783 lines
21 KiB
C
783 lines
21 KiB
C
/* Copyright (C) 2007-2020 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/>. */
|
|
|
|
#define DECNUMDIGITS 34 // work with up to 34 digits
|
|
|
|
#include "bid_internal.h"
|
|
#include "bid_b2d.h"
|
|
|
|
UINT32
|
|
bid_to_bid32 (UINT32 ba) {
|
|
UINT32 res;
|
|
UINT32 sign, comb, exp;
|
|
UINT32 trailing;
|
|
UINT32 bcoeff;
|
|
|
|
sign = (ba & 0x80000000ul);
|
|
comb = (ba & 0x7ff00000ul) >> 20;
|
|
trailing = (ba & 0x000ffffful);
|
|
|
|
if ((comb & 0x780) == 0x780) {
|
|
ba &= 0xfff0000ul;
|
|
return ba;
|
|
} else {
|
|
if ((comb & 0x600) == 0x600) { // G0..G1 = 11 -> exp is G2..G11
|
|
exp = (comb >> 1) & 0xff;
|
|
bcoeff = ((8 + (comb & 1)) << 20) | trailing;
|
|
} else {
|
|
exp = (comb >> 3) & 0xff;
|
|
bcoeff = ((comb & 7) << 20) | trailing;
|
|
}
|
|
if (bcoeff >= 10000000)
|
|
bcoeff = 0;
|
|
res = very_fast_get_BID32 (sign, exp, bcoeff);
|
|
}
|
|
return res;
|
|
}
|
|
|
|
UINT64
|
|
bid_to_bid64 (UINT64 ba) {
|
|
UINT64 res;
|
|
UINT64 sign, comb, exp;
|
|
UINT64 trailing;
|
|
UINT64 bcoeff;
|
|
|
|
sign = (ba & 0x8000000000000000ull);
|
|
comb = (ba & 0x7ffc000000000000ull) >> 50;
|
|
trailing = (ba & 0x0003ffffffffffffull);
|
|
|
|
if ((comb & 0x1e00) == 0x1e00) {
|
|
ba &= 0xfff000000000000ULL;
|
|
return ba;
|
|
} else {
|
|
if ((comb & 0x1800) == 0x1800) { // G0..G1 = 11 -> exp is G2..G11
|
|
exp = (comb >> 1) & 0x3ff;
|
|
bcoeff = ((8 + (comb & 1)) << 50) | trailing;
|
|
} else {
|
|
exp = (comb >> 3) & 0x3ff;
|
|
bcoeff = ((comb & 7) << 50) | trailing;
|
|
}
|
|
if (bcoeff >= 10000000000000000ull)
|
|
bcoeff = 0ull;
|
|
res = very_fast_get_BID64 (sign, exp, bcoeff);
|
|
}
|
|
return res;
|
|
}
|
|
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
|
void
|
|
bid_to_dpd32 (UINT32 * pres, UINT32 * pba) {
|
|
UINT32 ba = *pba;
|
|
#else
|
|
UINT32
|
|
bid_to_dpd32 (UINT32 ba) {
|
|
#endif
|
|
UINT32 res;
|
|
|
|
UINT32 sign, comb, exp, trailing;
|
|
UINT32 b0, b1, b2;
|
|
UINT32 bcoeff, dcoeff;
|
|
UINT32 nanb = 0;
|
|
|
|
sign = (ba & 0x80000000);
|
|
comb = (ba & 0x7ff00000) >> 20;
|
|
trailing = (ba & 0xfffff);
|
|
|
|
// Detect infinity, and return canonical infinity
|
|
if ((comb & 0x7c0) == 0x780) {
|
|
res = sign | 0x78000000;
|
|
BID_RETURN (res);
|
|
// Detect NaN, and canonicalize trailing
|
|
} else if ((comb & 0x7c0) == 0x7c0) {
|
|
if (trailing > 999999)
|
|
trailing = 0;
|
|
nanb = ba & 0xfe000000;
|
|
exp = 0;
|
|
bcoeff = trailing;
|
|
} else { // Normal number
|
|
if ((comb & 0x600) == 0x600) { // G0..G1 = 11 -> exp is G2..G11
|
|
exp = (comb >> 1) & 0xff;
|
|
bcoeff = ((8 + (comb & 1)) << 20) | trailing;
|
|
} else {
|
|
exp = (comb >> 3) & 0xff;
|
|
bcoeff = ((comb & 7) << 20) | trailing;
|
|
}
|
|
// Zero the coefficient if non-canonical (>= 10^7)
|
|
if (bcoeff >= 10000000)
|
|
bcoeff = 0;
|
|
}
|
|
|
|
b0 = bcoeff / 1000000;
|
|
b1 = (bcoeff / 1000) % 1000;
|
|
b2 = bcoeff % 1000;
|
|
dcoeff = (b2d[b1] << 10) | b2d[b2];
|
|
|
|
if (b0 >= 8) // is b0 8 or 9?
