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Diffstat (limited to 'libc-top-half/musl/src/complex/catan.c')
-rw-r--r-- | libc-top-half/musl/src/complex/catan.c | 107 |
1 files changed, 107 insertions, 0 deletions
diff --git a/libc-top-half/musl/src/complex/catan.c b/libc-top-half/musl/src/complex/catan.c new file mode 100644 index 0000000..ccc2fb5 --- /dev/null +++ b/libc-top-half/musl/src/complex/catan.c @@ -0,0 +1,107 @@ +/* origin: OpenBSD /usr/src/lib/libm/src/s_catan.c */ +/* + * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net> + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ +/* + * Complex circular arc tangent + * + * + * SYNOPSIS: + * + * double complex catan(); + * double complex z, w; + * + * w = catan (z); + * + * + * DESCRIPTION: + * + * If + * z = x + iy, + * + * then + * 1 ( 2x ) + * Re w = - arctan(-----------) + k PI + * 2 ( 2 2) + * (1 - x - y ) + * + * ( 2 2) + * 1 (x + (y+1) ) + * Im w = - log(------------) + * 4 ( 2 2) + * (x + (y-1) ) + * + * Where k is an arbitrary integer. + * + * catan(z) = -i catanh(iz). + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * DEC -10,+10 5900 1.3e-16 7.8e-18 + * IEEE -10,+10 30000 2.3e-15 8.5e-17 + * The check catan( ctan(z) ) = z, with |x| and |y| < PI/2, + * had peak relative error 1.5e-16, rms relative error + * 2.9e-17. See also clog(). + */ + +#include "complex_impl.h" + +#define MAXNUM 1.0e308 + +static const double DP1 = 3.14159265160560607910E0; +static const double DP2 = 1.98418714791870343106E-9; +static const double DP3 = 1.14423774522196636802E-17; + +static double _redupi(double x) +{ + double t; + long i; + + t = x/M_PI; + if (t >= 0.0) + t += 0.5; + else + t -= 0.5; + + i = t; /* the multiple */ + t = i; + t = ((x - t * DP1) - t * DP2) - t * DP3; + return t; +} + +double complex catan(double complex z) +{ + double complex w; + double a, t, x, x2, y; + + x = creal(z); + y = cimag(z); + + x2 = x * x; + a = 1.0 - x2 - (y * y); + + t = 0.5 * atan2(2.0 * x, a); + w = _redupi(t); + + t = y - 1.0; + a = x2 + (t * t); + + t = y + 1.0; + a = (x2 + t * t)/a; + w = CMPLX(w, 0.25 * log(a)); + return w; +} |