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231 lines
8.3 KiB
C
231 lines
8.3 KiB
C
/*
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* IBM Accurate Mathematical Library
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* written by International Business Machines Corp.
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* Copyright (C) 2001, 2011 Free Software Foundation
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU Lesser General Public License as published by
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* the Free Software Foundation; either version 2.1 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU Lesser General Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public License
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* along with this program; if not, see <http://www.gnu.org/licenses/>.
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*/
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/************************************************************************/
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/* MODULE_NAME: atnat.c */
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/* */
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/* FUNCTIONS: uatan */
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/* atanMp */
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/* signArctan */
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/* */
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/* */
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/* FILES NEEDED: dla.h endian.h mpa.h mydefs.h atnat.h */
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/* mpatan.c mpatan2.c mpsqrt.c */
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/* uatan.tbl */
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/* */
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/* An ultimate atan() routine. Given an IEEE double machine number x */
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/* it computes the correctly rounded (to nearest) value of atan(x). */
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/* */
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/* Assumption: Machine arithmetic operations are performed in */
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/* round to nearest mode of IEEE 754 standard. */
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/* */
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/************************************************************************/
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#include <dla.h>
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#include "mpa.h"
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#include "MathLib.h"
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#include "uatan.tbl"
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#include "atnat.h"
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#include "math.h"
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void __mpatan(mp_no *,mp_no *,int); /* see definition in mpatan.c */
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static double atanMp(double,const int[]);
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/* Fix the sign of y and return */
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static double __signArctan(double x,double y){
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return __copysign(y, x);
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}
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/* An ultimate atan() routine. Given an IEEE double machine number x, */
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/* routine computes the correctly rounded (to nearest) value of atan(x). */
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double atan(double x) {
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double cor,s1,ss1,s2,ss2,t1,t2,t3,t7,t8,t9,t10,u,u2,u3,
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v,vv,w,ww,y,yy,z,zz;
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#ifndef DLA_FMS
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double t4,t5,t6;
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#endif
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#if 0
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double y1,y2;
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#endif
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int i,ux,dx;
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#if 0
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int p;
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#endif
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static const int pr[M]={6,8,10,32};
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number num;
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#if 0
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mp_no mpt1,mpx,mpy,mpy1,mpy2,mperr;
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#endif
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num.d = x; ux = num.i[HIGH_HALF]; dx = num.i[LOW_HALF];
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/* x=NaN */
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if (((ux&0x7ff00000)==0x7ff00000) && (((ux&0x000fffff)|dx)!=0x00000000))
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return x+x;
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/* Regular values of x, including denormals +-0 and +-INF */
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u = (x<ZERO) ? -x : x;
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if (u<C) {
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if (u<B) {
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if (u<A) { /* u < A */
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return x; }
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else { /* A <= u < B */
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v=x*x; yy=x*v*(d3.d+v*(d5.d+v*(d7.d+v*(d9.d+v*(d11.d+v*d13.d)))));
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if ((y=x+(yy-U1*x)) == x+(yy+U1*x)) return y;
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EMULV(x,x,v,vv,t1,t2,t3,t4,t5) /* v+vv=x^2 */
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s1=v*(f11.d+v*(f13.d+v*(f15.d+v*(f17.d+v*f19.d))));
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ADD2(f9.d,ff9.d,s1,ZERO,s2,ss2,t1,t2)
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MUL2(v,vv,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(f7.d,ff7.d,s1,ss1,s2,ss2,t1,t2)
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MUL2(v,vv,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(f5.d,ff5.d,s1,ss1,s2,ss2,t1,t2)
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MUL2(v,vv,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(f3.d,ff3.d,s1,ss1,s2,ss2,t1,t2)
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MUL2(v,vv,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
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MUL2(x,ZERO,s1,ss1,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(x,ZERO,s2,ss2,s1,ss1,t1,t2)
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if ((y=s1+(ss1-U5*s1)) == s1+(ss1+U5*s1)) return y;
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return atanMp(x,pr);
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} }
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else { /* B <= u < C */
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i=(TWO52+TWO8*u)-TWO52; i-=16;
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z=u-cij[i][0].d;
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yy=z*(cij[i][2].d+z*(cij[i][3].d+z*(cij[i][4].d+
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z*(cij[i][5].d+z* cij[i][6].d))));
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t1=cij[i][1].d;
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if (i<112) {
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if (i<48) u2=U21; /* u < 1/4 */
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else u2=U22; } /* 1/4 <= u < 1/2 */
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else {
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if (i<176) u2=U23; /* 1/2 <= u < 3/4 */
