424 lines
13 KiB
C
424 lines
13 KiB
C
/* Copyright (C) 2007-2017 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"
|
|
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
|
void
|
|
bid64dq_mul (UINT64 * pres, UINT64 * px, UINT128 * py
|
|
_RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
|
_EXC_INFO_PARAM) {
|
|
UINT64 x = *px;
|
|
#if !DECIMAL_GLOBAL_ROUNDING
|
|
unsigned int rnd_mode = *prnd_mode;
|
|
#endif
|
|
#else
|
|
UINT64
|
|
bid64dq_mul (UINT64 x, UINT128 y
|
|
_RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
|
_EXC_INFO_PARAM) {
|
|
#endif
|
|
UINT64 res = 0xbaddbaddbaddbaddull;
|
|
UINT128 x1;
|
|
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
|
bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
|
|
bid64qq_mul (&res, &x1, py
|
|
_RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
|
|
_EXC_INFO_ARG);
|
|
#else
|
|
x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
|
|
res = bid64qq_mul (x1, y
|
|
_RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
|
|
_EXC_INFO_ARG);
|
|
#endif
|
|
BID_RETURN (res);
|
|
}
|
|
|
|
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
|
void
|
|
bid64qd_mul (UINT64 * pres, UINT128 * px, UINT64 * py
|
|
_RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
|
_EXC_INFO_PARAM) {
|
|
UINT64 y = *py;
|
|
#if !DECIMAL_GLOBAL_ROUNDING
|
|
unsigned int rnd_mode = *prnd_mode;
|
|
#endif
|
|
#else
|
|
UINT64
|
|
bid64qd_mul (UINT128 x, UINT64 y
|
|
_RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
|
_EXC_INFO_PARAM) {
|
|
#endif
|
|
UINT64 res = 0xbaddbaddbaddbaddull;
|
|
UINT128 y1;
|
|
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
|
bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
|
|
bid64qq_mul (&res, px, &y1
|
|
_RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
|
|
_EXC_INFO_ARG);
|
|
#else
|
|
y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
|
|
res = bid64qq_mul (x, y1
|
|
_RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
|
|
_EXC_INFO_ARG);
|
|
#endif
|
|
BID_RETURN (res);
|
|
}
|
|
|
|
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
|
void
|
|
bid64qq_mul (UINT64 * pres, UINT128 * px, UINT128 * py
|
|
_RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
|
_EXC_INFO_PARAM) {
|
|
UINT128 x = *px, y = *py;
|
|
#if !DECIMAL_GLOBAL_ROUNDING
|
|
unsigned int rnd_mode = *prnd_mode;
|
|
#endif
|
|
#else
|
|
UINT64
|
|
bid64qq_mul (UINT128 x, UINT128 y
|
|
_RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
|
_EXC_INFO_PARAM) {
|
|
#endif
|
|
|
|
UINT128 z = { {0x0000000000000000ull, 0x5ffe000000000000ull}
|
|
};
|
|
UINT64 res = 0xbaddbaddbaddbaddull;
|
|
UINT64 x_sign, y_sign, p_sign;
|
|
UINT64 x_exp, y_exp, p_exp;
|
|
int true_p_exp;
|
|
UINT128 C1, C2;
|
|
|
|
BID_SWAP128 (z);
|
|
// skip cases where at least one operand is NaN or infinity
|
|
if (!(((x.w[HIGH_128W] & MASK_NAN) == MASK_NAN) ||
|
|
((y.w[HIGH_128W] & MASK_NAN) == MASK_NAN) ||
|
|
((x.w[HIGH_128W] & MASK_ANY_INF) == MASK_INF) ||
|
|
((y.w[HIGH_128W] & MASK_ANY_INF) == MASK_INF))) {
|
|
// x, y are 0 or f but not inf or NaN => unpack the arguments and check
|
|
// for non-canonical values
|
|
|
|
x_sign = x.w[HIGH_128W] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
|
|
