/*
* IBM Accurate Mathematical Library
* written by International Business Machines Corp.
- * Copyright (C) 2001-2013 Free Software Foundation, Inc.
+ * Copyright (C) 2001-2016 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 "atnat2.h"
+#include <fenv.h>
+#include <float.h>
+#include <math.h>
#include <math_private.h>
+#include <stap-probe.h>
#ifndef SECTION
# define SECTION
/* Assumption: Machine arithmetic operations are performed in */
/* round to nearest mode of IEEE 754 standard. */
/************************************************************************/
-static double atan2Mp(double ,double ,const int[]);
+static double atan2Mp (double, double, const int[]);
/* Fix the sign and return after stage 1 or stage 2 */
-static double signArctan2(double y,double z)
+static double
+signArctan2 (double y, double z)
{
- return __copysign(z, y);
+ return __copysign (z, y);
}
-static double normalized(double ,double,double ,double);
-void __mpatan2(mp_no *,mp_no *,mp_no *,int);
+
+static double normalized (double, double, double, double);
+void __mpatan2 (mp_no *, mp_no *, mp_no *, int);
double
SECTION
-__ieee754_atan2(double y,double x) {
-
- int i,de,ux,dx,uy,dy;
-#if 0
- int p;
-#endif
- static const int pr[MM]={6,8,10,20,32};
- double ax,ay,u,du,u9,ua,v,vv,dv,t1,t2,t3,t7,t8,
- z,zz,cor,s1,ss1,s2,ss2;
+__ieee754_atan2 (double y, double x)
+{
+ int i, de, ux, dx, uy, dy;
+ static const int pr[MM] = { 6, 8, 10, 20, 32 };
+ double ax, ay, u, du, u9, ua, v, vv, dv, t1, t2, t3, t7, t8,
+ z, zz, cor, s1, ss1, s2, ss2;
#ifndef DLA_FMS
- double t4,t5,t6;
-#endif
-#if 0
- double z1,z2;
+ double t4, t5, t6;
#endif
number num;
-#if 0
- mp_no mperr,mpt1,mpx,mpy,mpz,mpz1,mpz2;
-#endif
- static const int ep= 59768832, /* 57*16**5 */
- em=-59768832; /* -57*16**5 */
+ static const int ep = 59768832, /* 57*16**5 */
+ em = -59768832; /* -57*16**5 */
/* x=NaN or y=NaN */
- num.d = x; ux = num.i[HIGH_HALF]; dx = num.i[LOW_HALF];
- if ((ux&0x7ff00000) ==0x7ff00000) {
- if (((ux&0x000fffff)|dx)!=0x00000000) return x+x; }
- num.d = y; uy = num.i[HIGH_HALF]; dy = num.i[LOW_HALF];
- if ((uy&0x7ff00000) ==0x7ff00000) {
- if (((uy&0x000fffff)|dy)!=0x00000000) return y+y; }
+ num.d = x;
+ ux = num.i[HIGH_HALF];
+ dx = num.i[LOW_HALF];
+ if ((ux & 0x7ff00000) == 0x7ff00000)
+ {
+ if (((ux & 0x000fffff) | dx) != 0x00000000)
+ return x + x;
+ }
+ num.d = y;
+ uy = num.i[HIGH_HALF];
+ dy = num.i[LOW_HALF];
+ if ((uy & 0x7ff00000) == 0x7ff00000)
+ {
+ if (((uy & 0x000fffff) | dy) != 0x00000000)
+ return y + y;
+ }
/* y=+-0 */
- if (uy==0x00000000) {
- if (dy==0x00000000) {
- if ((ux&0x80000000)==0x00000000) return ZERO;
- else return opi.d; } }
- else if (uy==0x80000000) {
