diff options
| -rw-r--r-- | ChangeLog | 4 | ||||
| -rw-r--r-- | sysdeps/ieee754/dbl-64/e_atan2.c | 804 |
2 files changed, 498 insertions, 310 deletions
diff --git a/ChangeLog b/ChangeLog index a6dd122a46..9a8bab6450 100644 --- a/ChangeLog +++ b/ChangeLog @@ -1,3 +1,7 @@ +2013-03-28 Siddhesh Poyarekar <siddhesh@redhat.com> + + * sysdeps/ieee-754/dbl-64/e_atan2.c: Reformat. + 2013-03-27 Joseph Myers <joseph@codesourcery.com> [BZ #15307] diff --git a/sysdeps/ieee754/dbl-64/e_atan2.c b/sysdeps/ieee754/dbl-64/e_atan2.c index 535010e3d8..bfe0b3b632 100644 --- a/sysdeps/ieee754/dbl-64/e_atan2.c +++ b/sysdeps/ieee754/dbl-64/e_atan2.c @@ -53,96 +53,171 @@ /* 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; - 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; + double t4, t5, t6; #endif number num; - 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 ZERO; + else + return opi.d; + } + } + else if (uy == 0x80000000) + { + if (dy == 0x00000000) + { + if ((ux & 0x80000000) == 0x00000000) + return MZERO; + else + return mopi.d; + } + } /* x=+-0 */ - if (x==ZERO) { - if ((uy&0x80000000)==0x00000000) return hpi.d; - else return mhpi.d; } + if (x == ZERO) + { + 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 ZERO; + else + return MZERO; + } + } } - } - 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; + } /* either x/y or y/x is very close to zero */ - ax = (x<ZERO) ? -x : x; ay = (y<ZERO) ? -y : y; + ax = (x < ZERO) ? -x : x; + ay = (y < ZERO) ? -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 > 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 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) @@ -152,268 +227,377 @@ __ieee754_atan2(double y,double x) { } /* 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 > 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); + } + + 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); + } + + /* (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, 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); + } + + 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); } - } - 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, 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); + } + + 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); } - /* (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, 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); } - } + + 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); } + #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) + return z1; + } + return z1; /*if impossible to do exact computing */ } |