| /* |
| * IBM Accurate Mathematical Library |
| * written by International Business Machines Corp. |
| * Copyright (C) 2001 Free Software Foundation |
| * |
| * This program is free software; you can redistribute it and/or modify |
| * it under the terms of the GNU Lesser General Public License as published by |
| * the Free Software Foundation; either version 2.1 of the License, or |
| * (at your option) any later version. |
| * |
| * This program 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 Lesser General Public License for more details. |
| * |
| * You should have received a copy of the GNU Lesser General Public License |
| * along with this program; if not, write to the Free Software |
| * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
| */ |
| /****************************************************************/ |
| /* MODULE_NAME: sincos32.c */ |
| /* */ |
| /* FUNCTIONS: ss32 */ |
| /* cc32 */ |
| /* c32 */ |
| /* sin32 */ |
| /* cos32 */ |
| /* mpsin */ |
| /* mpcos */ |
| /* mpranred */ |
| /* mpsin1 */ |
| /* mpcos1 */ |
| /* */ |
| /* FILES NEEDED: endian.h mpa.h sincos32.h */ |
| /* mpa.c */ |
| /* */ |
| /* Multi Precision sin() and cos() function with p=32 for sin()*/ |
| /* cos() arcsin() and arccos() routines */ |
| /* In addition mpranred() routine performs range reduction of */ |
| /* a double number x into multi precision number y, */ |
| /* such that y=x-n*pi/2, abs(y)<pi/4, n=0,+-1,+-2,.... */ |
| /****************************************************************/ |
| #include "endian.h" |
| #include "mpa.h" |
| #include "sincos32.h" |
| #include "math_private.h" |
| |
| /****************************************************************/ |
| /* Compute Multi-Precision sin() function for given p. Receive */ |
| /* Multi Precision number x and result stored at y */ |
| /****************************************************************/ |
| static void ss32(mp_no *x, mp_no *y, int p) { |
| int i; |
| double a; |
| #if 0 |
| double b; |
| static const mp_no mpone = {1,{1.0,1.0}}; |
| #endif |
| mp_no mpt1,x2,gor,sum ,mpk={1,{1.0}}; |
| #if 0 |
| mp_no mpt2; |
| #endif |
| for (i=1;i<=p;i++) mpk.d[i]=0; |
| |
| __mul(x,x,&x2,p); |
| __cpy(&oofac27,&gor,p); |
| __cpy(&gor,&sum,p); |
| for (a=27.0;a>1.0;a-=2.0) { |
| mpk.d[1]=a*(a-1.0); |
| __mul(&gor,&mpk,&mpt1,p); |
| __cpy(&mpt1,&gor,p); |
| __mul(&x2,&sum,&mpt1,p); |
| __sub(&gor,&mpt1,&sum,p); |
| } |
| __mul(x,&sum,y,p); |
| } |
| |
| /**********************************************************************/ |
| /* Compute Multi-Precision cos() function for given p. Receive Multi */ |
| /* Precision number x and result stored at y */ |
| /**********************************************************************/ |
| static void cc32(mp_no *x, mp_no *y, int p) { |
| int i; |
| double a; |
| #if 0 |
| double b; |
| static const mp_no mpone = {1,{1.0,1.0}}; |
| #endif |
| mp_no mpt1,x2,gor,sum ,mpk={1,{1.0}}; |
| #if 0 |
| mp_no mpt2; |
| #endif |
| for (i=1;i<=p;i++) mpk.d[i]=0; |
| |
| __mul(x,x,&x2,p); |
| mpk.d[1]=27.0; |
| __mul(&oofac27,&mpk,&gor,p); |
| __cpy(&gor,&sum,p); |
| for (a=26.0;a>2.0;a-=2.0) { |
| mpk.d[1]=a*(a-1.0); |
| __mul(&gor,&mpk,&mpt1,p); |
| __cpy(&mpt1,&gor,p); |
| __mul(&x2,&sum,&mpt1,p); |
| __sub(&gor,&mpt1,&sum,p); |
| } |
| __mul(&x2,&sum,y,p); |
| } |
| |
