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Implement and document csqrt(3) and csqrtf(3).
This commit is contained in:
David Schultz
parent
3eb5f519a5
commit
aaf70b2314
Notes:
svn2git
2020-12-20 02:59:44 +00:00
svn path=/head/; revision=174617
@ -1,5 +1,5 @@
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/*-
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* Copyright (c) 2001 The FreeBSD Project.
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* Copyright (c) 2001-2007 The FreeBSD Project.
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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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@ -57,6 +57,8 @@ 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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double complex csqrt(double complex);
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float complex csqrtf(float complex);
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__END_DECLS
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@ -40,7 +40,8 @@ COMMON_SRCS= b_exp.c b_log.c b_tgamma.c \
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k_tan.c k_tanf.c \
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s_asinh.c s_asinhf.c s_atan.c s_atanf.c s_carg.c s_cargf.c \
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s_cbrt.c s_cbrtf.c s_ceil.c s_ceilf.c s_ceill.c \
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s_copysign.c s_copysignf.c s_cos.c s_cosf.c s_erf.c s_erff.c \
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s_copysign.c s_copysignf.c s_cos.c s_cosf.c \
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s_csqrt.c s_csqrtf.c s_erf.c s_erff.c \
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s_exp2.c s_exp2f.c s_expm1.c s_expm1f.c s_fabsf.c s_fdim.c \
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s_finite.c s_finitef.c \
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s_floor.c s_floorf.c s_floorl.c s_fma.c s_fmaf.c \
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@ -93,7 +94,7 @@ SRCS= ${COMMON_SRCS} ${ARCH_SRCS}
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INCS= fenv.h math.h
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MAN= acos.3 acosh.3 asin.3 asinh.3 atan.3 atan2.3 atanh.3 ceil.3 \
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cimag.3 copysign.3 cos.3 cosh.3 erf.3 exp.3 fabs.3 fdim.3 \
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cimag.3 copysign.3 cos.3 cosh.3 csqrt.3 erf.3 exp.3 fabs.3 fdim.3 \
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feclearexcept.3 feenableexcept.3 fegetenv.3 \
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fegetround.3 fenv.3 floor.3 \
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fma.3 fmax.3 fmod.3 hypot.3 ieee.3 ieee_test.3 ilogb.3 j0.3 \
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@ -114,6 +115,7 @@ MLINKS+=cimag.3 cimagf.3 cimag.3 cimagl.3 \
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MLINKS+=copysign.3 copysignf.3 copysign.3 copysignl.3
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MLINKS+=cos.3 cosf.3
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MLINKS+=cosh.3 coshf.3
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MLINKS+=csqrt.3 csqrtf.3
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MLINKS+=erf.3 erfc.3 erf.3 erff.3 erf.3 erfcf.3
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MLINKS+=exp.3 expm1.3 exp.3 log.3 exp.3 log10.3 exp.3 log1p.3 exp.3 pow.3 \
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exp.3 exp2.3 exp.3 exp2f.3 exp.3 expf.3 \
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94
lib/msun/man/csqrt.3
Normal file
94
lib/msun/man/csqrt.3
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@ -0,0 +1,94 @@
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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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.\" $FreeBSD$
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.\"
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.Dd December 14, 2007
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.Dt CSQRT 3
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.Os
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.Sh NAME
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.Nm csqrt ,
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.Nm csqrtf
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.Nd complex square root functions
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.Sh LIBRARY
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.Lb libm
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.Sh SYNOPSIS
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.In complex.h
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.Ft double complex
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.Fn csqrt "double complex z"
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.Ft float complex
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.Fn csqrtf "float complex z"
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.Sh DESCRIPTION
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The
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.Fn csqrt
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and
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.Fn csqrtf
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functions compute the square root of
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.Fa z
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in the complex plane, with a branch cut along the negative real axis.
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In other words,
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.Fn csqrt
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and
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.Fn csqrtf
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always return the square root whose real part is non-negative.
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.Sh RETURN VALUES
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These functions return the requested square root.
