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KGC_TEST/KGCAPP/3rdparty/miracl/source/mrflsh3.c

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/***************************************************************************
*
Copyright 2013 CertiVox UK Ltd. *
*
This file is part of CertiVox MIRACL Crypto SDK. *
*
The CertiVox MIRACL Crypto SDK provides developers with an *
extensive and efficient set of cryptographic functions. *
For further information about its features and functionalities please *
refer to http://www.certivox.com *
*
* The CertiVox MIRACL Crypto SDK is free software: you can *
redistribute it and/or modify it under the terms of the *
GNU Affero General Public License as published by the *
Free Software Foundation, either version 3 of the License, *
or (at your option) any later version. *
*
* The CertiVox MIRACL Crypto SDK 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 Affero General Public License for more details. *
*
* You should have received a copy of the GNU Affero General Public *
License along with CertiVox MIRACL Crypto SDK. *
If not, see <http://www.gnu.org/licenses/>. *
*
You can be released from the requirements of the license by purchasing *
a commercial license. Buying such a license is mandatory as soon as you *
develop commercial activities involving the CertiVox MIRACL Crypto SDK *
without disclosing the source code of your own applications, or shipping *
the CertiVox MIRACL Crypto SDK with a closed source product. *
*
***************************************************************************/
/*
* MIRACL flash trig.
* mrflsh3.c
*/
#include <math.h>
#include "miracl.h"
#ifdef MR_FLASH
#define TAN 1
#define SIN 2
#define COS 3
static int norm(_MIPD_ int type,flash y)
{ /* convert y to first quadrant angle *
* and return sign of result */
int s;
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
if (mr_mip->ERNUM) return 0;
s=PLUS;
if (size(y)<0)
{
negify(y,y);
if (type!=COS) s=(-s);
}
fpi(_MIPP_ mr_mip->pi);
fpmul(_MIPP_ mr_mip->pi,1,2,mr_mip->w8);
if (fcomp(_MIPP_ y,mr_mip->w8)<=0) return s;
fpmul(_MIPP_ mr_mip->pi,2,1,mr_mip->w8);
if (fcomp(_MIPP_ y,mr_mip->w8)>0)
{ /* reduce mod 2.pi */
fdiv(_MIPP_ y,mr_mip->w8,mr_mip->w9);
ftrunc(_MIPP_ mr_mip->w9,mr_mip->w9,mr_mip->w9);
fmul(_MIPP_ mr_mip->w9,mr_mip->w8,mr_mip->w9);
fsub(_MIPP_ y,mr_mip->w9,y);
}
if (fcomp(_MIPP_ y,mr_mip->pi)>0)
{ /* if greater than pi */
fsub(_MIPP_ y,mr_mip->pi,y);
if (type!=TAN) s=(-s);
}
fpmul(_MIPP_ mr_mip->pi,1,2,mr_mip->w8);
if (fcomp(_MIPP_ y,mr_mip->w8)>0)
{ /* if greater than pi/2 */
fsub(_MIPP_ mr_mip->pi,y,y);
if (type!=SIN) s=(-s);
}
return s;
}
static int tan1(_MIPD_ big w,int n)
{ /* generator for C.F. of tan(1) */
if (n==0) return 1;
if (n%2==1) return 2*(n/2)+1;
else return 1;
}
void ftan(_MIPD_ flash x,flash y)
{ /* calculates y=tan(x) */
int i,n,nsq,m,sqrn,sgn,op[5];
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
copy(x,y);
if (mr_mip->ERNUM || size(y)==0) return;
MR_IN(57)
sgn=norm(_MIPP_ TAN,y);
ftrunc(_MIPP_ y,y,mr_mip->w10);
n=size(y);
if (n!=0) build(_MIPP_ y,tan1);
if (size(mr_mip->w10)==0)
{
insign(sgn,y);
MR_OUT
return;
}
sqrn=isqrt(mr_mip->lg2b*mr_mip->workprec,mr_mip->lg2b);
nsq=0;
copy(mr_mip->w10,mr_mip->w8);
frecip(_MIPP_ mr_mip->w10,mr_mip->w10);
ftrunc(_MIPP_ mr_mip->w10,mr_mip->w10,mr_mip->w10);
m=logb2(_MIPP_ mr_mip->w10);
if (m<sqrn)
{ /* scale fraction down */
nsq=sqrn-m;
expb2(_MIPP_ nsq,mr_mip->w10);
fdiv(_MIPP_ mr_mip->w8,mr_mip->w10,mr_mip->w8);
}
zero(mr_mip->w10);
fmul(_MIPP_ mr_mip->w8,mr_mip->w8,mr_mip->w9);
negify(mr_mip->w9,mr_mip->w9);
op[0]=0x4B; /* set up for x/(y+C) */
op[1]=op[3]=1;
op[2]=0;
for (m=sqrn;m>1;m--)
