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Add implementations of acosl(), asinl(), atanl(), atan2l(),

Browse Source 
and cargl().

Reviewed by:			bde
sparc64 testing resources from:	remko
This commit is contained in:
David Schultz 2008-07-31 22:41:26 +00:00
parent 4746c560a4
commit 17303c626f
Notes: svn2git 2020-12-20 02:59:44 +00:00 
svn path=/head/; revision=181074
20 changed files with 900 additions and 69 deletions
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20
lib/msun/Makefile
View File

@ -25,8 +25,10 @@ ARCH_SUBDIR= ${MACHINE_ARCH}
# long double format
.if ${LDBL_PREC} == 64
.PATH: ${.CURDIR}/ld80
CFLAGS+= -I${.CURDIR}/ld80
.elif ${LDBL_PREC} == 113
.PATH: ${.CURDIR}/ld128
CFLAGS+= -I${.CURDIR}/ld128
.endif
.PATH: ${.CURDIR}/bsdsrc
@ -48,7 +50,7 @@ COMMON_SRCS= b_exp.c b_log.c b_tgamma.c \
e_sinh.c e_sinhf.c e_sqrt.c e_sqrtf.c fenv.c \
k_cos.c k_cosf.c k_rem_pio2.c k_sin.c k_sinf.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_asinh.c s_asinhf.c s_atan.c s_atanf.c s_carg.c s_cargf.c s_cargl.c \
s_cbrt.c s_cbrtf.c s_ceil.c s_ceilf.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 \
@ -82,9 +84,10 @@ SYMBOL_MAPS= ${SYM_MAPS}
COMMON_SRCS+= s_copysignl.c s_fabsl.c s_llrintl.c s_lrintl.c s_modfl.c
.if ${LDBL_PREC} != 53
# If long double != double use these; otherwise, we alias the double versions.
COMMON_SRCS+= e_fmodl.c e_hypotl.c e_remainderl.c e_sqrtl.c \
k_cosl.c k_sinl.c k_tanl.c \
s_ceill.c s_cosl.c s_csqrtl.c s_exp2l.c s_floorl.c s_fmal.c \
COMMON_SRCS+= e_acosl.c e_asinl.c e_atan2l.c e_fmodl.c \
e_hypotl.c e_remainderl.c e_sqrtl.c \
invtrig.c k_cosl.c k_sinl.c k_tanl.c \
s_atanl.c s_ceill.c s_cosl.c s_csqrtl.c s_exp2l.c s_floorl.c s_fmal.c \
s_frexpl.c s_logbl.c s_nanl.c s_nextafterl.c s_nexttoward.c \
s_remquol.c s_rintl.c s_scalbnl.c \
s_sinl.c s_tanl.c s_truncl.c w_cabsl.c
@ -117,13 +120,14 @@ MAN= acos.3 acosh.3 asin.3 asinh.3 atan.3 atan2.3 atanh.3 ceil.3 \
nextafter.3 remainder.3 rint.3 \
round.3 scalbn.3 signbit.3 sin.3 sinh.3 sqrt.3 tan.3 tanh.3 trunc.3
MLINKS+=acos.3 acosf.3
MLINKS+=acos.3 acosf.3 acos.3 acosl.3
MLINKS+=acosh.3 acoshf.3
MLINKS+=asin.3 asinf.3
MLINKS+=asin.3 asinf.3 asin.3 asinl.3
MLINKS+=asinh.3 asinhf.3
MLINKS+=atan.3 atanf.3
MLINKS+=atan.3 atanf.3 atan.3 atanl.3
MLINKS+=atanh.3 atanhf.3
MLINKS+=atan2.3 atan2f.3 atan2.3 carg.3 atan2.3 cargf.3
MLINKS+=atan2.3 atan2f.3 atan2.3 atan2l.3 \
atan2.3 carg.3 atan2.3 cargf.3 atan2.3 cargl.3
MLINKS+=ceil.3 ceilf.3 ceil.3 ceill.3
MLINKS+=cimag.3 cimagf.3 cimag.3 cimagl.3 \
cimag.3 conj.3 cimag.3 conjf.3 cimag.3 conjl.3 \

