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gcc/libgcc/config/libbid/bid_div_macros.h

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/* Copyright (C) 2007-2022 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/>. */
#ifndef _DIV_MACROS_H_
#define _DIV_MACROS_H_
#include "bid_internal.h"
#define FENCE __fence
//#define FENCE
//#define DOUBLE_EXTENDED_ON
#if DOUBLE_EXTENDED_ON
__BID_INLINE__ void
__div_128_by_128 (UINT128 * pCQ, UINT128 * pCR, UINT128 CX, UINT128 CY) {
UINT128 CB, CB2, CB4, CB8, CQB, CA;
int_double d64, dm64, ds;
int_float t64;
double dx, dq, dqh;
BINARY80 lq, lx, ly;
UINT64 Rh, R, B2, B4, Ph, Ql, Ql2, carry, Qh;
if (!CY.w[1]) {
pCR->w[1] = 0;
if (!CX.w[1]) {
pCQ->w[0] = CX.w[0] / CY.w[0];
pCQ->w[1] = 0;
pCR->w[1] = 0;
pCR->w[0] = CX.w[0] - pCQ->w[0] * CY.w[0];
} else {
// This path works for CX<2^116 only
// 2^64
d64.i = 0x43f0000000000000;
// 2^64
dm64.i = 0x3bf0000000000000;
// 1.5*2^(-52)
ds.i = 0x3cb8000000000000;
dx = (BINARY80) CX.w[1] * d64.d + (BINARY80) CX.w[0];
dq = dx / (BINARY80) CY.w[0];
dq -= dq * (ds.d);
dqh = dq * dm64.d;
Qh = (UINT64) dqh;
Ql = (UINT64) (dq - ((double) Qh) * d64.d);
Rh = CX.w[0] - Ql * CY.w[0];
Ql2 = Rh / CY.w[0];
pCR->w[0] = Rh - Ql2 * CY.w[0];
__add_carry_out ((pCQ->w[0]), carry, Ql, Ql2);
pCQ->w[1] = Qh + carry;
}
return;
}
// now CY.w[1] > 0
// 2^64
t64.i = 0x5f800000;
lx = (BINARY80) CX.w[1] * (BINARY80) t64.d + (BINARY80) CX.w[0];
ly = (BINARY80) CY.w[1] * (BINARY80) t64.d + (BINARY80) CY.w[0];
lq = lx / ly;
pCQ->w[0] = (UINT64) lq;
pCQ->w[1] = 0;
if (!pCQ->w[0]) {
/*if(__unsigned_compare_ge_128(CX,CY))
{
pCQ->w[0] = 1;
__sub_128_128((*pCR), CX, CY);
}
else */
{
pCR->w[1] = CX.w[1];
pCR->w[0] = CX.w[0];
}
return;
}
if (CY.w[1] >= 16 || pCQ->w[0] <= 0x1000000000000000ull) {
pCQ->w[0] = (UINT64) lq - 1;
__mul_64x128_full (Ph, CQB, (pCQ->w[0]), CY);
__sub_128_128 (CA, CX, CQB);
if (__unsigned_compare_ge_128 (CA, CY)) {
__sub_128_128 (CA, CA, CY);
pCQ->w[0]++;
if (__unsigned_compare_ge_128 (CA, CY)) {
__sub_128_128 (CA, CA, CY);
pCQ->w[0]++;
}
}
pCR->w[1] = CA.w[1];
pCR->w[0] = CA.w[0];
} else {
pCQ->w[0] = (UINT64) lq - 6;
