| /* Copyright (C) 2007, 2009 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 |