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Add complex square root (#394)
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Steve Phillips
GitHub
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commit
92ebef16ee
3 changed files with 288 additions and 0 deletions
133
libc/tinymath/complex.h
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133
libc/tinymath/complex.h
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#ifndef _COMPLEX_H
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#define _COMPLEX_H
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#ifdef __cplusplus
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extern "C" {
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#endif
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#define complex _Complex
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#ifdef __GNUC__
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#define _Complex_I (__extension__ (0.0f+1.0fi))
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#else
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#define _Complex_I (0.0f+1.0fi)
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#endif
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#define I _Complex_I
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double complex cacos(double complex);
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float complex cacosf(float complex);
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long double complex cacosl(long double complex);
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double complex casin(double complex);
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float complex casinf(float complex);
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long double complex casinl(long double complex);
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double complex catan(double complex);
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float complex catanf(float complex);
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long double complex catanl(long double complex);
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double complex ccos(double complex);
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float complex ccosf(float complex);
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long double complex ccosl(long double complex);
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double complex csin(double complex);
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float complex csinf(float complex);
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long double complex csinl(long double complex);
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double complex ctan(double complex);
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float complex ctanf(float complex);
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long double complex ctanl(long double complex);
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double complex cacosh(double complex);
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float complex cacoshf(float complex);
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long double complex cacoshl(long double complex);
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double complex casinh(double complex);
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float complex casinhf(float complex);
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long double complex casinhl(long double complex);
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double complex catanh(double complex);
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float complex catanhf(float complex);
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long double complex catanhl(long double complex);
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double complex ccosh(double complex);
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float complex ccoshf(float complex);
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long double complex ccoshl(long double complex);
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double complex csinh(double complex);
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float complex csinhf(float complex);
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long double complex csinhl(long double complex);
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double complex ctanh(double complex);
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float complex ctanhf(float complex);
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long double complex ctanhl(long double complex);
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double complex cexp(double complex);
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float complex cexpf(float complex);
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long double complex cexpl(long double complex);
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double complex clog(double complex);
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float complex clogf(float complex);
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long double complex clogl(long double complex);
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double cabs(double complex);
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float cabsf(float complex);
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long double cabsl(long double complex);
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double complex cpow(double complex, double complex);
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float complex cpowf(float complex, float complex);
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long double complex cpowl(long double complex, long double complex);
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double complex csqrt(double complex);
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float complex csqrtf(float complex);
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long double complex csqrtl(long double complex);
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double carg(double complex);
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float cargf(float complex);
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long double cargl(long double complex);
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double cimag(double complex);
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float cimagf(float complex);
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long double cimagl(long double complex);
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double complex conj(double complex);
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float complex conjf(float complex);
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long double complex conjl(long double complex);
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double complex cproj(double complex);
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float complex cprojf(float complex);
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long double complex cprojl(long double complex);
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double creal(double complex);
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float crealf(float complex);
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long double creall(long double complex);
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#ifndef __cplusplus
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#define __CIMAG(x, t) \
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(+(union { _Complex t __z; t __xy[2]; }){(_Complex t)(x)}.__xy[1])
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#define creal(x) ((double)(x))
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#define crealf(x) ((float)(x))
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#define creall(x) ((long double)(x))
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#define cimag(x) __CIMAG(x, double)
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#define cimagf(x) __CIMAG(x, float)
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#define cimagl(x) __CIMAG(x, long double)
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#endif
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#if __STDC_VERSION__ >= 201112L
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#if defined(_Imaginary_I)
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#define __CMPLX(x, y, t) ((t)(x) + _Imaginary_I*(t)(y))
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#elif defined(__clang__)
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#define __CMPLX(x, y, t) (+(_Complex t){ (t)(x), (t)(y) })
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#else
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#define __CMPLX(x, y, t) (__builtin_complex((t)(x), (t)(y)))
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#endif
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#define CMPLX(x, y) __CMPLX(x, y, double)
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#define CMPLXF(x, y) __CMPLX(x, y, float)
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#define CMPLXL(x, y) __CMPLX(x, y, long double)
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#endif
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#ifdef __cplusplus
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}
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#endif
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#endif
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22
libc/tinymath/complex_impl.internal.h
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22
libc/tinymath/complex_impl.internal.h
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#ifndef _COMPLEX_IMPL_H
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#define _COMPLEX_IMPL_H
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#include <libc/tinymath/complex.h>
