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big.c
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big.c
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/**
* @file big.c
* @author Mike Scott
* @date 19th May 2015
* @brief AMCL basic functions for BIG type
*
* LICENSE
*
* Licensed to the Apache Software Foundation (ASF) under one
* or more contributor license agreements. See the NOTICE file
* distributed with this work for additional information
* regarding copyright ownership. The ASF licenses this file
* to you under the Apache License, Version 2.0 (the
* "License"); you may not use this file except in compliance
* with the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing,
* software distributed under the License is distributed on an
* "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
* KIND, either express or implied. See the License for the
* specific language governing permissions and limitations
* under the License.
*/
/* AMCL basic functions for BIG type */
/* SU=m, SU is Stack Usage */
#include "amcl.h"
/* Calculates x*y+c+*r */
#ifdef dchunk
/* Method required to calculate x*y+c+r, bottom half in r, top half returned */
chunk muladd(chunk x,chunk y,chunk c,chunk *r)
{
dchunk prod=(dchunk)x*y+c+*r;
*r=(chunk)prod&BMASK;
return (chunk)(prod>>BASEBITS);
}
#else
/* No integer type available that can store double the wordlength */
/* accumulate partial products */
/* Method required to calculate x*y+c+r, bottom half in r, top half returned */
chunk muladd(chunk x,chunk y,chunk c,chunk *r)
{
chunk x0,x1,y0,y1;
chunk bot,top,mid,carry;
x0=x&HMASK;
x1=(x>>HBITS);
y0=y&HMASK;
y1=(y>>HBITS);
bot=x0*y0;
top=x1*y1;
mid=x0*y1+x1*y0;
x0=mid&HMASK1;
x1=(mid>>HBITS1);
bot+=x0<<HBITS;
bot+=*r;
bot+=c;
#if HDIFF==1
bot+=(top&HDIFF)<<(BASEBITS-1);
top>>=HDIFF;
#endif
top+=x1;
carry=bot>>BASEBITS;
bot&=BMASK;
top+=carry;
*r=bot;
return top;
}
#endif
/*
// Alternative non Standard Solution required if no type available that can store double the wordlength
// The use of compiler intrinsics is permitted
#if CHUNK==64
#ifdef _WIN64
#include <intrin.h>
static INLINE chunk muladd(chunk x,chunk y,chunk c,chunk *r)
{
chunk t,e;
uchunk b;
b=_mul128(x,y,&t);
e=c+*r;
b+=e;
// make correction for possible carry to top half
if (e<0)
t-=(b>e);
else
t+=(b<e);
*r=b&MASK;
return (chunk)((t<<(CHUNK-BASEBITS)) | (b>>BASEBITS));
}
#endif
#endif
*/
/* Tests for BIG equal to zero */
int BIG_iszilch(BIG a)
{
int i;
for (i=0; i<NLEN; i++)
if (a[i]!=0) return 0;
return 1;
}
