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/* Copyright (C) 2007-2016 Free Software Foundation, Inc.
This file is part of GCC.
GCC is free software; you can redistribute it and/or modify it under
the terms of the GNU General Public License as published by the Free
Software Foundation; either version 3, or (at your option) any later
version.
GCC is distributed in the hope that it will be useful, but WITHOUT ANY
WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
for more details.
Under Section 7 of GPL version 3, you are granted additional
permissions described in the GCC Runtime Library Exception, version
3.1, as published by the Free Software Foundation.
You should have received a copy of the GNU General Public License and
a copy of the GCC Runtime Library Exception along with this program;
see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
<http://www.gnu.org/licenses/>. */
#include "bid_internal.h"
static const UINT64 mult_factor[16] = {
1ull, 10ull, 100ull, 1000ull,
10000ull, 100000ull, 1000000ull, 10000000ull,
100000000ull, 1000000000ull, 10000000000ull, 100000000000ull,
1000000000000ull, 10000000000000ull,
100000000000000ull, 1000000000000000ull
};
/*****************************************************************************
* BID64 non-computational functions:
* - bid64_isSigned
* - bid64_isNormal
* - bid64_isSubnormal
* - bid64_isFinite
* - bid64_isZero
* - bid64_isInf
* - bid64_isSignaling
* - bid64_isCanonical
* - bid64_isNaN
* - bid64_copy
* - bid64_negate
* - bid64_abs
* - bid64_copySign
* - bid64_class
* - bid64_sameQuantum
* - bid64_totalOrder
* - bid64_totalOrderMag
* - bid64_radix
****************************************************************************/
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_isSigned (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
UINT64 x = *px;
#else
int
bid64_isSigned (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
int res;
res = ((x & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// return 1 iff x is not zero, nor NaN nor subnormal nor infinity
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_isNormal (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
UINT64 x = *px;
#else
int
bid64_isNormal (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
int res;
UINT128 sig_x_prime;
UINT64 sig_x;
unsigned int exp_x;
if ((x & MASK_INF) == MASK_INF) { // x is either INF or NaN
res = 0;
} else {
// decode number into exponent and significand
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
// check for zero or non-canonical
if (sig_x > 9999999999999999ull || sig_x == 0) {
res = 0; // zero or non-canonical
BID_RETURN (res);
}
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
} else {
sig_x = (x & MASK_BINARY_SIG1);
if (sig_x == 0) {
res = 0; // zero
BID_RETURN (res);
}
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
}
// if exponent is less than -383, the number may be subnormal
// if (exp_x - 398 = -383) the number may be subnormal
if (exp_x < 15) {
__mul_64x64_to_128MACH (sig_x_prime, sig_x, mult_factor[exp_x]);
if (sig_x_prime.w[1] == 0
&& sig_x_prime.w[0] < 1000000000000000ull) {
res = 0; // subnormal
} else {
res = 1; // normal
}
} else {
res = 1; // normal
}
}
BID_RETURN (res);
}
// return 1 iff x is not zero, nor NaN nor normal nor infinity
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_isSubnormal (int *pres,
UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
UINT64 x = *px;
#else
int
bid64_isSubnormal (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
int res;
UINT128 sig_x_prime;
UINT64 sig_x;
unsigned int exp_x;
if ((x & MASK_INF) == MASK_INF) { // x is either INF or NaN
res = 0;
} else {
// decode number into exponent and significand
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
// check for zero or non-canonical
if (sig_x > 9999999999999999ull || sig_x == 0) {
res = 0; // zero or non-canonical
BID_RETURN (res);
}
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
} else {
sig_x = (x & MASK_BINARY_SIG1);
if (sig_x == 0) {
res = 0; // zero
BID_RETURN (res);
}
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
}
// if exponent is less than -383, the number may be subnormal
// if (exp_x - 398 = -383) the number may be subnormal
if (exp_x < 15) {
__mul_64x64_to_128MACH (sig_x_prime, sig_x, mult_factor[exp_x]);
if (sig_x_prime.w[1] == 0
&& sig_x_prime.w[0] < 1000000000000000ull) {
res = 1; // subnormal
} else {
res = 0; // normal
}
} else {
res = 0; // normal
}
}
BID_RETURN (res);
}
//iff x is zero, subnormal or normal (not infinity or NaN)
