/* 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/>. */
#undef IN_LIBGCC2
#include "bid-dpd.h"
/* get full 64x64bit product */
#define __mul_64x64_to_128(P, CX, CY) \
{ \
UINT64 CXH, CXL, CYH,CYL,PL,PH,PM,PM2; \
CXH = (CX) >> 32; \
CXL = (UINT32)(CX); \
CYH = (CY) >> 32; \
CYL = (UINT32)(CY); \
\
PM = CXH*CYL; \
PH = CXH*CYH; \
PL = CXL*CYL; \
PM2 = CXL*CYH; \
PH += (PM>>32); \
PM = (UINT64)((UINT32)PM)+PM2+(PL>>32); \
\
(P).w[1] = PH + (PM>>32); \
(P).w[0] = (PM<<32)+(UINT32)PL; \
}
/* add 64-bit value to 128-bit */
#define __add_128_64(R128, A128, B64) \
{ \
UINT64 R64H; \
R64H = (A128).w[1]; \
(R128).w[0] = (B64) + (A128).w[0]; \
if((R128).w[0] < (B64)) R64H ++; \
(R128).w[1] = R64H; \
}
/* add 128-bit value to 128-bit (assume no carry-out) */
#define __add_128_128(R128, A128, B128) \
{ \
UINT128 Q128; \
Q128.w[1] = (A128).w[1]+(B128).w[1]; \
Q128.w[0] = (B128).w[0] + (A128).w[0]; \
if(Q128.w[0] < (B128).w[0]) Q128.w[1] ++; \
(R128).w[1] = Q128.w[1]; \
(R128).w[0] = Q128.w[0]; \
}
#define __mul_128x128_high(Q, A, B) \
{ \
UINT128 ALBL, ALBH, AHBL, AHBH, QM, QM2; \
\
__mul_64x64_to_128(ALBH, (A).w[0], (B).w[1]); \
__mul_64x64_to_128(AHBL, (B).w[0], (A).w[1]); \
__mul_64x64_to_128(ALBL, (A).w[0], (B).w[0]); \
__mul_64x64_to_128(AHBH, (A).w[1],(B).w[1]); \
\
__add_128_128(QM, ALBH, AHBL); \
__add_128_64(QM2, QM, ALBL.w[1]); \
__add_128_64((Q), AHBH, QM2.w[1]); \
}
#include "bid2dpd_dpd2bid.h"
static const unsigned int dm103[] =
{ 0, 1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000, 11000 };
void _bid_to_dpd32 (_Decimal32 *, _Decimal32 *);
void
_bid_to_dpd32 (_Decimal32 *pres, _Decimal32 *px) {
unsigned int sign, coefficient_x, exp, dcoeff;
unsigned int b2, b1, b0, b01, res;
_Decimal32 x = *px;
sign = (x & 0x80000000);
if ((x & 0x60000000ul) == 0x60000000ul) {
/* special encodings */
if ((x & 0x78000000ul) == 0x78000000ul) {
*pres = x; /* NaN or Infinity */
return;
}
/* coefficient */
coefficient_x = (x & 0x001ffffful) | 0x00800000ul;
if (coefficient_x >= 10000000) coefficient_x = 0;
/* get exponent */
exp = (x >> 21) & 0xff;
} else {
exp = (x >> 23) & 0xff;
coefficient_x = (x & 0x007ffffful);
}
b01 = coefficient_x / 1000;
b2 = coefficient_x - 1000 * b01;
b0 = b01 / 1000;
b1 = b01 - 1000 * b0;
dcoeff = b2d[b2] | b2d2[b1];
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;
}
*pres = res;
}
void _dpd_to_bid32 (_Decimal32 *, _Decimal32 *);
void
_dpd_to_bid32 (_Decimal32 *pres, _Decimal32 *px) {
unsigned int r;
unsigned int sign, exp, bcoeff;
