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- Log ----------------------------------------------------------------- commit fdc6db4b7af14ce1ceb6e38e92135335a4921fa3 Author: Raymond Toy toy.raymond@gmail.com Date: Sat Aug 2 15:46:50 2014 -0700
Use fdlibm_atan instead of atan.
* fdlibm.h: * Declare fdlibm_atan * e_atan2.c: * Use fdlibm_atan instead of atan.
diff --git a/src/lisp/e_atan2.c b/src/lisp/e_atan2.c index f4c1c12..7e177e8 100644 --- a/src/lisp/e_atan2.c +++ b/src/lisp/e_atan2.c @@ -75,7 +75,7 @@ pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ if(((ix|((lx|-lx)>>31))>0x7ff00000)|| ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */ return x+y; - if((hx-0x3ff00000|lx)==0) return atan(y); /* x=1.0 */ + if((hx-0x3ff00000|lx)==0) return fdlibm_atan(y); /* x=1.0 */ m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */
/* when y = 0 */ @@ -115,7 +115,7 @@ pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ k = (iy-ix)>>20; if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */ else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */ - else z=atan(fabs(y/x)); /* safe to do y/x */ + else z=fdlibm_atan(fabs(y/x)); /* safe to do y/x */ switch (m) { case 0: return z ; /* atan(+,+) */ case 1: diff --git a/src/lisp/fdlibm.h b/src/lisp/fdlibm.h index 72f57f8..9d25664 100644 --- a/src/lisp/fdlibm.h +++ b/src/lisp/fdlibm.h @@ -53,6 +53,7 @@ extern double fdlibm_cos(double x); extern double fdlibm_tan(double x); extern double fdlibm_expm1(double x); extern double fdlibm_log1p(double x); +extern double fdlibm_atan(double x); extern double __ieee754_exp(double x); extern double __ieee754_log(double x);
commit 797b00817a9ecfb6e13badf1aa2b88ff87acc2ac Author: Raymond Toy toy.raymond@gmail.com Date: Sat Aug 2 15:43:49 2014 -0700
Fix up atan2 by using unions.
diff --git a/src/lisp/e_atan2.c b/src/lisp/e_atan2.c index 4e731ba..f4c1c12 100644 --- a/src/lisp/e_atan2.c +++ b/src/lisp/e_atan2.c @@ -63,11 +63,15 @@ pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ double z; int k,m,hx,hy,ix,iy; unsigned lx,ly; + union { int i[2]; double d; } ux; + union { int i[2]; double d; } uy;
- hx = __HI(x); ix = hx&0x7fffffff; - lx = __LO(x); - hy = __HI(y); iy = hy&0x7fffffff; - ly = __LO(y); + ux.d = x; + hx = ux.i[HIWORD]; ix = hx&0x7fffffff; + lx = ux.i[LOWORD]; + uy.d = y; + hy = uy.i[HIWORD]; iy = hy&0x7fffffff; + ly = uy.i[LOWORD]; if(((ix|((lx|-lx)>>31))>0x7ff00000)|| ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */ return x+y; @@ -114,7 +118,10 @@ pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ else z=atan(fabs(y/x)); /* safe to do y/x */ switch (m) { case 0: return z ; /* atan(+,+) */ - case 1: __HI(z) ^= 0x80000000; + case 1: + ux.d = z; + ux.i[HIWORD] ^= 0x80000000; + z = ux.d; return z ; /* atan(-,+) */ case 2: return pi-(z-pi_lo);/* atan(+,-) */ default: /* case 3 */
commit d2e935a5b3a1a3922be0c52059fa99a332178483 Author: Raymond Toy toy.raymond@gmail.com Date: Sat Aug 2 15:40:31 2014 -0700
Import atan2 function from fdlibm, as is.
diff --git a/src/lisp/e_atan2.c b/src/lisp/e_atan2.c new file mode 100644 index 0000000..4e731ba --- /dev/null +++ b/src/lisp/e_atan2.c @@ -0,0 +1,123 @@ + +/* @(#)e_atan2.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + */ + +/* __ieee754_atan2(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 "fdlibm.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +tiny = 1.0e-300, +zero = 0.0, +pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */ +pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */ +pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */ +pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ + +#ifdef __STDC__ + double __ieee754_atan2(double y, double x) +#else + double __ieee754_atan2(y,x) + double y,x; +#endif +{ + double z; + int k,m,hx,hy,ix,iy; + unsigned lx,ly; + + hx = __HI(x); ix = hx&0x7fffffff; + lx = __LO(x); + hy = __HI(y); iy = hy&0x7fffffff; + ly = __LO(y); + if(((ix|((lx|-lx)>>31))>0x7ff00000)|| + ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */ + return x+y; + if((hx-0x3ff00000|lx)==0) return atan(y); /* x=1.0 */ + m = ((hy>>31)&1)|((hx>>30)&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==0x7ff00000) { + if(iy==0x7ff00000) { + 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==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; + + /* compute y/x */ + k = (iy-ix)>>20; + if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */ + else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */ + else z=atan(fabs(y/x)); /* safe to do y/x */ + switch (m) { + case 0: return z ; /* atan(+,+) */ + case 1: __HI(z) ^= 0x80000000; + return z ; /* atan(-,+) */ + case 2: return pi-(z-pi_lo);/* atan(+,-) */ + default: /* case 3 */ + return (z-pi_lo)-pi;/* atan(-,-) */ + } +}
-----------------------------------------------------------------------
Summary of changes: src/lisp/e_atan2.c | 130 ++++++++++++++++++++++++++++++++++++++++++++++++++++ src/lisp/fdlibm.h | 1 + 2 files changed, 131 insertions(+) create mode 100644 src/lisp/e_atan2.c
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