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Format s_atan.c
This commit is contained in:
Siddhesh Poyarekar
parent
0f6a8d4b0b
commit
d26dd3eb00
@ -1,5 +1,7 @@
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2013-03-29 Siddhesh Poyarekar <siddhesh@redhat.com>
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2013-03-29 Siddhesh Poyarekar <siddhesh@redhat.com>
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* sysdeps/ieee754/dbl-64/s_atan.c: Fix formatting.
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* sysdeps/ieee754/dbl-64/e_log.c: Fix formatting.
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* sysdeps/ieee754/dbl-64/e_log.c: Fix formatting.
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2013-03-28 Roland McGrath <roland@hack.frob.com>
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2013-03-28 Roland McGrath <roland@hack.frob.com>
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@ -43,177 +43,272 @@
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#include "atnat.h"
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#include "atnat.h"
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#include <math.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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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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static double atanMp (double, const int[]);
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/* Fix the sign of y and return */
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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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static double
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return __copysign(y, x);
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__signArctan (double x, double y)
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{
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return __copysign (y, x);
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}
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}
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/* An ultimate atan() routine. Given an IEEE double machine number x, */
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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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/* routine computes the correctly rounded (to nearest) value of atan(x). */
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double atan(double x) {
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double
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atan (double x)
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{
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double cor,s1,ss1,s2,ss2,t1,t2,t3,t7,t8,t9,t10,u,u2,u3,
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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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v, vv, w, ww, y, yy, z, zz;
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#ifndef DLA_FMS
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#ifndef DLA_FMS
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double t4,t5,t6;
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double t4, t5, t6;
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#endif
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#endif
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int i,ux,dx;
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int i, ux, dx;
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static const int pr[M]={6,8,10,32};
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static const int pr[M] = { 6, 8, 10, 32 };
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number num;
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number num;
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num.d = x; ux = num.i[HIGH_HALF]; dx = num.i[LOW_HALF];
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num.d = x;
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ux = num.i[HIGH_HALF];
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dx = num.i[LOW_HALF];
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/* x=NaN */
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/* x=NaN */
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if (((ux&0x7ff00000)==0x7ff00000) && (((ux&0x000fffff)|dx)!=0x00000000))
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if (((ux & 0x7ff00000) == 0x7ff00000)
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return x+x;
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&& (((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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/* Regular values of x, including denormals +-0 and +-INF */
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u = (x<ZERO) ? -x : x;
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u = (x < ZERO) ? -x : x;
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if (u<C) {
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if (u < C)
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if (u<B) {
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{
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if (u<A) { /* u < A */
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if (u < B)
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return x; }
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{
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else { /* A <= u < B */
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if (u < A)
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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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return x;
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if ((y=x+(yy-U1*x)) == x+(yy+U1*x)) return y;
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else
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{ /* A <= u < B */
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v = x * x;
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yy = d11.d + v * d13.d;
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yy = d9.d + v * yy;
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yy = d7.d + v * yy;
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yy = d5.d + v * yy;
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yy = d3.d + v * yy;