__mul_64x128_full (Ph, CQB, (pCQ->w[0]), CY);
__sub_128_128 (CA, CX, CQB);
CB8.w[1] = (CY.w[1] << 3) | (CY.w[0] >> 61);
CB8.w[0] = CY.w[0] << 3;
CB4.w[1] = (CY.w[1] << 2) | (CY.w[0] >> 62);
CB4.w[0] = CY.w[0] << 2;
CB2.w[1] = (CY.w[1] << 1) | (CY.w[0] >> 63);
CB2.w[0] = CY.w[0] << 1;
if (__unsigned_compare_ge_128 (CA, CB8)) {
pCQ->w[0] += 8;
__sub_128_128 (CA, CA, CB8);
}
if (__unsigned_compare_ge_128 (CA, CB4)) {
pCQ->w[0] += 4;
__sub_128_128 (CA, CA, CB4);
}
if (__unsigned_compare_ge_128 (CA, CB2)) {
pCQ->w[0] += 2;
__sub_128_128 (CA, CA, CB2);
}
if (__unsigned_compare_ge_128 (CA, CY)) {
pCQ->w[0] += 1;
__sub_128_128 (CA, CA, CY);
}
pCR->w[1] = CA.w[1];
pCR->w[0] = CA.w[0];
}
}
__BID_INLINE__ void
__div_256_by_128 (UINT128 * pCQ, UINT256 * pCA4, UINT128 CY) {
UINT256 CQ2Y;
UINT128 CQ2, CQ3Y;
UINT64 Q3, carry64;
int_double d64;
BINARY80 lx, ly, lq, l64, l128;
// 2^64
d64.i = 0x43f0000000000000ull;
l64 = (BINARY80) d64.d;
// 2^128
l128 = l64 * l64;
lx =
((BINARY80) (*pCA4).w[3] * l64 +
(BINARY80) (*pCA4).w[2]) * l128 +
(BINARY80) (*pCA4).w[1] * l64 + (BINARY80) (*pCA4).w[0];
ly = (BINARY80) CY.w[1] * l128 + (BINARY80) CY.w[0] * l64;
lq = lx / ly;
CQ2.w[1] = (UINT64) lq;
lq = (lq - CQ2.w[1]) * l64;
CQ2.w[0] = (UINT64) lq;
// CQ2*CY
__mul_128x128_to_256 (CQ2Y, CY, CQ2);
// CQ2Y <= (*pCA4) ?
if (CQ2Y.w[3] < (*pCA4).w[3]
|| (CQ2Y.w[3] == (*pCA4).w[3]
&& (CQ2Y.w[2] < (*pCA4).w[2]
|| (CQ2Y.w[2] == (*pCA4).w[2]
&& (CQ2Y.w[1] < (*pCA4).w[1]
|| (CQ2Y.w[1] == (*pCA4).w[1]
&& (CQ2Y.w[0] <= (*pCA4).w[0]))))))) {
// (*pCA4) -CQ2Y, guaranteed below 5*2^49*CY < 5*2^(49+128)
__sub_borrow_out ((*pCA4).w[0], carry64, (*pCA4).w[0], CQ2Y.w[0]);
__sub_borrow_in_out ((*pCA4).w[1], carry64, (*pCA4).w[1], CQ2Y.w[1],
carry64);
(*pCA4).w[2] = (*pCA4).w[2] - CQ2Y.w[2] - carry64;
lx = ((BINARY80) (*pCA4).w[2] * l128 +
((BINARY80) (*pCA4).w[1] * l64 +
(BINARY80) (*pCA4).w[0])) * l64;
lq = lx / ly;
Q3 = (UINT64) lq;
if (Q3) {
Q3--;
__mul_64x128_short (CQ3Y, Q3, CY);
__sub_borrow_out ((*pCA4).w[0], carry64, (*pCA4).w[0], CQ3Y.w[0]);
(*pCA4).w[1] = (*pCA4).w[1] - CQ3Y.w[1] - carry64;
if ((*pCA4).w[1] > CY.w[1]
|| ((*pCA4).w[1] == CY.w[1] && (*pCA4).w[0] >= CY.w[0])) {
Q3++;