5
lib/msun/Symbol.map
View File

@ -209,4 +209,9 @@ FBSD_1.1 {
remquol;
remainderl;
fmodl;
acosl;
asinl;
atan2l;
atanl;
cargl;
};

100
lib/msun/ld128/invtrig.c Normal file
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@ -0,0 +1,100 @@
/*-
* Copyright (c) 2008 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 "invtrig.h"
/*
* asinl() and acosl()
*/
const long double
pS0 = 1.66666666666666666666666666666700314e-01L,
pS1 = -7.32816946414566252574527475428622708e-01L,
pS2 = 1.34215708714992334609030036562143589e+00L,
pS3 = -1.32483151677116409805070261790752040e+00L,
pS4 = 7.61206183613632558824485341162121989e-01L,
pS5 = -2.56165783329023486777386833928147375e-01L,
pS6 = 4.80718586374448793411019434585413855e-02L,
pS7 = -4.42523267167024279410230886239774718e-03L,
pS8 = 1.44551535183911458253205638280410064e-04L,
pS9 = -2.10558957916600254061591040482706179e-07L,
qS1 = -4.84690167848739751544716485245697428e+00L,
qS2 = 9.96619113536172610135016921140206980e+00L,
qS3 = -1.13177895428973036660836798461641458e+01L,
qS4 = 7.74004374389488266169304117714658761e+00L,
qS5 = -3.25871986053534084709023539900339905e+00L,
qS6 = 8.27830318881232209752469022352928864e-01L,
qS7 = -1.18768052702942805423330715206348004e-01L,
qS8 = 8.32600764660522313269101537926539470e-03L,
qS9 = -1.99407384882605586705979504567947007e-04L;
/*
* atanl()
*/
const long double atanhi[] = {
4.63647609000806116214256231461214397e-01L,
7.85398163397448309615660845819875699e-01L,
9.82793723247329067985710611014666038e-01L,
1.57079632679489661923132169163975140e+00L,
};
const long double atanlo[] = {
4.89509642257333492668618435220297706e-36L,
2.16795253253094525619926100651083806e-35L,
-2.31288434538183565909319952098066272e-35L,
4.33590506506189051239852201302167613e-35L,
};
const long double aT[] = {
3.33333333333333333333333333333333125e-01L,
-1.99999999999999999999999999999180430e-01L,
1.42857142857142857142857142125269827e-01L,
-1.11111111111111111111110834490810169e-01L,
9.09090909090909090908522355708623681e-02L,
-7.69230769230769230696553844935357021e-02L,
6.66666666666666660390096773046256096e-02L,
-5.88235294117646671706582985209643694e-02L,
5.26315789473666478515847092020327506e-02L,
-4.76190476189855517021024424991436144e-02L,
4.34782608678695085948531993458097026e-02L,
-3.99999999632663469330634215991142368e-02L,
3.70370363987423702891250829918659723e-02L,
-3.44827496515048090726669907612335954e-02L,
3.22579620681420149871973710852268528e-02L,
-3.03020767654269261041647570626778067e-02L,
2.85641979882534783223403715930946138e-02L,
-2.69824879726738568189929461383741323e-02L,
2.54194698498808542954187110873675769e-02L,
-2.35083879708189059926183138130183215e-02L,
2.04832358998165364349957325067131428e-02L,
-1.54489555488544397858507248612362957e-02L,
8.64492360989278761493037861575248038e-03L,
-2.58521121597609872727919154569765469e-03L,
};
const long double pi_lo = 8.67181013012378102479704402604335225e-35L;

