1201 lines
38 KiB
C
1201 lines
38 KiB
C
/* 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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<http://www.gnu.org/licenses/>. */
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#include "bid_internal.h"
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/*****************************************************************************
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*
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* BID128 non-computational functions:
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* - bid128_isSigned
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* - bid128_isNormal
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* - bid128_isSubnormal
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* - bid128_isFinite
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* - bid128_isZero
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* - bid128_isInf
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* - bid128_isSignaling
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* - bid128_isCanonical
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* - bid128_isNaN
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* - bid128_copy
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* - bid128_negate
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* - bid128_abs
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* - bid128_copySign
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* - bid128_class
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* - bid128_totalOrder
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* - bid128_totalOrderMag
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* - bid128_sameQuantum
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* - bid128_radix
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****************************************************************************/
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#if DECIMAL_CALL_BY_REFERENCE
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void
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bid128_isSigned (int *pres,
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UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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UINT128 x = *px;
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#else
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int
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bid128_isSigned (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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#endif
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int res;
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res = ((x.w[HIGH_128W] & MASK_SIGN) == MASK_SIGN);
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BID_RETURN (res);
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}
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// return 1 iff x is not zero, nor NaN nor subnormal nor infinity
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#if DECIMAL_CALL_BY_REFERENCE
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void
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bid128_isNormal (int *pres,
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UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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UINT128 x = *px;
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#else
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int
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bid128_isNormal (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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#endif
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int res;
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UINT64 x_exp, C1_hi, C1_lo;
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BID_UI64DOUBLE tmp1;
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int exp, q, x_nr_bits;
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BID_SWAP128 (x);
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// test for special values - infinity or NaN
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if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
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// x is special
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res = 0;
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BID_RETURN (res);
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}
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// unpack x
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x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions
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C1_hi = x.w[1] & MASK_COEFF;
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C1_lo = x.w[0];
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// test for zero
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if (C1_hi == 0 && C1_lo == 0) {
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res = 0;
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BID_RETURN (res);
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}
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// test for non-canonical values of the argument x
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if ((((C1_hi > 0x0001ed09bead87c0ull)
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|| ((C1_hi == 0x0001ed09bead87c0ull)
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&& (C1_lo > 0x378d8e63ffffffffull)))
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&& ((x.w[1] & 0x6000000000000000ull) != 0x6000000000000000ull))
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|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
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res = 0;
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BID_RETURN (res);
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}
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// x is subnormal or normal
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// determine the number of digits q in the significand
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// q = nr. of decimal digits in x
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// determine first the nr. of bits in x
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if (C1_hi == 0) {
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if (C1_lo >= 0x0020000000000000ull) { // x >= 2^53
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// split the 64-bit value in two 32-bit halves to avoid rounding errors
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if (C1_lo >= 0x0000000100000000ull) { // x >= 2^32
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tmp1.d = (double) (C1_lo >> 32); // exact conversion
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x_nr_bits =
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33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
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} else { // x < 2^32
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tmp1.d = (double) (C1_lo); // exact conversion
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x_nr_bits =
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1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
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}
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} else { // if x < 2^53
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tmp1.d = (double) C1_lo; // exact conversion
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x_nr_bits =
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1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
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}
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} else { // C1_hi != 0 => nr. bits = 64 + nr_bits (C1_hi)
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tmp1.d = (double) C1_hi; // exact conversion
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x_nr_bits =
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65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
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}
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q = nr_digits[x_nr_bits - 1].digits;
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if (q == 0) {
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q = nr_digits[x_nr_bits - 1].digits1;
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if (C1_hi > nr_digits[x_nr_bits - 1].threshold_hi ||
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(C1_hi == nr_digits[x_nr_bits - 1].threshold_hi &&
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C1_lo >= nr_digits[x_nr_bits - 1].threshold_lo))
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q++;
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}
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exp = (int) (x_exp >> 49) - 6176;
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// test for subnormal values of x
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if (exp + q <= -6143) {
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res = 0;
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BID_RETURN (res);
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} else {
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res = 1;
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BID_RETURN (res);
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}
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}
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// return 1 iff x is not zero, nor NaN nor normal nor infinity
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#if DECIMAL_CALL_BY_REFERENCE
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void
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bid128_isSubnormal (int *pres,
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UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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UINT128 x = *px;
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#else
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int
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bid128_isSubnormal (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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#endif
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int res;
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UINT64 x_exp, C1_hi, C1_lo;
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BID_UI64DOUBLE tmp1;
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int exp, q, x_nr_bits;
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BID_SWAP128 (x);