C1.w[1] = x.w[HIGH_128W] & MASK_COEFF;
|
|
C1.w[0] = x.w[LOW_128W];
|
|
// check for non-canonical values - treated as zero
|
|
if ((x.w[HIGH_128W] & 0x6000000000000000ull) ==
|
|
0x6000000000000000ull) {
|
|
// G0_G1=11 => non-canonical
|
|
x_exp = (x.w[HIGH_128W] << 2) & MASK_EXP; // biased and shifted left 49 bits
|
|
C1.w[1] = 0; // significand high
|
|
C1.w[0] = 0; // significand low
|
|
} else { // G0_G1 != 11
|
|
x_exp = x.w[HIGH_128W] & MASK_EXP; // biased and shifted left 49 bits
|
|
if (C1.w[1] > 0x0001ed09bead87c0ull ||
|
|
(C1.w[1] == 0x0001ed09bead87c0ull &&
|
|
C1.w[0] > 0x378d8e63ffffffffull)) {
|
|
// x is non-canonical if coefficient is larger than 10^34 -1
|
|
C1.w[1] = 0;
|
|
C1.w[0] = 0;
|
|
} else { // canonical
|
|
;
|
|
}
|
|
}
|
|
y_sign = y.w[HIGH_128W] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
|
|
C2.w[1] = y.w[HIGH_128W] & MASK_COEFF;
|
|
C2.w[0] = y.w[LOW_128W];
|
|
// check for non-canonical values - treated as zero
|
|
if ((y.w[HIGH_128W] & 0x6000000000000000ull) ==
|
|
0x6000000000000000ull) {
|
|
// G0_G1=11 => non-canonical
|
|
y_exp = (y.w[HIGH_128W] << 2) & MASK_EXP; // biased and shifted left 49 bits
|
|
C2.w[1] = 0; // significand high
|
|
C2.w[0] = 0; // significand low
|
|
} else { // G0_G1 != 11
|
|
y_exp = y.w[HIGH_128W] & MASK_EXP; // biased and shifted left 49 bits
|
|
if (C2.w[1] > 0x0001ed09bead87c0ull ||
|
|
(C2.w[1] == 0x0001ed09bead87c0ull &&
|
|
C2.w[0] > 0x378d8e63ffffffffull)) {
|
|
// y is non-canonical if coefficient is larger than 10^34 -1
|
|
C2.w[1] = 0;
|
|
C2.w[0] = 0;
|
|
} else { // canonical
|
|
;
|
|
}
|
|
}
|
|
p_sign = x_sign ^ y_sign; // sign of the product
|
|
|
|
true_p_exp = (x_exp >> 49) - 6176 + (y_exp >> 49) - 6176;
|
|
// true_p_exp, p_exp are used only for 0 * 0, 0 * f, or f * 0
|
|
if (true_p_exp < -398)
|
|
p_exp = 0; // cannot be less than EXP_MIN
|
|
else if (true_p_exp > 369)
|
|
p_exp = (UINT64) (369 + 398) << 53; // cannot be more than EXP_MAX
|
|
else
|
|
p_exp = (UINT64) (true_p_exp + 398) << 53;
|
|
|
|
if ((C1.w[1] == 0x0 && C1.w[0] == 0x0) ||
|
|
(C2.w[1] == 0x0 && C2.w[0] == 0x0)) {
|
|
// x = 0 or y = 0
|
|
// the result is 0
|
|
res = p_sign | p_exp; // preferred exponent in [EXP_MIN, EXP_MAX]
|
|
BID_RETURN (res)
|
|
} // else continue
|
|
}
|
|
// swap x and y - ensure that a NaN in x has 'higher precedence' than one in y
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
|
bid64qqq_fma (&res, &y, &x, &z
|
|
_RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
|
|
_EXC_INFO_ARG);
|
|
#else
|
|
res = bid64qqq_fma (y, x, z
|
|
_RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
|
|
_EXC_INFO_ARG);
|
|
#endif
|
|
BID_RETURN (res);
|
|
}
|
|
|
|
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
|
void
|
|
bid128dd_mul (UINT128 * pres, UINT64 * px, UINT64 * py
|
|
_RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
|
_EXC_INFO_PARAM) {
|
|
UINT64 x = *px, y = *py;
|
|
#if !DECIMAL_GLOBAL_ROUNDING
|
|
unsigned int rnd_mode = *prnd_mode;
|
|
#endif
|
|
#else
|
|
UINT128
|
|
bid128dd_mul (UINT64 x, UINT64 y
|
|
_RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
|
_EXC_INFO_PARAM) {
|
|
#endif
|
|
UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull}
|
|
};
|
|
UINT128 x1, y1;