113
lib/msun/ld128/invtrig.h Normal file
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@ -0,0 +1,113 @@
/*-
* Copyright (c) 2008 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.
*
* $FreeBSD$
*/
#include <float.h>
#include "fpmath.h"
#define BIAS (LDBL_MAX_EXP - 1)
#define MANH_SIZE (LDBL_MANH_SIZE + 1)
/* Approximation thresholds. */
#define ASIN_LINEAR (BIAS - 56) /* 2**-56 */
#define ACOS_CONST (BIAS - 113) /* 2**-113 */
#define ATAN_CONST (BIAS + 113) /* 2**113 */
#define ATAN_LINEAR (BIAS - 56) /* 2**-56 */
/* 0.95 */
#define THRESH ((0xe666666666666666ULL>>(64-(MANH_SIZE-1)))|LDBL_NBIT)
/* Constants shared by the long double inverse trig functions. */
#define pS0 _ItL_pS0
#define pS1 _ItL_pS1
#define pS2 _ItL_pS2
#define pS3 _ItL_pS3
#define pS4 _ItL_pS4
#define pS5 _ItL_pS5
#define pS6 _ItL_pS6
#define pS7 _ItL_pS7
#define pS8 _ItL_pS8
#define pS9 _ItL_pS9
#define qS1 _ItL_qS1
#define qS2 _ItL_qS2
#define qS3 _ItL_qS3
#define qS4 _ItL_qS4
#define qS5 _ItL_qS5
#define qS6 _ItL_qS6
#define qS7 _ItL_qS7
#define qS8 _ItL_qS8
#define qS9 _ItL_qS9
#define atanhi _ItL_atanhi
#define atanlo _ItL_atanlo
#define aT _ItL_aT
#define pi_lo _ItL_pi_lo
#define pio2_hi atanhi[3]
#define pio2_lo atanlo[3]
#define pio4_hi atanhi[1]
/* Constants shared by the long double inverse trig functions. */
extern const long double pS0, pS1, pS2, pS3, pS4, pS5, pS6, pS7, pS8, pS9;
extern const long double qS1, qS2, qS3, qS4, qS5, qS6, qS7, qS8, qS9;
extern const long double atanhi[], atanlo[], aT[];
extern const long double pi_lo;
static inline long double
P(long double x)
{
return (x * (pS0 + x * (pS1 + x * (pS2 + x * (pS3 + x * \
(pS4 + x * (pS5 + x * (pS6 + x * (pS7 + x * (pS8 + x * \
pS9))))))))));
}
static inline long double
Q(long double x)
{
return (1.0 + x * (qS1 + x * (qS2 + x * (qS3 + x * (qS4 + x * \
(qS5 + x * (qS6 + x * (qS7 + x * (qS8 + x * qS9)))))))));
}
static inline long double
T_even(long double x)
{
return (aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] + x * \
(aT[8] + x * (aT[10] + x * (aT[12] + x * (aT[14] + x * \
(aT[16] + x * (aT[18] + x * (aT[20] + x * aT[22])))))))))));
}
static inline long double
T_odd(long double x)
{
return (aT[1] + x * (aT[3] + x * (aT[5] + x * (aT[7] + x * \
(aT[9] + x * (aT[11] + x * (aT[13] + x * (aT[15] + x * \
(aT[17] + x * (aT[19] + x * (aT[21] + x * aT[23])))))))))));
}

82
lib/msun/ld80/invtrig.c Normal file
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@ -0,0 +1,82 @@
/*-
* Copyright (c) 2008 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 "invtrig.h"
/*
* asinl() and acosl()
*/
const long double
pS0 = 1.66666666666666666631e-01L,
pS1 = -4.16313987993683104320e-01L,
pS2 = 3.69068046323246813704e-01L,
pS3 = -1.36213932016738603108e-01L,
pS4 = 1.78324189708471965733e-02L,
pS5 = -2.19216428382605211588e-04L,
pS6 = -7.10526623669075243183e-06L,
qS1 = -2.94788392796209867269e+00L,
qS2 = 3.27309890266528636716e+00L,
qS3 = -1.68285799854822427013e+00L,
qS4 = 3.90699412641738801874e-01L,
qS5 = -3.14365703596053263322e-02L;
/*
* atanl()
*/
const long double atanhi[] = {
4.63647609000806116202e-01L,
7.85398163397448309628e-01L,
9.82793723247329067960e-01L,
1.57079632679489661926e+00L,
};
const long double atanlo[] = {
1.18469937025062860669e-20L,
-1.25413940316708300586e-20L,
2.55232234165405176172e-20L,
-2.50827880633416601173e-20L,
};
const long double aT[] = {
3.33333333333333333017e-01L,
-1.99999999999999632011e-01L,
1.42857142857046531280e-01L,
-1.11111111100562372733e-01L,
9.09090902935647302252e-02L,
-7.69230552476207730353e-02L,
6.66661718042406260546e-02L,
-5.88158892835030888692e-02L,
5.25499891539726639379e-02L,
-4.70119845393155721494e-02L,
4.03539201366454414072e-02L,
-2.91303858419364158725e-02L,
1.24822046299269234080e-02L,
};
const long double pi_lo = -5.01655761266833202345e-20L;