/* Tests for DBIG equal to zero */
int BIG_diszilch(DBIG a)
{
int i;
for (i=0; i<DNLEN; i++)
if (a[i]!=0) return 0;
return 1;
}
/* SU= 56, Outputs a BIG number to the console */
void BIG_output(BIG a)
{
BIG b;
int i,len;
len=BIG_nbits(a);
if (len%4==0) len/=4;
else
{
len/=4;
len++;
}
if (len<MODBYTES*2) len=MODBYTES*2;
for (i=len-1; i>=0; i--)
{
BIG_copy(b,a);
BIG_shr(b,i*4);
printf("%01x",(unsigned int) b[0]&15);
}
}
/* SU= 16, Outputs a BIG number to the console in raw form (for debugging) */
void BIG_rawoutput(BIG a)
{
int i;
printf("(");
for (i=0; i<NLEN-1; i++)
#if CHUNK==64
printf("%"PRId64",",(uint64_t) a[i]);
printf("%"PRId64")",(uint64_t) a[NLEN-1]);
#else
printf("%x,",(unsigned int) a[i]);
printf("%x)",(unsigned int) a[NLEN-1]);
#endif
}
/*
void BIG_rawdoutput(DBIG a)
{
int i;
printf("(");
for (i=0;i<DNLEN-1;i++)
#if CHUNK==64
printf("%llx,",(long long unsigned int) a[i]);
printf("%llx)",(long long unsigned int) a[DNLEN-1]);
#else
printf("%x,",(unsigned int) a[i]);
printf("%x)",(unsigned int) a[NLEN-1]);
#endif
}
*/
/* Conditional constant time swap of two BIG numbers */
void BIG_cswap(BIG a,BIG b,int d)
{
int i;
chunk t,c=d;
c=~(c-1);
#ifdef DEBUG_NORM
for (i=0; i<=NLEN; i++)
#else
for (i=0; i<NLEN; i++)
#endif
{
t=c&(a[i]^b[i]);
a[i]^=t;
b[i]^=t;
}
}
/* Conditional copy of BIG number */
void BIG_cmove(BIG f,BIG g,int d)
{
int i;
chunk b=(chunk)-d;
#ifdef DEBUG_NORM
for (i=0; i<=NLEN; i++)
#else
for (i=0; i<NLEN; i++)
#endif
{
f[i]^=(f[i]^g[i])&b;
}
}
/* Move g to f if d=1 */
void BIG_dcmove(DBIG f,DBIG g,int d)
{
int i;
chunk b=(chunk)-d;
#ifdef DEBUG_NORM
for (i=0;i<=DNLEN;i++)
#else
for (i=0;i<DNLEN;i++)
#endif
{
f[i]^=(f[i]^g[i])&b;
}
}
/* SU= 64, Convert from BIG number to byte array */
void BIG_toBytes(char *b,BIG a)
{
int i;
BIG c;
BIG_norm(a);
BIG_copy(c,a);
for (i=MODBYTES-1; i>=0; i--)
{
b[i]=c[0]&0xff;
BIG_fshr(c,8);
}
}
/* SU= 16, Convert to BIG number from byte array */
void BIG_fromBytes(BIG a,char *b)
{
int i;
BIG_zero(a);
for (i=0; i<MODBYTES; i++)
{
BIG_fshl(a,8);
a[0]+=(int)(unsigned char)b[i];
//BIG_inc(a,(int)(unsigned char)b[i]); BIG_norm(a);
}
#ifdef DEBUG_NORM
a[NLEN]=0;
#endif
}
/* Convert to BIG number from byte array of given length */
void BIG_fromBytesLen(BIG a,char *b,int s)
{
int i,len=s;
BIG_zero(a);
if (s>MODBYTES) s=MODBYTES;
for (i=0; i<len; i++)
{
BIG_fshl(a,8);
a[0]+=(int)(unsigned char)b[i];
}
#ifdef DEBUG_NORM
a[NLEN]=0;
#endif
}
/* Convert to DBIG number from byte array of given length */
void BIG_dfromBytesLen(DBIG a,char *b,int s)
