mirror of
https://github.com/freebsd/freebsd-src
synced 2024-07-22 02:37:15 +00:00
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 @@
|
|||
/*-
|
||||
* 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
|
||||
|
||||
|
|
|
|||
|
|
@ -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
94
lib/msun/man/csqrt.3
Normal 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
104
lib/msun/src/s_csqrt.c
Normal 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
88
lib/msun/src/s_csqrtf.c
Normal 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)));
|
||||
}
|
||||
}
|
||||
Loading…
Reference in a new issue