/*
* IBM Accurate Mathematical Library
* written by International Business Machines Corp.
- * Copyright (C) 2001, 2011 Free Software Foundation
+ * Copyright (C) 2001-2019 Free Software Foundation, Inc.
*
* 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
#include "MathLib.h"
#include "uatan.tbl"
#include "atnat.h"
+#include <fenv.h>
+#include <float.h>
+#include <libm-alias-double.h>
#include <math.h>
+#include <fenv_private.h>
+#include <math-underflow.h>
+#include <stap-probe.h>
-void __mpatan(mp_no *,mp_no *,int); /* see definition in mpatan.c */
-static double atanMp(double,const int[]);
+void __mpatan (mp_no *, mp_no *, int); /* see definition in mpatan.c */
+static double atanMp (double, const int[]);
/* Fix the sign of y and return */
-static double __signArctan(double x,double y){
- return __copysign(y, x);
+static double
+__signArctan (double x, double y)
+{
+ return copysign (y, x);
}
/* An ultimate atan() routine. Given an IEEE double machine number x, */
/* routine computes the correctly rounded (to nearest) value of atan(x). */
-double atan(double x) {
-
-
- double cor,s1,ss1,s2,ss2,t1,t2,t3,t7,t8,t9,t10,u,u2,u3,
- v,vv,w,ww,y,yy,z,zz;
+double
+__atan (double x)
+{
+ double cor, s1, ss1, s2, ss2, t1, t2, t3, t7, t8, t9, t10, u, u2, u3,
+ v, vv, w, ww, y, yy, z, zz;
#ifndef DLA_FMS
- double t4,t5,t6;
-#endif
-#if 0
- double y1,y2;
-#endif
- int i,ux,dx;
-#if 0
- int p;
+ double t4, t5, t6;
#endif
- static const int pr[M]={6,8,10,32};
+ int i, ux, dx;
+ static const int pr[M] = { 6, 8, 10, 32 };
number num;
-#if 0
- mp_no mpt1,mpx,mpy,mpy1,mpy2,mperr;
-#endif
- num.d = x; ux = num.i[HIGH_HALF]; dx = num.i[LOW_HALF];
+ num.d = x;
+ ux = num.i[HIGH_HALF];
+ dx = num.i[LOW_HALF];
/* x=NaN */
- if (((ux&0x7ff00000)==0x7ff00000) && (((ux&0x000fffff)|dx)!=0x00000000))
- return x+x;
+ if (((ux & 0x7ff00000) == 0x7ff00000)
+ && (((ux & 0x000fffff) | dx) != 0x00000000))
+ return x + x;
/* Regular values of x, including denormals +-0 and +-INF */
- u = (x<ZERO) ? -x : x;
- if (u<C) {
- if (u<B) {
- if (u<A) { /* u < A */
- return x; }
- else { /* A <= u < B */
- v=x*x; yy=x*v*(d3.d+v*(d5.d+v*(d7.d+v*(d9.d+v*(d11.d+v*d13.d)))));
- if ((y=x+(yy-U1*x)) == x+(yy+U1*x)) return y;
-
- EMULV(x,x,v,vv,t1,t2,t3,t4,t5) /* v+vv=x^2 */
- s1=v*(f11.d+v*(f13.d+v*(f15.d+v*(f17.d+v*f19.d))));
- 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(x,ZERO,s1,ss1,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
- ADD2(x,ZERO,s2,ss2,s1,ss1,t1,t2)
- if ((y=s1+(ss1-U5*s1)) == s1+(ss1+U5*s1)) return y;
-
- return atanMp(x,pr);
- } }
- else { /* B <= u < C */
- i=(TWO52+TWO8*u)-TWO52; i-=16;
- z=u-cij[i][0].d;
- yy=z*(cij[i][2].d+z*(cij[i][3].d+z*(cij[i][4].d+
- z*(cij[i][5].d+z* cij[i][6].d))));
- t1=cij[i][1].d;
- if (i<112) {
- if (i<48) u2=U21; /* u < 1/4 */
- else u2=U22; } /* 1/4 <= u < 1/2 */
- else {
- if (i<176) u2=U23; /* 1/2 <= u < 3/4 */
- else u2=U24; } /* 3/4 <= u <= 1 */
- if ((y=t1+(yy-u2*t1)) == t1+(yy+u2*t1)) return __signArctan(x,y);
-
- z=u-hij[i][0].d;
- s1=z*(hij[i][11].d+z*(hij[i][12].d+z*(hij[i][13].d+
- z*(hij[i][14].d+z* hij[i][15].d))));
- ADD2(hij[i][9].d,hij[i][10].d,s1,ZERO,s2,ss2,t1,t2)
- MUL2(z,ZERO,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,ZERO,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,ZERO,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,ZERO,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)
- if ((y=s2+(ss2-U6*s2)) == s2+(ss2+U6*s2)) return __signArctan(x,y);
-
- return atanMp(x,pr);
- }
- }
- else {
- if (u<D) { /* C <= u < D */
- w=ONE/u;
- 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=HPI1-z*(cij[i][2].d+z*(cij[i][3].d+z*(cij[i][4].d+
- z*(cij[i][5].d+z* cij[i][6].d))));
- 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=z*(hij[i][11].d+z*(hij[i][12].d+z*(hij[i][13].d+