|
|
res =
|
|
sign |
|
|
((0x600 | ((exp >> 6) << 7) | ((b0 & 1) << 6) | (exp & 0x3f)) <<
|
|
20) | dcoeff;
|
|
else // else b0 is 0..7
|
|
res =
|
|
sign | ((((exp >> 6) << 9) | (b0 << 6) | (exp & 0x3f)) << 20) |
|
|
dcoeff;
|
|
|
|
res |= nanb;
|
|
|
|
BID_RETURN (res);
|
|
}
|
|
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
|
void
|
|
bid_to_dpd64 (UINT64 * pres, UINT64 * pba) {
|
|
UINT64 ba = *pba;
|
|
#else
|
|
UINT64
|
|
bid_to_dpd64 (UINT64 ba) {
|
|
#endif
|
|
UINT64 res;
|
|
|
|
UINT64 sign, comb, exp;
|
|
UINT64 trailing;
|
|
UINT32 b0, b1, b2, b3, b4, b5;
|
|
UINT64 bcoeff;
|
|
UINT64 dcoeff;
|
|
UINT32 yhi, ylo;
|
|
UINT64 nanb = 0;
|
|
|
|
//printf("arg bid "FMT_LLX16" \n", ba);
|
|
sign = (ba & 0x8000000000000000ull);
|
|
comb = (ba & 0x7ffc000000000000ull) >> 50;
|
|
trailing = (ba & 0x0003ffffffffffffull);
|
|
|
|
// Detect infinity, and return canonical infinity
|
|
if ((comb & 0x1f00) == 0x1e00) {
|
|
res = sign | 0x7800000000000000ull;
|
|
BID_RETURN (res);
|
|
// Detect NaN, and canonicalize trailing
|
|
} else if ((comb & 0x1e00) == 0x1e00) {
|
|
if (trailing > 999999999999999ull)
|
|
trailing = 0;
|
|
nanb = ba & 0xfe00000000000000ull;
|
|
exp = 0;
|
|
bcoeff = trailing;
|
|
} else { // Normal number
|
|
if ((comb & 0x1800) == 0x1800) { // G0..G1 = 11 -> exp is G2..G11
|
|
exp = (comb >> 1) & 0x3ff;
|
|
bcoeff = ((8 + (comb & 1)) << 50) | trailing;
|
|
} else {
|
|
exp = (comb >> 3) & 0x3ff;
|
|
bcoeff = ((comb & 7) << 50) | trailing;
|
|
}
|
|
|
|
// Zero the coefficient if it is non-canonical (>= 10^16)
|
|
if (bcoeff >= 10000000000000000ull)
|
|
bcoeff = 0;
|
|
}
|
|
|
|
// Floor(2^61 / 10^9)
|
|
#define D61 (2305843009ull)
|
|
|
|
// Multipy the binary coefficient by ceil(2^64 / 1000), and take the upper
|
|
// 64-bits in order to compute a division by 1000.
|
|
|
|
#if 1
|
|
yhi =
|
|
((UINT64) D61 *
|
|
(UINT64) (UINT32) (bcoeff >> (UINT64) 27)) >> (UINT64) 34;
|
|
ylo = bcoeff - 1000000000ull * yhi;
|
|
if (ylo >= 1000000000) {
|
|
ylo = ylo - 1000000000;
|
|
yhi = yhi + 1;
|
|
}
|
|
#else
|
|
yhi = bcoeff / 1000000000ull;
|
|
ylo = bcoeff % 1000000000ull;
|
|
#endif
|
|
|
|
// yhi = ABBBCCC ylo = DDDEEEFFF
|
|
b5 = ylo % 1000; // b5 = FFF
|
|
b3 = ylo / 1000000; // b3 = DDD
|
|
b4 = (ylo / 1000) - (1000 * b3); // b4 = EEE
|
|
b2 = yhi % 1000; // b2 = CCC
|
|
b0 = yhi / 1000000; // b0 = A
|
|
b1 = (yhi / 1000) - (1000 * b0); // b1 = BBB
|
|
|
|
dcoeff = b2d[b5] | b2d2[b4] | b2d3[b3] | b2d4[b2] | b2d5[b1];
|
|
|
|
if (b0 >= 8) // is b0 8 or 9?
