| /* e_atan2l.c -- long double version of e_atan2.c. |
| * Conversion to long double by Ulrich Drepper, |
| * Cygnus Support, drepper@cygnus.com. |
| */ |
| |
| /* |
| * ==================================================== |
| * 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. |
| * ==================================================== |
| */ |
| |
| #if defined(LIBM_SCCS) && !defined(lint) |
| static char rcsid[] = "$NetBSD: $"; |
| #endif |
| |
| /* __ieee754_atan2l(y,x) |
| * Method : |
| * 1. Reduce y to positive by atan2(y,x)=-atan2(-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 "math.h" |
| #include "math_private.h" |
| |
| #ifdef __STDC__ |
| static const long double |
| #else |
| static long double |
| #endif |
| tiny = 1.0e-4900L, |
| zero = 0.0, |
| pi_o_4 = 7.85398163397448309628202E-01L, /* 0x3FFE, 0xC90FDAA2, 0x2168C235 */ |
| pi_o_2 = 1.5707963267948966192564E+00L, /* 0x3FFF, 0xC90FDAA2, 0x2168C235 */ |
| pi = 3.14159265358979323851281E+00L, /* 0x4000, 0xC90FDAA2, 0x2168C235 */ |
| pi_lo = -5.01655761266833202345176e-20L;/* 0xBFBE, 0xECE675D1, 0xFC8F8CBB */ |
| |
| #ifdef __STDC__ |
| long double __ieee754_atan2l(long double y, long double x) |
| #else |
| long double __ieee754_atan2l(y,x) |
| long double y,x; |
| #endif |
| { |
| long double z; |
| int32_t k,m,hx,hy,ix,iy; |
| u_int32_t sx,sy,lx,ly; |
| |
| GET_LDOUBLE_WORDS(sx,hx,lx,x); |
| ix = sx&0x7fff; |
| lx |= hx & 0x7fffffff; |
| GET_LDOUBLE_WORDS(sy,hy,ly,y); |
| iy = sy&0x7fff; |
| ly |= hy & 0x7fffffff; |
| if(((2*ix|((lx|-lx)>>31))>0xfffe)|| |
| ((2*iy|((ly|-ly)>>31))>0xfffe)) /* x or y is NaN */ |
| return x+y; |
| if(((sx-0x3fff)|lx)==0) return __atanl(y); /* x=1.0 */ |
| m = ((sy>>15)&1)|((sx>>14)&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 (sy>=0x8000)? -pi_o_2-tiny: pi_o_2+tiny; |
| |
| /* when x is INF */ |
| if(ix==0x7fff) { |
| if(iy==0x7fff) { |
| 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 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/ |
| case 3: return -3.0*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==0x7fff) return (sy>=0x8000)? -pi_o_2-tiny: pi_o_2+tiny; |
| |
| /* compute y/x */ |
| k = sy-sx; |
| if(k > 70) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**70 */ |
| else if(sx>=0x8000&&k<-70) z=0.0; /* |y|/x < -2**70 */ |
| else z=__atanl(fabsl(y/x)); /* safe to do y/x */ |
| switch (m) { |
| case 0: return z ; /* atan(+,+) */ |
| case 1: { |
| u_int32_t sz; |
| GET_LDOUBLE_EXP(sz,z); |
| SET_LDOUBLE_EXP(z,sz ^ 0x8000); |
| } |
| return z ; /* atan(-,+) */ |
| case 2: return pi-(z-pi_lo);/* atan(+,-) */ |
| default: /* case 3 */ |
| return (z-pi_lo)-pi;/* atan(-,-) */ |
| } |
| } |