1 /* atan2q.c -- __float128 version of e_atan2.c. * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz. */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ /* atan2q(y,x) * Method : * 1. Reduce y to positive by atan2q(y,x)=-atan2q(-y,x). * 2. Reduce x to positive by (if x and y are unexceptional): * ARG (x+iy) = arctan(y/x) ... if x > 0, * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0, * * Special cases: * * ATAN2((anything), NaN ) is NaN; * ATAN2(NAN , (anything) ) is NaN; * ATAN2(+-0, +(anything but NaN)) is +-0 ; * ATAN2(+-0, -(anything but NaN)) is +-pi ; * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2; * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ; * ATAN2(+-(anything but INF and NaN), -INF) is +-pi; * ATAN2(+-INF,+INF ) is +-pi/4 ; * ATAN2(+-INF,-INF ) is +-3pi/4; * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2; * * Constants: * The hexadecimal values are the intended ones for the following * constants. The decimal values may be used, provided that the * compiler will convert from decimal to binary accurately enough * to produce the hexadecimal values shown. */ #include "quadmath-imp.h" static const __float128 tiny = 1.0e-4900Q, zero = 0.0, pi_o_4 = 7.85398163397448309615660845819875699e-01Q, /* 3ffe921fb54442d18469898cc51701b8 */ pi_o_2 = 1.57079632679489661923132169163975140e+00Q, /* 3fff921fb54442d18469898cc51701b8 */ pi = 3.14159265358979323846264338327950280e+00Q, /* 4000921fb54442d18469898cc51701b8 */ pi_lo = 8.67181013012378102479704402604335225e-35Q; /* 3f8dcd129024e088a67cc74020bbea64 */ __float128 atan2q (__float128 y, __float128 x) { __float128 z; int64_t k,m,hx,hy,ix,iy; uint64_t lx,ly; GET_FLT128_WORDS64(hx,lx,x); ix = hx&0x7fffffffffffffffLL; GET_FLT128_WORDS64(hy,ly,y); iy = hy&0x7fffffffffffffffLL; if(((ix|((lx|-lx)>>63))>0x7fff000000000000LL)|| ((iy|((ly|-ly)>>63))>0x7fff000000000000LL)) /* x or y is NaN */ return x+y; if(((hx-0x3fff000000000000LL)|lx)==0) return atanq(y); /* x=1.0Q */ m = ((hy>>63)&1)|((hx>>62)&2); /* 2*sign(x)+sign(y) */ /* when y = 0 */ if((iy|ly)==0) { switch(m) { case 0: case 1: return y; /* atan(+-0,+anything)=+-0 */ case 2: return pi+tiny;/* atan(+0,-anything) = pi */ case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ } } /* when x = 0 */ if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; /* when x is INF */ if(ix==0x7fff000000000000LL) { if(iy==0x7fff000000000000LL) { switch(m) { case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ case 2: return 3.0Q*pi_o_4+tiny;/*atan(+INF,-INF)*/ case 3: return -3.0Q*pi_o_4-tiny;/*atan(-INF,-INF)*/ } } else { switch(m) { case 0: return zero ; /* atan(+...,+INF) */ case 1: return -zero ; /* atan(-...,+INF) */ case 2: return pi+tiny ; /* atan(+...,-INF) */ case 3: return -pi-tiny ; /* atan(-...,-INF) */ } } } /* when y is INF */ if(iy==0x7fff000000000000LL) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; /* compute y/x */ k = (iy-ix)>>48; if(k > 120) z=pi_o_2+0.5Q*pi_lo; /* |y/x| > 2**120 */ else if(hx<0&&k<-120) z=0.0Q; /* |y|/x < -2**120 */ else z=atanq(fabsq(y/x)); /* safe to do y/x */ switch (m) { case 0: return z ; /* atan(+,+) */ case 1: { uint64_t zh; GET_FLT128_MSW64(zh,z); SET_FLT128_MSW64(z,zh ^ 0x8000000000000000ULL); } return z ; /* atan(-,+) */ case 2: return pi-(z-pi_lo);/* atan(+,-) */ default: /* case 3 */ return (z-pi_lo)-pi;/* atan(-,-) */ } }