|
|
res =
|
|
sign |
|
|
((0x1800 | ((exp >> 8) << 9) | ((b0 & 1) << 8) | (exp & 0xff)) <<
|
|
50) | dcoeff;
|
|
else // else b0 is 0..7
|
|
res =
|
|
sign | ((((exp >> 8) << 11) | (b0 << 8) | (exp & 0xff)) << 50) |
|
|
dcoeff;
|
|
|
|
res |= nanb;
|
|
|
|
BID_RETURN (res);
|
|
}
|
|
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
|
void
|
|
dpd_to_bid32 (UINT32 * pres, UINT32 * pda) {
|
|
UINT32 da = *pda;
|
|
#else
|
|
UINT32
|
|
dpd_to_bid32 (UINT32 da) {
|
|
#endif
|
|
UINT32 in = *(UINT32 *) & da;
|
|
UINT32 res;
|
|
|
|
UINT32 sign, comb, exp;
|
|
UINT32 trailing;
|
|
UINT32 d0 = 0, d1, d2;
|
|
UINT64 bcoeff;
|
|
UINT32 nanb = 0;
|
|
|
|
sign = (in & 0x80000000);
|
|
comb = (in & 0x7ff00000) >> 20;
|
|
trailing = (in & 0x000fffff);
|
|
|
|
if ((comb & 0x7e0) == 0x780) { // G0..G4 = 1111 -> Inf
|
|
res = in & 0xf8000000;
|
|
BID_RETURN (res);
|
|
} else if ((comb & 0x7c0) == 0x7c0) { // G0..G5 = 11111 -> NaN
|
|
nanb = in & 0xfe000000;
|
|
exp = 0;
|
|
} else { // Normal number
|
|
if ((comb & 0x600) == 0x600) { // G0..G1 = 11 -> d0 = 8 + G4
|
|
d0 = ((comb >> 6) & 1) | 8;
|
|
exp = ((comb & 0x180) >> 1) | (comb & 0x3f);
|
|
} else {
|
|
d0 = (comb >> 6) & 0x7;
|
|
exp = ((comb & 0x600) >> 3) | (comb & 0x3f);
|
|
}
|
|
}
|
|
d1 = d2b2[(trailing >> 10) & 0x3ff];
|
|
d2 = d2b[(trailing) & 0x3ff];
|
|
|
|
bcoeff = d2 + d1 + (1000000 * d0);
|
|
if (bcoeff < 0x800000) {
|
|
res = (exp << 23) | bcoeff | sign;
|
|
} else {
|
|
res = (exp << 21) | sign | 0x60000000 | (bcoeff & 0x1fffff);
|
|
}
|
|
|
|
res |= nanb;
|
|
|
|
BID_RETURN (res);
|
|
}
|
|
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
|
void
|
|
dpd_to_bid64 (UINT64 * pres, UINT64 * pda) {
|
|
UINT64 da = *pda;
|
|
#else
|
|
UINT64
|
|
dpd_to_bid64 (UINT64 da) {
|
|
#endif
|
|
UINT64 in = *(UINT64 *) & da;
|
|
UINT64 res;
|
|
|
|
UINT64 sign, comb, exp;
|
|
UINT64 trailing;
|
|
// UINT64 d0, d1, d2, d3, d4, d5;
|
|
|
|
UINT64 d1, d2;
|
|
UINT32 d0, d3, d4, d5;
|
|
UINT64 bcoeff;
|
|
UINT64 nanb = 0;
|
|
|
|
//printf("arg dpd "FMT_LLX16" \n", in);
|
|
sign = (in & 0x8000000000000000ull);
|
|
comb = (in & 0x7ffc000000000000ull) >> 50;
|
|
trailing = (in & 0x0003ffffffffffffull);
|
|
|
|
if ((comb & 0x1f00) == 0x1e00) { // G0..G4 = 1111 -> Inf
|
|
res = in & 0xf800000000000000ull;
|
|
BID_RETURN (res);
|
|
} else if ((comb & 0x1f00) == 0x1f00) { // G0..G5 = 11111 -> NaN
|
|
nanb = in & 0xfe00000000000000ull;
|
|
exp = 0;
|
|
d0 = 0;
|
|
} else { // Normal number