{
int i,len=s;
BIG_dzero(a);
for (i=0; i<len; i++)
{
BIG_dshl(a,8);
a[0]+=(int)(unsigned char)b[i];
}
#ifdef DEBUG_NORM
a[NLEN]=0;
#endif
}
/* SU= 88, Outputs a DBIG number to the console */
void BIG_doutput(DBIG a)
{
DBIG b;
int i,len;
BIG_dnorm(a);
len=BIG_dnbits(a);
if (len%4==0) len/=4;
else
{
len/=4;
len++;
}
for (i=len-1; i>=0; i--)
{
BIG_dcopy(b,a);
BIG_dshr(b,i*4);
printf("%01x",(unsigned int) b[0]&15);
}
}
/* Copy b=a, Copy BIG to another BIG */
void BIG_copy(BIG b,BIG a)
{
int i;
for (i=0; i<NLEN; i++)
b[i]=a[i];
#ifdef DEBUG_NORM
b[NLEN]=a[NLEN];
#endif
}
/* Copy from ROM b=a, Copy BIG from Read-Only Memory to a BIG */
void BIG_rcopy(BIG b,const BIG a)
{
int i;
for (i=0; i<NLEN; i++)
b[i]=a[i];
#ifdef DEBUG_NORM
b[NLEN]=0;
#endif
}
/* double length DBIG copy b=a */
void BIG_dcopy(DBIG b,DBIG a)
{
int i;
for (i=0; i<DNLEN; i++)
b[i]=a[i];
#ifdef DEBUG_NORM
b[DNLEN]=a[DNLEN];
#endif
}
/* Copy BIG to lower half of DBIG */
void BIG_dscopy(DBIG b,BIG a)
{
int i;
for (i=0; i<NLEN-1; i++)
b[i]=a[i];
b[NLEN-1]=a[NLEN-1]&BMASK; /* top word normalized */
b[NLEN]=a[NLEN-1]>>BASEBITS;
for (i=NLEN+1; i<DNLEN; i++) b[i]=0;
#ifdef DEBUG_NORM
b[DNLEN]=a[NLEN];
#endif
}
/* Copy BIG to upper half of DBIG */
void BIG_dsucopy(DBIG b,BIG a)
{
int i;
for (i=0; i<NLEN; i++)
b[i]=0;
for (i=NLEN; i<DNLEN; i++)
b[i]=a[i-NLEN];
#ifdef DEBUG_NORM
b[DNLEN]=a[NLEN];
#endif
}
/* Copy lower half of DBIG to a BIG */
void BIG_sdcopy(BIG b,DBIG a)
{
int i;
for (i=0; i<NLEN; i++)
b[i]=a[i];
#ifdef DEBUG_NORM
b[NLEN]=a[DNLEN];
#endif
}
/* Copy upper half of DBIG to a BIG */
void BIG_sducopy(BIG b,DBIG a)
{
int i;
for (i=0; i<NLEN; i++)
b[i]=a[i+NLEN];
#ifdef DEBUG_NORM
b[NLEN]=a[DNLEN];
#endif
}
/* Set BIG to zero */
void BIG_zero(BIG a)
{
int i;
for (i=0; i<NLEN; i++)
a[i]=0;
#ifdef DEBUG_NORM
a[NLEN]=0;
#endif
}
/* Set DBIG to zero */
void BIG_dzero(DBIG a)
{
int i;
for (i=0; i<DNLEN; i++)
a[i]=0;
#ifdef DEBUG_NORM
a[DNLEN]=0;
#endif
}
/* Set BIG to one (unity) */
void BIG_one(BIG a)
{
int i;
a[0]=1;
for (i=1; i<NLEN; i++)
a[i]=0;
#ifdef DEBUG_NORM
a[NLEN]=0;
#endif
}
/* SU= 8, Set BIG to sum of two BIGs - output not normalised */
void BIG_add(BIG c,BIG a,BIG b)
{
int i;
for (i=0; i<NLEN; i++)
c[i]=a[i]+b[i];
#ifdef DEBUG_NORM
c[NLEN]=a[NLEN]+b[NLEN]+1;
if (c[NLEN]>=NEXCESS) printf("add problem - digit overflow %lu\n",c[NLEN]);
#endif
}
/* Increment BIG by a small integer - output not normalised */
void BIG_inc(BIG c,int d)
{
BIG_norm(c);
c[0]+=(chunk)d;
#ifdef DEBUG_NORM
c[NLEN]=1;
#endif