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#include "libc/math.h"
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#undef __CMPLX
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#undef CMPLX
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#undef CMPLXF
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#undef CMPLXL
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#define __CMPLX(x, y, t) \
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((union { _Complex t __z; t __xy[2]; }){.__xy = {(x),(y)}}.__z)
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#define CMPLX(x, y) __CMPLX(x, y, double)
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#define CMPLXF(x, y) __CMPLX(x, y, float)
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#define CMPLXL(x, y) __CMPLX(x, y, long double)
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hidden double complex __ldexp_cexp(double complex,int);
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hidden float complex __ldexp_cexpf(float complex,int);
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#endif
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133
libc/tinymath/csqrt.c
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133
libc/tinymath/csqrt.c
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/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-│
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│vi: set et ft=c ts=8 tw=8 fenc=utf-8 :vi│
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╚──────────────────────────────────────────────────────────────────────────────╝
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│ │
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│ Musl Libc │
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│ Copyright © 2005-2014 Rich Felker, et al. │
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│ │
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│ Permission is hereby granted, free of charge, to any person obtaining │
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│ a copy of this software and associated documentation files (the │
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│ "Software"), to deal in the Software without restriction, including │
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│ without limitation the rights to use, copy, modify, merge, publish, │
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│ distribute, sublicense, and/or sell copies of the Software, and to │
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│ permit persons to whom the Software is furnished to do so, subject to │
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│ the following conditions: │
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│ │
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│ The above copyright notice and this permission notice shall be │
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│ included in all copies or substantial portions of the Software. │
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│ │
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│ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, │
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│ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF │
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│ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. │
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│ IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY │
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│ CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, │
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│ TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE │
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│ SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. │
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│ │
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╚─────────────────────────────────────────────────────────────────────────────*/
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#include "libc/tinymath/complex_impl.internal.h"
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asm(".ident\t\"\\n\\n\
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Musl libc (MIT License)\\n\
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Copyright 2005-2014 Rich Felker, et. al.\"");
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asm(".include \"libc/disclaimer.inc\"");
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/* clang-format off */
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/* origin: FreeBSD /usr/src/lib/msun/src/s_csqrt.c */
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/*-
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* Copyright (c) 2007 David Schultz <das@FreeBSD.ORG>
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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*
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* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*/
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/*
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* gcc doesn't implement complex multiplication or division correctly,
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* so we need to handle infinities specially. We turn on this pragma to
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* notify conforming c99 compilers that the fast-but-incorrect code that
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* gcc generates is acceptable, since the special cases have already been
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* handled.
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*/
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#pragma STDC CX_LIMITED_RANGE ON
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/* We risk spurious overflow for components >= DBL_MAX / (1 + sqrt(2)). */
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#define THRESH 0x1.a827999fcef32p+1022
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double complex csqrt(double complex z)
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{
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double complex result;
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double a, b;
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double t;
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int scale;
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a = creal(z);
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b = cimag(z);
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/* Handle special cases. */
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if (z == 0)
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return CMPLX(0, b);
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if (isinf(b))
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return CMPLX(INFINITY, b);
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if (isnan(a)) {
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t = (b - b) / (b - b); /* raise invalid if b is not a NaN */
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return CMPLX(a, t); /* return NaN + NaN i */
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}
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if (isinf(a)) {
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/*
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* csqrt(inf + NaN i) = inf + NaN i
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* csqrt(inf + y i) = inf + 0 i
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* csqrt(-inf + NaN i) = NaN +- inf i
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* csqrt(-inf + y i) = 0 + inf i
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*/
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if (signbit(a))
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return CMPLX(fabs(b - b), copysign(a, b));
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else
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return CMPLX(a, copysign(b - b, b));
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}
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/*
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* The remaining special case (b is NaN) is handled just fine by
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* the normal code path below.
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*/
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/* Scale to avoid overflow. */
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if (fabs(a) >= THRESH || fabs(b) >= THRESH) {
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a *= 0.25;
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b *= 0.25;
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scale = 1;
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} else {
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scale = 0;
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}
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/* Algorithm 312, CACM vol 10, Oct 1967. */
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if (a >= 0) {
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t = sqrt((a + hypot(a, b)) * 0.5);
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result = CMPLX(t, b / (2 * t));
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} else {
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t = sqrt((-a + hypot(a, b)) * 0.5);
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result = CMPLX(fabs(b) / (2 * t), copysign(t, b));
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}
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/* Rescale. */
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if (scale)
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result *= 2;
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return result;
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}
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