|
|
if ((comb & 0x1800) == 0x1800) { // G0..G1 = 11 -> d0 = 8 + G4
|
|
d0 = ((comb >> 8) & 1) | 8;
|
|
// d0 = (comb & 0x0100 ? 9 : 8);
|
|
exp = (comb & 0x600) >> 1;
|
|
// exp = (comb & 0x0400 ? 1 : 0) * 0x200 + (comb & 0x0200 ? 1 : 0) * 0x100; // exp leading bits are G2..G3
|
|
} else {
|
|
d0 = (comb >> 8) & 0x7;
|
|
exp = (comb & 0x1800) >> 3;
|
|
// exp = (comb & 0x1000 ? 1 : 0) * 0x200 + (comb & 0x0800 ? 1 : 0) * 0x100; // exp loading bits are G0..G1
|
|
}
|
|
}
|
|
d1 = d2b5[(trailing >> 40) & 0x3ff];
|
|
d2 = d2b4[(trailing >> 30) & 0x3ff];
|
|
d3 = d2b3[(trailing >> 20) & 0x3ff];
|
|
d4 = d2b2[(trailing >> 10) & 0x3ff];
|
|
d5 = d2b[(trailing) & 0x3ff];
|
|
|
|
bcoeff = (d5 + d4 + d3) + d2 + d1 + (1000000000000000ull * d0);
|
|
exp += (comb & 0xff);
|
|
res = very_fast_get_BID64 (sign, exp, bcoeff);
|
|
|
|
res |= nanb;
|
|
|
|
BID_RETURN (res);
|
|
}
|
|
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
|
void
|
|
bid_to_dpd128 (UINT128 * pres, UINT128 * pba) {
|
|
UINT128 ba = *pba;
|
|
#else
|
|
UINT128
|
|
bid_to_dpd128 (UINT128 ba) {
|
|
#endif
|
|
UINT128 res;
|
|
|
|
UINT128 sign;
|
|
UINT32 comb, exp;
|
|
UINT128 trailing;
|
|
UINT128 d0, d1, d2, d3, d4, d5, d6, d7, d8, d9, d10, d11;
|
|
UINT128 bcoeff;
|
|
UINT128 dcoeff;
|
|
UINT64 nanb = 0;
|
|
|
|
sign.w[1] = (ba.w[HIGH_128W] & 0x8000000000000000ull);
|
|
sign.w[0] = 0;
|
|
comb = (ba.w[HIGH_128W] & 0x7fffc00000000000ull) >> 46;
|
|
trailing.w[1] = (ba.w[HIGH_128W] & 0x00003fffffffffffull);
|
|
trailing.w[0] = ba.w[LOW_128W];
|
|
exp = 0;
|
|
|
|
if ((comb & 0x1f000) == 0x1e000) { // G0..G4 = 1111 -> Inf
|
|
res.w[HIGH_128W] = ba.w[HIGH_128W] & 0xf800000000000000ull;
|
|
res.w[LOW_128W] = 0;
|
|
BID_RETURN (res);
|
|
// Detect NaN, and canonicalize trailing
|
|
} else if ((comb & 0x1f000) == 0x1f000) {
|
|
if ((trailing.w[1] > 0x0000314dc6448d93ULL) || // significand is non-canonical
|
|
((trailing.w[1] == 0x0000314dc6448d93ULL)
|
|
&& (trailing.w[0] >= 0x38c15b0a00000000ULL))
|
|
// significand is non-canonical
|
|
) {
|
|
trailing.w[1] = trailing.w[0] = 0ull;
|
|
}
|
|
bcoeff.w[1] = trailing.w[1];
|
|
bcoeff.w[0] = trailing.w[0];
|
|
nanb = ba.w[HIGH_128W] & 0xfe00000000000000ull;
|
|
exp = 0;
|
|
} else { // Normal number
|
|
if ((comb & 0x18000) == 0x18000) { // G0..G1 = 11 -> exp is G2..G11
|
|
exp = (comb >> 1) & 0x3fff;
|
|
bcoeff.w[1] =
|
|
((UINT64) (8 + (comb & 1)) << (UINT64) 46) | trailing.w[1];
|
|
bcoeff.w[0] = trailing.w[0];
|
|
} else {