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yy *= x * v;
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EMULV(x,x,v,vv,t1,t2,t3,t4,t5) /* v+vv=x^2 */
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if ((y = x + (yy - U1 * x)) == x + (yy + U1 * x))
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s1=v*(f11.d+v*(f13.d+v*(f15.d+v*(f17.d+v*f19.d))));
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return y;
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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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EMULV (x, x, v, vv, t1, t2, t3, t4, t5); /* v+vv=x^2 */
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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 = f17.d + v * f19.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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s1 = f15.d + v * s1;
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z*(hij[i][14].d+z* hij[i][15].d))));
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s1 = f13.d + v * s1;
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ADD2(hij[i][9].d,hij[i][10].d,s1,ZERO,s2,ss2,t1,t2)
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s1 = f11.d + v * s1;
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MUL2(z,ZERO,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
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s1 *= v;
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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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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,
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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))
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return y;
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return atanMp (x, pr);
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}
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}
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}
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}
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else {
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else
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if (u<D) { /* C <= u < D */
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{ /* B <= u < C */
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w=ONE/u;
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i = (TWO52 + TWO8 * u) - TWO52;
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EMULV(w,u,t1,t2,t3,t4,t5,t6,t7)
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i -= 16;
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ww=w*((ONE-t1)-t2);
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z = u - cij[i][0].d;
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i=(TWO52+TWO8*w)-TWO52; i-=16;
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yy = cij[i][5].d + z * cij[i][6].d;
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z=(w-cij[i][0].d)+ww;
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yy = cij[i][4].d + z * yy;
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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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yy = cij[i][3].d + z * yy;
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z*(cij[i][5].d+z* cij[i][6].d))));
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yy = cij[i][2].d + z * yy;
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t1=HPI-cij[i][1].d;
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yy *= z;
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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 = cij[i][1].d;
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t1=w-hij[i][0].d;
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if (i < 112)
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EADD(t1,ww,z,zz)
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{
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s1=z*(hij[i][11].d+z*(hij[i][12].d+z*(hij[i][13].d+
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if (i < 48)
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z*(hij[i][14].d+z* hij[i][15].d))));
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u2 = U21; /* u < 1/4 */
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ADD2(hij[i][9].d,hij[i][10].d,s1,ZERO,s2,ss2,t1,t2)
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else
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MUL2(z,zz,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
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u2 = U22;
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ADD2(hij[i][7].d,hij[i][8].d,s1,ss1,s2,ss2,t1,t2)
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} /* 1/4 <= u < 1/2 */
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MUL2(z,zz,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
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else
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ADD2(hij[i][5].d,hij[i][6].d,s1,ss1,s2,ss2,t1,t2)
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{
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MUL2(z,zz,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
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if (i < 176)
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ADD2(hij[i][3].d,hij[i][4].d,s1,ss1,s2,ss2,t1,t2)
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u2 = U23; /* 1/2 <= u < 3/4 */
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MUL2(z,zz,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
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else
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ADD2(hij[i][1].d,hij[i][2].d,s1,ss1,s2,ss2,t1,t2)
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u2 = U24;
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SUB2(HPI,HPI1,s2,ss2,s1,ss1,t1,t2)
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} /* 3/4 <= u <= 1 */
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if ((y=s1+(ss1-U7)) == s1+(ss1+U7)) return __signArctan(x,y);
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if ((y = t1 + (yy - u2 * t1)) == t1 + (yy + u2 * t1))
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return __signArctan (x, y);
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return atanMp(x,pr);