}
/* SU= 8, Set BIG to difference of two BIGs */
void BIG_sub(BIG c,BIG a,BIG b)
{
int i;
for (i=0; i<NLEN; i++)
c[i]=a[i]-b[i];
#ifdef DEBUG_NORM
c[NLEN]=a[NLEN]+b[NLEN]+1;
if (c[NLEN]>=NEXCESS) printf("sub problem - digit overflow %d\n",c[NLEN]);
#endif
}
/* SU= 8, Set DBIG to difference of two DBIGs */
void BIG_dsub(DBIG c,DBIG a,DBIG b)
{
int i;
for (i=0; i<DNLEN; i++)
c[i]=a[i]-b[i];
#ifdef DEBUG_NORM
c[DNLEN]=a[DNLEN]+b[DNLEN]+1;
if (c[DNLEN]>=NEXCESS) printf("sub problem - digit overflow %d\n",c[DNLEN]);
#endif
}
/* Decrement BIG by a small integer - output not normalised */
void BIG_dec(BIG c,int d)
{
BIG_norm(c);
c[0]-=(chunk)d;
#ifdef DEBUG_NORM
c[NLEN]=1;
#endif
}
/* Multiply BIG by a small integer - output not normalised. r=a*c by c<=NEXCESS */
void BIG_imul(BIG r,BIG a,int c)
{
int i;
for (i=0; i<NLEN; i++) r[i]=a[i]*c;
#ifdef DEBUG_NORM
r[NLEN]=(a[NLEN]+1)*c-1;
if (r[NLEN]>=NEXCESS) printf("int mul problem - digit overflow %d\n",r[NLEN]);
#endif
}
/* SU= 24, Multiply BIG by not-so-small small integer - output normalised. r=a*c by larger integer - c<=FEXCESS */
chunk BIG_pmul(BIG r,BIG a,int c)
{
int i;
chunk ak,carry=0;
BIG_norm(a);
for (i=0; i<NLEN; i++)
{
ak=a[i];
r[i]=0;
carry=muladd(ak,(chunk)c,carry,&r[i]);
}
#ifdef DEBUG_NORM
r[NLEN]=0;
#endif
return carry;
}
/* SU= 16, Divide BIG by 3 - output normalised */
int BIG_div3(BIG r)
{
int i;
chunk ak,base,carry=0;
BIG_norm(r);
base=((chunk)1<<BASEBITS);
for (i=NLEN-1; i>=0; i--)
{
ak=(carry*base+r[i]);
r[i]=ak/3;
carry=ak%3;
}
return (int)carry;
}
/* SU= 24. Multiply BIG by even bigger small integer resulting in a DBIG - output normalised. c=a*b by even larger integer b>FEXCESS, resulting in DBIG */
void BIG_pxmul(DBIG c,BIG a,int b)
{
int j;
chunk carry;
BIG_dzero(c);
carry=0;
for (j=0; j<NLEN; j++)
carry=muladd(a[j],(chunk)b,carry,&c[j]);
c[NLEN]=carry;
#ifdef DEBUG_NORM
c[DNLEN]=0;
#endif
}
/* SU= 72, Multiply BIG by another BIG resulting in DBIG - inputs normalised and output normalised */
void BIG_mul(DBIG c,BIG a,BIG b)
{
int i;
#ifdef dchunk
dchunk t,co;
dchunk s;
dchunk d[NLEN];
int k;
#endif
/* change here - a and b MUST be normed on input */
// BIG_norm(a); /* needed here to prevent overflow from addition of partial products */
// BIG_norm(b);
/* Faster to Combafy it.. Let the compiler unroll the loops! */
#ifdef COMBA
/* faster pseudo-Karatsuba method */
for (i=0; i<NLEN; i++)
d[i]=(dchunk)a[i]*b[i];
s=d[0];
t=s;
c[0]=(chunk)t&BMASK;
co=t>>BASEBITS;
for (k=1; k<NLEN; k++)
{
s+=d[k];
t=co+s;