|
|
exp = (comb >> 3) & 0x3fff;
|
|
bcoeff.w[1] =
|
|
((UINT64) (comb & 7) << (UINT64) 46) | trailing.w[1];
|
|
bcoeff.w[0] = trailing.w[0];
|
|
}
|
|
// Zero the coefficient if non-canonical (>= 10^34)
|
|
if (bcoeff.w[1] > 0x1ed09bead87c0ull ||
|
|
(bcoeff.w[1] == 0x1ed09bead87c0ull
|
|
&& bcoeff.w[0] >= 0x378D8E6400000000ull)) {
|
|
bcoeff.w[0] = bcoeff.w[1] = 0;
|
|
}
|
|
}
|
|
// Constant 2^128 / 1000 + 1
|
|
{
|
|
UINT128 t;
|
|
UINT64 t2;
|
|
UINT128 d1000;
|
|
UINT128 b11, b10, b9, b8, b7, b6, b5, b4, b3, b2, b1;
|
|
d1000.w[1] = 0x4189374BC6A7EFull;
|
|
d1000.w[0] = 0x9DB22D0E56041894ull;
|
|
__mul_128x128_high (b11, bcoeff, d1000);
|
|
__mul_128x128_high (b10, b11, d1000);
|
|
__mul_128x128_high (b9, b10, d1000);
|
|
__mul_128x128_high (b8, b9, d1000);
|
|
__mul_128x128_high (b7, b8, d1000);
|
|
__mul_128x128_high (b6, b7, d1000);
|
|
__mul_128x128_high (b5, b6, d1000);
|
|
__mul_128x128_high (b4, b5, d1000);
|
|
__mul_128x128_high (b3, b4, d1000);
|
|
__mul_128x128_high (b2, b3, d1000);
|
|
__mul_128x128_high (b1, b2, d1000);
|
|
|
|
|
|
__mul_64x128_full (t2, t, 1000ull, b11);
|
|
__sub_128_128 (d11, bcoeff, t);
|
|
__mul_64x128_full (t2, t, 1000ull, b10);
|
|
__sub_128_128 (d10, b11, t);
|
|
__mul_64x128_full (t2, t, 1000ull, b9);
|
|
__sub_128_128 (d9, b10, t);
|
|
__mul_64x128_full (t2, t, 1000ull, b8);
|
|
__sub_128_128 (d8, b9, t);
|
|
__mul_64x128_full (t2, t, 1000ull, b7);
|
|
__sub_128_128 (d7, b8, t);
|
|
__mul_64x128_full (t2, t, 1000ull, b6);
|
|
__sub_128_128 (d6, b7, t);
|
|
__mul_64x128_full (t2, t, 1000ull, b5);
|
|
__sub_128_128 (d5, b6, t);
|
|
__mul_64x128_full (t2, t, 1000ull, b4);
|
|
__sub_128_128 (d4, b5, t);
|
|
__mul_64x128_full (t2, t, 1000ull, b3);
|
|
__sub_128_128 (d3, b4, t);
|
|
__mul_64x128_full (t2, t, 1000ull, b2);
|
|
__sub_128_128 (d2, b3, t);
|
|
__mul_64x128_full (t2, t, 1000ull, b1);
|
|
__sub_128_128 (d1, b2, t);
|
|
d0 = b1;
|
|
|
|
}
|
|
|
|
dcoeff.w[0] = b2d[d11.w[0]] | (b2d[d10.w[0]] << 10) |
|
|
(b2d[d9.w[0]] << 20) | (b2d[d8.w[0]] << 30) | (b2d[d7.w[0]] << 40) |
|
|
(b2d[d6.w[0]] << 50) | (b2d[d5.w[0]] << 60);
|
|
dcoeff.w[1] =
|
|
(b2d[d5.w[0]] >> 4) | (b2d[d4.w[0]] << 6) | (b2d[d3.w[0]] << 16) |
|
|
(b2d[d2.w[0]] << 26) | (b2d[d1.w[0]] << 36);
|
|
|
|
res.w[0] = dcoeff.w[0];
|
|
if (d0.w[0] >= 8) {
|
|
res.w[1] =
|
|
sign.
|
|
w[1] |
|
|
((0x18000 | ((exp >> 12) << 13) | ((d0.w[0] & 1) << 12) |
|
|
(exp & 0xfff)) << 46) | dcoeff.w[1];
|
|
} else {
|
|
res.w[1] =
|
|
sign.