- if (dy==0x00000000) {
- if ((ux&0x80000000)==0x00000000) return MZERO;
- else return mopi.d;} }
+ if (uy == 0x00000000)
+ {
+ if (dy == 0x00000000)
+ {
+ if ((ux & 0x80000000) == 0x00000000)
+ return 0;
+ else
+ return opi.d;
+ }
+ }
+ else if (uy == 0x80000000)
+ {
+ if (dy == 0x00000000)
+ {
+ if ((ux & 0x80000000) == 0x00000000)
+ return -0.0;
+ else
+ return mopi.d;
+ }
+ }
/* x=+-0 */
- if (x==ZERO) {
- if ((uy&0x80000000)==0x00000000) return hpi.d;
- else return mhpi.d; }
+ if (x == 0)
+ {
+ if ((uy & 0x80000000) == 0x00000000)
+ return hpi.d;
+ else
+ return mhpi.d;
+ }
/* x=+-INF */
- if (ux==0x7ff00000) {
- if (dx==0x00000000) {
- if (uy==0x7ff00000) {
- if (dy==0x00000000) return qpi.d; }
- else if (uy==0xfff00000) {
- if (dy==0x00000000) return mqpi.d; }
- else {
- if ((uy&0x80000000)==0x00000000) return ZERO;
- else return MZERO; }
+ if (ux == 0x7ff00000)
+ {
+ if (dx == 0x00000000)
+ {
+ if (uy == 0x7ff00000)
+ {
+ if (dy == 0x00000000)
+ return qpi.d;
+ }
+ else if (uy == 0xfff00000)
+ {
+ if (dy == 0x00000000)
+ return mqpi.d;
+ }
+ else
+ {
+ if ((uy & 0x80000000) == 0x00000000)
+ return 0;
+ else
+ return -0.0;
+ }
+ }
}
- }
- else if (ux==0xfff00000) {
- if (dx==0x00000000) {
- if (uy==0x7ff00000) {
- if (dy==0x00000000) return tqpi.d; }
- else if (uy==0xfff00000) {
- if (dy==0x00000000) return mtqpi.d; }
- else {
- if ((uy&0x80000000)==0x00000000) return opi.d;
- else return mopi.d; }
+ else if (ux == 0xfff00000)
+ {
+ if (dx == 0x00000000)
+ {
+ if (uy == 0x7ff00000)
+ {
+ if (dy == 0x00000000)
+ return tqpi.d;
+ }
+ else if (uy == 0xfff00000)
+ {
+ if (dy == 0x00000000)
+ return mtqpi.d;
+ }
+ else
+ {
+ if ((uy & 0x80000000) == 0x00000000)
+ return opi.d;
+ else
+ return mopi.d;
+ }
+ }
}
- }
/* y=+-INF */
- if (uy==0x7ff00000) {
- if (dy==0x00000000) return hpi.d; }
- else if (uy==0xfff00000) {
- if (dy==0x00000000) return mhpi.d; }
+ if (uy == 0x7ff00000)
+ {
+ if (dy == 0x00000000)
+ return hpi.d;
+ }
+ else if (uy == 0xfff00000)
+ {
+ if (dy == 0x00000000)
+ return mhpi.d;
+ }
+ SET_RESTORE_ROUND (FE_TONEAREST);
/* either x/y or y/x is very close to zero */
- ax = (x<ZERO) ? -x : x; ay = (y<ZERO) ? -y : y;
+ ax = (x < 0) ? -x : x;
+ ay = (y < 0) ? -y : y;
de = (uy & 0x7ff00000) - (ux & 0x7ff00000);
- if (de>=ep) { return ((y>ZERO) ? hpi.d : mhpi.d); }
- else if (de<=em) {
- if (x>ZERO) {
- if ((z=ay/ax)<TWOM1022) return normalized(ax,ay,y,z);
- else return signArctan2(y,z); }
- else { return ((y>ZERO) ? opi.d : mopi.d); } }
+ if (de >= ep)
+ {
+ return ((y > 0) ? hpi.d : mhpi.d);
+ }
+ else if (de <= em)
+ {
+ if (x > 0)
+ {
+ double ret;
+ if ((z = ay / ax) < TWOM1022)
+ ret = normalized (ax, ay, y, z);
