| /* origin: OpenBSD /usr/src/lib/libm/src/s_catanl.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: |
| * |
| * long double complex catanl(); |
| * long double complex z, w; |
| * |
| * w = catanl( 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. |
| * |
| * |
| * 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.h> |
| #include <float.h> |
| #include "complex_impl.h" |
| |
| #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 |
| long double complex catanl(long double complex z) |
| { |
| return catan(z); |
| } |
| #else |
| static const long double PIL = 3.141592653589793238462643383279502884197169L; |
| static const long double DP1 = 3.14159265358979323829596852490908531763125L; |
| static const long double DP2 = 1.6667485837041756656403424829301998703007e-19L; |
| static const long double DP3 = 1.8830410776607851167459095484560349402753e-39L; |
| |
| static long double redupil(long double x) |
| { |
| long double t; |
| long i; |
| |
| t = x / PIL; |
| if (t >= 0.0L) |
| t += 0.5L; |
| else |
| t -= 0.5L; |
| |
| i = t; /* the multiple */ |
| t = i; |
| t = ((x - t * DP1) - t * DP2) - t * DP3; |
| return t; |
| } |
| |
| long double complex catanl(long double complex z) |
| { |
| long double complex w; |
| long double a, t, x, x2, y; |
| |
| x = creall(z); |
| y = cimagl(z); |
| |
| x2 = x * x; |
| a = 1.0L - x2 - (y * y); |
| |
| t = atan2l(2.0L * x, a) * 0.5L; |
| w = redupil(t); |
| |
| t = y - 1.0L; |
| a = x2 + (t * t); |
| |
| t = y + 1.0L; |
| a = (x2 + (t * t)) / a; |
| w = CMPLXF(w, 0.25L * logl(a)); |
| return w; |
| } |
| #endif |