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diff --git a/gcc-4.9/libgcc/config/libbid/bid128_noncomp.c b/gcc-4.9/libgcc/config/libbid/bid128_noncomp.c
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+++ b/gcc-4.9/libgcc/config/libbid/bid128_noncomp.c
@@ -0,0 +1,1200 @@
+/* Copyright (C) 2007-2014 Free Software Foundation, Inc.
+
+This file is part of GCC.
+
+GCC is free software; you can redistribute it and/or modify it under
+the terms of the GNU General Public License as published by the Free
+Software Foundation; either version 3, or (at your option) any later
+version.
+
+GCC is distributed in the hope that it will be useful, but WITHOUT ANY
+WARRANTY; without even the implied warranty of MERCHANTABILITY or
+FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
+for more details.
+
+Under Section 7 of GPL version 3, you are granted additional
+permissions described in the GCC Runtime Library Exception, version
+3.1, as published by the Free Software Foundation.
+
+You should have received a copy of the GNU General Public License and
+a copy of the GCC Runtime Library Exception along with this program;
+see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
+<http://www.gnu.org/licenses/>. */
+
+#include "bid_internal.h"
+
+/*****************************************************************************
+ *
+ * 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);
+}
generated by cgit v1.2.3 (git 2.25.1) at 2024-04-19 10:15:21 +0000