Implement and document csqrt(3) and csqrtf(3).

This commit is contained in:
David Schultz 2007-12-15 08:38:44 +00:00
parent 3eb5f519a5
commit aaf70b2314
Notes: svn2git 2020-12-20 02:59:44 +00:00
svn path=/head/; revision=174617
5 changed files with 293 additions and 3 deletions

View File

@ -1,5 +1,5 @@
/*-
* Copyright (c) 2001 The FreeBSD Project.
* Copyright (c) 2001-2007 The FreeBSD Project.
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
@ -57,6 +57,8 @@ long double complex
double creal(double complex);
float crealf(float complex);
long double creall(long double complex);
double complex csqrt(double complex);
float complex csqrtf(float complex);
__END_DECLS

View File

@ -40,7 +40,8 @@ COMMON_SRCS= b_exp.c b_log.c b_tgamma.c \
k_tan.c k_tanf.c \
s_asinh.c s_asinhf.c s_atan.c s_atanf.c s_carg.c s_cargf.c \
s_cbrt.c s_cbrtf.c s_ceil.c s_ceilf.c s_ceill.c \
s_copysign.c s_copysignf.c s_cos.c s_cosf.c s_erf.c s_erff.c \
s_copysign.c s_copysignf.c s_cos.c s_cosf.c \
s_csqrt.c s_csqrtf.c s_erf.c s_erff.c \
s_exp2.c s_exp2f.c s_expm1.c s_expm1f.c s_fabsf.c s_fdim.c \
s_finite.c s_finitef.c \
s_floor.c s_floorf.c s_floorl.c s_fma.c s_fmaf.c \
@ -93,7 +94,7 @@ SRCS= ${COMMON_SRCS} ${ARCH_SRCS}
INCS= fenv.h math.h
MAN= acos.3 acosh.3 asin.3 asinh.3 atan.3 atan2.3 atanh.3 ceil.3 \
cimag.3 copysign.3 cos.3 cosh.3 erf.3 exp.3 fabs.3 fdim.3 \
cimag.3 copysign.3 cos.3 cosh.3 csqrt.3 erf.3 exp.3 fabs.3 fdim.3 \
feclearexcept.3 feenableexcept.3 fegetenv.3 \
fegetround.3 fenv.3 floor.3 \
fma.3 fmax.3 fmod.3 hypot.3 ieee.3 ieee_test.3 ilogb.3 j0.3 \
@ -114,6 +115,7 @@ MLINKS+=cimag.3 cimagf.3 cimag.3 cimagl.3 \
MLINKS+=copysign.3 copysignf.3 copysign.3 copysignl.3
MLINKS+=cos.3 cosf.3
MLINKS+=cosh.3 coshf.3
MLINKS+=csqrt.3 csqrtf.3
MLINKS+=erf.3 erfc.3 erf.3 erff.3 erf.3 erfcf.3
MLINKS+=exp.3 expm1.3 exp.3 log.3 exp.3 log10.3 exp.3 log1p.3 exp.3 pow.3 \
exp.3 exp2.3 exp.3 exp2f.3 exp.3 expf.3 \

94
lib/msun/man/csqrt.3 Normal file
View File

@ -0,0 +1,94 @@
.\" Copyright (c) 2007 David Schultz <das@FreeBSD.org>
.\" All rights reserved.
.\"
.\" Redistribution and use in source and binary forms, with or without
.\" modification, are permitted provided that the following conditions
.\" are met:
.\" 1. Redistributions of source code must retain the above copyright
.\" notice, this list of conditions and the following disclaimer.
.\" 2. Redistributions in binary form must reproduce the above copyright
.\" notice, this list of conditions and the following disclaimer in the
.\" documentation and/or other materials provided with the distribution.
.\"
.\" THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
.\" ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
.\" SUCH DAMAGE.
.\"
.\" $FreeBSD$
.\"
.Dd December 14, 2007
.Dt CSQRT 3
.Os
.Sh NAME
.Nm csqrt ,
.Nm csqrtf
.Nd complex square root functions
.Sh LIBRARY
.Lb libm
.Sh SYNOPSIS
.In complex.h
.Ft double complex
.Fn csqrt "double complex z"
.Ft float complex
.Fn csqrtf "float complex z"
.Sh DESCRIPTION
The
.Fn csqrt
and
.Fn csqrtf
functions compute the square root of
.Fa z
in the complex plane, with a branch cut along the negative real axis.
In other words,
.Fn csqrt
and
.Fn csqrtf
always return the square root whose real part is non-negative.
.Sh RETURN VALUES
These functions return the requested square root.
The square root of 0 is
.Li +0 \*(Pm 0 ,
where the imaginary parts of the input and respective result have
the same sign.
For infinities and \*(Nas, the following rules apply, with the
earlier rules having precedence:
.Bl -column -offset indent "-\*(If + \*(Na*I" "\*(If \*(Pm \*(If*I " "(for all k)"
.Em Input Result
k + \*(If*I \*(If + \*(If*I (for all k)
-\*(If + \*(Na*I \*(Na \*(Pm \*(If*I
\*(If + \*(Na*I \*(If + \*(Na*I
k + \*(Na*I \*(Na + \*(Na*I
\*(Na + k*I \*(Na + \*(Na*I
-\*(If + k*I +0 + \*(If*I
\*(If + k*I \*(If + 0*I
.El
.Pp
For numbers with negative imaginary parts, the above special cases
apply given the identity:
.Dl csqrt(conj(z) = conj(sqrt(z))
Note that the sign of \*(Na is indeterminate.
Also, if the real or imaginary part of the input is finite and
an \*(Na is generated, an invalid exception will be thrown.
.Sh SEE ALSO
.Xr cabs 3 ,
.Xr fenv 3 ,
.Xr math 3 ,
.Sh STANDARDS
The
.Fn csqrt
and
.Fn csqrtf
functions conform to
.St -isoC-99 .
.Sh BUGS
For
.Fn csqrt ,
inexact results are not correctly rounded in general.