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_isFinite (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
UINT64 x = *px;
#else
int
bid64_isFinite (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
int res;
res = ((x & MASK_INF) != MASK_INF);
BID_RETURN (res);
}
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_isZero (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
UINT64 x = *px;
#else
int
bid64_isZero (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
int res;
// if infinity or nan, return 0
if ((x & MASK_INF) == MASK_INF) {
res = 0;
} else if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1]
// => sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
// if(sig_x > 9999999999999999ull) {return 1;}
res =
(((x & MASK_BINARY_SIG2) | MASK_BINARY_OR2) >
9999999999999999ull);
} else {
res = ((x & MASK_BINARY_SIG1) == 0);
}
BID_RETURN (res);
}
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_isInf (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
UINT64 x = *px;
#else
int
bid64_isInf (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
int res;
res = ((x & MASK_INF) == MASK_INF) && ((x & MASK_NAN) != MASK_NAN);
BID_RETURN (res);
}
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_isSignaling (int *pres,
UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
UINT64 x = *px;
#else
int
bid64_isSignaling (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
int res;
res = ((x & MASK_SNAN) == MASK_SNAN);
BID_RETURN (res);
}
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_isCanonical (int *pres,
UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
UINT64 x = *px;
#else
int
bid64_isCanonical (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
int res;
if ((x & MASK_NAN) == MASK_NAN) { // NaN
if (x & 0x01fc000000000000ull) {
res = 0;
} else if ((x & 0x0003ffffffffffffull) > 999999999999999ull) { // payload
res = 0;
} else {
res = 1;
}
} else if ((x & MASK_INF) == MASK_INF) {
if (x & 0x03ffffffffffffffull) {
res = 0;
} else {
res = 1;
}
} else if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { // 54-bit coeff.
res =
(((x & MASK_BINARY_SIG2) | MASK_BINARY_OR2) <=
9999999999999999ull);
} else { // 53-bit coeff.
res = 1;
}
BID_RETURN (res);
}
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_isNaN (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
UINT64 x = *px;
#else
int
bid64_isNaN (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
int res;
res = ((x & MASK_NAN) == MASK_NAN);
BID_RETURN (res);
}
// copies a floating-point operand x to destination y, with no change
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_copy (UINT64 * pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
UINT64 x = *px;
#else
UINT64
bid64_copy (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
UINT64 res;
res = x;
BID_RETURN (res);
}
// copies a floating-point operand x to destination y, reversing the sign
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_negate (UINT64 * pres,
UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
UINT64 x = *px;
#else
UINT64
bid64_negate (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
UINT64 res;
res = x ^ MASK_SIGN;
BID_RETURN (res);
}
// copies a floating-point operand x to destination y, changing the sign to positive
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_abs (UINT64 * pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
UINT64 x = *px;
#else
UINT64
bid64_abs (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
UINT64 res;
res = x & ~MASK_SIGN;
BID_RETURN (res);
}
// copies operand x to destination in the same format as x, but
// with the sign of y
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_copySign (UINT64 * pres, UINT64 * px,
UINT64 * py _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
UINT64 x = *px;
UINT64 y = *py;
#else
UINT64
bid64_copySign (UINT64 x, UINT64 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
UINT64 res;
res = (x & ~MASK_SIGN) | (y & MASK_SIGN);
BID_RETURN (res);
}
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_class (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
UINT64 x = *px;
#else
int
bid64_class (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
int res;
UINT128 sig_x_prime;
UINT64 sig_x;
int exp_x;
if ((x & MASK_NAN) == MASK_NAN) {
// is the NaN signaling?
if ((x & MASK_SNAN) == MASK_SNAN) {
res = signalingNaN;
BID_RETURN (res);
}
// if NaN and not signaling, must be quietNaN
res = quietNaN;
BID_RETURN (res);
} else if ((x & MASK_INF) == MASK_INF) {
// is the Infinity negative?