+ else
+ ret = signArctan2 (y, z);
+ if (fabs (ret) < DBL_MIN)
+ {
+ double vret = ret ? ret : DBL_MIN;
+ double force_underflow = vret * vret;
+ math_force_eval (force_underflow);
+ }
+ return ret;
+ }
+ else
+ {
+ return ((y > 0) ? opi.d : mopi.d);
+ }
+ }
/* if either x or y is extremely close to zero, scale abs(x), abs(y). */
- if (ax<twom500.d || ay<twom500.d) { ax*=two500.d; ay*=two500.d; }
+ if (ax < twom500.d || ay < twom500.d)
+ {
+ ax *= two500.d;
+ ay *= two500.d;
+ }
/* Likewise for large x and y. */
if (ax > two500.d || ay > two500.d)
}
/* x,y which are neither special nor extreme */
- if (ay<ax) {
- u=ay/ax;
- EMULV(ax,u,v,vv,t1,t2,t3,t4,t5)
- du=((ay-v)-vv)/ax; }
- else {
- u=ax/ay;
- EMULV(ay,u,v,vv,t1,t2,t3,t4,t5)
- du=((ax-v)-vv)/ay; }
-
- if (x>ZERO) {
-
- /* (i) x>0, abs(y)< abs(x): atan(ay/ax) */
- if (ay<ax) {
- if (u<inv16.d) {
- v=u*u; zz=du+u*v*(d3.d+v*(d5.d+v*(d7.d+v*(d9.d+v*(d11.d+v*d13.d)))));
- if ((z=u+(zz-u1.d*u)) == u+(zz+u1.d*u)) return signArctan2(y,z);
-
- MUL2(u,du,u,du,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(u,du,s1,ss1,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
- ADD2(u,du,s2,ss2,s1,ss1,t1,t2)
- if ((z=s1+(ss1-u5.d*s1)) == s1+(ss1+u5.d*s1)) return signArctan2(y,z);
- return atan2Mp(x,y,pr);
- }
- else {
- i=(TWO52+TWO8*u)-TWO52; i-=16;
- t3=u-cij[i][0].d;
- EADD(t3,du,v,dv)
- t1=cij[i][1].d; t2=cij[i][2].d;
- zz=v*t2+(dv*t2+v*v*(cij[i][3].d+v*(cij[i][4].d+
- v*(cij[i][5].d+v* cij[i][6].d))));
- if (i<112) {
- if (i<48) u9=u91.d; /* u < 1/4 */
- else u9=u92.d; } /* 1/4 <= u < 1/2 */
- else {
- if (i<176) u9=u93.d; /* 1/2 <= u < 3/4 */
- else u9=u94.d; } /* 3/4 <= u <= 1 */
- if ((z=t1+(zz-u9*t1)) == t1+(zz+u9*t1)) return signArctan2(y,z);
-
- t1=u-hij[i][0].d;
- EADD(t1,du,v,vv)
- s1=v*(hij[i][11].d+v*(hij[i][12].d+v*(hij[i][13].d+
- v*(hij[i][14].d+v* hij[i][15].d))));
- ADD2(hij[i][9].d,hij[i][10].d,s1,ZERO,s2,ss2,t1,t2)
- MUL2(v,vv,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(v,vv,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(v,vv,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(v,vv,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 ((z=s2+(ss2-ub.d*s2)) == s2+(ss2+ub.d*s2)) return signArctan2(y,z);
- return atan2Mp(x,y,pr);
- }
+ if (ay < ax)
+ {
+ u = ay / ax;
+ EMULV (ax, u, v, vv, t1, t2, t3, t4, t5);
+ du = ((ay - v) - vv) / ax;
+ }
+ else
+ {
+ u = ax / ay;
+ EMULV (ay, u, v, vv, t1, t2, t3, t4, t5);
+ du = ((ax - v) - vv) / ay;
}
- /* (ii) x>0, abs(x)<=abs(y): pi/2-atan(ax/ay) */
- else {
- if (u<inv16.d) {
- v=u*u;
- zz=u*v*(d3.d+v*(d5.d+v*(d7.d+v*(d9.d+v*(d11.d+v*d13.d)))));
- ESUB(hpi.d,u,t2,cor)
- t3=((hpi1.d+cor)-du)-zz;