|
|
w[1] | ((((exp >> 12) << 15) | (d0.w[0] << 12) | (exp & 0xfff))
|
|
<< 46) | dcoeff.w[1];
|
|
}
|
|
|
|
res.w[1] |= nanb;
|
|
|
|
BID_SWAP128 (res);
|
|
BID_RETURN (res);
|
|
}
|
|
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
|
void
|
|
dpd_to_bid128 (UINT128 * pres, UINT128 * pda) {
|
|
UINT128 da = *pda;
|
|
#else
|
|
UINT128
|
|
dpd_to_bid128 (UINT128 da) {
|
|
#endif
|
|
UINT128 in = *(UINT128 *) & da;
|
|
UINT128 res;
|
|
|
|
UINT128 sign;
|
|
UINT64 exp, comb;
|
|
UINT128 trailing;
|
|
UINT64 d0, d1, d2, d3, d4, d5, d6, d7, d8, d9, d10, d11;
|
|
UINT128 bcoeff;
|
|
UINT64 tl, th;
|
|
UINT64 nanb = 0;
|
|
|
|
sign.w[1] = (in.w[HIGH_128W] & 0x8000000000000000ull);
|
|
sign.w[0] = 0;
|
|
comb = (in.w[HIGH_128W] & 0x7fffc00000000000ull) >> 46;
|
|
trailing.w[1] = (in.w[HIGH_128W] & 0x00003fffffffffffull);
|
|
trailing.w[0] = in.w[LOW_128W];
|
|
exp = 0;
|
|
|
|
if ((comb & 0x1f000) == 0x1e000) { // G0..G4 = 1111 -> Inf
|
|
res.w[HIGH_128W] = in.w[HIGH_128W] & 0xf800000000000000ull;
|
|
res.w[LOW_128W] = 0ull;
|
|
BID_RETURN (res);
|
|
} else if ((comb & 0x1f000) == 0x1f000) { // G0..G4 = 11111 -> NaN
|
|
nanb = in.w[HIGH_128W] & 0xfe00000000000000ull;
|
|
exp = 0;
|
|
d0 = 0;
|
|
} else { // Normal number
|
|
if ((comb & 0x18000) == 0x18000) { // G0..G1 = 11 -> d0 = 8 + G4
|
|
d0 = 8 + (comb & 0x01000 ? 1 : 0);
|
|
exp =
|
|
(comb & 0x04000 ? 1 : 0) * 0x2000 +
|
|
(comb & 0x02000 ? 1 : 0) * 0x1000;
|
|
// exp leading bits are G2..G3
|
|
} else {
|
|
d0 =
|
|
4 * (comb & 0x04000 ? 1 : 0) + 2 * (comb & 0x2000 ? 1 : 0) +
|
|
(comb & 0x1000 ? 1 : 0);
|
|
exp =
|
|
(comb & 0x10000 ? 1 : 0) * 0x2000 +
|
|
(comb & 0x08000 ? 1 : 0) * 0x1000;
|
|
// exp loading bits are G0..G1
|
|
}
|
|
}
|
|
|
|
d11 = d2b[(trailing.w[0]) & 0x3ff];
|
|
d10 = d2b[(trailing.w[0] >> 10) & 0x3ff];
|
|
d9 = d2b[(trailing.w[0] >> 20) & 0x3ff];
|
|
d8 = d2b[(trailing.w[0] >> 30) & 0x3ff];
|
|
d7 = d2b[(trailing.w[0] >> 40) & 0x3ff];
|
|
d6 = d2b[(trailing.w[0] >> 50) & 0x3ff];
|
|
d5 = d2b[(trailing.w[0] >> 60) | ((trailing.w[1] & 0x3f) << 4)];
|
|
d4 = d2b[(trailing.w[1] >> 6) & 0x3ff];
|
|
d3 = d2b[(trailing.w[1] >> 16) & 0x3ff];
|
|
d2 = d2b[(trailing.w[1] >> 26) & 0x3ff];
|
|
d1 = d2b[(trailing.w[1] >> 36) & 0x3ff];
|
|
|
|
tl =
|
|
d11 + (d10 * 1000ull) + (d9 * 1000000ull) + (d8 * 1000000000ull) +
|
|
(d7 * 1000000000000ull) + (d6 * 1000000000000000ull);
|
|
th =
|
|
d5 + (d4 * 1000ull) + (d3 * 1000000ull) + (d2 * 1000000000ull) +
|
|
(d1 * 1000000000000ull) + (d0 * 1000000000000000ull);
|
|
__mul_64x64_to_128 (bcoeff, th, 1000000000000000000ull);
|
|
__add_128_64 (bcoeff, bcoeff, tl);
|
|
|
|
if (!nanb)
|
|
exp += (comb & 0xfff);
|
|
|
|
res.w[0] = bcoeff.w[0];
|
|
res.w[1] = (exp << 49) | sign.w[1] | bcoeff.w[1];
|
|
|
|
res.w[1] |= nanb;
|
|
|
|
BID_SWAP128 (res);
|
|
BID_RETURN (res);
|
|
}
|
|
|
|
UINT128
|
|
bid_to_bid128 (UINT128 bq) {
|
|
UINT128 res;
|
|
UINT64 sign, comb, exp;
|
|
UINT64 trailing;
|
|
UINT64 bcoeff;
|
|
|
|
UINT128 rq;
|
|
UINT128 qcoeff;
|
|
UINT64 ba, bb;
|
|
|
|
ba = *((UINT64 *) & bq + HIGH_128W);
|
|
bb = *((UINT64 *) & bq + LOW_128W);
|
|
|
|
sign = (ba & 0x8000000000000000ull);
|
|
comb = (ba & 0x7fffc00000000000ull) >> 46;
|
|
trailing = (ba & 0x00003fffffffffffull);
|
|
|
|
if ((comb & 0x18000) == 0x18000) { // G0..G1 = 11 -> exp is G2..G11
|
|
exp = (comb >> 1) & 0x3fff;
|
|
bcoeff = ((8 + (comb & 1)) << 46) | trailing;
|
|
} else {
|
|
exp = (comb >> 3) & 0x3fff;
|
|
bcoeff = ((comb & 7) << 46) | trailing;
|
|
}
|
|
|
|
if ((comb & 0x1f000) == 0x1f000) { //NaN
|
|
ba &= 0xfe003fffffffffffULL; // make exponent 0
|
|
bcoeff &= 0x00003fffffffffffull; // NaN payloat is only T.