for (i=k; i>=1+k/2; i--) t+=(dchunk)(a[i]-a[k-i])*(b[k-i]-b[i]);
c[k]=(chunk)t&BMASK;
co=t>>BASEBITS;
}
for (k=NLEN; k<2*NLEN-1; k++)
{
s-=d[k-NLEN];
t=co+s;
for (i=NLEN-1; i>=1+k/2; i--) t+=(dchunk)(a[i]-a[k-i])*(b[k-i]-b[i]);
c[k]=(chunk)t&BMASK;
co=t>>BASEBITS;
}
c[2*NLEN-1]=(chunk)co;
#else
int j;
chunk carry;
BIG_dzero(c);
for (i=0; i<NLEN; i++)
{
carry=0;
for (j=0; j<NLEN; j++)
carry=muladd(a[i],b[j],carry,&c[i+j]);
c[NLEN+i]=carry;
}
#endif
#ifdef DEBUG_NORM
c[DNLEN]=0;
#endif
}
/* SU= 40, Multiply BIG by another BIG resulting in another BIG - inputs normalised and output normalised. */
void BIG_smul(BIG c,BIG a,BIG b)
{
int i,j;
chunk carry;
BIG_norm(a);
BIG_norm(b);
BIG_zero(c);
for (i=0; i<NLEN; i++)
{
carry=0;
for (j=0; j<NLEN; j++)
{
if (i+j<NLEN)
carry=muladd(a[i],b[j],carry,&c[i+j]);
}
}
#ifdef DEBUG_NORM
c[NLEN]=0;
#endif
}
/* SU= 80, Square BIG resulting in a DBIG - input normalised and output normalised */
void BIG_sqr(DBIG c,BIG a)
{
int i,j,last;
#ifdef dchunk
dchunk t,co;
#endif
/* change here - a MUST be normed on input */
// BIG_norm(a);
/* Note 2*a[i] in loop below and extra addition */
#ifdef COMBA
t=(dchunk)a[0]*a[0];
c[0]=(chunk)t&BMASK;
co=t>>BASEBITS;
t=(dchunk)a[1]*a[0];
t+=t;
t+=co;
c[1]=(chunk)t&BMASK;
co=t>>BASEBITS;
last=NLEN-NLEN%2;
for (j=2; j<last; j+=2)
{
t=(dchunk)a[j]*a[0];
for (i=1; i<(j+1)/2; i++) t+=(dchunk)a[j-i]*a[i];
t+=t;
t+=co;
t+=(dchunk)a[j/2]*a[j/2];
c[j]=(chunk)t&BMASK;
co=t>>BASEBITS;
t=(dchunk)a[j+1]*a[0];
for (i=1; i<(j+2)/2; i++) t+=(dchunk)a[j+1-i]*a[i];
t+=t;
t+=co;
c[j+1]=(chunk)t&BMASK;
co=t>>BASEBITS;
}
j=last;
#if NLEN%2==1
t=(dchunk)a[j]*a[0];
for (i=1; i<(j+1)/2; i++) t+=(dchunk)a[j-i]*a[i];
t+=t;
t+=co;
t+=(dchunk)a[j/2]*a[j/2];
c[j]=(chunk)t&BMASK;
co=t>>BASEBITS;
j++;
t=(dchunk)a[NLEN-1]*a[j-NLEN+1];
for (i=j-NLEN+2; i<(j+1)/2; i++) t+=(dchunk)a[j-i]*a[i];
t+=t;
t+=co;
c[j]=(chunk)t&BMASK;
co=t>>BASEBITS;
j++;
#endif
for (; j<DNLEN-2; j+=2)
{
t=(dchunk)a[NLEN-1]*a[j-NLEN+1];
for (i=j-NLEN+2; i<(j+1)/2; i++) t+=(dchunk)a[j-i]*a[i];
t+=t;
t+=co;
t+=(dchunk)a[j/2]*a[j/2];
c[j]=(chunk)t&BMASK;
co=t>>BASEBITS;
t=(dchunk)a[NLEN-1]*a[j-NLEN+2];
for (i=j-NLEN+3; i<(j+2)/2; i++) t+=(dchunk)a[j+1-i]*a[i];
t+=t;
t+=co;
c[j+1]=(chunk)t&BMASK;
co=t>>BASEBITS;
}
t=(dchunk)a[NLEN-1]*a[NLEN-1]+co;
c[DNLEN-2]=(chunk)t&BMASK;
co=t>>BASEBITS;
c[DNLEN-1]=(chunk)co;
#else
chunk carry;
BIG_dzero(c);
for (i=0; i<NLEN; i++)
{
carry=0;
for (j=i+1; j<NLEN; j++)
carry=muladd(a[i],a[j],carry,&c[i+j]);
c[NLEN+i]=carry;
}
for (i=0; i<DNLEN; i++) c[i]*=2;
