256 lines
8.1 KiB
C
256 lines
8.1 KiB
C
/*
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dnl Copyright 2009 Jason Moxham
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dnl This file is part of the MPIR Library.
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dnl The MPIR Library is free software; you can redistribute it and/or modify
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dnl it under the terms of the GNU Lesser General Public License as published
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dnl by the Free Software Foundation; either version 2.1 of the License, or (at
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dnl your option) any later version.
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dnl The MPIR Library is distributed in the hope that it will be useful, but
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dnl WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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dnl or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
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dnl License for more details.
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dnl You should have received a copy of the GNU Lesser General Public License
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dnl along with the MPIR Library; see the file COPYING.LIB. If not, write
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dnl to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
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dnl Boston, MA 02110-1301, USA.
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*/
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#include "mpir.h"
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#include "gmp-impl.h"
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#include "longlong.h"
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mp_limb_t mpn_mod_1_1_wrap(mp_srcptr xp,mp_size_t xn,mp_limb_t d)// in each round we hack off a limb from the body , ie k=1
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{mp_limb_t crap,h,l,sh,sl,ret,i,c,ds,db[2],rem[2];
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mp_size_t j;
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ASSERT_MPN(xp,xn);
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if(xn==0)return 0;
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if(xn==1)return xp[0]%d;
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ASSERT(d-1<=GMP_LIMB_HIGHBIT);
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count_leading_zeros(c,d);ds=d<<c;
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invert_limb(i,ds);
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udiv_qrnnd_preinv(crap,db[0],((mp_limb_t)1)<<c,0,ds,i); // is B%ds
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udiv_qrnnd_preinv(crap,db[1],db[0],0,ds,i);// is B^2%ds could calc indep of db[0]
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db[0]>>=c;db[1]>>=c;// are now B^i %d
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mpn_mod_1_1(rem,xp,xn,db);
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/*
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h=xp[xn-1];l=xp[xn-2];
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for(j=xn-3;j>=0;j--)
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{umul_ppmm(sh,sl,l,db[0]);
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add_ssaaaa(sh,sl,sh,sl,0,xp[j]);
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umul_ppmm(h,l,h,db[1]);
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add_ssaaaa(h,l,h,l,sh,sl);}
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umul_ppmm(sh,sl,h,db[0]);
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add_ssaaaa(sh,sl,sh,sl,0,l);
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*/
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sh=rem[1];sl=rem[0];
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ASSERT(sh<d);
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udiv_qrnnd_preinv(crap,ret,(sh<<c)|((sl>>(GMP_LIMB_BITS-1-c))>>1),sl<<c,ds,i);
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return ret>>c;}
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mp_limb_t mpn_mod_1_2_wrap(mp_srcptr xp,mp_size_t xn,mp_limb_t d)// in each round we hack off two limbs from the body , ie k=2
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{mp_limb_t crap,h,l,sh,sl,th,tl,i,ret,ds,c,db[3],rem[2];
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mp_size_t j;
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ASSERT_MPN(xp,xn);
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if(xn==0)return 0;
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if(xn==1)return xp[0]%d;
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umul_ppmm(h,l,d-1,3);ASSERT(h==0 || (h==1 && l==0));// ie (k+1)(d-1)<=B
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count_leading_zeros(c,d);ds=d<<c;
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invert_limb(i,ds);
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udiv_qrnnd_preinv(crap,db[0],((mp_limb_t)1)<<c,0,ds,i);
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udiv_qrnnd_preinv(crap,db[1],db[0],0,ds,i);db[0]>>=c;
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udiv_qrnnd_preinv(crap,db[2],db[1],0,ds,i);db[1]>>=c;
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db[2]>>=c;
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mpn_mod_1_2(rem,xp,xn,db);
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h=rem[1];l=rem[0];
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/*
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tl=xp[xn-2];th=xp[xn-1];
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for(j=xn-4;j>=0;j-=2)
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{umul_ppmm(sh,sl,xp[j+1],db[0]);
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add_ssaaaa(sh,sl,sh,sl,0,xp[j]);
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umul_ppmm(h,l,tl,db[1]);
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add_ssaaaa(sh,sl,sh,sl,h,l);
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umul_ppmm(th,tl,th,db[2]);
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add_ssaaaa(th,tl,th,tl,sh,sl);}
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if(j>-2)// we have at least three limbs to do still ie xp[0],...,tl,th
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{umul_ppmm(sh,sl,tl,db[0]);
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add_ssaaaa(sh,sl,sh,sl,0,xp[0]);