101
lib/msun/ld80/invtrig.h Normal file
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@ -0,0 +1,101 @@
/*-
* Copyright (c) 2008 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.
*
* $FreeBSD$
*/
#include <float.h>
#include "fpmath.h"
#define BIAS (LDBL_MAX_EXP - 1)
#define MANH_SIZE LDBL_MANH_SIZE
/* Approximation thresholds. */
#define ASIN_LINEAR (BIAS - 32) /* 2**-32 */
#define ACOS_CONST (BIAS - 65) /* 2**-65 */
#define ATAN_CONST (BIAS + 65) /* 2**65 */
#define ATAN_LINEAR (BIAS - 32) /* 2**-32 */
/* 0.95 */
#define THRESH ((0xe666666666666666ULL>>(64-(MANH_SIZE-1)))|LDBL_NBIT)
/* Constants shared by the long double inverse trig functions. */
#define pS0 _ItL_pS0
#define pS1 _ItL_pS1
#define pS2 _ItL_pS2
#define pS3 _ItL_pS3
#define pS4 _ItL_pS4
#define pS5 _ItL_pS5
#define pS6 _ItL_pS6
#define qS1 _ItL_qS1
#define qS2 _ItL_qS2
#define qS3 _ItL_qS3
#define qS4 _ItL_qS4
#define qS5 _ItL_qS5
#define atanhi _ItL_atanhi
#define atanlo _ItL_atanlo
#define aT _ItL_aT
#define pi_lo _ItL_pi_lo
#define pio2_hi atanhi[3]
#define pio2_lo atanlo[3]
#define pio4_hi atanhi[1]
extern const long double pS0, pS1, pS2, pS3, pS4, pS5, pS6;
extern const long double qS1, qS2, qS3, qS4, qS5;
extern const long double atanhi[], atanlo[], aT[];
extern const long double pi_lo;
static inline long double
P(long double x)
{
return (x * (pS0 + x * (pS1 + x * (pS2 + x * (pS3 + x * \
(pS4 + x * (pS5 + x * pS6)))))));
}
static inline long double
Q(long double x)
{
return (1.0 + x * (qS1 + x * (qS2 + x * (qS3 + x * (qS4 + x * qS5)))));
}
static inline long double
T_even(long double x)
{
return (aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] + x * \
(aT[8] + x * (aT[10] + x * aT[12]))))));
}
static inline long double
T_odd(long double x)
{
return (aT[1] + x * (aT[3] + x * (aT[5] + x * (aT[7] + x * \
(aT[9] + x * aT[11])))));
}

33
lib/msun/man/acos.3
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@ -28,12 +28,13 @@
.\" from: @(#)acos.3 5.1 (Berkeley) 5/2/91
.\" $FreeBSD$
.\"
.Dd January 14, 2005
.Dd July 31, 2008
.Dt ACOS 3
.Os
.Sh NAME
.Nm acos ,
.Nm acosf
.Nm acosf ,
.Nm acosl
.Nd arc cosine functions
.Sh LIBRARY
.Lb libm
@ -43,23 +44,18 @@
.Fn acos "double x"
.Ft float
.Fn acosf "float x"
.Ft long double
.Fn acosl "long double x"
.Sh DESCRIPTION
The
.Fn acos
and the
.Fn acosf
.Fn acos ,
.Fn acosf ,
and
.Fn acosl
functions compute the principal value of the arc cosine of
.Fa x .
A domain error occurs for arguments not in the range
.Bq -1 , +1 .
For a discussion of error due to roundoff, see
.Xr math 3 .
.Sh RETURN VALUES
The
.Fn acos
and the
.Fn acosf
functions return the arc cosine in the range
These functions return the arc cosine in the range
.Bq 0 , \*(Pi
radians.
If:
@ -83,6 +79,9 @@ raises an invalid exception and returns an \*(Na.
.Xr tanh 3
.Sh STANDARDS
The
.Fn acos
function conforms to
.St -isoC .
.Fn acos ,
.Fn acosf ,
and
.Fn acosl
functions conform to
.St -isoC-99 .