104
lib/msun/src/s_csqrt.c Normal file
View File

@ -0,0 +1,104 @@
/*-
* Copyright (c) 2007 David Schultz <das@FreeBSD.ORG>
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*/
#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");
#include <complex.h>
#include <math.h>
#include "math_private.h"
/*
* gcc doesn't implement complex multiplication or division correctly,
* so we need to handle infinities specially. We turn on this pragma to
* notify conforming c99 compilers that the fast-but-incorrect code that
* gcc generates is acceptable, since the special cases have already been
* handled.
*/
#pragma STDC CX_LIMITED_RANGE on
/* We risk spurious overflow for components >= DBL_MAX/(1+sqrt(2)) */
#define THRESH 0x1.a827999fcef32p+1022
double complex
csqrt(double complex z)
{
double a = creal(z), b = cimag(z);
double t;
double complex result;
int scale;
/* Handle special cases. */
if (z == 0)
return (cpack(0, b));
if (isinf(b))
return (cpack(INFINITY, b));
if (isnan(a)) {
t = (b - b) / (b - b); /* raise invalid if b is not a NaN */
return (cpack(t, t)); /* return NaN + NaN i */
}
if (isinf(a)) {
/*
* csqrt(inf + nan i) = inf + nan i
* csqrt(inf + y i) = inf + 0 i
* csqrt(-inf + nan i) = nan +- inf i
* csqrt(-inf + y i) = 0 + inf i
*/
if (signbit(a))
return (cpack(fabs(b - b), copysign(a, b)));
else
return (cpack(a, copysign(b - b, b)));
}
/*
* The remaining special case (b is NaN) is handled just fine by
* the normal code path below.
*/
/* Scale to avoid overflow. */
if (a >= THRESH || b >= THRESH) {
a *= 0.25;
b *= 0.25;
scale = 1;
} else {
scale = 0;
}
/* Algorithm 312, CACM vol 10, Oct 1967 */
if (a >= 0) {
t = sqrt((a + hypot(a, b)) * 0.5);
result = cpack(t, b / (2 * t));
} else {
t = sqrt((-a + hypot(a, b)) * 0.5);
result = cpack(fabs(b) / (2 * t), copysign(t, b));
}
/* Rescale */
if (scale)
return (result * 2);
else
return (result);
}

88
lib/msun/src/s_csqrtf.c Normal file
View File

@ -0,0 +1,88 @@
/*-
* Copyright (c) 2007 David Schultz <das@FreeBSD.ORG>
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*/
#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");
#include <complex.h>
#include <math.h>
#include "math_private.h"
/*
* gcc doesn't implement complex multiplication or division correctly,
* so we need to handle infinities specially. We turn on this pragma to
* notify conforming c99 compilers that the fast-but-incorrect code that
* gcc generates is acceptable, since the special cases have already been
* handled.
*/
#pragma STDC CX_LIMITED_RANGE on
float complex
csqrtf(float complex z)
{
float a = crealf(z), b = cimagf(z);
double t;
/* Handle special cases. */
if (z == 0)
return (cpackf(0, b));
if (isinf(b))
return (cpackf(INFINITY, b));
if (isnan(a)) {
t = (b - b) / (b - b); /* raise invalid if b is not a NaN */
return (cpackf(t, t)); /* return NaN + NaN i */
}
if (isinf(a)) {
/*
* csqrtf(inf + nan i) = inf + nan i
* csqrtf(inf + y i) = inf + 0 i
* csqrtf(-inf + nan i) = nan +- inf i
* csqrtf(-inf + y i) = 0 + inf i
*/
if (signbit(a))
return (cpackf(fabsf(b - b), copysignf(a, b)));
else
return (cpackf(a, copysignf(b - b, b)));
}
/*
* The remaining special case (b is NaN) is handled just fine by
* the normal code path below.
*/
/*
* We compute t in double precision to avoid overflow and to
* provide correct rounding in nearly all cases.
* This is Algorithm 312, CACM vol 10, Oct 1967.
*/
if (a >= 0) {
t = sqrt((a + hypot(a, b)) * 0.5);
return (cpackf(t, b / (2.0 * t)));
} else {
t = sqrt((-a + hypot(a, b)) * 0.5);
return (cpackf(fabsf(b) / (2.0 * t), copysignf(t, b)));
}
}