for (i=0; i<NLEN; i++)
c[2*i+1]+=muladd(a[i],a[i],0,&c[2*i]);
BIG_dnorm(c);
#endif
#ifdef DEBUG_NORM
c[DNLEN]=0;
#endif
}
/* SU= 32, Shifts a BIG left by any number of bits - input must be normalised, output normalised */
void BIG_shl(BIG a,int k)
{
int i;
int n=k%BASEBITS;
int m=k/BASEBITS;
// a[NLEN-1]=((a[NLEN-1-m]<<n))|(a[NLEN-m-2]>>(BASEBITS-n));
a[NLEN-1]=((a[NLEN-1-m]<<n));
if (NLEN>=m+2) a[NLEN-1]|=(a[NLEN-m-2]>>(BASEBITS-n));
for (i=NLEN-2; i>m; i--)
a[i]=((a[i-m]<<n)&BMASK)|(a[i-m-1]>>(BASEBITS-n));
a[m]=(a[0]<<n)&BMASK;
for (i=0; i<m; i++) a[i]=0;
}
/* SU= 16, Fast shifts a BIG left by a small number of bits - input must be normalised, output will be normalised */
chunk BIG_fshl(BIG a,int n)
{
int i;
a[NLEN-1]=((a[NLEN-1]<<n))|(a[NLEN-2]>>(BASEBITS-n)); /* top word not masked */
for (i=NLEN-2; i>0; i--)
a[i]=((a[i]<<n)&BMASK)|(a[i-1]>>(BASEBITS-n));
a[0]=(a[0]<<n)&BMASK;
return (a[NLEN-1]>>((8*MODBYTES)%BASEBITS)); /* return excess - only used in ff.c */
}
/* SU= 32, Shifts a DBIG left by any number of bits - input must be normalised, output normalised */
void BIG_dshl(DBIG a,int k)
{
int i;
int n=k%BASEBITS;
int m=k/BASEBITS;
a[DNLEN-1]=((a[DNLEN-1-m]<<n))|(a[DNLEN-m-2]>>(BASEBITS-n));
for (i=DNLEN-2; i>m; i--)
a[i]=((a[i-m]<<n)&BMASK)|(a[i-m-1]>>(BASEBITS-n));
a[m]=(a[0]<<n)&BMASK;
for (i=0; i<m; i++) a[i]=0;
}
/* SU= 32, Shifts a BIG right by any number of bits - input must be normalised, output normalised */
void BIG_shr(BIG a,int k)
{
int i;
int n=k%BASEBITS;
int m=k/BASEBITS;
for (i=0; i<NLEN-m-1; i++)
a[i]=(a[m+i]>>n)|((a[m+i+1]<<(BASEBITS-n))&BMASK);
if (NLEN>m) a[NLEN-m-1]=a[NLEN-1]>>n;
for (i=NLEN-m; i<NLEN; i++) a[i]=0;
}
/* SU= 16, Fast shifts a BIG right by a small number of bits - input must be normalised, output will be normalised */
chunk BIG_fshr(BIG a,int k)
{
int i;
chunk r=a[0]&(((chunk)1<<k)-1); /* shifted out part */
for (i=0; i<NLEN-1; i++)
a[i]=(a[i]>>k)|((a[i+1]<<(BASEBITS-k))&BMASK);
a[NLEN-1]=a[NLEN-1]>>k;
return r;
}
/* SU= 32, Shifts a DBIG right by any number of bits - input must be normalised, output normalised */
void BIG_dshr(DBIG a,int k)
{
int i;
int n=k%BASEBITS;
int m=k/BASEBITS;
for (i=0; i<DNLEN-m-1; i++)
a[i]=(a[m+i]>>n)|((a[m+i+1]<<(BASEBITS-n))&BMASK);
a[DNLEN-m-1]=a[DNLEN-1]>>n;
for (i=DNLEN-m; i<DNLEN; i++ ) a[i]=0;
}
/* SU= 24, Splits a DBIG into two BIGs - input must be normalised, outputs normalised */
chunk BIG_split(BIG t,BIG b,DBIG d,int n)
{
int i;
chunk nw,carry=0;
int m=n%BASEBITS;
// BIG_dnorm(d);