| /***************************************************************************/ |
| /* c32() computes both sin(x), cos(x) as Multi precision numbers */ |
| /***************************************************************************/ |
| void __c32(mp_no *x, mp_no *y, mp_no *z, int p) { |
| static const mp_no mpt={1,{1.0,2.0}}, one={1,{1.0,1.0}}; |
| mp_no u,t,t1,t2,c,s; |
| int i; |
| __cpy(x,&u,p); |
| u.e=u.e-1; |
| cc32(&u,&c,p); |
| ss32(&u,&s,p); |
| for (i=0;i<24;i++) { |
| __mul(&c,&s,&t,p); |
| __sub(&s,&t,&t1,p); |
| __add(&t1,&t1,&s,p); |
| __sub(&mpt,&c,&t1,p); |
| __mul(&t1,&c,&t2,p); |
| __add(&t2,&t2,&c,p); |
| } |
| __sub(&one,&c,y,p); |
| __cpy(&s,z,p); |
| } |
| |
| /************************************************************************/ |
| /*Routine receive double x and two double results of sin(x) and return */ |
| /*result which is more accurate */ |
| /*Computing sin(x) with multi precision routine c32 */ |
| /************************************************************************/ |
| double __sin32(double x, double res, double res1) { |
| int p; |
| mp_no a,b,c; |
| p=32; |
| __dbl_mp(res,&a,p); |
| __dbl_mp(0.5*(res1-res),&b,p); |
| __add(&a,&b,&c,p); |
| if (x>0.8) |
| { __sub(&hp,&c,&a,p); |
| __c32(&a,&b,&c,p); |
| } |
| else __c32(&c,&a,&b,p); /* b=sin(0.5*(res+res1)) */ |
| __dbl_mp(x,&c,p); /* c = x */ |
| __sub(&b,&c,&a,p); |
| /* if a>0 return min(res,res1), otherwise return max(res,res1) */ |
| if (a.d[0]>0) return (res<res1)?res:res1; |
| else return (res>res1)?res:res1; |
| } |
| |
| /************************************************************************/ |
| /*Routine receive double x and two double results of cos(x) and return */ |
| /*result which is more accurate */ |
| /*Computing cos(x) with multi precision routine c32 */ |
| /************************************************************************/ |
| double __cos32(double x, double res, double res1) { |
| int p; |
| mp_no a,b,c; |
| p=32; |
| __dbl_mp(res,&a,p); |
| __dbl_mp(0.5*(res1-res),&b,p); |
| __add(&a,&b,&c,p); |
| if (x>2.4) |
| { __sub(&pi,&c,&a,p); |
| __c32(&a,&b,&c,p); |
| b.d[0]=-b.d[0]; |
| } |
| else if (x>0.8) |
| { __sub(&hp,&c,&a,p); |
| __c32(&a,&c,&b,p); |
| } |
| else __c32(&c,&b,&a,p); /* b=cos(0.5*(res+res1)) */ |
| __dbl_mp(x,&c,p); /* c = x */ |
| __sub(&b,&c,&a,p); |
| /* if a>0 return max(res,res1), otherwise return min(res,res1) */ |
| if (a.d[0]>0) return (res>res1)?res:res1; |
| else return (res<res1)?res:res1; |
| } |
| |
| /*******************************************************************/ |
| /*Compute sin(x+dx) as Multi Precision number and return result as */ |
| /* double */ |
| /*******************************************************************/ |
| double __mpsin(double x, double dx) { |
| int p; |
| double y; |
| mp_no a,b,c; |
| p=32; |
| __dbl_mp(x,&a,p); |
| __dbl_mp(dx,&b,p); |
| __add(&a,&b,&c,p); |
| if (x>0.8) { __sub(&hp,&c,&a,p); __c32(&a,&b,&c,p); } |
| else __c32(&c,&a,&b,p); /* b = sin(x+dx) */ |
| __mp_dbl(&b,&y,p); |
| return y; |
| } |
| |
| /*******************************************************************/ |
| /* Compute cos()of double-length number (x+dx) as Multi Precision */ |
| /* number and return result as double */ |
| /*******************************************************************/ |
| double __mpcos(double x, double dx) { |
| int p; |
| double y; |