__sub_borrow_out ((*pCA4).w[0], carry64, (*pCA4).w[0], CY.w[0]);
(*pCA4).w[1] = (*pCA4).w[1] - CY.w[1] - carry64;
if ((*pCA4).w[1] > CY.w[1]
|| ((*pCA4).w[1] == CY.w[1] && (*pCA4).w[0] >= CY.w[0])) {
Q3++;
__sub_borrow_out ((*pCA4).w[0], carry64, (*pCA4).w[0],
CY.w[0]);
(*pCA4).w[1] = (*pCA4).w[1] - CY.w[1] - carry64;
}
}
// add Q3 to Q2
__add_carry_out (CQ2.w[0], carry64, Q3, CQ2.w[0]);
CQ2.w[1] += carry64;
}
} else {
// CQ2Y - (*pCA4), guaranteed below 5*2^(49+128)
__sub_borrow_out ((*pCA4).w[0], carry64, CQ2Y.w[0], (*pCA4).w[0]);
__sub_borrow_in_out ((*pCA4).w[1], carry64, CQ2Y.w[1], (*pCA4).w[1],
carry64);
(*pCA4).w[2] = CQ2Y.w[2] - (*pCA4).w[2] - carry64;
lx =
((BINARY80) (*pCA4).w[2] * l128 +
(BINARY80) (*pCA4).w[1] * l64 + (BINARY80) (*pCA4).w[0]) * l64;
lq = lx / ly;
Q3 = 1 + (UINT64) lq;
__mul_64x128_short (CQ3Y, Q3, CY);
__sub_borrow_out ((*pCA4).w[0], carry64, CQ3Y.w[0], (*pCA4).w[0]);
(*pCA4).w[1] = CQ3Y.w[1] - (*pCA4).w[1] - carry64;
if ((SINT64) (*pCA4).w[1] > (SINT64) CY.w[1]
|| ((*pCA4).w[1] == CY.w[1] && (*pCA4).w[0] >= CY.w[0])) {
Q3--;
__sub_borrow_out ((*pCA4).w[0], carry64, (*pCA4).w[0], CY.w[0]);
(*pCA4).w[1] = (*pCA4).w[1] - CY.w[1] - carry64;
} else if ((SINT64) (*pCA4).w[1] < 0) {
Q3++;
__add_carry_out ((*pCA4).w[0], carry64, (*pCA4).w[0], CY.w[0]);
(*pCA4).w[1] = (*pCA4).w[1] + CY.w[1] + carry64;
}
// subtract Q3 from Q2
__sub_borrow_out (CQ2.w[0], carry64, CQ2.w[0], Q3);
CQ2.w[1] -= carry64;
}
// (*pCQ) + CQ2 + carry
__add_carry_out ((*pCQ).w[0], carry64, CQ2.w[0], (*pCQ).w[0]);
(*pCQ).w[1] = (*pCQ).w[1] + CQ2.w[1] + carry64;
}
#else
__BID_INLINE__ void
__div_128_by_128 (UINT128 * pCQ, UINT128 * pCR, UINT128 CX0, UINT128 CY) {
UINT128 CY36, CY51, CQ, A2, CX, CQT;
UINT64 Q;
int_double t64, d49, d60;
double lx, ly, lq;
if (!CX0.w[1] && !CY.w[1]) {
pCQ->w[0] = CX0.w[0] / CY.w[0];
pCQ->w[1] = 0;
pCR->w[1] = pCR->w[0] = 0;
pCR->w[0] = CX0.w[0] - pCQ->w[0] * CY.w[0];
return;
}
CX.w[1] = CX0.w[1];
CX.w[0] = CX0.w[0];
// 2^64
t64.i = 0x43f0000000000000ull;
lx = (double) CX.w[1] * t64.d + (double) CX.w[0];
ly = (double) CY.w[1] * t64.d + (double) CY.w[0];
lq = lx / ly;
CY36.w[1] = CY.w[0] >> (64 - 36);
CY36.w[0] = CY.w[0] << 36;
CQ.w[1] = CQ.w[0] = 0;
// Q >= 2^100 ?