if ((x & MASK_SIGN) == MASK_SIGN) {
res = negativeInfinity;
} else {
// otherwise, must be positive infinity
res = positiveInfinity;
}
BID_RETURN (res);
} else if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
// decode number into exponent and significand
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
// check for zero or non-canonical
if (sig_x > 9999999999999999ull || sig_x == 0) {
if ((x & MASK_SIGN) == MASK_SIGN) {
res = negativeZero;
} else {
res = positiveZero;
}
BID_RETURN (res);
}
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
} else {
sig_x = (x & MASK_BINARY_SIG1);
if (sig_x == 0) {
res =
((x & MASK_SIGN) == MASK_SIGN) ? negativeZero : positiveZero;
BID_RETURN (res);
}
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
}
// if exponent is less than -383, number may be subnormal
// if (exp_x - 398 < -383)
if (exp_x < 15) { // sig_x *10^exp_x
__mul_64x64_to_128MACH (sig_x_prime, sig_x, mult_factor[exp_x]);
if (sig_x_prime.w[1] == 0
&& (sig_x_prime.w[0] < 1000000000000000ull)) {
res =
((x & MASK_SIGN) ==
MASK_SIGN) ? negativeSubnormal : positiveSubnormal;
BID_RETURN (res);
}
}
// otherwise, normal number, determine the sign
res =
((x & MASK_SIGN) == MASK_SIGN) ? negativeNormal : positiveNormal;
BID_RETURN (res);
}
// true if the exponents of x and y are the same, false otherwise.
// The special cases of sameQuantum (NaN, NaN) and sameQuantum (Inf, Inf) are
// true.
// If exactly one operand is infinite or exactly one operand is NaN, then false
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_sameQuantum (int *pres, UINT64 * px,
UINT64 * py _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
UINT64 x = *px;
UINT64 y = *py;
#else
int
bid64_sameQuantum (UINT64 x, UINT64 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
int res;
unsigned int exp_x, exp_y;
// if both operands are NaN, return true; if just one is NaN, return false
if ((x & MASK_NAN) == MASK_NAN || ((y & MASK_NAN) == MASK_NAN)) {
res = ((x & MASK_NAN) == MASK_NAN && (y & MASK_NAN) == MASK_NAN);
BID_RETURN (res);
}
// if both operands are INF, return true; if just one is INF, return false
if ((x & MASK_INF) == MASK_INF || (y & MASK_INF) == MASK_INF) {
res = ((x & MASK_INF) == MASK_INF && (y & MASK_INF) == MASK_INF);
BID_RETURN (res);
}
// decode exponents for both numbers, and return true if they match
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
} else {
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
}
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
} else {
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
}
res = (exp_x == exp_y);
BID_RETURN (res);
}
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_totalOrder (int *pres, UINT64 * px,
UINT64 * py _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
UINT64 x = *px;
UINT64 y = *py;
#else
int
bid64_totalOrder (UINT64 x, UINT64 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
int res;
int exp_x, exp_y;
UINT64 sig_x, sig_y, pyld_y, pyld_x;
UINT128 sig_n_prime;
char x_is_zero = 0, y_is_zero = 0;
// NaN (CASE1)
// if x and y are unordered numerically because either operand is NaN
// (1) totalOrder(-NaN, number) is true
// (2) totalOrder(number, +NaN) is true
// (3) if x and y are both NaN:
// i) negative sign bit < positive sign bit
// ii) signaling < quiet for +NaN, reverse for -NaN
// iii) lesser payload < greater payload for +NaN (reverse for -NaN)
// iv) else if bitwise identical (in canonical form), return 1
if ((x & MASK_NAN) == MASK_NAN) {
// if x is -NaN
if ((x & MASK_SIGN) == MASK_SIGN) {
// return true, unless y is -NaN also
if ((y & MASK_NAN) != MASK_NAN || (y & MASK_SIGN) != MASK_SIGN) {
res = 1; // y is a number, return 1
BID_RETURN (res);
} else { // if y and x are both -NaN
// if x and y are both -sNaN or both -qNaN, we have to compare payloads
// this xnor statement evaluates to true if both are sNaN or qNaN
if (!
(((y & MASK_SNAN) == MASK_SNAN) ^ ((x & MASK_SNAN) ==
MASK_SNAN))) {
// it comes down to the payload. we want to return true if x has a
// larger payload, or if the payloads are equal (canonical forms
// are bitwise identical)
pyld_y = y & 0x0003ffffffffffffull;
pyld_x = x & 0x0003ffffffffffffull;
if (pyld_y > 999999999999999ull || pyld_y == 0) {
// if y is zero, x must be less than or numerically equal
// y's payload is 0
res = 1;
BID_RETURN (res);
}
// if x is zero and y isn't, x has the smaller payload
// definitely (since we know y isn't 0 at this point)
if (pyld_x > 999999999999999ull || pyld_x == 0) {
// x's payload is 0
res = 0;
BID_RETURN (res);
}
res = (pyld_x >= pyld_y);
BID_RETURN (res);
} else {
// either x = -sNaN and y = -qNaN or x = -qNaN and y = -sNaN
res = (y & MASK_SNAN) == MASK_SNAN; // totalOrder(-qNaN, -sNaN) == 1
BID_RETURN (res);
}
}
} else { // x is +NaN
// return false, unless y is +NaN also
if ((y & MASK_NAN) != MASK_NAN || (y & MASK_SIGN) == MASK_SIGN) {
res = 0; // y is a number, return 1
BID_RETURN (res);
} else {
// x and y are both +NaN;
// must investigate payload if both quiet or both signaling
// this xnor statement will be true if both x and y are +qNaN or +sNaN
if (!