- if ((z=t2+(t3-u2.d)) == t2+(t3+u2.d)) return signArctan2(y,z);
-
- MUL2(u,du,u,du,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(u,du,s1,ss1,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
- ADD2(u,du,s2,ss2,s1,ss1,t1,t2)
- SUB2(hpi.d,hpi1.d,s1,ss1,s2,ss2,t1,t2)
- if ((z=s2+(ss2-u6.d)) == s2+(ss2+u6.d)) return signArctan2(y,z);
- return atan2Mp(x,y,pr);
- }
- else {
- i=(TWO52+TWO8*u)-TWO52; i-=16;
- v=(u-cij[i][0].d)+du;
- zz=hpi1.d-v*(cij[i][2].d+v*(cij[i][3].d+v*(cij[i][4].d+
- v*(cij[i][5].d+v* cij[i][6].d))));
- t1=hpi.d-cij[i][1].d;
- if (i<112) ua=ua1.d; /* w < 1/2 */
- else ua=ua2.d; /* w >= 1/2 */
- if ((z=t1+(zz-ua)) == t1+(zz+ua)) return signArctan2(y,z);
-
- t1=u-hij[i][0].d;
- EADD(t1,du,v,vv)
- s1=v*(hij[i][11].d+v*(hij[i][12].d+v*(hij[i][13].d+
- v*(hij[i][14].d+v* hij[i][15].d))));
- ADD2(hij[i][9].d,hij[i][10].d,s1,ZERO,s2,ss2,t1,t2)
- MUL2(v,vv,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(v,vv,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(v,vv,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(v,vv,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.d,hpi1.d,s2,ss2,s1,ss1,t1,t2)
- if ((z=s1+(ss1-uc.d)) == s1+(ss1+uc.d)) return signArctan2(y,z);
- return atan2Mp(x,y,pr);
- }
+ if (x > 0)
+ {
+ /* (i) x>0, abs(y)< abs(x): atan(ay/ax) */
+ if (ay < ax)
+ {
+ if (u < inv16.d)
+ {
+ v = u * u;
+
+ zz = du + u * v * (d3.d
+ + v * (d5.d
+ + v * (d7.d
+ + v * (d9.d
+ + v * (d11.d
+ + v * d13.d)))));
+
+ if ((z = u + (zz - u1.d * u)) == u + (zz + u1.d * u))
+ return signArctan2 (y, z);
+
+ MUL2 (u, du, u, du, 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, 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 (u, du, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
+ ADD2 (u, du, s2, ss2, s1, ss1, t1, t2);
+
+ if ((z = s1 + (ss1 - u5.d * s1)) == s1 + (ss1 + u5.d * s1))
+ return signArctan2 (y, z);
+
+ return atan2Mp (x, y, pr);
+ }
+
+ i = (TWO52 + TWO8 * u) - TWO52;
+ i -= 16;
+ t3 = u - cij[i][0].d;
+ EADD (t3, du, v, dv);
+ t1 = cij[i][1].d;
+ t2 = cij[i][2].d;
+ zz = v * t2 + (dv * t2
+ + v * v * (cij[i][3].d
+ + v * (cij[i][4].d
+ + v * (cij[i][5].d
+ + v * cij[i][6].d))));
+ if (i < 112)
+ {
+ if (i < 48)
+ u9 = u91.d; /* u < 1/4 */
+ else
+ u9 = u92.d;
+ } /* 1/4 <= u < 1/2 */
+ else
+ {
+ if (i < 176)
+ u9 = u93.d; /* 1/2 <= u < 3/4 */
+ else
+ u9 = u94.d;
+ } /* 3/4 <= u <= 1 */
+ if ((z = t1 + (zz - u9 * t1)) == t1 + (zz + u9 * t1))
+ return signArctan2 (y, z);
+
+ t1 = u - hij[i][0].d;
+ EADD (t1, du, v, vv);
+ s1 = v * (hij[i][11].d
+ + v * (hij[i][12].d
+ + v * (hij[i][13].d
+ + v * (hij[i][14].d
+ + v * hij[i][15].d))));
+ ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2);