if (!CY.w[1] && !CY36.w[1] && (CX.w[1] >= CY36.w[0])) {
// then Q >= 2^100
// 2^(-60)*CX/CY
d60.i = 0x3c30000000000000ull;
lq *= d60.d;
Q = (UINT64) lq - 4ull;
// Q*CY
__mul_64x64_to_128 (A2, Q, CY.w[0]);
// A2 <<= 60
A2.w[1] = (A2.w[1] << 60) | (A2.w[0] >> (64 - 60));
A2.w[0] <<= 60;
__sub_128_128 (CX, CX, A2);
lx = (double) CX.w[1] * t64.d + (double) CX.w[0];
lq = lx / ly;
CQ.w[1] = Q >> (64 - 60);
CQ.w[0] = Q << 60;
}
CY51.w[1] = (CY.w[1] << 51) | (CY.w[0] >> (64 - 51));
CY51.w[0] = CY.w[0] << 51;
if (CY.w[1] < (UINT64) (1 << (64 - 51))
&& (__unsigned_compare_gt_128 (CX, CY51))) {
// Q > 2^51
// 2^(-49)*CX/CY
d49.i = 0x3ce0000000000000ull;
lq *= d49.d;
Q = (UINT64) lq - 1ull;
// Q*CY
__mul_64x64_to_128 (A2, Q, CY.w[0]);
A2.w[1] += Q * CY.w[1];
// A2 <<= 49
A2.w[1] = (A2.w[1] << 49) | (A2.w[0] >> (64 - 49));
A2.w[0] <<= 49;
__sub_128_128 (CX, CX, A2);
CQT.w[1] = Q >> (64 - 49);
CQT.w[0] = Q << 49;
__add_128_128 (CQ, CQ, CQT);
lx = (double) CX.w[1] * t64.d + (double) CX.w[0];
lq = lx / ly;
}
Q = (UINT64) lq;
__mul_64x64_to_128 (A2, Q, CY.w[0]);
A2.w[1] += Q * CY.w[1];
__sub_128_128 (CX, CX, A2);
if ((SINT64) CX.w[1] < 0) {
Q--;
CX.w[0] += CY.w[0];
if (CX.w[0] < CY.w[0])
CX.w[1]++;
CX.w[1] += CY.w[1];
if ((SINT64) CX.w[1] < 0) {
Q--;
CX.w[0] += CY.w[0];
if (CX.w[0] < CY.w[0])
CX.w[1]++;
CX.w[1] += CY.w[1];
}
} else if (__unsigned_compare_ge_128 (CX, CY)) {
Q++;
__sub_128_128 (CX, CX, CY);
}
__add_128_64 (CQ, CQ, Q);
pCQ->w[1] = CQ.w[1];
pCQ->w[0] = CQ.w[0];
pCR->w[1] = CX.w[1];
pCR->w[0] = CX.w[0];
return;
}
__BID_INLINE__ void
__div_256_by_128 (UINT128 * pCQ, UINT256 * pCA4, UINT128 CY) {
UINT256 CA4, CA2, CY51, CY36;
UINT128 CQ, A2, A2h, CQT;
UINT64 Q, carry64;
int_double t64, d49, d60;
double lx, ly, lq, d128, d192;
// the quotient is assumed to be at most 113 bits,
// as needed by BID128 divide routines
// initial dividend
CA4.w[3] = (*pCA4).w[3];
CA4.w[2] = (*pCA4).w[2];
CA4.w[1] = (*pCA4).w[1];
CA4.w[0] = (*pCA4).w[0];
CQ.w[1] = (*pCQ).w[1];
CQ.w[0] = (*pCQ).w[0];
// 2^64
t64.i = 0x43f0000000000000ull;
d128 = t64.d * t64.d;
d192 = d128 * t64.d;
lx = (double) CA4.w[3] * d192 + ((double) CA4.w[2] * d128 +
((double) CA4.w[1] * t64.d +
(double) CA4.w[0]));
ly = (double) CY.w[1] * t64.d + (double) CY.w[0];
lq = lx / ly;
CY36.w[2] = CY.w[1] >> (64 - 36);
CY36.w[1] = (CY.w[1] << 36) | (CY.w[0] >> (64 - 36));
CY36.w[0] = CY.w[0] << 36;
CQ.w[1] = (*pCQ).w[1];
CQ.w[0] = (*pCQ).w[0];
// Q >= 2^100 ?