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umul_ppmm(th,tl,th,db[1]);
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add_ssaaaa(th,tl,th,tl,sh,sl);}
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umul_ppmm(h,l,th,db[0]);
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add_ssaaaa(h,l,h,l,0,tl);
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*/
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ASSERT(h<d);
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udiv_qrnnd_preinv(crap,ret,(h<<c)|((l>>(GMP_LIMB_BITS-1-c))>>1),l<<c,ds,i);
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return ret>>c;}
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mp_limb_t mpn_mod_1_3_wrap(mp_srcptr xp,mp_size_t xn,mp_limb_t d)// in each round we hack off 3 limbs from the body
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{mp_limb_t crap,h,l,sh,sl,th,tl,i,ret,ds,c,db[4],rem[2];
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mp_size_t j,jj;
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ASSERT_MPN(xp,xn);
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if(xn==0)return 0;
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if(xn==1)return xp[0]%d;
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umul_ppmm(h,l,d-1,4);ASSERT(h==0 || (h==1 && l==0));// ie (k+1)(d-1)<=B
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count_leading_zeros(c,d);ds=d<<c;
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invert_limb(i,ds);
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udiv_qrnnd_preinv(crap,db[0],((mp_limb_t)1)<<c,0,ds,i);
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udiv_qrnnd_preinv(crap,db[1],db[0],0,ds,i);db[0]>>=c;
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udiv_qrnnd_preinv(crap,db[2],db[1],0,ds,i);db[1]>>=c;
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udiv_qrnnd_preinv(crap,db[3],db[2],0,ds,i);db[2]>>=c;
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db[3]>>=c;
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mpn_mod_1_3(rem,xp,xn,db);
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h=rem[1];l=rem[0];
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/*
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tl=xp[xn-2];th=xp[xn-1];
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for(j=xn-5;j>=0;j-=3)
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{umul_ppmm(sh,sl,xp[j+1],db[0]);
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add_ssaaaa(sh,sl,sh,sl,0,xp[j]);
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umul_ppmm(h,l,xp[j+2],db[1]);
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add_ssaaaa(sh,sl,sh,sl,h,l);
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umul_ppmm(h,l,tl,db[2]);
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add_ssaaaa(sh,sl,sh,sl,h,l);
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umul_ppmm(th,tl,th,db[3]);
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add_ssaaaa(th,tl,th,tl,sh,sl);}
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if(j>-3)// we have at least three limbs to do still ie xp[0],...,tl,th
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{sh=0;sl=xp[0];jj=1;
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if(j==-1)
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{umul_ppmm(sh,sl,xp[1],db[0]);
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add_ssaaaa(sh,sl,sh,sl,0,xp[0]);
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jj=2;}
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umul_ppmm(h,l,tl,db[jj-1]);
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add_ssaaaa(sh,sl,sh,sl,h,l);
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umul_ppmm(th,tl,th,db[jj]);
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add_ssaaaa(th,tl,th,tl,sh,sl);}
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umul_ppmm(h,l,th,db[0]);
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add_ssaaaa(h,l,h,l,0,tl);
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*/
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ASSERT(h<d);
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udiv_qrnnd_preinv(crap,ret,(h<<c)|((l>>(GMP_LIMB_BITS-1-c))>>1),l<<c,ds,i);
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return ret>>c;}
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// This is a generic version for k>=2
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mp_limb_t mpn_mod_1_k(mp_srcptr xp,mp_size_t xn,mp_limb_t d,mp_size_t k)// in each round we hack off k limbs from the body
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{mp_limb_t crap,h,l,sh,sl,th,tl,i,ret,ds,c,db[30];//need k+1 entries in array
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mp_size_t j,jj;
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ASSERT_MPN(xp,xn);
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if(xn==0)return 0;
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if(xn==1)return xp[0]%d;
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ASSERT(k>=2);
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umul_ppmm(h,l,d-1,k+1);ASSERT(h==0 || (h==1 && l==0));// ie (k+1)(d-1)<=B
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count_leading_zeros(c,d);ds=d<<c;
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invert_limb(i,ds);
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udiv_qrnnd_preinv(crap,db[0],((mp_limb_t)1)<<c,0,ds,i);
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ASSERT_ALWAYS(k+1<=numberof(db));
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for(j=1;j<=k;j++){udiv_qrnnd_preinv(crap,db[j],db[j-1],0,ds,i);db[j-1]>>=c;}// so db[j]=B^j %d
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db[k]>>=c;tl=xp[xn-2];th=xp[xn-1];
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for(j=xn-k-2;j>=0;j-=k)
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{umul_ppmm(sh,sl,xp[j+1],db[0]);
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add_ssaaaa(sh,sl,sh,sl,0,xp[j]);
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for(jj=2;jj<=k-1;jj++)
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{umul_ppmm(h,l,xp[j+jj],db[jj-1]);
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add_ssaaaa(sh,sl,sh,sl,h,l);}
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umul_ppmm(h,l,tl,db[k-1]);
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add_ssaaaa(sh,sl,sh,sl,h,l);
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umul_ppmm(th,tl,th,db[k]);
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add_ssaaaa(th,tl,th,tl,sh,sl);}