(((y & MASK_SNAN) == MASK_SNAN) ^ ((x & MASK_SNAN) ==
MASK_SNAN))) {
// it comes down to the payload. we want to return true if x has a
// smaller payload, or if the payloads are equal (canonical forms
// are bitwise identical)
pyld_y = y & 0x0003ffffffffffffull;
pyld_x = x & 0x0003ffffffffffffull;
// if x is zero and y isn't, x has the smaller
// payload definitely (since we know y isn't 0 at this point)
if (pyld_x > 999999999999999ull || pyld_x == 0) {
res = 1;
BID_RETURN (res);
}
if (pyld_y > 999999999999999ull || pyld_y == 0) {
// if y is zero, x must be less than or numerically equal
res = 0;
BID_RETURN (res);
}
res = (pyld_x <= pyld_y);
BID_RETURN (res);
} else {
// return true if y is +qNaN and x is +sNaN
// (we know they're different bc of xor if_stmt above)
res = ((x & MASK_SNAN) == MASK_SNAN);
BID_RETURN (res);
}
}
}
} else if ((y & MASK_NAN) == MASK_NAN) {
// x is certainly not NAN in this case.
// return true if y is positive
res = ((y & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// SIMPLE (CASE2)
// if all the bits are the same, these numbers are equal.
if (x == y) {
res = 1;
BID_RETURN (res);
}
// OPPOSITE SIGNS (CASE 3)
// if signs are opposite, return 1 if x is negative
// (if x<y, totalOrder is true)
if (((x & MASK_SIGN) == MASK_SIGN) ^ ((y & MASK_SIGN) == MASK_SIGN)) {
res = (x & MASK_SIGN) == MASK_SIGN;
BID_RETURN (res);
}
// INFINITY (CASE4)
if ((x & MASK_INF) == MASK_INF) {
// if x==neg_inf, return (y == neg_inf)?1:0;
if ((x & MASK_SIGN) == MASK_SIGN) {
res = 1;
BID_RETURN (res);
} else {
// x is positive infinity, only return1 if y
// is positive infinity as well
// (we know y has same sign as x)
res = ((y & MASK_INF) == MASK_INF);
BID_RETURN (res);
}
} else if ((y & MASK_INF) == MASK_INF) {
// x is finite, so:
// if y is +inf, x<y
// if y is -inf, x>y
res = ((y & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (sig_x > 9999999999999999ull || sig_x == 0) {
x_is_zero = 1;
}
} else {
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
sig_x = (x & MASK_BINARY_SIG1);
if (sig_x == 0) {
x_is_zero = 1;
}
}
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (sig_y > 9999999999999999ull || sig_y == 0) {
y_is_zero = 1;
}
} else {
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
sig_y = (y & MASK_BINARY_SIG1);
if (sig_y == 0) {
y_is_zero = 1;
}
}
// ZERO (CASE 5)
// if x and y represent the same entities, and
// both are negative , return true iff exp_x <= exp_y
if (x_is_zero && y_is_zero) {
if (!((x & MASK_SIGN) == MASK_SIGN) ^
((y & MASK_SIGN) == MASK_SIGN)) {
// if signs are the same:
// totalOrder(x,y) iff exp_x >= exp_y for negative numbers
// totalOrder(x,y) iff exp_x <= exp_y for positive numbers
if (exp_x == exp_y) {
res = 1;
BID_RETURN (res);
}
res = (exp_x <= exp_y) ^ ((x & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
} else {
// signs are different.