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else u2=U24; } /* 3/4 <= u <= 1 */
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if ((y=t1+(yy-u2*t1)) == t1+(yy+u2*t1)) return __signArctan(x,y);
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z=u-hij[i][0].d;
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s1=z*(hij[i][11].d+z*(hij[i][12].d+z*(hij[i][13].d+
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z*(hij[i][14].d+z* hij[i][15].d))));
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ADD2(hij[i][9].d,hij[i][10].d,s1,ZERO,s2,ss2,t1,t2)
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MUL2(z,ZERO,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(hij[i][7].d,hij[i][8].d,s1,ss1,s2,ss2,t1,t2)
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MUL2(z,ZERO,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(hij[i][5].d,hij[i][6].d,s1,ss1,s2,ss2,t1,t2)
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MUL2(z,ZERO,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(hij[i][3].d,hij[i][4].d,s1,ss1,s2,ss2,t1,t2)
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MUL2(z,ZERO,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(hij[i][1].d,hij[i][2].d,s1,ss1,s2,ss2,t1,t2)
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if ((y=s2+(ss2-U6*s2)) == s2+(ss2+U6*s2)) return __signArctan(x,y);
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return atanMp(x,pr);
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}
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}
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else {
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if (u<D) { /* C <= u < D */
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w=ONE/u;
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EMULV(w,u,t1,t2,t3,t4,t5,t6,t7)
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ww=w*((ONE-t1)-t2);
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i=(TWO52+TWO8*w)-TWO52; i-=16;
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z=(w-cij[i][0].d)+ww;
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yy=HPI1-z*(cij[i][2].d+z*(cij[i][3].d+z*(cij[i][4].d+
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z*(cij[i][5].d+z* cij[i][6].d))));
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t1=HPI-cij[i][1].d;
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if (i<112) u3=U31; /* w < 1/2 */
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else u3=U32; /* w >= 1/2 */
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if ((y=t1+(yy-u3)) == t1+(yy+u3)) return __signArctan(x,y);
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DIV2(ONE,ZERO,u,ZERO,w,ww,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
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t1=w-hij[i][0].d;
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EADD(t1,ww,z,zz)
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s1=z*(hij[i][11].d+z*(hij[i][12].d+z*(hij[i][13].d+
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z*(hij[i][14].d+z* hij[i][15].d))));
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ADD2(hij[i][9].d,hij[i][10].d,s1,ZERO,s2,ss2,t1,t2)
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MUL2(z,zz,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(hij[i][7].d,hij[i][8].d,s1,ss1,s2,ss2,t1,t2)
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MUL2(z,zz,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(hij[i][5].d,hij[i][6].d,s1,ss1,s2,ss2,t1,t2)
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MUL2(z,zz,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(hij[i][3].d,hij[i][4].d,s1,ss1,s2,ss2,t1,t2)
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MUL2(z,zz,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(hij[i][1].d,hij[i][2].d,s1,ss1,s2,ss2,t1,t2)
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SUB2(HPI,HPI1,s2,ss2,s1,ss1,t1,t2)
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if ((y=s1+(ss1-U7)) == s1+(ss1+U7)) return __signArctan(x,y);
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return atanMp(x,pr);
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}
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else {
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if (u<E) { /* D <= u < E */
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w=ONE/u; v=w*w;
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EMULV(w,u,t1,t2,t3,t4,t5,t6,t7)
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yy=w*v*(d3.d+v*(d5.d+v*(d7.d+v*(d9.d+v*(d11.d+v*d13.d)))));
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ww=w*((ONE-t1)-t2);
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ESUB(HPI,w,t3,cor)
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yy=((HPI1+cor)-ww)-yy;
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if ((y=t3+(yy-U4)) == t3+(yy+U4)) return __signArctan(x,y);
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DIV2(ONE,ZERO,u,ZERO,w,ww,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
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MUL2(w,ww,w,ww,v,vv,t1,t2,t3,t4,t5,t6,t7,t8)
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s1=v*(f11.d+v*(f13.d+v*(f15.d+v*(f17.d+v*f19.d))));
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ADD2(f9.d,ff9.d,s1,ZERO,s2,ss2,t1,t2)
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MUL2(v,vv,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(f7.d,ff7.d,s1,ss1,s2,ss2,t1,t2)
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MUL2(v,vv,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(f5.d,ff5.d,s1,ss1,s2,ss2,t1,t2)
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MUL2(v,vv,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(f3.d,ff3.d,s1,ss1,s2,ss2,t1,t2)
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MUL2(v,vv,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
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MUL2(w,ww,s1,ss1,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2(w,ww,s2,ss2,s1,ss1,t1,t2)
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SUB2(HPI,HPI1,s1,ss1,s2,ss2,t1,t2)
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if ((y=s2+(ss2-U8)) == s2+(ss2+U8)) return __signArctan(x,y);
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return atanMp(x,pr);
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}
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else {
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/* u >= E */
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if (x>0) return HPI;
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else return MHPI; }
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}
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}
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}
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/* Final stages. Compute atan(x) by multiple precision arithmetic */
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static double atanMp(double x,const int pr[]){
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mp_no mpx,mpy,mpy2,mperr,mpt1,mpy1;
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double y1,y2;
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int i,p;
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for (i=0; i<M; i++) {
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p = pr[i];
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__dbl_mp(x,&mpx,p); __mpatan(&mpx,&mpy,p);
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__dbl_mp(u9[i].d,&mpt1,p); __mul(&mpy,&mpt1,&mperr,p);
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__add(&mpy,&mperr,&mpy1,p); __sub(&mpy,&mperr,&mpy2,p);
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__mp_dbl(&mpy1,&y1,p); __mp_dbl(&mpy2,&y2,p);
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if (y1==y2) return y1;
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}
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return y1; /*if unpossible to do exact computing */
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}
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#ifdef NO_LONG_DOUBLE
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weak_alias (atan, atanl)
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#endif
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