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if(j+k>0)// we have at least three limbs to do still ie xp[0],...,tl,th
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{sh=0;sl=xp[0];
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for(jj=1;jj<j+k;jj++)
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{umul_ppmm(h,l,xp[jj],db[jj-1]);
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add_ssaaaa(sh,sl,sh,sl,h,l);}
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umul_ppmm(h,l,tl,db[jj-1]);
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add_ssaaaa(sh,sl,sh,sl,h,l);
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umul_ppmm(th,tl,th,db[jj]);
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add_ssaaaa(th,tl,th,tl,sh,sl);}
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umul_ppmm(h,l,th,db[0]);
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add_ssaaaa(h,l,h,l,0,tl);
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ASSERT(h<d);
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udiv_qrnnd_preinv(crap,ret,(h<<c)|(l>>(GMP_LIMB_BITS-c)),l<<c,ds,i);
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return ret>>c;}
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// d is mormalized
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#define udiv_inverse(i,d) do{mp_limb_t __X;udiv_qrnnd(i,__X,~(d),GMP_LIMB_MAX,d);}while(0)
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// note double lenght inverse can easily be calculated from single length inverse
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// d is normalize
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#define udiv_double_inverse(ih,il,d) \
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do{mp_limb_t __X;udiv_qrnnd(ih,__X,~(d),GMP_LIMB_MAX,d);udiv_qrnnd(il,__X,__X,GMP_LIMB_MAX,d);}while(0)
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// set to 1=store or 0=not store
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#define STORE_QUOTIENT 0
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// set to 0=udiv 1=gmp-preinv 2-barrett
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#define UDIV_METHOD 1
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#if UDIV_NEEDS_NORMALIZATION==1 || UDIV_METHOD==1
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#define NORMALIZE 1
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#else
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#define NORMALIZE 0
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#endif
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#if UDIV_METHOD==0
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#define UDIV(q,r,h,l,d,i) udiv_qrnnd(q,r,h,l,d)
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#endif
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#if UDIV_METHOD==1
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#define UDIV udiv_qrnnd_preinv
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#endif
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#if UDIV_METHOD==2
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#define UDIV udiv_qrnnd_barrett
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#endif
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#if STORE_QUOTIENT
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mp_limb_t mpn_divrem_euclidean_qr_1(mp_ptr qp,mp_size_t qxn,mp_srcptr xp,mp_size_t n,mp_limb_t d)
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#else
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mp_limb_t mpn_divrem_euclidean_r_1(mp_srcptr xp,mp_size_t n,mp_limb_t d)
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#endif
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{mp_size_t j;
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mp_limb_t r=0,s=0,h,l,q,i;
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#if STORE_QUOTIENT
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ASSET_ALWAYS(qxn==0);
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#endif
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ASSERT(n>0);ASSERT(d!=0);ASSERT_MPN(xp,n);
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#if STORE_QUOTIENT
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ASSERT(MPN_SAME_OR_SEPARATE_P(qp,xp,n));
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#endif
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if(d<=GMP_LIMB_HIGHBIT/2+1 && ABOVE_THRESHOLD(n,MOD_1_3_THRESHOLD))return mpn_mod_1_3_wrap(xp,n,d);
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if(d<=MP_LIMB_T_MAX/3+1 && ABOVE_THRESHOLD(n,MOD_1_2_THRESHOLD))return mpn_mod_1_2_wrap(xp,n,d);
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if(d<=GMP_LIMB_HIGHBIT+1 && ABOVE_THRESHOLD(n,MOD_1_1_THRESHOLD))return mpn_mod_1_1_wrap(xp,n,d);
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// for n=1 or n=2 probably faster to do a special case
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#if NORMALIZE==1
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count_leading_zeros(s,d);d=d<<s;
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invert_limb(i,d);
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#endif
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for(j=n-1;j>=0;j--)
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{l=xp[j]; // out dlimb is (h=r,l)
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h=(l>>((GMP_LIMB_BITS-1-s))>>1);l=l<<s;// shift dlimb left by s
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h=h+r; // carry in
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UDIV(q,r,h,l,d,i); // carry out , carry-out to carry-in is the critical latency bottleneck
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#if STORE_QUOTIENT
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qp[j]=q;
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#endif
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}
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ASSERT((r<<(GMP_LIMB_BITS-1-s)<<1)==0);// ie bottom s bits of r are zero
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r>>=s;
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return r;} // so (xp,n) = (qp,n)*d +r and 0 <= r < d
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/*
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in hensel-div we use shiftout which means we can use mmx shifting and dont need to always use it
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in euclid-div shiftout needs a final div for the remainder
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*/
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