res = ((x.w[1] & MASK_SIGN) != MASK_SIGN); BID_RETURN (res); } if (exp_y - exp_x > 19) { // adjust the y significand upwards __mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[exp_y - exp_x - 20]); // if x and y represent the same entities and both are negative // return true iff exp_x <= exp_y if ((sig_n_prime256.w[3] == 0) && (sig_n_prime256.w[2] == 0) && (sig_n_prime256.w[1] == sig_x.w[1]) && (sig_n_prime256.w[0] == sig_x.w[0])) { res = (exp_x <= exp_y) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } // values are not equal, for positive numbers return 1 if x is less than y // and 0 otherwise res = (((sig_n_prime256.w[3] != 0) || // if upper128 bits of compensated y are non-zero, y is bigger (sig_n_prime256.w[2] != 0) || // if upper128 bits of compensated y are non-zero, y is bigger (sig_n_prime256.w[1] > sig_x.w[1]) || // if compensated y is bigger, y is bigger (sig_n_prime256.w[1] == sig_x.w[1] && sig_n_prime256.w[0] > sig_x.w[0])) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN)); BID_RETURN (res); } __mul_64x128_to_192 (sig_n_prime192, ten2k64[exp_y - exp_x], sig_y); if ((sig_n_prime192.w[2] == 0) && (sig_n_prime192.w[1] == sig_x.w[1]) && (sig_n_prime192.w[0] == sig_x.w[0])) { res = (exp_x <= exp_y) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN); BID_RETURN (res); } res = (((sig_n_prime192.w[2] != 0) || // if upper128 bits of compensated y are non-zero, y is bigger (sig_n_prime192.w[1] > sig_x.w[1]) || // if compensated y is bigger, y is bigger (sig_n_prime192.w[1] == sig_x.w[1] && sig_n_prime192.w[0] > sig_x.w[0])) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN)); BID_RETURN (res); } #if DECIMAL_CALL_BY_REFERENCE void bid128_totalOrderMag (int *pres, UINT128 * px, UINT128 * py _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT128 x = *px; UINT128 y = *py; #else int bid128_totalOrderMag (UINT128 x, UINT128 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; int exp_x, exp_y; UINT128 sig_x, sig_y, pyld_y, pyld_x; UINT192 sig_n_prime192; UINT256 sig_n_prime256; char x_is_zero = 0, y_is_zero = 0; BID_SWAP128 (x); BID_SWAP128 (y); x.w[1] = x.w[1] & 0x7fffffffffffffffull; y.w[1] = y.w[1] & 0x7fffffffffffffffull; // 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.w[1] & MASK_NAN) == MASK_NAN) { // x is +NaN // return false, unless y is +NaN also if ((y.w[1] & MASK_NAN) != MASK_NAN) { res = 0; // y is a number, return 0 BID_RETURN (res); } else { // x and y are both +NaN; pyld_x.w[1] = x.w[1] & 0x00003fffffffffffull; pyld_x.w[0] = x.w[0]; pyld_y.w[1] = y.w[1] & 0x00003fffffffffffull; pyld_y.w[0] = y.w[0]; if ((pyld_x.w[1] > 0x0000314dc6448d93ull) || ((pyld_x.w[1] == 0x0000314dc6448d93ull) && (pyld_x.w[0] > 0x38c15b09ffffffffull))) { pyld_x.w[1] = 0; pyld_x.w[0] = 0; } if ((pyld_y.w[1] > 0x0000314dc6448d93ull) || ((pyld_y.w[1] == 0x0000314dc6448d93ull) && (pyld_y.w[0] > 0x38c15b09ffffffffull))) { pyld_y.w[1] = 0; pyld_y.w[0] = 0; } // if x and y are both +SNaN or both +QNaN, we have to compare payloads // this statement evaluates to true if both are SNaN or QNaN if (! (((y.w[1] & MASK_SNAN) == MASK_SNAN) ^ ((x.w[1] & 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) if ((pyld_x.w[1] < pyld_y.w[1]) || ((pyld_x.w[1] == pyld_y.w[1]) && (pyld_x.w[0] <= pyld_y.w[0]))) { res = 1; } else { res = 0; } BID_RETURN (res); } else { // either x = SNaN and y = QNaN or x = QNaN and y = SNaN res = ((x.w[1] & MASK_SNAN) == MASK_SNAN); // totalOrder (-QNaN, -SNaN) == 1 BID_RETURN (res); } } } else if ((y.w[1] & MASK_NAN) == MASK_NAN) { // x is certainly not NAN in this case. // return true because y is positive res = 1; BID_RETURN (res); } // SIMPLE (CASE 2) // if all the bits are the same, the numbers are equal. if ((x.w[1] == y.w[1]) && (x.w[0] == y.w[0])) { res = 1; BID_RETURN (res); } // INFINITY (CASE 3) if ((x.w[1] & MASK_INF) == MASK_INF) { // x is positive infinity, only return 1 if y is positive infinity as well res = ((y.w[1] & MASK_INF) == MASK_INF); BID_RETURN (res); // (we know y has same sign as x) } else if ((y.w[1] & MASK_INF) == MASK_INF) { // x is finite, so: // since y is +inf, x<y res = 1; BID_RETURN (res); } else { ; // continue } // CONVERT x sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull; sig_x.w[0] = x.w[0]; exp_x = (x.w[1] >> 49) & 0x000000000003fffull; // CHECK IF x IS CANONICAL // 9999999999999999999999999999999999 (decimal) = // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) // [0, 10^34) is the 754r supported canonical range. // If the value exceeds that, it is interpreted as 0. if ((((sig_x.w[1] > 0x0001ed09bead87c0ull) || ((sig_x.w[1] == 0x0001ed09bead87c0ull) && (sig_x.w[0] > 0x378d8e63ffffffffull))) && ((x.w[1] & 0x6000000000000000ull) != 0x6000000000000000ull)) || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) { x_is_zero = 1; // check for the case where the exponent is shifted right by 2 bits! if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { exp_x = (x.w[1] >> 47) & 0x000000000003fffull; } } // CONVERT y exp_y = (y.w[1] >> 49) & 0x0000000000003fffull; sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull; sig_y.w[0] = y.w[0]; // CHECK IF y IS CANONICAL // 9999999999999999999999999999999999(decimal) = // 1ed09_bead87c0_378d8e63_ffffffff(hexadecimal) // [0, 10^34) is the 754r supported canonical range. // If the value exceeds that, it is interpreted as 0. if ((((sig_y.w[1] > 0x0001ed09bead87c0ull) || ((sig_y.w[1] == 0x0001ed09bead87c0ull) && (sig_y.w[0] > 0x378d8e63ffffffffull))) && ((y.w[1] & 0x6000000000000000ull) != 0x6000000000000000ull)) || ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) { y_is_zero = 1; // check for the case where the exponent is shifted right by 2 bits! if ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { exp_y = (y.w[1] >> 47) & 0x000000000003fffull; } } // ZERO (CASE 4) if (x_is_zero && y_is_zero) { // we know that signs must be the same because we would have caught it // in case3 if signs were different // 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); 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 (CASE 5) // if both components are either bigger or smaller if (((sig_x.w[1] > sig_y.w[1]) || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0])) && exp_x >= exp_y) { res = 0; BID_RETURN (res); } if (((sig_x.w[1] < sig_y.w[1]) || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0])) && exp_x <= exp_y) { res = 1; BID_RETURN (res); } // if |exp_x - exp_y| < 33, it comes down to the compensated significand if (exp_x > exp_y) { // if exp_x is 33 greater than exp_y, it is definitely larger, // so no need for compensation if (exp_x - exp_y > 33) { res = 0; // difference cannot be greater than 10^33 BID_RETURN (res); } // otherwise adjust the x significand upwards if (exp_x - exp_y > 19) { __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[exp_x - exp_y - 20]); // the compensated significands are equal (ie "x and y represent the same // entities") return 1 if (negative && expx > expy) || // (positive && expx < expy) if ((sig_n_prime256.w[3] == 0) && (sig_n_prime256.w[2] == 0) && (sig_n_prime256.w[1] == sig_y.w[1]) && (sig_n_prime256.w[0] == sig_y.w[0])) { // the case (exp_x == exp_y) cannot occur, because all bits must be // the same - would have been caught if (x == y) res = (exp_x <= exp_y); BID_RETURN (res); } // since positive, return 1 if adjusted x is smaller than y res = ((sig_n_prime256.w[3] == 0) && (sig_n_prime256.w[2] == 0) && ((sig_n_prime256.w[1] < sig_y.w[1]) || (sig_n_prime256.w[1] == sig_y.w[1] && sig_n_prime256.w[0] < sig_y.w[0]))); BID_RETURN (res); } __mul_64x128_to_192 (sig_n_prime192, ten2k64[exp_x - exp_y], sig_x); // if positive, return whichever significand is larger // (converse if negative) if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1] && (sig_n_prime192.w[0] == sig_y.w[0])) { res = (exp_x <= exp_y); BID_RETURN (res); } res = ((sig_n_prime192.w[2] == 0) && ((sig_n_prime192.w[1] < sig_y.w[1]) || (sig_n_prime192.w[1] == sig_y.w[1] && sig_n_prime192.w[0] < sig_y.w[0]))); BID_RETURN (res); } // if exp_x is 33 less than exp_y, it is definitely smaller, // no need for compensation if (exp_y - exp_x > 33) { res = 1; BID_RETURN (res); } if (exp_y - exp_x > 19) { // adjust the y significand upwards __mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[exp_y - exp_x - 20]); if ((sig_n_prime256.w[3] == 0) && (sig_n_prime256.w[2] == 0) && (sig_n_prime256.w[1] == sig_x.w[1]) && (sig_n_prime256.w[0] == sig_x.w[0])) { res = (exp_x <= exp_y); BID_RETURN (res); } // values are not equal, for positive numbers return 1 if x is less than y // and 0 otherwise res = ((sig_n_prime256.w[3] != 0) || // if upper128 bits of compensated y are non-zero, y is bigger (sig_n_prime256.w[2] != 0) || // if upper128 bits of compensated y are non-zero, y is bigger (sig_n_prime256.w[1] > sig_x.w[1]) || // if compensated y is bigger, y is bigger (sig_n_prime256.w[1] == sig_x.w[1] && sig_n_prime256.w[0] > sig_x.w[0])); BID_RETURN (res); } __mul_64x128_to_192 (sig_n_prime192, ten2k64[exp_y - exp_x], sig_y); if ((sig_n_prime192.w[2] == 0) && (sig_n_prime192.w[1] == sig_x.w[1]) && (sig_n_prime192.w[0] == sig_x.w[0])) { res = (exp_x <= exp_y); BID_RETURN (res); } res = ((sig_n_prime192.w[2] != 0) || // if upper128 bits of compensated y are non-zero, y is bigger (sig_n_prime192.w[1] > sig_x.w[1]) || // if compensated y is bigger, y is bigger (sig_n_prime192.w[1] == sig_x.w[1] && sig_n_prime192.w[0] > sig_x.w[0])); BID_RETURN (res); } #if DECIMAL_CALL_BY_REFERENCE void bid128_radix (int *pres, UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT128 x = *px; #else int bid128_radix (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif int res; if (x.w[LOW_128W]) // dummy test res = 10; else res = 10; BID_RETURN (res); }
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