// totalOrder(-0, +0) is true
// totalOrder(+0, -0) is false
res = ((x & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
}
// if x is zero and y isn't, clearly x has the smaller payload.
if (x_is_zero) {
res = ((y & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// if y is zero, and x isn't, clearly y has the smaller payload.
if (y_is_zero) {
res = ((x & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// REDUNDANT REPRESENTATIONS (CASE6)
// if both components are either bigger or smaller,
// it is clear what needs to be done
if (sig_x > sig_y && exp_x >= exp_y) {
res = ((x & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
if (sig_x < sig_y && exp_x <= exp_y) {
res = ((x & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// if exp_x is 15 greater than exp_y, it is
// definitely larger, so no need for compensation
if (exp_x - exp_y > 15) {
// difference cannot be greater than 10^15
res = ((x & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// if exp_x is 15 less than exp_y, it is
// definitely smaller, no need for compensation
if (exp_y - exp_x > 15) {
res = ((x & MASK_SIGN) != MASK_SIGN);
BID_RETURN (res);
}
// if |exp_x - exp_y| < 15, it comes down
// to the compensated significand
if (exp_x > exp_y) {
// otherwise adjust the x significand upwards
__mul_64x64_to_128MACH (sig_n_prime, sig_x,
mult_factor[exp_x - exp_y]);
// if x and y represent the same entities,
// and both are negative, return true iff exp_x <= exp_y
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
// case cannot occure, because all bits must
// be the same - would have been caught if (x==y)
res = (exp_x <= exp_y) ^ ((x & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// if positive, return 1 if adjusted x is smaller than y
res = ((sig_n_prime.w[1] == 0)
&& sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) ==
MASK_SIGN);
BID_RETURN (res);
}
// adjust the y significand upwards
__mul_64x64_to_128MACH (sig_n_prime, sig_y,
mult_factor[exp_y - exp_x]);
// if x and y represent the same entities,
// and both are negative, return true iff exp_x <= exp_y
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
// Cannot occur, because all bits must be the same.
// Case would have been caught if (x==y)
res = (exp_x <= exp_y) ^ ((x & MASK_SIGN) == MASK_SIGN);
BID_RETURN (res);
}
// values are not equal, for positive numbers return 1
// if x is less than y. 0 otherwise
res = ((sig_n_prime.w[1] > 0)
|| (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) ==
MASK_SIGN);
BID_RETURN (res);
}
// totalOrderMag is TotalOrder(abs(x), abs(y))
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_totalOrderMag (int *pres, UINT64 * px,
UINT64 * py _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
UINT64 x = *px;
UINT64 y = *py;
#else
int
bid64_totalOrderMag (UINT64 x,
UINT64 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
int res;
int exp_x, exp_y;
UINT64 sig_x, sig_y, pyld_y, pyld_x;
UINT128 sig_n_prime;
char x_is_zero = 0, y_is_zero = 0;
// NaN (CASE 1)
// if x and y are unordered numerically because either operand is NaN
// (1) totalOrder(number, +NaN) is true
// (2) if x and y are both NaN:
// i) signaling < quiet for +NaN
// ii) lesser payload < greater payload for +NaN
// iii) else if bitwise identical (in canonical form), return 1
if ((x & MASK_NAN) == MASK_NAN) {
// x is +NaN
// return false, unless y is +NaN also
if ((y & MASK_NAN) != MASK_NAN) {
res = 0; // y is a number, return 1
BID_RETURN (res);
} else {
// x and y are both +NaN;
// must investigate payload if both quiet or both signaling
// this xnor statement will be true if both x and y are +qNaN or +sNaN
if (!
(((y & MASK_SNAN) == MASK_SNAN) ^ ((x & MASK_SNAN) ==
MASK_SNAN))) {
// it comes down to the payload. we want to return true if x has a
// smaller payload, or if the payloads are equal (canonical forms
// are bitwise identical)
pyld_y = y & 0x0003ffffffffffffull;
pyld_x = x & 0x0003ffffffffffffull;
// if x is zero and y isn't, x has the smaller
// payload definitely (since we know y isn't 0 at this point)
if (pyld_x > 999999999999999ull || pyld_x == 0) {
res = 1;
BID_RETURN (res);
}
if (pyld_y > 999999999999999ull || pyld_y == 0) {
// if y is zero, x must be less than or numerically equal
res = 0;
BID_RETURN (res);
}
res = (pyld_x <= pyld_y);
BID_RETURN (res);
} else {
// return true if y is +qNaN and x is +sNaN
// (we know they're different bc of xor if_stmt above)
res = ((x & MASK_SNAN) == MASK_SNAN);
BID_RETURN (res);
}
}
} else if ((y & MASK_NAN) == MASK_NAN) {
// x is certainly not NAN in this case.