| mp_no a,b,c; |
| p=32; |
| __dbl_mp(x,&a,p); |
| __dbl_mp(dx,&b,p); |
| __add(&a,&b,&c,p); |
| if (x>0.8) |
| { __sub(&hp,&c,&b,p); |
| __c32(&b,&c,&a,p); |
| } |
| else __c32(&c,&a,&b,p); /* a = cos(x+dx) */ |
| __mp_dbl(&a,&y,p); |
| return y; |
| } |
| |
| /******************************************************************/ |
| /* mpranred() performs range reduction of a double number x into */ |
| /* multi precision number y, such that y=x-n*pi/2, abs(y)<pi/4, */ |
| /* n=0,+-1,+-2,.... */ |
| /* Return int which indicates in which quarter of circle x is */ |
| /******************************************************************/ |
| int __mpranred(double x, mp_no *y, int p) |
| { |
| number v; |
| double t,xn; |
| int i,k,n; |
| static const mp_no one = {1,{1.0,1.0}}; |
| mp_no a,b,c; |
| |
| if (ABS(x) < 2.8e14) { |
| t = (x*hpinv.d + toint.d); |
| xn = t - toint.d; |
| v.d = t; |
| n =v.i[LOW_HALF]&3; |
| __dbl_mp(xn,&a,p); |
| __mul(&a,&hp,&b,p); |
| __dbl_mp(x,&c,p); |
| __sub(&c,&b,y,p); |
| return n; |
| } |
| else { /* if x is very big more precision required */ |
| __dbl_mp(x,&a,p); |
| a.d[0]=1.0; |
| k = a.e-5; |
| if (k < 0) k=0; |
| b.e = -k; |
| b.d[0] = 1.0; |
| for (i=0;i<p;i++) b.d[i+1] = toverp[i+k]; |
| __mul(&a,&b,&c,p); |
| t = c.d[c.e]; |
| for (i=1;i<=p-c.e;i++) c.d[i]=c.d[i+c.e]; |
| for (i=p+1-c.e;i<=p;i++) c.d[i]=0; |
| c.e=0; |
| if (c.d[1] >= 8388608.0) |
| { t +=1.0; |
| __sub(&c,&one,&b,p); |
| __mul(&b,&hp,y,p); |
| } |
| else __mul(&c,&hp,y,p); |
| n = (int) t; |
| if (x < 0) { y->d[0] = - y->d[0]; n = -n; } |
| return (n&3); |
| } |
| } |
| |
| /*******************************************************************/ |
| /* Multi-Precision sin() function subroutine, for p=32. It is */ |
| /* based on the routines mpranred() and c32(). */ |
| /*******************************************************************/ |
| double __mpsin1(double x) |
| { |
| int p; |
| int n; |
| mp_no u,s,c; |
| double y; |
| p=32; |
| n=__mpranred(x,&u,p); /* n is 0, 1, 2 or 3 */ |
| __c32(&u,&c,&s,p); |
| switch (n) { /* in which quarter of unit circle y is*/ |
| case 0: |
| __mp_dbl(&s,&y,p); |
| return y; |
| break; |
| |
| case 2: |
| __mp_dbl(&s,&y,p); |
| return -y; |
| break; |
| |
| case 1: |
| __mp_dbl(&c,&y,p); |
| return y; |
| break; |
| |
| case 3: |
| __mp_dbl(&c,&y,p); |
| return -y; |
| break; |
| |
| } |
| return 0; /* unreachable, to make the compiler happy */ |
| } |
| |
| /*****************************************************************/ |
| /* Multi-Precision cos() function subroutine, for p=32. It is */ |
| /* based on the routines mpranred() and c32(). */ |
| /*****************************************************************/ |
| |
| double __mpcos1(double x) |
| { |
| int p; |
| int n; |
| mp_no u,s,c; |
| double y; |
| |
| p=32; |
| n=__mpranred(x,&u,p); /* n is 0, 1, 2 or 3 */ |
| __c32(&u,&c,&s,p); |
| switch (n) { /* in what quarter of unit circle y is*/ |
| |
| case 0: |
| __mp_dbl(&c,&y,p); |
| return y; |
| break; |
| |
| case 2: |
| __mp_dbl(&c,&y,p); |
| return -y; |
| break; |
| |
| case 1: |
| __mp_dbl(&s,&y,p); |
| return -y; |
| break; |
| |
| case 3: |
| __mp_dbl(&s,&y,p); |
| return y; |
| break; |
| |
| } |
| return 0; /* unreachable, to make the compiler happy */ |
| } |
| /******************************************************************/ |