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The square root of 0 is
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.Li +0 \*(Pm 0 ,
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where the imaginary parts of the input and respective result have
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the same sign.
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For infinities and \*(Nas, the following rules apply, with the
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earlier rules having precedence:
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.Bl -column -offset indent "-\*(If + \*(Na*I" "\*(If \*(Pm \*(If*I " "(for all k)"
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.Em Input Result
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k + \*(If*I \*(If + \*(If*I (for all k)
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-\*(If + \*(Na*I \*(Na \*(Pm \*(If*I
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\*(If + \*(Na*I \*(If + \*(Na*I
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k + \*(Na*I \*(Na + \*(Na*I
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\*(Na + k*I \*(Na + \*(Na*I
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-\*(If + k*I +0 + \*(If*I
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\*(If + k*I \*(If + 0*I
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.El
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.Pp
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For numbers with negative imaginary parts, the above special cases
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apply given the identity:
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.Dl csqrt(conj(z) = conj(sqrt(z))
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Note that the sign of \*(Na is indeterminate.
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Also, if the real or imaginary part of the input is finite and
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an \*(Na is generated, an invalid exception will be thrown.
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.Sh SEE ALSO
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.Xr cabs 3 ,
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.Xr fenv 3 ,
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.Xr math 3 ,
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.Sh STANDARDS
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The
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.Fn csqrt
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and
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.Fn csqrtf
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functions conform to
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.St -isoC-99 .
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.Sh BUGS
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For
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.Fn csqrt ,
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inexact results are not correctly rounded in general.
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104
lib/msun/src/s_csqrt.c
Normal file
104
lib/msun/src/s_csqrt.c
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@ -0,0 +1,104 @@
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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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#include <sys/cdefs.h>
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__FBSDID("$FreeBSD$");
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#include <complex.h>
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#include <math.h>
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#include "math_private.h"
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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
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csqrt(double complex z)
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{
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double a = creal(z), b = cimag(z);
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double t;
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double complex result;
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int scale;
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/* Handle special cases. */
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if (z == 0)
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return (cpack(0, b));
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if (isinf(b))
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return (cpack(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 (cpack(t, 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 (cpack(fabs(b - b), copysign(a, b)));
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else
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return (cpack(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 (a >= THRESH || 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 = cpack(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 = cpack(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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return (result * 2);
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else
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return (result);
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}
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88
lib/msun/src/s_csqrtf.c
Normal file
88
lib/msun/src/s_csqrtf.c
Normal file
@ -0,0 +1,88 @@
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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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#include <sys/cdefs.h>
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__FBSDID("$FreeBSD$");
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#include <complex.h>
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#include <math.h>
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#include "math_private.h"
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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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float complex
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csqrtf(float complex z)
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{
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float a = crealf(z), b = cimagf(z);
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double t;
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/* Handle special cases. */
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if (z == 0)
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return (cpackf(0, b));
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if (isinf(b))
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return (cpackf(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 (cpackf(t, t)); /* return NaN + NaN i */
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}
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if (isinf(a)) {
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/*
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* csqrtf(inf + nan i) = inf + nan i
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* csqrtf(inf + y i) = inf + 0 i
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* csqrtf(-inf + nan i) = nan +- inf i
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* csqrtf(-inf + y i) = 0 + inf i
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*/
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if (signbit(a))
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return (cpackf(fabsf(b - b), copysignf(a, b)));
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else
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return (cpackf(a, copysignf(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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/*
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* We compute t in double precision to avoid overflow and to
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* provide correct rounding in nearly all cases.
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* This is Algorithm 312, CACM vol 10, Oct 1967.
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*/
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if (a >= 0) {
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t = sqrt((a + hypot(a, b)) * 0.5);
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return (cpackf(t, b / (2.0 * t)));
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} else {
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t = sqrt((-a + hypot(a, b)) * 0.5);
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return (cpackf(fabsf(b) / (2.0 * t), copysignf(t, b)));
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}
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}
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