|
|
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
|
bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
|
|
bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
|
|
bid128_mul (&res, &x1, &y1
|
|
_RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
|
|
_EXC_INFO_ARG);
|
|
#else
|
|
x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
|
|
y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
|
|
res = bid128_mul (x1, y1
|
|
_RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
|
|
_EXC_INFO_ARG);
|
|
#endif
|
|
BID_RETURN (res);
|
|
}
|
|
|
|
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
|
void
|
|
bid128dq_mul (UINT128 * pres, UINT64 * px, UINT128 * py
|
|
_RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
|
_EXC_INFO_PARAM) {
|
|
UINT64 x = *px;
|
|
#if !DECIMAL_GLOBAL_ROUNDING
|
|
unsigned int rnd_mode = *prnd_mode;
|
|
#endif
|
|
#else
|
|
UINT128
|
|
bid128dq_mul (UINT64 x, UINT128 y
|
|
_RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
|
_EXC_INFO_PARAM) {
|
|
#endif
|
|
UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull}
|
|
};
|
|
UINT128 x1;
|
|
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
|
bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
|
|
bid128_mul (&res, &x1, py
|
|
_RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
|
|
_EXC_INFO_ARG);
|
|
#else
|
|
x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
|
|
res = bid128_mul (x1, y
|
|
_RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
|
|
_EXC_INFO_ARG);
|
|
#endif
|
|
BID_RETURN (res);
|
|
}
|
|
|
|
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
|
void
|
|
bid128qd_mul (UINT128 * pres, UINT128 * px, UINT64 * py
|
|
_RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
|
_EXC_INFO_PARAM) {
|
|
UINT64 y = *py;
|
|
#if !DECIMAL_GLOBAL_ROUNDING
|
|
unsigned int rnd_mode = *prnd_mode;
|
|
#endif
|
|
#else
|
|
UINT128
|
|
bid128qd_mul (UINT128 x, UINT64 y
|
|
_RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
|
_EXC_INFO_PARAM) {
|
|
#endif
|
|
UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull}
|
|
};
|
|
UINT128 y1;
|
|
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
|
bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
|
|
bid128_mul (&res, px, &y1
|
|
_RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
|
|
_EXC_INFO_ARG);
|
|
#else
|
|
y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
|
|
res = bid128_mul (x, y1
|
|
_RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
|
|
_EXC_INFO_ARG);
|
|
#endif
|
|
BID_RETURN (res);
|
|
}
|
|
|
|
|
|
// bid128_mul stands for bid128qq_mul
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
|
void
|
|
bid128_mul (UINT128 * pres, UINT128 * px,
|
|
UINT128 *
|
|
py _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
|
_EXC_INFO_PARAM) {
|
|
UINT128 x = *px, y = *py;
|
|
|
|
#if !DECIMAL_GLOBAL_ROUNDING
|
|
unsigned int rnd_mode = *prnd_mode;
|
|
|
|
#endif
|
|
#else
|
|
UINT128
|
|
bid128_mul (UINT128 x,
|
|
UINT128 y _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
|
_EXC_INFO_PARAM) {
|
|
|
|
#endif
|
|
UINT128 z = { {0x0000000000000000ull, 0x5ffe000000000000ull}
|
|
};
|
|
UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull}
|
|
};
|
|
UINT64 x_sign, y_sign, p_sign;