33
lib/msun/man/asin.3
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@ -28,12 +28,13 @@
.\" from: @(#)asin.3 5.1 (Berkeley) 5/2/91
.\" $FreeBSD$
.\"
.Dd January 14, 2005
.Dd July 31, 2008
.Dt ASIN 3
.Os
.Sh NAME
.Nm asin ,
.Nm asinf
.Nm asinf ,
.Nm asinl
.Nd arc sine functions
.Sh LIBRARY
.Lb libm
@ -43,23 +44,18 @@
.Fn asin "double x"
.Ft float
.Fn asinf "float x"
.Ft long double
.Fn asinl "long double x"
.Sh DESCRIPTION
The
.Fn asin
and the
.Fn asinf
.Fn asin ,
.Fn asinf ,
and
.Fn asinl
functions compute the principal value of the arc sine of
.Fa x .
A domain error occurs for arguments not in the range
.Bq -1 , +1 .
For a discussion of error due to roundoff, see
.Xr math 3 .
.Sh RETURN VALUES
The
.Fn asin
and the
.Fn asinf
functions return the arc sine in the range
These functions return the arc sine in the range
.Bk -words
.Bq -\*(Pi/2 , +\*(Pi/2
.Ek
@ -85,6 +81,9 @@ raises an invalid exception and returns an \*(Na.
.Xr tanh 3
.Sh STANDARDS
The
.Fn asin
function conforms to
.St -isoC .
.Fn asin ,
.Fn asinf ,
and
.Fn asinl
functions conform to
.St -isoC-99 .

31
lib/msun/man/atan.3
View File

@ -28,12 +28,13 @@
.\" from: @(#)atan.3 5.1 (Berkeley) 5/2/91
.\" $FreeBSD$
.\"
.Dd May 2, 1991
.Dd July 31, 2008
.Dt ATAN 3
.Os
.Sh NAME
.Nm atan ,
.Nm atanf
.Nm atanf ,
.Nm atanl
.Nd arc tangent functions of one variable
.Sh LIBRARY
.Lb libm
@ -43,21 +44,18 @@
.Fn atan "double x"
.Ft float
.Fn atanf "float x"
.Ft long double
.Fn atanl "long double x"
.Sh DESCRIPTION
The
.Fn atan
and the
.Fn atanf
.Fn atan ,
.Fn atanf ,
and
.Fn atanl
functions compute the principal value of the arc tangent of
.Fa x .
For a discussion of error due to roundoff, see
.Xr math 3 .
.Sh RETURN VALUES
The
.Fn atan
and the
.Fn atanf
function returns the arc tangent in the range
These functions return the arc tangent in the range
.Bk -words
.Bq -\*(Pi/2 , +\*(Pi/2
.Ek
@ -75,6 +73,9 @@ radians.
.Xr tanh 3
.Sh STANDARDS
The
.Fn atan
function conforms to
.St -isoC .
.Fn atan ,
.Fn atanf ,
and
.Fn atanl
functions conform to
.St -isoC-99 .

