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; #ifndef DLA_FMS double t4, t5, t6; #endif number num; 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; } /* y=+-0 */ 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 == 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 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; } } } /* y=+-INF */ 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 < 0) ? -x : x; ay = (y < 0) ? -y : y; de = (uy & 0x7ff00000) - (ux & 0x7ff00000); if (de >= ep) { return ((y > 0) ? hpi.d : mhpi.d); } else if (de <= em) { if (x > 0) { if ((z = ay / ax) < TWOM1022) return normalized (ax, ay, y, z); else return signArctan2 (y, z); } 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; } /* Likewise for large x and y. */ if (ax > two500.d || ay > two500.d) { ax *= twom500.d; ay *= twom500.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 > 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); } /* (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) */ 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); }
/* 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; #ifndef DLA_FMS double t4, t5, t6; #endif int i, ux, dx; static const int pr[M] = { 6, 8, 10, 32 }; number num; 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; /* Regular values of x, including denormals +-0 and +-INF */ 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; } } } }