UINT64 trailing;
unsigned int d0, d1, d2;
_Decimal32 x = *px;
sign = (x & 0x80000000);
trailing = (x & 0x000fffff);
if ((x & 0x78000000) == 0x78000000) {
*pres = x;
return;
}
/* normal number */
if ((x & 0x60000000) == 0x60000000) { /* G0..G1 = 11 -> d0 = 8 + G4 */
d0 = d2b3[((x >> 26) & 1) | 8]; /* d0 = (comb & 0x0100 ? 9 : 8); */
exp = (x >> 27) & 3; /* exp leading bits are G2..G3 */
} else {
d0 = d2b3[(x >> 26) & 0x7];
exp = (x >> 29) & 3; /* exp loading bits are G0..G1 */
}
d1 = d2b2[(trailing >> 10) & 0x3ff];
d2 = d2b[(trailing) & 0x3ff];
bcoeff = d2 + d1 + d0;
exp = (exp << 6) + ((x >> 20) & 0x3f);
if (bcoeff < (1 << 23)) {
r = exp;
r <<= 23;
r |= (bcoeff | sign);
} else {
r = exp;
r <<= 21;
r |= (sign | 0x60000000ul);
/* add coeff, without leading bits */
r |= (((unsigned int) bcoeff) & 0x1fffff);
}
*pres = r;
}
void _bid_to_dpd64 (_Decimal64 *, _Decimal64 *);
void
_bid_to_dpd64 (_Decimal64 *pres, _Decimal64 *px) {
UINT64 res;
UINT64 sign, comb, exp, B34, B01;
UINT64 d103, D61;
UINT64 b0, b2, b3, b5;
unsigned int b1, b4;
UINT64 bcoeff;
UINT64 dcoeff;
unsigned int yhi, ylo;
_Decimal64 x = *px;
sign = (x & 0x8000000000000000ull);
comb = (x & 0x7ffc000000000000ull) >> 51;
if ((comb & 0xf00) == 0xf00) {
*pres = x;
return;
}
/* Normal number */
if ((comb & 0xc00) == 0xc00) { /* G0..G1 = 11 -> exp is G2..G11 */
exp = (comb) & 0x3ff;
bcoeff = (x & 0x0007ffffffffffffull) | 0x0020000000000000ull;
if (bcoeff >= 10000000000000000ull)
bcoeff = 0;
} else {
exp = (comb >> 2) & 0x3ff;
bcoeff = (x & 0x001fffffffffffffull);
}
D61 = 2305843009ull; /* Floor(2^61 / 10^9) */
/* Multiply the binary coefficient by ceil(2^64 / 1000), and take the upper
64-bits in order to compute a division by 1000. */
yhi = (D61 * (UINT64)(bcoeff >> (UINT64)27)) >> (UINT64)34;
ylo = bcoeff - 1000000000ull * yhi;
if (ylo >= 1000000000) {
ylo = ylo - 1000000000;
yhi = yhi + 1;
}
d103 = 0x4189374c;
B34 = ((UINT64) ylo * d103) >> (32 + 8);
B01 = ((UINT64) yhi * d103) >> (32 + 8);
b5 = ylo - B34 * 1000;
b2 = yhi - B01 * 1000;
b3 = ((UINT64) B34 * d103) >> (32 + 8);
b0 = ((UINT64) B01 * d103) >> (32 + 8);
b4 = (unsigned int) B34 - (unsigned int) b3 *1000;
b1 = (unsigned int) B01 - (unsigned int) dm103[b0];
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;
*pres = res;
}
void _dpd_to_bid64 (_Decimal64 *, _Decimal64 *);
void
_dpd_to_bid64 (_Decimal64 *pres, _Decimal64 *px) {
UINT64 res;
UINT64 sign, comb, exp;
UINT64 trailing;
UINT64 d0, d1, d2;
unsigned int d3, d4, d5;
UINT64 bcoeff, mask;
_Decimal64 x = *px;