|
|
if ((bcoeff > 0x0000314dc6448d93ULL) || // significand is non-canonical
|
|
((bcoeff == 0x0000314dc6448d93ULL)
|
|
&& (bb >= 0x38c15b0a00000000ULL))
|
|
// significand is non-canonical
|
|
) {
|
|
bcoeff = 0ull;
|
|
ba &= ~0x00003fffffffffffull;
|
|
bb = 0ull;
|
|
}
|
|
*((UINT64 *) & rq + HIGH_128W) = ba;
|
|
*((UINT64 *) & rq + LOW_128W) = bb;
|
|
return rq;
|
|
} else if ((comb & 0x1e000) == 0x1e000) { //Inf
|
|
ba &= 0xf800000000000000ULL; // make exponent and significand 0
|
|
bb = 0;
|
|
*((UINT64 *) & rq + HIGH_128W) = ba;
|
|
*((UINT64 *) & rq + LOW_128W) = bb;
|
|
return rq;
|
|
}
|
|
|
|
if ((bcoeff > 0x0001ed09bead87c0ull)
|
|
|| ((bcoeff == 0x0001ed09bead87c0ull)
|
|
&& (bb > 0x378d8e63ffffffffull))) {
|
|
// significand is non-canonical
|
|
bcoeff = 0ull;
|
|
bb = 0ull;
|
|
}
|
|
|
|
*((UINT64 *) & qcoeff + 1) = bcoeff;
|
|
*((UINT64 *) & qcoeff + 0) = bb;
|
|
|
|
get_BID128_fast (&res, sign, exp, qcoeff);
|
|
|
|
BID_SWAP128 (res);
|
|
return res;
|
|
}
|
|
|
|
UINT32
|
|
bid32_canonize (UINT32 ba) {
|
|
FPSC bidrnd;
|
|
unsigned int rnd = 0;
|
|
|
|
UINT32 res;
|
|
UINT32 sign, comb, exp;
|
|
UINT32 trailing;
|
|
UINT32 bcoeff;
|
|
|
|
sign = (ba & 0x80000000);
|
|
comb = (ba & 0x7ff00000) >> 20;
|
|
trailing = (ba & 0x000fffff);
|
|
|
|
if ((comb & 0x600) == 0x600) { // G0..G1 = 11 -> exp is G2..G11
|
|
exp = (comb >> 1) & 0xff;
|
|
bcoeff = ((8 + (comb & 1)) << 20) | trailing;
|
|
} else {
|
|
exp = (comb >> 3) & 0xff;
|
|
bcoeff = ((comb & 7) << 20) | trailing;
|
|
}
|
|
|
|
if ((comb & 0x7c0) == 0x7c0) { //NaN
|
|
ba &= 0xfe0fffff; // make exponent 0
|
|
bcoeff &= 0x000fffff; // NaN payloat is only T.
|
|
if (bcoeff >= 1000000)
|
|
ba &= 0xfff00000; //treat non-canonical significand
|
|
return ba;
|
|
} else if ((comb & 0x780) == 0x780) { //Inf
|
|
ba &= 0xf8000000; // make exponent and significand 0
|
|
return ba;
|
|
}
|
|
|
|
if (bcoeff >= 10000000)
|
|
bcoeff = 0;
|
|
rnd = bidrnd = ROUNDING_TO_NEAREST;
|
|
res = get_BID32 (sign, exp, bcoeff, rnd, &bidrnd);
|
|
return res;
|
|
}
|
|
|
|
UINT64
|
|
bid64_canonize (UINT64 ba) {
|
|
UINT64 res;
|
|
UINT64 sign, comb, exp;
|
|
UINT64 trailing;
|
|
UINT64 bcoeff;
|
|
|
|
sign = (ba & 0x8000000000000000ull);
|
|
comb = (ba & 0x7ffc000000000000ull) >> 50;
|
|
trailing = (ba & 0x0003ffffffffffffull);
|
|
|
|
|
|
if ((comb & 0x1800) == 0x1800) { // G0..G1 = 11 -> exp is G2..G11
|
|
exp = (comb >> 1) & 0x3ff;
|
|
bcoeff = ((8 + (comb & 1)) << 50) | trailing;
|
|
} else {
|
|
exp = (comb >> 3) & 0x3ff;
|
|
bcoeff = ((comb & 7) << 50) | trailing;
|
|
}
|
|
|
|
if ((comb & 0x1f00) == 0x1f00) { //NaN
|
|
ba &= 0xfe03ffffffffffffULL; // make exponent 0
|
|
bcoeff &= 0x0003ffffffffffffull; // NaN payloat is only T.