// return true if y is positive
res = 1;
BID_RETURN (res);
}
// SIMPLE (CASE2)
// if all the bits (except sign bit) are the same,
// these numbers are equal.
if ((x & ~MASK_SIGN) == (y & ~MASK_SIGN)) {
res = 1;
BID_RETURN (res);
}
// INFINITY (CASE3)
if ((x & MASK_INF) == MASK_INF) {
// x is positive infinity, only return1
// if y is positive infinity as well
res = ((y & MASK_INF) == MASK_INF);
BID_RETURN (res);
} else if ((y & MASK_INF) == MASK_INF) {
// x is finite, so:
// if y is +inf, x<y
res = 1;
BID_RETURN (res);
}
// if steering bits are 11 (condition will be 0),
// then exponent is G[0:w+1] =>
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (sig_x > 9999999999999999ull || sig_x == 0) {
x_is_zero = 1;
}
} else {
exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
sig_x = (x & MASK_BINARY_SIG1);
if (sig_x == 0) {
x_is_zero = 1;
}
}
// if steering bits are 11 (condition will be 0),
// then exponent is G[0:w+1] =>
if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (sig_y > 9999999999999999ull || sig_y == 0) {
y_is_zero = 1;
}
} else {
exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
sig_y = (y & MASK_BINARY_SIG1);
if (sig_y == 0) {
y_is_zero = 1;
}
}
// ZERO (CASE 5)
// if x and y represent the same entities,
// and both are negative , return true iff exp_x <= exp_y
if (x_is_zero && y_is_zero) {
// totalOrder(x,y) iff exp_x <= exp_y for positive numbers
res = (exp_x <= exp_y);
BID_RETURN (res);
}
// if x is zero and y isn't, clearly x has the smaller payload.
if (x_is_zero) {
res = 1;
BID_RETURN (res);
}
// if y is zero, and x isn't, clearly y has the smaller payload.
if (y_is_zero) {
res = 0;
BID_RETURN (res);
}
// REDUNDANT REPRESENTATIONS (CASE6)
// if both components are either bigger or smaller
if (sig_x > sig_y && exp_x >= exp_y) {
res = 0;
BID_RETURN (res);
}
if (sig_x < sig_y && exp_x <= exp_y) {
res = 1;
BID_RETURN (res);
}
// if exp_x is 15 greater than exp_y, it is definitely
// larger, so no need for compensation
if (exp_x - exp_y > 15) {
res = 0; // difference cannot be greater than 10^15
BID_RETURN (res);
}
// if exp_x is 15 less than exp_y, it is definitely
// smaller, no need for compensation
if (exp_y - exp_x > 15) {
res = 1;
BID_RETURN (res);
}
// if |exp_x - exp_y| < 15, it comes down
// to the compensated significand
if (exp_x > exp_y) {
// otherwise adjust the x significand upwards
__mul_64x64_to_128MACH (sig_n_prime, sig_x,
mult_factor[exp_x - exp_y]);
// if x and y represent the same entities,
// and both are negative, return true iff exp_x <= exp_y
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
// case cannot occur, because all bits
// must be the same - would have been caught if (x==y)
res = (exp_x <= exp_y);
BID_RETURN (res);
}
// if positive, return 1 if adjusted x is smaller than y
res = ((sig_n_prime.w[1] == 0) && sig_n_prime.w[0] < sig_y);
BID_RETURN (res);
}
// adjust the y significand upwards
__mul_64x64_to_128MACH (sig_n_prime, sig_y,
mult_factor[exp_y - exp_x]);
// if x and y represent the same entities,
// and both are negative, return true iff exp_x <= exp_y
if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
res = (exp_x <= exp_y);
BID_RETURN (res);
}
// values are not equal, for positive numbers
// return 1 if x is less than y. 0 otherwise
res = ((sig_n_prime.w[1] > 0) || (sig_x < sig_n_prime.w[0]));
BID_RETURN (res);
}
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_radix (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
UINT64 x = *px;
#else
int
bid64_radix (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
int res;
if (x) // dummy test
res = 10;
else
res = 10;
BID_RETURN (res);
}
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