38
lib/msun/man/atan2.3
View File

@ -28,14 +28,16 @@
.\" from: @(#)atan2.3 5.1 (Berkeley) 5/2/91
.\" $FreeBSD$
.\"
.Dd December 12, 2007
.Dd July 31, 2008
.Dt ATAN2 3
.Os
.Sh NAME
.Nm atan2 ,
.Nm atan2f ,
.Nm atan2l ,
.Nm carg ,
.Nm cargf
.Nm cargf ,
.Nm cargl
.Nd arc tangent and complex phase angle functions
.Sh LIBRARY
.Lb libm
@ -45,15 +47,21 @@
.Fn atan2 "double y" "double x"
.Ft float
.Fn atan2f "float y" "float x"
.Ft long double
.Fn atan2l "long double y" "long double x"
.In complex.h
.Ft double
.Fn carg "double complex z"
.Ft float
.Fn cargf "float complex z"
.Ft long double
.Fn cargl "long double complex z"
.Sh DESCRIPTION
The
.Fn atan2
and the
.Fn atan2f
.Fn atan2 ,
.Fn atan2f ,
and
.Fn atan2l
functions compute the principal value of the arc tangent of
.Fa y/ Ns Ar x ,
using the signs of both arguments to determine the quadrant of
@ -66,9 +74,10 @@ the return value.
.\}
.Pp
The
.Fn carg
.Fn carg ,
.Fn cargf ,
and
.Fn cargf
.Fn cargl
functions compute the complex argument (or phase angle) of
.Fa z .
The complex argument is the number \*(Th such that
@ -80,12 +89,15 @@ The call
is equivalent to
.Li atan2(cimag(z), creal(z)) ,
and similarly for
.Fn cargf .
.Fn cargf
and
.Fn cargl .
.Sh RETURN VALUES
The
.Fn atan2
and the
.Fn atan2f
.Fn atan2 ,
.Fn atan2f ,
and
.Fn atan2l
functions, if successful,
return the arc tangent of
.Fa y/ Ns Ar x
@ -210,8 +222,10 @@ r := \(sr(x\(**x+y\(**y);\0\0if r = 0 then x := copysign(1,x);
The
.Fn atan2 ,
.Fn atan2f ,
.Fn atan2l ,
.Fn carg ,
.Fn cargf ,
and
.Fn cargf
.Fn cargl
functions conform to
.St -isoC-99 .

6
lib/msun/src/e_acos.c
View File

@ -38,6 +38,8 @@ __FBSDID("$FreeBSD$");
* Function needed: sqrt
*/
#include <float.h>
#include "math.h"
#include "math_private.h"
@ -103,3 +105,7 @@ __ieee754_acos(double x)
return 2.0*(df+w);
}
}
#if LDBL_MANT_DIG == 53
__weak_reference(acos, acosl);
#endif

77
lib/msun/src/e_acosl.c Normal file
View File

@ -0,0 +1,77 @@
/* @(#)e_acos.c 1.3 95/01/18 */
/* FreeBSD: head/lib/msun/src/e_acos.c 176451 2008-02-22 02:30:36Z das */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");
/*
* See comments in e_acos.c.
* Converted to long double by David Schultz <das@FreeBSD.ORG>.
*/
#include <float.h>
#include "invtrig.h"
#include "math.h"
#include "math_private.h"
static const long double
one= 1.00000000000000000000e+00,
pi = 3.14159265358979323846264338327950280e+00L;
long double
acosl(long double x)
{
union IEEEl2bits u;
long double z,p,q,r,w,s,c,df;
int16_t expsign, expt;
u.e = x;
expsign = u.xbits.expsign;
expt = expsign & 0x7fff;
if(expt >= BIAS) { /* |x| >= 1 */
if(expt==BIAS && ((u.bits.manh&~LDBL_NBIT)|u.bits.manl)==0) {
if (expsign>0) return 0.0; /* acos(1) = 0 */
else return pi+2.0*pio2_lo; /* acos(-1)= pi */
}
return (x-x)/(x-x); /* acos(|x|>1) is NaN */
}
if(expt<BIAS-1) { /* |x| < 0.5 */
if(expt<ACOS_CONST) return pio2_hi+pio2_lo;/*x tiny: acosl=pi/2*/
z = x*x;
p = P(z);
q = Q(z);
r = p/q;
return pio2_hi - (x - (pio2_lo-x*r));
} else if (expsign<0) { /* x < -0.5 */
z = (one+x)*0.5;
p = P(z);
q = Q(z);
s = sqrtl(z);
r = p/q;
w = r*s-pio2_lo;
return pi - 2.0*(s+w);
} else { /* x > 0.5 */
z = (one-x)*0.5;
s = sqrtl(z);
u.e = s;
u.bits.manl = 0;
df = u.e;
c = (z-df*df)/(s+df);
p = P(z);
q = Q(z);
r = p/q;
w = r*s+c;
return 2.0*(df+w);
}
}