+ MUL2 (v, vv, 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 (v, vv, 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 (v, vv, 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 (v, vv, 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 ((z = s2 + (ss2 - ub.d * s2)) == s2 + (ss2 + ub.d * s2))
+ return signArctan2 (y, z);
+ return atan2Mp (x, y, pr);
+ }
+
+ /* (ii) x>0, abs(x)<=abs(y): pi/2-atan(ax/ay) */
+ if (u < inv16.d)
+ {
+ v = u * u;
+ zz = u * v * (d3.d
+ + v * (d5.d
+ + v * (d7.d
+ + v * (d9.d
+ + v * (d11.d
+ + v * d13.d)))));
+ ESUB (hpi.d, u, t2, cor);
+ t3 = ((hpi1.d + cor) - du) - zz;
+ if ((z = t2 + (t3 - u2.d)) == t2 + (t3 + u2.d))
+ return signArctan2 (y, z);
+
+ MUL2 (u, du, u, du, 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, 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 (u, du, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
+ ADD2 (u, du, s2, ss2, s1, ss1, t1, t2);
+ SUB2 (hpi.d, hpi1.d, s1, ss1, s2, ss2, t1, t2);
+
+ if ((z = s2 + (ss2 - u6.d)) == s2 + (ss2 + u6.d))
+ return signArctan2 (y, z);
+ return atan2Mp (x, y, pr);
+ }
+
+ i = (TWO52 + TWO8 * u) - TWO52;
+ i -= 16;
+ v = (u - cij[i][0].d) + du;
+
+ zz = hpi1.d - v * (cij[i][2].d
+ + v * (cij[i][3].d
+ + v * (cij[i][4].d
+ + v * (cij[i][5].d
+ + v * cij[i][6].d))));
+ t1 = hpi.d - cij[i][1].d;
+ if (i < 112)
+ ua = ua1.d; /* w < 1/2 */
+ else
+ ua = ua2.d; /* w >= 1/2 */
+ if ((z = t1 + (zz - ua)) == t1 + (zz + ua))
+ return signArctan2 (y, z);
+
+ t1 = u - hij[i][0].d;
+ EADD (t1, du, v, vv);
+
+ s1 = v * (hij[i][11].d
+ + v * (hij[i][12].d
+ + v * (hij[i][13].d
+ + v * (hij[i][14].d
+ + v * hij[i][15].d))));
+
+ ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2);
+ MUL2 (v, vv, 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 (v, vv, 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 (v, vv, 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 (v, vv, 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.d, hpi1.d, s2, ss2, s1, ss1, t1, t2);
+
+ if ((z = s1 + (ss1 - uc.d)) == s1 + (ss1 + uc.d))
+ return signArctan2 (y, z);
+ return atan2Mp (x, y, pr);
}
- }
- else {
-
- /* (iii) x<0, abs(x)< abs(y): pi/2+atan(ax/ay) */
- if (ax<ay) {
- if (u<inv16.d) {
- v=u*u;
- zz=u*v*(d3.d+v*(d5.d+v*(d7.d+v*(d9.d+v*(d11.d+v*d13.d)))));
- EADD(hpi.d,u,t2,cor)
- t3=((hpi1.d+cor)+du)+zz;
- if ((z=t2+(t3-u3.d)) == t2+(t3+u3.d)) return signArctan2(y,z);
-
- MUL2(u,du,u,du,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(u,du,s1,ss1,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
- ADD2(u,du,s2,ss2,s1,ss1,t1,t2)
- ADD2(hpi.d,hpi1.d,s1,ss1,s2,ss2,t1,t2)
- if ((z=s2+(ss2-u7.d)) == s2+(ss2+u7.d)) return signArctan2(y,z);