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// test for special values - infinity or NaN
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if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
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// x is special
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res = 0;
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BID_RETURN (res);
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}
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// unpack x
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x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions
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C1_hi = x.w[1] & MASK_COEFF;
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C1_lo = x.w[0];
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// test for zero
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if (C1_hi == 0 && C1_lo == 0) {
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res = 0;
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BID_RETURN (res);
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}
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// test for non-canonical values of the argument x
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if ((((C1_hi > 0x0001ed09bead87c0ull)
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|| ((C1_hi == 0x0001ed09bead87c0ull)
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&& (C1_lo > 0x378d8e63ffffffffull)))
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&& ((x.w[1] & 0x6000000000000000ull) != 0x6000000000000000ull))
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|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
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res = 0;
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BID_RETURN (res);
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}
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// x is subnormal or normal
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// determine the number of digits q in the significand
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// q = nr. of decimal digits in x
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// determine first the nr. of bits in x
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if (C1_hi == 0) {
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if (C1_lo >= 0x0020000000000000ull) { // x >= 2^53
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// split the 64-bit value in two 32-bit halves to avoid rounding errors
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if (C1_lo >= 0x0000000100000000ull) { // x >= 2^32
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tmp1.d = (double) (C1_lo >> 32); // exact conversion
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x_nr_bits =
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33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
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} else { // x < 2^32
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tmp1.d = (double) (C1_lo); // exact conversion
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x_nr_bits =
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1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
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}
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} else { // if x < 2^53
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tmp1.d = (double) C1_lo; // exact conversion
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x_nr_bits =
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1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
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}
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} else { // C1_hi != 0 => nr. bits = 64 + nr_bits (C1_hi)
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tmp1.d = (double) C1_hi; // exact conversion
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x_nr_bits =
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65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
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}
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q = nr_digits[x_nr_bits - 1].digits;
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if (q == 0) {
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q = nr_digits[x_nr_bits - 1].digits1;
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if (C1_hi > nr_digits[x_nr_bits - 1].threshold_hi ||
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(C1_hi == nr_digits[x_nr_bits - 1].threshold_hi &&
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C1_lo >= nr_digits[x_nr_bits - 1].threshold_lo))
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q++;
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}
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exp = (int) (x_exp >> 49) - 6176;
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// test for subnormal values of x
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if (exp + q <= -6143) {
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res = 1;
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} else {
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res = 0;
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}
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BID_RETURN (res);
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}
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#if DECIMAL_CALL_BY_REFERENCE
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void
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bid128_isFinite (int *pres,
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UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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UINT128 x = *px;
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#else
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int
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bid128_isFinite (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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#endif
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int res;
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res = ((x.w[HIGH_128W] & MASK_INF) != MASK_INF);
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BID_RETURN (res);
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}
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#if DECIMAL_CALL_BY_REFERENCE
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void
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bid128_isZero (int *pres, UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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UINT128 x = *px;
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#else
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int
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bid128_isZero (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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#endif
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int res;
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UINT128 sig_x;
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BID_SWAP128 (x);
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if ((x.w[1] & MASK_INF) == MASK_INF) {
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res = 0;
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BID_RETURN (res);
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}
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sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
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sig_x.w[0] = x.w[0];
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if ((sig_x.w[1] > 0x0001ed09bead87c0ull) || // significand is non-canonical
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((sig_x.w[1] == 0x0001ed09bead87c0ull) && (sig_x.w[0] > 0x378d8e63ffffffffull)) || // significand is non-canonical
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((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull && (x.w[1] & MASK_INF) != MASK_INF) || // significand is non-canonical
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(sig_x.w[1] == 0 && sig_x.w[0] == 0)) { // significand is 0
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res = 1;
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BID_RETURN (res);
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}
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res = 0;
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BID_RETURN (res);
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}
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#if DECIMAL_CALL_BY_REFERENCE
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void
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bid128_isInf (int *pres, UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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UINT128 x = *px;
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#else
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int
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bid128_isInf (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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#endif
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int res;
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res = ((x.w[HIGH_128W] & MASK_INF) == MASK_INF)
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&& ((x.w[HIGH_128W] & MASK_NAN) != MASK_NAN);
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BID_RETURN (res);
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}
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#if DECIMAL_CALL_BY_REFERENCE
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void
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bid128_isSignaling (int *pres,
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UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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UINT128 x = *px;
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#else
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int
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bid128_isSignaling (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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#endif
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int res;
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res = ((x.w[HIGH_128W] & MASK_SNAN) == MASK_SNAN);
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BID_RETURN (res);
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}
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// return 1 iff x is a canonical number ,infinity, or NaN.