5
lib/msun/src/e_asin.c
View File

@ -44,6 +44,7 @@ __FBSDID("$FreeBSD$");
*
*/
#include <float.h>
#include "math.h"
#include "math_private.h"
@ -110,3 +111,7 @@ __ieee754_asin(double x)
}
if(hx>0) return t; else return -t;
}
#if LDBL_MANT_DIG == 53
__weak_reference(asin, asinl);
#endif

77
lib/msun/src/e_asinl.c Normal file
View File

@ -0,0 +1,77 @@
/* @(#)e_asin.c 1.3 95/01/18 */
/* FreeBSD: head/lib/msun/src/e_asin.c 176451 2008-02-22 02:30:36Z das */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");
/*
* See comments in e_asin.c.
* Converted to long double by David Schultz <das@FreeBSD.ORG>.
*/
#include <float.h>
#include "invtrig.h"
#include "math.h"
#include "math_private.h"
static const long double
one = 1.00000000000000000000e+00,
huge = 1.000e+300;
long double
asinl(long double x)
{
union IEEEl2bits u;
long double t=0.0,w,p,q,c,r,s;
int16_t expsign, expt;
u.e = x;
expsign = u.xbits.expsign;
expt = expsign & 0x7fff;
if(expt >= BIAS) { /* |x|>= 1 */
if(expt==BIAS && ((u.bits.manh&~LDBL_NBIT)|u.bits.manl)==0)
/* asin(1)=+-pi/2 with inexact */
return x*pio2_hi+x*pio2_lo;
return (x-x)/(x-x); /* asin(|x|>1) is NaN */
} else if (expt<BIAS-1) { /* |x|<0.5 */
if(expt<ASIN_LINEAR) { /* if |x| is small, asinl(x)=x */
if(huge+x>one) return x;/* return x with inexact if x!=0*/
} else
t = x*x;
p = P(t);
q = Q(t);
w = p/q;
return x+x*w;
}
/* 1> |x|>= 0.5 */
w = one-fabsl(x);
t = w*0.5;
p = P(t);
q = Q(t);
s = sqrtl(t);
if(u.bits.manh>=THRESH) { /* if |x| is close to 1 */
w = p/q;
t = pio2_hi-(2.0*(s+s*w)-pio2_lo);
} else {
u.e = s;
u.bits.manl = 0;
w = u.e;
c = (t-w*w)/(s+w);
r = p/q;
p = 2.0*s*r-(pio2_lo-2.0*c);
q = pio4_hi-2.0*w;
t = pio4_hi-(p-q);
}
if(expsign>0) return t; else return -t;
}

6
lib/msun/src/e_atan2.c
View File

@ -42,6 +42,8 @@ __FBSDID("$FreeBSD$");
* to produce the hexadecimal values shown.
*/
#include <float.h>
#include "math.h"
#include "math_private.h"
@ -123,3 +125,7 @@ __ieee754_atan2(double y, double x)
return (z-pi_lo)-pi;/* atan(-,-) */
}
}
#if LDBL_MANT_DIG == 53
__weak_reference(atan2, atan2l);
#endif

