gcc/libgcc/config/libbid/bid_div_macros.h

/* Copyright (C) 2007  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 2, or (at your option) any later
version.

In addition to the permissions in the GNU General Public License, the
Free Software Foundation gives you unlimited permission to link the
compiled version of this file into combinations with other programs,
and to distribute those combinations without any restriction coming
from the use of this file.  (The General Public License restrictions
do apply in other respects; for example, they cover modification of
the file, and distribution when not linked into a combine
executable.)

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.

You should have received a copy of the GNU General Public License
along with GCC; see the file COPYING.  If not, write to the Free
Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA
02110-1301, USA.  */

#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