|
|
UINT64 x_exp, y_exp, p_exp;
|
|
int true_p_exp;
|
|
UINT128 C1, C2;
|
|
|
|
BID_SWAP128 (x);
|
|
BID_SWAP128 (y);
|
|
// skip cases where at least one operand is NaN or infinity
|
|
if (!(((x.w[1] & MASK_NAN) == MASK_NAN) ||
|
|
((y.w[1] & MASK_NAN) == MASK_NAN) ||
|
|
((x.w[1] & MASK_ANY_INF) == MASK_INF) ||
|
|
((y.w[1] & MASK_ANY_INF) == MASK_INF))) {
|
|
// x, y are 0 or f but not inf or NaN => unpack the arguments and check
|
|
// for non-canonical values
|
|
|
|
x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
|
|
C1.w[1] = x.w[1] & MASK_COEFF;
|
|
C1.w[0] = x.w[0];
|
|
// check for non-canonical values - treated as zero
|
|
if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) {
|
|
// G0_G1=11 => non-canonical
|
|
x_exp = (x.w[1] << 2) & MASK_EXP; // biased and shifted left 49 bits
|
|
C1.w[1] = 0; // significand high
|
|
C1.w[0] = 0; // significand low
|
|
} else { // G0_G1 != 11
|
|
x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bits
|
|
if (C1.w[1] > 0x0001ed09bead87c0ull ||
|
|
(C1.w[1] == 0x0001ed09bead87c0ull &&
|
|
C1.w[0] > 0x378d8e63ffffffffull)) {
|
|
// x is non-canonical if coefficient is larger than 10^34 -1
|
|
C1.w[1] = 0;
|
|
C1.w[0] = 0;
|
|
} else { // canonical
|
|
;
|
|
}
|
|
}
|
|
y_sign = y.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
|
|
C2.w[1] = y.w[1] & MASK_COEFF;
|
|
C2.w[0] = y.w[0];
|
|
// check for non-canonical values - treated as zero
|
|
if ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) {
|
|
// G0_G1=11 => non-canonical
|
|
y_exp = (y.w[1] << 2) & MASK_EXP; // biased and shifted left 49 bits
|
|
C2.w[1] = 0; // significand high
|
|
C2.w[0] = 0; // significand low
|
|
} else { // G0_G1 != 11
|
|
y_exp = y.w[1] & MASK_EXP; // biased and shifted left 49 bits
|
|
if (C2.w[1] > 0x0001ed09bead87c0ull ||
|
|
(C2.w[1] == 0x0001ed09bead87c0ull &&
|
|
C2.w[0] > 0x378d8e63ffffffffull)) {
|
|
// y is non-canonical if coefficient is larger than 10^34 -1
|
|
C2.w[1] = 0;
|
|
C2.w[0] = 0;
|
|
} else { // canonical
|
|
;
|
|
}
|
|
}
|
|
p_sign = x_sign ^ y_sign; // sign of the product
|
|
|
|
true_p_exp = (x_exp >> 49) - 6176 + (y_exp >> 49) - 6176;
|
|
// true_p_exp, p_exp are used only for 0 * 0, 0 * f, or f * 0
|
|
if (true_p_exp < -6176)
|
|
p_exp = 0; // cannot be less than EXP_MIN
|
|
else if (true_p_exp > 6111)
|
|
p_exp = (UINT64) (6111 + 6176) << 49; // cannot be more than EXP_MAX
|
|
else
|
|
p_exp = (UINT64) (true_p_exp + 6176) << 49;
|
|
|
|
if ((C1.w[1] == 0x0 && C1.w[0] == 0x0) ||
|
|
(C2.w[1] == 0x0 && C2.w[0] == 0x0)) {
|
|
// x = 0 or y = 0
|
|
// the result is 0
|
|
res.w[1] = p_sign | p_exp; // preferred exponent in [EXP_MIN, EXP_MAX]
|
|
res.w[0] = 0x0;
|
|
BID_SWAP128 (res);
|
|
BID_RETURN (res)
|
|
} // else continue
|
|
}
|
|
|
|
BID_SWAP128 (x);
|
|
BID_SWAP128 (y);
|
|
BID_SWAP128 (z);
|
|
// swap x and y - ensure that a NaN in x has 'higher precedence' than one in y
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
|
bid128_fma (&res, &y, &x, &z
|
|
_RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
|
|
_EXC_INFO_ARG);
|
|
#else
|
|
res = bid128_fma (y, x, z
|
|
_RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
|
|
_EXC_INFO_ARG);
|
|
#endif
|
|
BID_RETURN (res);
|
|
}
|