- return atan2Mp(x,y,pr);
- }
- else {
- i=(TWO52+TWO8*u)-TWO52; i-=16;
- v=(u-cij[i][0].d)+du;
- zz=hpi1.d+v*(cij[i][2].d+v*(cij[i][3].d+v*(cij[i][4].d+
- v*(cij[i][5].d+v* cij[i][6].d))));
- t1=hpi.d+cij[i][1].d;
- if (i<112) ua=ua1.d; /* w < 1/2 */
- else ua=ua2.d; /* w >= 1/2 */
- if ((z=t1+(zz-ua)) == t1+(zz+ua)) return signArctan2(y,z);
-
- t1=u-hij[i][0].d;
- EADD(t1,du,v,vv)
- s1=v*(hij[i][11].d+v*(hij[i][12].d+v*(hij[i][13].d+
- v*(hij[i][14].d+v* hij[i][15].d))));
- ADD2(hij[i][9].d,hij[i][10].d,s1,ZERO,s2,ss2,t1,t2)
- MUL2(v,vv,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(v,vv,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(v,vv,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(v,vv,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)
- ADD2(hpi.d,hpi1.d,s2,ss2,s1,ss1,t1,t2)
- if ((z=s1+(ss1-uc.d)) == s1+(ss1+uc.d)) return signArctan2(y,z);
- return atan2Mp(x,y,pr);
- }
+
+ /* (iii) x<0, abs(x)< abs(y): pi/2+atan(ax/ay) */
+ if (ax < ay)
+ {
+ if (u < inv16.d)
+ {
+ v = u * u;
+ zz = u * v * (d3.d
+ + v * (d5.d
+ + v * (d7.d
+ + v * (d9.d
+ + v * (d11.d + v * d13.d)))));
+ EADD (hpi.d, u, t2, cor);
+ t3 = ((hpi1.d + cor) + du) + zz;
+ if ((z = t2 + (t3 - u3.d)) == t2 + (t3 + u3.d))
+ return signArctan2 (y, z);
+
+ MUL2 (u, du, u, du, 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, 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 (u, du, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
+ ADD2 (u, du, s2, ss2, s1, ss1, t1, t2);
+ ADD2 (hpi.d, hpi1.d, s1, ss1, s2, ss2, t1, t2);
+
+ if ((z = s2 + (ss2 - u7.d)) == s2 + (ss2 + u7.d))
+ return signArctan2 (y, z);
+ return atan2Mp (x, y, pr);
+ }
+
+ i = (TWO52 + TWO8 * u) - TWO52;
+ i -= 16;
+ v = (u - cij[i][0].d) + du;
+ zz = hpi1.d + v * (cij[i][2].d
+ + v * (cij[i][3].d
+ + v * (cij[i][4].d
+ + v * (cij[i][5].d
+ + v * cij[i][6].d))));
+ t1 = hpi.d + cij[i][1].d;
+ if (i < 112)
+ ua = ua1.d; /* w < 1/2 */
+ else
+ ua = ua2.d; /* w >= 1/2 */
+ if ((z = t1 + (zz - ua)) == t1 + (zz + ua))
+ return signArctan2 (y, z);
+
+ t1 = u - hij[i][0].d;
+ EADD (t1, du, v, vv);
+ s1 = v * (hij[i][11].d
+ + v * (hij[i][12].d
+ + v * (hij[i][13].d
+ + v * (hij[i][14].d
+ + v * hij[i][15].d))));
+ ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2);
+ MUL2 (v, vv, 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 (v, vv, 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 (v, vv, 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 (v, vv, 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);
+ ADD2 (hpi.d, hpi1.d, s2, ss2, s1, ss1, t1, t2);
+
+ if ((z = s1 + (ss1 - uc.d)) == s1 + (ss1 + uc.d))
+ return signArctan2 (y, z);