sign = (x & 0x8000000000000000ull);
comb = (x & 0x7ffc000000000000ull) >> 50;
trailing = (x & 0x0003ffffffffffffull);
if ((comb & 0x1e00) == 0x1e00) {
*pres = x;
return;
}
/* normal number */
if ((comb & 0x1800) == 0x1800) { /* G0..G1 = 11 -> d0 = 8 + G4 */
d0 = d2b6[((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 = d2b6[(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 + d0;
exp += (comb & 0xff);
mask = 1;
mask <<= 53;
if (bcoeff < mask) { /* check whether coefficient fits in 10*5+3 bits */
res = exp;
res <<= 53;
res |= (bcoeff | sign);
*pres = res;
return;
}
/* special format */
res = (exp << 51) | (sign | 0x6000000000000000ull);
/* add coeff, without leading bits */
mask = (mask >> 2) - 1;
bcoeff &= mask;
res |= bcoeff;
*pres = res;
}
void _bid_to_dpd128 (_Decimal128 *, _Decimal128 *);
void
_bid_to_dpd128 (_Decimal128 *pres, _Decimal128 *px) {
UINT128 res;
UINT128 sign;
unsigned int comb;
UINT128 bcoeff;
UINT128 dcoeff;
UINT128 BH, d1018, BT2, BT1;
UINT64 exp, BL, d109;
UINT64 d106, d103;
UINT64 k1, k2, k4, k5, k7, k8, k10, k11;
unsigned int BHH32, BLL32, BHL32, BLH32, k0, k3, k6, k9, amount;
_Decimal128 x = *px;
sign.w[1] = (x.w[1] & 0x8000000000000000ull);
sign.w[0] = 0;
comb = (x.w[1] /*& 0x7fffc00000000000ull */ ) >> 46;
exp = 0;
if ((comb & 0x1e000) == 0x1e000) {
res = x;
} else { /* normal number */
if ((comb & 0x18000) == 0x18000) {
/* Noncanonical significand (prepending 8 or 9 to any 110-bit
trailing significand field produces a value above 10^34). */
exp = (comb & 0x7fff) >> 1;
bcoeff.w[1] = 0;
bcoeff.w[0] = 0;
} else {
exp = ((x.w[1] & 0x7fff000000000000ull) >> 49) & 0x3fff;
bcoeff.w[1] = (x.w[1] & 0x0001ffffffffffffull);
bcoeff.w[0] = x.w[0];
if (bcoeff.w[1] > 0x1ed09bead87c0ull
|| (bcoeff.w[1] == 0x1ed09bead87c0ull
&& bcoeff.w[0] >= 0x378d8e6400000000ull)) {
bcoeff.w[1] = 0;
bcoeff.w[0] = 0;
}
}
d1018 = reciprocals10_128[18];
__mul_128x128_high (BH, bcoeff, d1018);
amount = recip_scale[18];
BH.w[0] = (BH.w[0] >> amount) | (BH.w[1] << (64 - amount));
BL = bcoeff.w[0] - BH.w[0] * 1000000000000000000ull;
d109 = reciprocals10_64[9];
__mul_64x64_to_128 (BT1, BH.w[0], d109);
BHH32 = (unsigned int) (BT1.w[1] >> short_recip_scale[9]);
BHL32 = (unsigned int) BH.w[0] - BHH32 * 1000000000;
__mul_64x64_to_128 (BT2, BL, d109);
BLH32 = (unsigned int) (BT2.w[1] >> short_recip_scale[9]);
BLL32 = (unsigned int) BL - BLH32 * 1000000000;
d106 = 0x431BDE83;
d103 = 0x4189374c;
k0 = ((UINT64) BHH32 * d106) >> (32 + 18);
BHH32 -= (unsigned int) k0 *1000000;