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z = u - hij[i][0].d;
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s1 = hij[i][14].d + z * hij[i][15].d;
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s1 = hij[i][13].d + z * s1;
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s1 = hij[i][12].d + z * s1;
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s1 = hij[i][11].d + z * s1;
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s1 *= z;
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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))
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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<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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}
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else {
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else
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{
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if (u < D)
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{ /* C <= u < D */
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w = ONE / u;
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||||||
|
EMULV (w, u, t1, t2, t3, t4, t5, t6, t7);
|
||||||
|
ww = w * ((ONE - t1) - t2);
|
||||||
|
i = (TWO52 + TWO8 * w) - TWO52;
|
||||||
|
i -= 16;
|
||||||
|
z = (w - cij[i][0].d) + ww;
|
||||||
|
|
||||||
|
yy = cij[i][5].d + z * cij[i][6].d;
|
||||||
|
yy = cij[i][4].d + z * yy;
|
||||||
|
yy = cij[i][3].d + z * yy;
|
||||||
|
yy = cij[i][2].d + z * yy;
|
||||||
|
yy = HPI1 - z * yy;
|
||||||
|
|
||||||
|
t1 = HPI - cij[i][1].d;
|
||||||
|
if (i < 112)
|
||||||
|
u3 = U31; /* w < 1/2 */
|
||||||
|
else
|
||||||
|
u3 = U32; /* w >= 1/2 */
|
||||||
|
if ((y = t1 + (yy - u3)) == t1 + (yy + u3))
|
||||||
|
return __signArctan (x, y);
|
||||||
|
|
||||||
|
DIV2 (ONE, ZERO, u, ZERO, w, ww, t1, t2, t3, t4, t5, t6, t7, t8, t9,
|
||||||
|
t10);
|
||||||
|
t1 = w - hij[i][0].d;
|
||||||
|
EADD (t1, ww, z, zz);
|
||||||
|
|
||||||
|
s1 = hij[i][14].d + z * hij[i][15].d;
|
||||||
|
s1 = hij[i][13].d + z * s1;
|
||||||
|
s1 = hij[i][12].d + z * s1;
|
||||||
|
s1 = hij[i][11].d + z * s1;
|
||||||
|
s1 *= z;
|
||||||
|
|
||||||
|
ADD2 (hij[i][9].d, hij[i][10].d, s1, ZERO, s2, ss2, t1, t2);
|
||||||
|
MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
|
ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2);
|
||||||
|
MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
|
ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2);
|
||||||
|
MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
|
ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2);
|
||||||
|
MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
|
ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2);
|
||||||
|
SUB2 (HPI, HPI1, s2, ss2, s1, ss1, t1, t2);
|
||||||
|
if ((y = s1 + (ss1 - U7)) == s1 + (ss1 + U7))
|
||||||
|
return __signArctan (x, y);
|
||||||
|
|
||||||
|
return atanMp (x, pr);
|
||||||
|
}
|
||||||
|
else
|
||||||
|
{
|
||||||
|
if (u < E)
|
||||||
|
{ /* D <= u < E */
|
||||||
|
w = ONE / u;
|
||||||
|
v = w * w;
|
||||||
|
EMULV (w, u, t1, t2, t3, t4, t5, t6, t7);
|
||||||
|
|
||||||
|
yy = d11.d + v * d13.d;
|
||||||
|
yy = d9.d + v * yy;
|
||||||
|
yy = d7.d + v * yy;
|
||||||
|
yy = d5.d + v * yy;
|
||||||
|
yy = d3.d + v * yy;
|
||||||
|
yy *= w * v;
|
||||||
|
|
||||||
|
ww = w * ((ONE - t1) - t2);
|
||||||
|
ESUB (HPI, w, t3, cor);
|
||||||
|
yy = ((HPI1 + cor) - ww) - yy;
|
||||||
|
if ((y = t3 + (yy - U4)) == t3 + (yy + U4))
|
||||||
|
return __signArctan (x, y);
|
||||||
|
|
||||||
|
DIV2 (ONE, ZERO, u, ZERO, w, ww, t1, t2, t3, t4, t5, t6, t7, t8,
|
||||||
|
t9, t10);
|
||||||
|
MUL2 (w, ww, w, ww, v, vv, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
|
|
||||||
|
s1 = f17.d + v * f19.d;
|
||||||
|
s1 = f15.d + v * s1;
|
||||||
|
s1 = f13.d + v * s1;
|
||||||
|
s1 = f11.d + v * s1;
|
||||||
|
s1 *= v;
|
||||||
|
|
||||||
|
ADD2 (f9.d, ff9.d, s1, ZERO, s2, ss2, t1, t2);
|
||||||
|
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
|
ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2);
|
||||||
|
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
|
ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2);
|
||||||
|
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
|
ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2);
|
||||||
|
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
|
MUL2 (w, ww, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
|
ADD2 (w, ww, s2, ss2, s1, ss1, t1, t2);
|
||||||
|
SUB2 (HPI, HPI1, s1, ss1, s2, ss2, t1, t2);
|
||||||
|
|
||||||
|
if ((y = s2 + (ss2 - U8)) == s2 + (ss2 + U8))
|
||||||
|
return __signArctan (x, y);
|
||||||
|
|
||||||
|
return atanMp (x, pr);
|
||||||
|
}
|
||||||
|
else
|
||||||
|
{
|
||||||
/* u >= E */
|
/* u >= E */
|
||||||
if (x>0) return HPI;
|
if (x > 0)
|
||||||
else return MHPI; }
|
return HPI;
|
||||||
|
else
|
||||||
|
return MHPI;
|
||||||
|
}
|
||||||
}
|
}
|
||||||
}
|
}
|
||||||
|
|
||||||
}
|
}
|
||||||
|
|
||||||
/* Final stages. Compute atan(x) by multiple precision arithmetic */
|
/* Final stages. Compute atan(x) by multiple precision arithmetic */
|
||||||
static double atanMp(double x,const int pr[]){
|
static double
|
||||||
mp_no mpx,mpy,mpy2,mperr,mpt1,mpy1;
|
atanMp (double x, const int pr[])
|
||||||
double y1,y2;
|
{
|
||||||
int i,p;
|
mp_no mpx, mpy, mpy2, mperr, mpt1, mpy1;
|
||||||
|
double y1, y2;
|
||||||
|
int i, p;
|
||||||
|
|
||||||
for (i=0; i<M; i++) {
|
for (i = 0; i < M; i++)
|
||||||
|
{
|
||||||
p = pr[i];
|
p = pr[i];
|
||||||
__dbl_mp(x,&mpx,p); __mpatan(&mpx,&mpy,p);
|
__dbl_mp (x, &mpx, p);
|
||||||
__dbl_mp(u9[i].d,&mpt1,p); __mul(&mpy,&mpt1,&mperr,p);
|
__mpatan (&mpx, &mpy, p);
|
||||||
__add(&mpy,&mperr,&mpy1,p); __sub(&mpy,&mperr,&mpy2,p);
|
__dbl_mp (u9[i].d, &mpt1, p);
|
||||||
__mp_dbl(&mpy1,&y1,p); __mp_dbl(&mpy2,&y2,p);
|
__mul (&mpy, &mpt1, &mperr, p);
|
||||||
if (y1==y2) return y1;
|
__add (&mpy, &mperr, &mpy1, p);
|
||||||
|
__sub (&mpy, &mperr, &mpy2, p);
|
||||||
|
__mp_dbl (&mpy1, &y1, p);
|
||||||
|
__mp_dbl (&mpy2, &y2, p);
|
||||||
|
if (y1 == y2)
|
||||||
|
return y1;
|
||||||
}
|
}
|
||||||
return y1; /*if unpossible to do exact computing */
|
return y1; /*if impossible to do exact computing */
|
||||||
}
|
}
|
||||||
|
|
||||||
#ifdef NO_LONG_DOUBLE
|
#ifdef NO_LONG_DOUBLE
|
||||||
|
|||||||
Loading…
Reference in New Issue
Block a user