+ return atan2Mp (x, y, pr);
}
- /* (iv) x<0, abs(y)<=abs(x): pi-atan(ax/ay) */
- else {
- if (u<inv16.d) {
- v=u*u;
- zz=u*v*(d3.d+v*(d5.d+v*(d7.d+v*(d9.d+v*(d11.d+v*d13.d)))));
- ESUB(opi.d,u,t2,cor)
- t3=((opi1.d+cor)-du)-zz;
- if ((z=t2+(t3-u4.d)) == t2+(t3+u4.d)) return signArctan2(y,z);
-
- MUL2(u,du,u,du,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(u,du,s1,ss1,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
- ADD2(u,du,s2,ss2,s1,ss1,t1,t2)
- SUB2(opi.d,opi1.d,s1,ss1,s2,ss2,t1,t2)
- if ((z=s2+(ss2-u8.d)) == s2+(ss2+u8.d)) return signArctan2(y,z);
- return atan2Mp(x,y,pr);
- }
- else {
- i=(TWO52+TWO8*u)-TWO52; i-=16;
- v=(u-cij[i][0].d)+du;
- zz=opi1.d-v*(cij[i][2].d+v*(cij[i][3].d+v*(cij[i][4].d+
- v*(cij[i][5].d+v* cij[i][6].d))));
- t1=opi.d-cij[i][1].d;
- if (i<112) ua=ua1.d; /* w < 1/2 */
- else ua=ua2.d; /* w >= 1/2 */
- if ((z=t1+(zz-ua)) == t1+(zz+ua)) return signArctan2(y,z);
-
- t1=u-hij[i][0].d;
- EADD(t1,du,v,vv)
- s1=v*(hij[i][11].d+v*(hij[i][12].d+v*(hij[i][13].d+
- v*(hij[i][14].d+v* hij[i][15].d))));
- ADD2(hij[i][9].d,hij[i][10].d,s1,ZERO,s2,ss2,t1,t2)
- MUL2(v,vv,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(v,vv,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(v,vv,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(v,vv,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(opi.d,opi1.d,s2,ss2,s1,ss1,t1,t2)
- if ((z=s1+(ss1-uc.d)) == s1+(ss1+uc.d)) return signArctan2(y,z);
- return atan2Mp(x,y,pr);
- }
+ /* (iv) x<0, abs(y)<=abs(x): pi-atan(ax/ay) */
+ if (u < inv16.d)
+ {
+ v = u * u;
+ zz = u * v * (d3.d
+ + v * (d5.d
+ + v * (d7.d
+ + v * (d9.d + v * (d11.d + v * d13.d)))));
+ ESUB (opi.d, u, t2, cor);
+ t3 = ((opi1.d + cor) - du) - zz;
+ if ((z = t2 + (t3 - u4.d)) == t2 + (t3 + u4.d))
+ return signArctan2 (y, z);
+
+ MUL2 (u, du, u, du, 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, 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 (u, du, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
+ ADD2 (u, du, s2, ss2, s1, ss1, t1, t2);
+ SUB2 (opi.d, opi1.d, s1, ss1, s2, ss2, t1, t2);
+
+ if ((z = s2 + (ss2 - u8.d)) == s2 + (ss2 + u8.d))
+ return signArctan2 (y, z);
+ return atan2Mp (x, y, pr);
}
- }
+
+ i = (TWO52 + TWO8 * u) - TWO52;
+ i -= 16;
+ v = (u - cij[i][0].d) + du;
+ zz = opi1.d - v * (cij[i][2].d
+ + v * (cij[i][3].d
+ + v * (cij[i][4].d
+ + v * (cij[i][5].d + v * cij[i][6].d))));
+ t1 = opi.d - cij[i][1].d;
+ if (i < 112)
+ ua = ua1.d; /* w < 1/2 */
+ else
+ ua = ua2.d; /* w >= 1/2 */
+ if ((z = t1 + (zz - ua)) == t1 + (zz + ua))
+ return signArctan2 (y, z);
+
+ t1 = u - hij[i][0].d;
+
+ EADD (t1, du, v, vv);
+
+ s1 = v * (hij[i][11].d