|
|
if (bcoeff >= 1000000000000000ull)
|
|
ba &= 0xfe00000000000000ull; // treat non canonical significand and zero G6-G12
|
|
return ba;
|
|
} else if ((comb & 0x1e00) == 0x1e00) { //Inf
|
|
ba &= 0xf800000000000000ULL; // make exponent and significand 0
|
|
return ba;
|
|
}
|
|
|
|
if (bcoeff >= 10000000000000000ull) {
|
|
bcoeff = 0ull;
|
|
}
|
|
res = very_fast_get_BID64 (sign, exp, bcoeff);
|
|
return res;
|
|
}
|
|
|
|
UINT128
|
|
bid128_canonize (UINT128 bq) {
|
|
UINT128 res;
|
|
UINT64 sign, comb, exp;
|
|
UINT64 trailing;
|
|
UINT64 bcoeff;
|
|
|
|
UINT128 rq;
|
|
UINT128 qcoeff;
|
|
UINT64 ba, bb;
|
|
|
|
ba = *((UINT64 *) & bq + HIGH_128W);
|
|
bb = *((UINT64 *) & bq + LOW_128W);
|
|
|
|
sign = (ba & 0x8000000000000000ull);
|
|
comb = (ba & 0x7fffc00000000000ull) >> 46;
|
|
trailing = (ba & 0x00003fffffffffffull);
|
|
|
|
if ((comb & 0x18000) == 0x18000) { // G0..G1 = 11 -> exp is G2..G11
|
|
exp = (comb >> 1) & 0x3fff;
|
|
bcoeff = ((8 + (comb & 1)) << 46) | trailing;
|
|
} else {
|
|
exp = (comb >> 3) & 0x3fff;
|
|
bcoeff = ((comb & 7) << 46) | trailing;
|
|
}
|
|
|
|
if ((comb & 0x1f000) == 0x1f000) { //NaN
|
|
ba &= 0xfe003fffffffffffULL; // make exponent 0
|
|
bcoeff &= 0x00003fffffffffffull; // NaN payload is only T.
|
|
|
|
if ((bcoeff > 0x0000314dc6448d93ULL) || // significand is non-canonical
|
|
((bcoeff == 0x0000314dc6448d93ULL)
|
|
&& (bb >= 0x38c15b0a00000000ULL))
|
|
// significand is non-canonical
|
|
) {
|
|
bcoeff = 0ull;
|
|
ba &= ~0x00003fffffffffffull;
|
|
bb = 0ull;
|
|
}
|
|
*((UINT64 *) & rq + HIGH_128W) = ba;
|
|
*((UINT64 *) & rq + LOW_128W) = bb;
|
|
return rq;
|
|
} else if ((comb & 0x1e000) == 0x1e000) { //Inf
|
|
ba &= 0xf800000000000000ULL; // make exponent and significand 0
|
|
bb = 0;
|
|
*((UINT64 *) & rq + HIGH_128W) = ba;
|
|
*((UINT64 *) & rq + LOW_128W) = bb;
|
|
return rq;
|
|
}
|
|
|
|
if ((bcoeff > 0x0001ed09bead87c0ull) || // significand is non-canonical
|
|
((bcoeff == 0x0001ed09bead87c0ull)
|
|
&& (bb > 0x378d8e63ffffffffull))
|
|
// significand is non-canonical
|
|
) {
|
|
bcoeff = 0ull;
|
|
bb = 0ull;
|
|
}
|
|
|
|
*((UINT64 *) & qcoeff + 1) = bcoeff;
|
|
*((UINT64 *) & qcoeff + 0) = bb;
|
|
|
|
get_BID128_fast (&res, sign, exp, qcoeff);
|
|
BID_SWAP128 (res);
|
|
return res;
|
|
}
|