{ /* Unwind C.F for tan(x)=z/(1-z^2/(3-z^2/(5-...)))))) */
op[4]=2*m-1;
flop(_MIPP_ mr_mip->w9,mr_mip->w10,op,mr_mip->w10);
}
op[4]=1;
flop(_MIPP_ mr_mip->w8,mr_mip->w10,op,mr_mip->w10);
op[0]=0x6C; /* set up for tan(x+y)=tan(x)+tan(y)/(1-tan(x).tan(y)) */
op[1]=op[2]=op[3]=1;
op[4]=(-1);
for (i=0;i<nsq;i++)
{ /* now square it back up again */
flop(_MIPP_ mr_mip->w10,mr_mip->w10,op,mr_mip->w10);
}
flop(_MIPP_ y,mr_mip->w10,op,y);
insign(sgn,y);
MR_OUT
}
void fatan(_MIPD_ flash x,flash y)
{ /* calculate y=atan(x) */
int s,c,op[5];
BOOL inv,hack;
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
copy(x,y);
if (mr_mip->ERNUM || size(y)==0) return;
MR_IN(58)
s=exsign(y);
insign(PLUS,y);
inv=FALSE;
fpi(_MIPP_ mr_mip->pi);
fconv(_MIPP_ 1,1,mr_mip->w11);
c=fcomp(_MIPP_ y,mr_mip->w11);
if (c==0)
{ /* atan(1)=pi/4 */
fpmul(_MIPP_ mr_mip->pi,1,4,y);
insign(s,y);
MR_OUT
return;
}
if (c>0)
{ /* atan(x)=pi/2 - atan(1/x) for x>1 */
inv=TRUE;
frecip(_MIPP_ y,y);
}
hack=FALSE;
if (mr_lent(y)<=2)
{ /* for 'simple' values of y */
hack=TRUE;
fconv(_MIPP_ 3,1,mr_mip->w11);
froot(_MIPP_ mr_mip->w11,2,mr_mip->w11);
op[0]=0xC6;
op[2]=op[3]=op[4]=1;
op[1]=(-1);
flop(_MIPP_ y,mr_mip->w11,op,y);
}
op[0]=0x4B;
op[1]=op[3]=op[4]=1;
op[2]=0;
mr_mip->workprec=mr_mip->stprec;
dconv(_MIPP_ atan(fdsize(_MIPP_ y)),mr_mip->w11);
while (mr_mip->workprec!=mr_mip->nib)
{ /* Newtons iteration w11=w11+(y-tan(w11))/(tan(w11)^2+1) */
if (mr_mip->workprec<mr_mip->nib) mr_mip->workprec*=2;
if (mr_mip->workprec>=mr_mip->nib) mr_mip->workprec=mr_mip->nib;
else if (mr_mip->workprec*2>mr_mip->nib) mr_mip->workprec=(mr_mip->nib+1)/2;
ftan(_MIPP_ mr_mip->w11,mr_mip->w12);
fsub(_MIPP_ y,mr_mip->w12,mr_mip->w8);
fmul(_MIPP_ mr_mip->w12,mr_mip->w12,mr_mip->w12);
flop(_MIPP_ mr_mip->w8,mr_mip->w12,op,mr_mip->w12); /* w12=w8/(w12+1) */
fadd(_MIPP_ mr_mip->w12,mr_mip->w11,mr_mip->w11);
}
copy(mr_mip->w11,y);
op[0]=0x6C;
op[1]=op[3]=6;
op[2]=1;
op[4]=0;
if (hack) flop(_MIPP_ y,mr_mip->pi,op,y);
op[1]=(-2);
op[3]=2;
if (inv) flop(_MIPP_ y,mr_mip->pi,op,y);
insign(s,y);
MR_OUT
}
void fsin(_MIPD_ flash x,flash y)
{ /* calculate y=sin(x) */
int sgn,op[5];
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
copy(x,y);
if (mr_mip->ERNUM || size(y)==0) return;
MR_IN(59)
sgn=norm(_MIPP_ SIN,y);
fpmul(_MIPP_ y,1,2,y);
ftan(_MIPP_ y,y);
op[0]=0x6C;
op[1]=op[2]=op[3]=op[4]=1;
flop(_MIPP_ y,y,op,y);
insign(sgn,y);
MR_OUT
}
void fasin(_MIPD_ flash x,flash y)
{ /* calculate y=asin(x) */
int s,op[5];
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
copy(x,y);
if (mr_mip->ERNUM || size(y)==0) return;
MR_IN(60)
s=exsign(y);
insign(PLUS,y);
op[0]=0x3C;
op[1]=(-1);
op[2]=op[3]=1;
op[4]=0;
flop(_MIPP_ y,y,op,mr_mip->w11); /* mr_w11 = -(y.y-1) */
froot(_MIPP_ mr_mip->w11,2,mr_mip->w11);
if (size(mr_mip->w11)==0)
{
fpi(_MIPP_ mr_mip->pi);
fpmul(_MIPP_ mr_mip->pi,1,2,y);
}
else
{
fdiv(_MIPP_ y,mr_mip->w11,y);
fatan(_MIPP_ y,y);
}
insign(s,y);
MR_OUT
}
void fcos(_MIPD_ flash x,flash y)
{ /* calculate y=cos(x) */
int sgn,op[5];
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
copy(x,y);
if (mr_mip->ERNUM || size(y)==0)
{
convert(_MIPP_ 1,y);
return;
}
MR_IN(61)
sgn=norm(_MIPP_ COS,y);
fpmul(_MIPP_ y,1,2,y);
ftan(_MIPP_ y,y);
op[0]=0x33;
op[1]=op[3]=op[4]=1;
op[2]=(-1);
flop(_MIPP_ y,y,op,y);
insign(sgn,y);
MR_OUT
}
void facos(_MIPD_ flash x,flash y)
{ /* calculate y=acos(x) */
int op[5];
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
if (mr_mip->ERNUM) return;
MR_IN(62)
fasin(_MIPP_ x,y);
fpi(_MIPP_ mr_mip->pi);
op[0]=0x6C;
op[1]=(-2);
op[2]=1;
op[3]=2;
op[4]=0;
flop(_MIPP_ y,mr_mip->pi,op,y); /* y = pi/2 - y */
MR_OUT
}
#endif
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