+ + v * (hij[i][12].d
+ + v * (hij[i][13].d
+ + v * (hij[i][14].d + v * hij[i][15].d))));
+
+ ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2);
+ MUL2 (v, vv, 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 (v, vv, 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 (v, vv, 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 (v, vv, 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 (opi.d, opi1.d, s2, ss2, s1, ss1, t1, t2);
+
+ if ((z = s1 + (ss1 - uc.d)) == s1 + (ss1 + uc.d))
+ return signArctan2 (y, z);
+ return atan2Mp (x, y, pr);
}
+
#ifndef __ieee754_atan2
strong_alias (__ieee754_atan2, __atan2_finite)
#endif
- /* Treat the Denormalized case */
+/* Treat the Denormalized case */
static double
SECTION
-normalized(double ax,double ay,double y, double z)
- { int p;
- mp_no mpx,mpy,mpz,mperr,mpz2,mpt1;
- p=6;
- __dbl_mp(ax,&mpx,p); __dbl_mp(ay,&mpy,p); __dvd(&mpy,&mpx,&mpz,p);
- __dbl_mp(ue.d,&mpt1,p); __mul(&mpz,&mpt1,&mperr,p);
- __sub(&mpz,&mperr,&mpz2,p); __mp_dbl(&mpz2,&z,p);
- return signArctan2(y,z);
+normalized (double ax, double ay, double y, double z)
+{
+ int p;
+ mp_no mpx, mpy, mpz, mperr, mpz2, mpt1;
+ p = 6;
+ __dbl_mp (ax, &mpx, p);
+ __dbl_mp (ay, &mpy, p);
+ __dvd (&mpy, &mpx, &mpz, p);
+ __dbl_mp (ue.d, &mpt1, p);
+ __mul (&mpz, &mpt1, &mperr, p);
+ __sub (&mpz, &mperr, &mpz2, p);
+ __mp_dbl (&mpz2, &z, p);
+ return signArctan2 (y, z);
}
- /* Stage 3: Perform a multi-Precision computation */
+
+/* Stage 3: Perform a multi-Precision computation */
static double
SECTION
-atan2Mp(double x,double y,const int pr[])
+atan2Mp (double x, double y, const int pr[])
{
- double z1,z2;
- int i,p;
- mp_no mpx,mpy,mpz,mpz1,mpz2,mperr,mpt1;
- for (i=0; i<MM; i++) {
- p = pr[i];
- __dbl_mp(x,&mpx,p); __dbl_mp(y,&mpy,p);
- __mpatan2(&mpy,&mpx,&mpz,p);
- __dbl_mp(ud[i].d,&mpt1,p); __mul(&mpz,&mpt1,&mperr,p);
- __add(&mpz,&mperr,&mpz1,p); __sub(&mpz,&mperr,&mpz2,p);
- __mp_dbl(&mpz1,&z1,p); __mp_dbl(&mpz2,&z2,p);
- if (z1==z2) return z1;
- }
- return z1; /*if unpossible to do exact computing */
+ double z1, z2;
+ int i, p;
+ mp_no mpx, mpy, mpz, mpz1, mpz2, mperr, mpt1;
+ for (i = 0; i < MM; i++)
+ {
+ p = pr[i];
+ __dbl_mp (x, &mpx, p);
+ __dbl_mp (y, &mpy, p);
+ __mpatan2 (&mpy, &mpx, &mpz, p);
+ __dbl_mp (ud[i].d, &mpt1, p);
+ __mul (&mpz, &mpt1, &mperr, p);
+ __add (&mpz, &mperr, &mpz1, p);
+ __sub (&mpz, &mperr, &mpz2, p);
+ __mp_dbl (&mpz1, &z1, p);
+ __mp_dbl (&mpz2, &z2, p);
+ if (z1 == z2)
+ {
+ LIBC_PROBE (slowatan2, 4, &p, &x, &y, &z1);
+ return z1;
+ }
+ }
+ LIBC_PROBE (slowatan2_inexact, 4, &p, &x, &y, &z1);
+ return z1; /*if impossible to do exact computing */
}
projects / thirdparty / glibc.git / blobdiff