if (m==0)
{
for (i=0; i<NLEN; i++) b[i]=d[i];
if (t!=b)
{
for (i=NLEN; i<2*NLEN; i++) t[i-NLEN]=d[i];
carry=t[NLEN-1]>>BASEBITS;
t[NLEN-1]=t[NLEN-1]&BMASK; /* top word normalized */
}
return carry;
}
for (i=0; i<NLEN-1; i++) b[i]=d[i];
b[NLEN-1]=d[NLEN-1]&(((chunk)1<<m)-1);
if (t!=b)
{
carry=(d[DNLEN-1]<<(BASEBITS-m));
for (i=DNLEN-2; i>=NLEN-1; i--)
{
nw=(d[i]>>m)|carry;
carry=(d[i]<<(BASEBITS-m))&BMASK;
t[i-NLEN+1]=nw;
}
}
#ifdef DEBUG_NORM
t[NLEN]=0;
b[NLEN]=0;
#endif
return carry;
}
/* you gotta keep the sign of carry! Look - no branching! */
/* Note that sign bit is needed to disambiguate between +ve and -ve values */
/* Normalizes a BIG number - output normalised, force all digits < 2^BASEBITS */
chunk BIG_norm(BIG a)
{
int i;
chunk d,carry=0;
for (i=0; i<NLEN-1; i++)
{
d=a[i]+carry;
a[i]=d&BMASK;
carry=d>>BASEBITS;
}
a[NLEN-1]=(a[NLEN-1]+carry);
#ifdef DEBUG_NORM
a[NLEN]=0;
#endif
return (a[NLEN-1]>>((8*MODBYTES)%BASEBITS)); /* only used in ff.c */
}
/* Normalizes a DBIG number - output normalised */
void BIG_dnorm(DBIG a)
{
int i;
chunk d,carry=0;
for (i=0; i<DNLEN-1; i++)
{
d=a[i]+carry;
a[i]=d&BMASK;
carry=d>>BASEBITS;
}
a[DNLEN-1]=(a[DNLEN-1]+carry);
#ifdef DEBUG_NORM
a[DNLEN]=0;
#endif
}
/* Compare a and b. Return 1 for a>b, -1 for a<b, 0 for a==b */
/* a and b MUST be normalised before call */
int BIG_comp(BIG a,BIG b)
{
int i;
for (i=NLEN-1; i>=0; i--)
{
if (a[i]==b[i]) continue;
if (a[i]>b[i]) return 1;
else return -1;
}
return 0;
}
/* Compares two DBIG numbers. Inputs must be normalised externally */
int BIG_dcomp(DBIG a,DBIG b)
{
int i;
for (i=DNLEN-1; i>=0; i--)
{
if (a[i]==b[i]) continue;
if (a[i]>b[i]) return 1;
else return -1;
}
return 0;
}
/* SU= 8, Calculate number of bits in a BIG - output normalised */
int BIG_nbits(BIG a)
{
int bts,k=NLEN-1;
chunk c;
BIG_norm(a);
while (k>=0 && a[k]==0) k--;
if (k<0) return 0;
bts=BASEBITS*k;
c=a[k];
while (c!=0)
{
c/=2;
bts++;
}
return bts;
}
/* SU= 8, Calculate number of bits in a DBIG - output normalised */
int BIG_dnbits(DBIG a)
{
int bts,k=DNLEN-1;
chunk c;
BIG_dnorm(a);
while (k>=0 && a[k]==0) k--;
if (k<0) return 0;
bts=BASEBITS*k;
c=a[k];
while (c!=0)
{
c/=2;
bts++;
}
return bts;
}
/* SU= 16, Reduce x mod n - input and output normalised, constant time. */
void BIG_mod(BIG b,BIG c)
{
int k=0;
BIG r; /**/
BIG_norm(b);
if (BIG_comp(b,c)<0)
return;
do
{
BIG_fshl(c,1);
k++;
}
while (BIG_comp(b,c)>=0);
while (k>0)
{
BIG_fshr(c,1);
BIG_sub(r,b,c);
BIG_norm(r);
BIG_cmove(b,r,1-((r[NLEN-1]>>(CHUNK-1))&1));
k--;
}
}