- z*(hij[i][14].d+z* hij[i][15].d))));
- 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=w*v*(d3.d+v*(d5.d+v*(d7.d+v*(d9.d+v*(d11.d+v*d13.d)))));
- 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=v*(f11.d+v*(f13.d+v*(f15.d+v*(f17.d+v*f19.d))));
- 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 */
- if (x>0) return HPI;
- else return MHPI; }
+ SET_RESTORE_ROUND (FE_TONEAREST);
+ u = (x < 0) ? -x : x;
+ if (u < C)
+ {
+ if (u < B)
+ {
+ if (u < A)
+ {
+ math_check_force_underflow_nonneg (u);
+ return x;
+ }
+ else
+ { /* A <= u < B */
+ v = x * x;
+ 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 *= x * v;
+
+ if ((y = x + (yy - U1 * x)) == x + (yy + U1 * x))
+ return y;
+
+ EMULV (x, x, v, vv, t1, t2, t3, t4, t5); /* v+vv=x^2 */
+
+ 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, 0, 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 (x, 0, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7,
+ t8);
+ ADD2 (x, 0, s2, ss2, s1, ss1, t1, t2);
+ if ((y = s1 + (ss1 - U5 * s1)) == s1 + (ss1 + U5 * s1))
+ return y;
+
+ return atanMp (x, pr);
+ }
+ }
+ else
+ { /* B <= u < C */
+ i = (TWO52 + TWO8 * u) - TWO52;
+ i -= 16;
+ z = u - cij[i][0].d;
+ 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 *= z;
+
+ t1 = cij[i][1].d;
+ if (i < 112)
+ {
+ if (i < 48)
+ u2 = U21; /* u < 1/4 */
+ else
+ u2 = U22;
+ } /* 1/4 <= u < 1/2 */
+ else
+ {
+ if (i < 176)
+ u2 = U23; /* 1/2 <= u < 3/4 */
+ else
+ u2 = U24;
+ } /* 3/4 <= u <= 1 */
+ if ((y = t1 + (yy - u2 * t1)) == t1 + (yy + u2 * t1))
+ return __signArctan (x, y);
+
+ z = u - hij[i][0].d;
+
+ 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, 0, s2, ss2, t1, t2);
+ MUL2 (z, 0, 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, 0, 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, 0, 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, 0, 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);
+ if ((y = s2 + (ss2 - U6 * s2)) == s2 + (ss2 + U6 * s2))
+ return __signArctan (x, y);
+
+ return atanMp (x, pr);
+ }
}
- }
+ else
+ {
+ if (u < D)
+ { /* C <= u < D */
+ w = 1 / u;
+ EMULV (w, u, t1, t2, t3, t4, t5, t6, t7);
+ ww = w * ((1 - 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 (1, 0, u, 0, 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, 0, 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 = 1 / 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 * ((1 - 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 (1, 0, u, 0, 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, 0, 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 */
+ if (x > 0)
+ return HPI;
+ else
+ return MHPI;
+ }
+ }
+ }
}
/* Final stages. Compute atan(x) by multiple precision arithmetic */
-static double atanMp(double x,const int pr[]){
- mp_no mpx,mpy,mpy2,mperr,mpt1,mpy1;
- double y1,y2;
- int i,p;
-
-for (i=0; i<M; i++) {
- p = pr[i];
- __dbl_mp(x,&mpx,p); __mpatan(&mpx,&mpy,p);
- __dbl_mp(u9[i].d,&mpt1,p); __mul(&mpy,&mpt1,&mperr,p);
- __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 */
+static double
+atanMp (double x, const int pr[])
+{
+ mp_no mpx, mpy, mpy2, mperr, mpt1, mpy1;
+ double y1, y2;
+ int i, p;
+
+ for (i = 0; i < M; i++)
+ {
+ p = pr[i];
+ __dbl_mp (x, &mpx, p);
+ __mpatan (&mpx, &mpy, p);
+ __dbl_mp (u9[i].d, &mpt1, p);
+ __mul (&mpy, &mpt1, &mperr, p);
+ __add (&mpy, &mperr, &mpy1, p);
+ __sub (&mpy, &mperr, &mpy2, p);
+ __mp_dbl (&mpy1, &y1, p);
+ __mp_dbl (&mpy2, &y2, p);
+ if (y1 == y2)
+ {
+ LIBC_PROBE (slowatan, 3, &p, &x, &y1);
+ return y1;
+ }
+ }
+ LIBC_PROBE (slowatan_inexact, 3, &p, &x, &y1);
+ return y1; /*if impossible to do exact computing */
}
-#ifdef NO_LONG_DOUBLE
-weak_alias (atan, atanl)
+#ifndef __atan
+libm_alias_double (__atan, atan)
#endif
projects / thirdparty / glibc.git / blobdiff