if (CA4.w[3] > CY36.w[2]
|| (CA4.w[3] == CY36.w[2]
&& (CA4.w[2] > CY36.w[1]
|| (CA4.w[2] == CY36.w[1] && CA4.w[1] >= CY36.w[0])))) {
// 2^(-60)*CA4/CY
d60.i = 0x3c30000000000000ull;
lq *= d60.d;
Q = (UINT64) lq - 4ull;
// Q*CY
__mul_64x128_to_192 (CA2, Q, CY);
// CA2 <<= 60
// CA2.w[3] = CA2.w[2] >> (64-60);
CA2.w[2] = (CA2.w[2] << 60) | (CA2.w[1] >> (64 - 60));
CA2.w[1] = (CA2.w[1] << 60) | (CA2.w[0] >> (64 - 60));
CA2.w[0] <<= 60;
// CA4 -= CA2
__sub_borrow_out (CA4.w[0], carry64, CA4.w[0], CA2.w[0]);
__sub_borrow_in_out (CA4.w[1], carry64, CA4.w[1], CA2.w[1],
carry64);
CA4.w[2] = CA4.w[2] - CA2.w[2] - carry64;
lx = ((double) CA4.w[2] * d128 +
((double) CA4.w[1] * t64.d + (double) CA4.w[0]));
lq = lx / ly;
CQT.w[1] = Q >> (64 - 60);
CQT.w[0] = Q << 60;
__add_128_128 (CQ, CQ, CQT);
}
CY51.w[2] = CY.w[1] >> (64 - 51);
CY51.w[1] = (CY.w[1] << 51) | (CY.w[0] >> (64 - 51));
CY51.w[0] = CY.w[0] << 51;
if (CA4.w[2] > CY51.w[2] || ((CA4.w[2] == CY51.w[2])
&&
(__unsigned_compare_gt_128 (CA4, CY51))))
{
// Q > 2^51
// 2^(-49)*CA4/CY
d49.i = 0x3ce0000000000000ull;
lq *= d49.d;
Q = (UINT64) lq - 1ull;
// Q*CY
__mul_64x64_to_128 (A2, Q, CY.w[0]);
__mul_64x64_to_128 (A2h, Q, CY.w[1]);
A2.w[1] += A2h.w[0];
if (A2.w[1] < A2h.w[0])
A2h.w[1]++;
// A2 <<= 49
CA2.w[2] = (A2h.w[1] << 49) | (A2.w[1] >> (64 - 49));
CA2.w[1] = (A2.w[1] << 49) | (A2.w[0] >> (64 - 49));
CA2.w[0] = A2.w[0] << 49;
__sub_borrow_out (CA4.w[0], carry64, CA4.w[0], CA2.w[0]);
__sub_borrow_in_out (CA4.w[1], carry64, CA4.w[1], CA2.w[1],
carry64);
CA4.w[2] = CA4.w[2] - CA2.w[2] - carry64;
CQT.w[1] = Q >> (64 - 49);
CQT.w[0] = Q << 49;
__add_128_128 (CQ, CQ, CQT);
lx = ((double) CA4.w[2] * d128 +
((double) CA4.w[1] * t64.d + (double) CA4.w[0]));
lq = lx / ly;
}
Q = (UINT64) lq;
__mul_64x64_to_128 (A2, Q, CY.w[0]);
A2.w[1] += Q * CY.w[1];
__sub_128_128 (CA4, CA4, A2);
if ((SINT64) CA4.w[1] < 0) {
Q--;
CA4.w[0] += CY.w[0];
if (CA4.w[0] < CY.w[0])
CA4.w[1]++;
CA4.w[1] += CY.w[1];
if ((SINT64) CA4.w[1] < 0) {
Q--;
CA4.w[0] += CY.w[0];
if (CA4.w[0] < CY.w[0])
CA4.w[1]++;
CA4.w[1] += CY.w[1];
}
} else if (__unsigned_compare_ge_128 (CA4, CY)) {
Q++;
__sub_128_128 (CA4, CA4, CY);
}
__add_128_64 (CQ, CQ, Q);
pCQ->w[1] = CQ.w[1];
pCQ->w[0] = CQ.w[0];
pCA4->w[1] = CA4.w[1];
pCA4->w[0] = CA4.w[0];
return;
}
#endif
#endif
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