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#if DECIMAL_CALL_BY_REFERENCE
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void
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bid128_isCanonical (int *pres,
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UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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UINT128 x = *px;
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#else
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int
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bid128_isCanonical (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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#endif
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int res;
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UINT128 sig_x;
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BID_SWAP128 (x);
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if ((x.w[1] & MASK_NAN) == MASK_NAN) { // NaN
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if (x.w[1] & 0x01ffc00000000000ull) {
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res = 0;
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BID_RETURN (res);
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}
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sig_x.w[1] = x.w[1] & 0x00003fffffffffffull; // 46 bits
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sig_x.w[0] = x.w[0]; // 64 bits
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// payload must be < 10^33 = 0x0000314dc6448d93_38c15b0a00000000
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if (sig_x.w[1] < 0x0000314dc6448d93ull
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|| (sig_x.w[1] == 0x0000314dc6448d93ull
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&& sig_x.w[0] < 0x38c15b0a00000000ull)) {
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res = 1;
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} else {
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res = 0;
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}
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BID_RETURN (res);
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} else if ((x.w[1] & MASK_INF) == MASK_INF) { // infinity
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if ((x.w[1] & 0x03ffffffffffffffull) || x.w[0]) {
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res = 0;
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} else {
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res = 1;
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}
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BID_RETURN (res);
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}
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// not NaN or infinity; extract significand to ensure it is canonical
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sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
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sig_x.w[0] = x.w[0];
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// a canonical number has a coefficient < 10^34
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// (0x0001ed09_bead87c0_378d8e64_00000000)
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if ((sig_x.w[1] > 0x0001ed09bead87c0ull) || // significand is non-canonical
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((sig_x.w[1] == 0x0001ed09bead87c0ull) && (sig_x.w[0] > 0x378d8e63ffffffffull)) || // significand is non-canonical
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((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
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res = 0;
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} else {
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res = 1;
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}
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BID_RETURN (res);
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}
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#if DECIMAL_CALL_BY_REFERENCE
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void
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bid128_isNaN (int *pres, UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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UINT128 x = *px;
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#else
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int
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bid128_isNaN (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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#endif
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int res;
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res = ((x.w[HIGH_128W] & MASK_NAN) == MASK_NAN);
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BID_RETURN (res);
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}
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// copies a floating-point operand x to destination y, with no change
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#if DECIMAL_CALL_BY_REFERENCE
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void
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bid128_copy (UINT128 * pres,
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UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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UINT128 x = *px;
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#else
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UINT128
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bid128_copy (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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#endif
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UINT128 res;
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res = x;
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BID_RETURN (res);
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}
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// copies a floating-point operand x to destination y, reversing the sign
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#if DECIMAL_CALL_BY_REFERENCE
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void
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bid128_negate (UINT128 * pres,
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UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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UINT128 x = *px;
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#else
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UINT128
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bid128_negate (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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#endif
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UINT128 res;
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x.w[HIGH_128W] ^= MASK_SIGN;
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res = x;
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BID_RETURN (res);
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}
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// copies a floating-point operand x to destination y, changing the sign to positive
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#if DECIMAL_CALL_BY_REFERENCE
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void
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bid128_abs (UINT128 * pres,
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UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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UINT128 x = *px;
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#else
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UINT128
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bid128_abs (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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#endif
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UINT128 res;
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x.w[HIGH_128W] &= ~MASK_SIGN;
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res = x;
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BID_RETURN (res);
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}
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// copies operand x to destination in the same format as x, but with the sign of y
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#if DECIMAL_CALL_BY_REFERENCE
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void
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bid128_copySign (UINT128 * pres, UINT128 * px,
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UINT128 * py _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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UINT128 x = *px;
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UINT128 y = *py;
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#else
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UINT128
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bid128_copySign (UINT128 x, UINT128 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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#endif
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UINT128 res;
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x.w[HIGH_128W] =
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(x.w[HIGH_128W] & ~MASK_SIGN) | (y.w[HIGH_128W] & MASK_SIGN);
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res = x;
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BID_RETURN (res);
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}
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#if DECIMAL_CALL_BY_REFERENCE
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void
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bid128_class (int *pres, UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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UINT128 x = *px;
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#else
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int
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bid128_class (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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#endif
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int res;
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UINT256 sig_x_prime256;
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UINT192 sig_x_prime192;
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UINT128 sig_x;
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int exp_x;
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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);
|
|
}
|