k1 = ((UINT64) BHH32 * d103) >> (32 + 8);
k2 = BHH32 - (unsigned int) k1 *1000;
k3 = ((UINT64) BHL32 * d106) >> (32 + 18);
BHL32 -= (unsigned int) k3 *1000000;
k4 = ((UINT64) BHL32 * d103) >> (32 + 8);
k5 = BHL32 - (unsigned int) k4 *1000;
k6 = ((UINT64) BLH32 * d106) >> (32 + 18);
BLH32 -= (unsigned int) k6 *1000000;
k7 = ((UINT64) BLH32 * d103) >> (32 + 8);
k8 = BLH32 - (unsigned int) k7 *1000;
k9 = ((UINT64) BLL32 * d106) >> (32 + 18);
BLL32 -= (unsigned int) k9 *1000000;
k10 = ((UINT64) BLL32 * d103) >> (32 + 8);
k11 = BLL32 - (unsigned int) k10 *1000;
dcoeff.w[1] = (b2d[k5] >> 4) | (b2d[k4] << 6) | (b2d[k3] << 16) |
(b2d[k2] << 26) | (b2d[k1] << 36);
dcoeff.w[0] = b2d[k11] | (b2d[k10] << 10) | (b2d[k9] << 20) |
(b2d[k8] << 30) | (b2d[k7] << 40) | (b2d[k6] << 50) | (b2d[k5] << 60);
res.w[0] = dcoeff.w[0];
if (k0 >= 8) {
res.w[1] = sign.w[1] | ((0x18000 | ((exp >> 12) << 13) |
((k0 & 1) << 12) | (exp & 0xfff)) << 46) | dcoeff.w[1];
} else {
res.w[1] = sign.w[1] | ((((exp >> 12) << 15) | (k0 << 12) |
(exp & 0xfff)) << 46) | dcoeff.w[1];
}
}
*pres = res;
}
void _dpd_to_bid128 (_Decimal128 *, _Decimal128 *);
void
_dpd_to_bid128 (_Decimal128 *pres, _Decimal128 *px) {
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;
_Decimal128 x = *px;
sign.w[1] = (x.w[1] & 0x8000000000000000ull);
sign.w[0] = 0;
comb = (x.w[1] & 0x7fffc00000000000ull) >> 46;
trailing.w[1] = x.w[1];
trailing.w[0] = x.w[0];
if ((comb & 0x1e000) == 0x1e000) {
*pres = x;
return;
}
if ((comb & 0x18000) == 0x18000) { /* G0..G1 = 11 -> d0 = 8 + G4 */
d0 = d2b6[8 + ((comb & 0x01000) >> 12)];
exp = (comb & 0x06000) >> 1; /* exp leading bits are G2..G3 */
} else {
d0 = d2b6[((comb & 0x07000) >> 12)];
exp = (comb & 0x18000) >> 3; /* exp loading bits are G0..G1 */
}
d11 = d2b[(trailing.w[0]) & 0x3ff];
d10 = d2b2[(trailing.w[0] >> 10) & 0x3ff];
d9 = d2b3[(trailing.w[0] >> 20) & 0x3ff];
d8 = d2b4[(trailing.w[0] >> 30) & 0x3ff];
d7 = d2b5[(trailing.w[0] >> 40) & 0x3ff];
d6 = d2b6[(trailing.w[0] >> 50) & 0x3ff];
d5 = d2b[(trailing.w[0] >> 60) | ((trailing.w[1] & 0x3f) << 4)];
d4 = d2b2[(trailing.w[1] >> 6) & 0x3ff];
d3 = d2b3[(trailing.w[1] >> 16) & 0x3ff];
d2 = d2b4[(trailing.w[1] >> 26) & 0x3ff];
d1 = d2b5[(trailing.w[1] >> 36) & 0x3ff];
tl = d11 + d10 + d9 + d8 + d7 + d6;
th = d5 + d4 + d3 + d2 + d1 + d0;
__mul_64x64_to_128 (bcoeff, th, 1000000000000000000ull);
__add_128_64 (bcoeff, bcoeff, tl);
exp += (comb & 0xfff);
res.w[0] = bcoeff.w[0];
res.w[1] = (exp << 49) | sign.w[1] | bcoeff.w[1];
*pres = res;
}