107
lib/msun/src/e_atan2l.c Normal file
View File

@ -0,0 +1,107 @@
/* @(#)e_atan2.c 1.3 95/01/18 */
/* FreeBSD: head/lib/msun/src/e_atan2.c 176451 2008-02-22 02:30:36Z das */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");
/*
* See comments in e_atan2.c.
* Converted to long double by David Schultz <das@FreeBSD.ORG>.
*/
#include <float.h>
#include "invtrig.h"
#include "math.h"
#include "math_private.h"
static volatile long double
tiny = 1.0e-300;
static const long double
zero = 0.0,
pi = 3.14159265358979323846264338327950280e+00L;
long double
atan2l(long double y, long double x)
{
union IEEEl2bits ux, uy;
long double z;
int32_t k,m;
int16_t exptx, expsignx, expty, expsigny;
uy.e = y;
expsigny = uy.xbits.expsign;
expty = expsigny & 0x7fff;
ux.e = x;
expsignx = ux.xbits.expsign;
exptx = expsignx & 0x7fff;
if ((exptx==BIAS+LDBL_MAX_EXP &&
((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)!=0) || /* x is NaN */
(expty==BIAS+LDBL_MAX_EXP &&
((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0)) /* y is NaN */
return x+y;
if (expsignx==BIAS && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0)
return atanl(y); /* x=1.0 */
m = ((expsigny>>15)&1)|((expsignx>>14)&2); /* 2*sign(x)+sign(y) */
/* when y = 0 */
if(expty==0 && ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)==0) {
switch(m) {
case 0:
case 1: return y; /* atan(+-0,+anything)=+-0 */
case 2: return pi+tiny;/* atan(+0,-anything) = pi */
case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
}
}
/* when x = 0 */
if(exptx==0 && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0)
return (expsigny<0)? -pio2_hi-tiny: pio2_hi+tiny;
/* when x is INF */
if(exptx==BIAS+LDBL_MAX_EXP) {
if(expty==BIAS+LDBL_MAX_EXP) {
switch(m) {
case 0: return pio2_hi*0.5+tiny;/* atan(+INF,+INF) */
case 1: return -pio2_hi*0.5-tiny;/* atan(-INF,+INF) */
case 2: return 1.5*pio2_hi+tiny;/*atan(+INF,-INF)*/
case 3: return -1.5*pio2_hi-tiny;/*atan(-INF,-INF)*/
}
} else {
switch(m) {
case 0: return zero ; /* atan(+...,+INF) */
case 1: return -zero ; /* atan(-...,+INF) */
case 2: return pi+tiny ; /* atan(+...,-INF) */
case 3: return -pi-tiny ; /* atan(-...,-INF) */
}
}
}
/* when y is INF */
if(expty==BIAS+LDBL_MAX_EXP)
return (expsigny<0)? -pio2_hi-tiny: pio2_hi+tiny;
/* compute y/x */
k = expty-exptx;
if(k > LDBL_MANT_DIG+2) z=pio2_hi+pio2_lo; /* |y/x| huge */
else if(expsignx<0&&k<-LDBL_MANT_DIG-2) z=0.0; /* |y/x| tiny, x<0 */
else z=atanl(fabsl(y/x)); /* safe to do y/x */
switch (m) {
case 0: return z ; /* atan(+,+) */
case 1: return -z ; /* atan(-,+) */
case 2: return pi-(z-pi_lo);/* atan(+,-) */
default: /* case 3 */
return (z-pi_lo)-pi;/* atan(-,-) */
}
}

6
lib/msun/src/math.h
View File

@ -394,12 +394,18 @@ float significandf(float);
#if __ISO_C_VISIBLE >= 1999
#if 0
long double acoshl(long double);
#endif
long double acosl(long double);
#if 0
long double asinhl(long double);
#endif
long double asinl(long double);
long double atan2l(long double, long double);
#if 0
long double atanhl(long double);
#endif
long double atanl(long double);
#if 0
long double cbrtl(long double);
#endif
long double ceill(long double);

6
lib/msun/src/s_atan.c
View File

@ -33,6 +33,8 @@ __FBSDID("$FreeBSD$");
* to produce the hexadecimal values shown.
*/
#include <float.h>
#include "math.h"
#include "math_private.h"
@ -116,3 +118,7 @@ atan(double x)
return (hx<0)? -z:z;
}
}
#if LDBL_MANT_DIG == 53
__weak_reference(atan, atanl);
#endif

85
lib/msun/src/s_atanl.c Normal file
View File

@ -0,0 +1,85 @@
/* @(#)s_atan.c 5.1 93/09/24 */
/* FreeBSD: head/lib/msun/src/s_atan.c 176451 2008-02-22 02:30:36Z das */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");
/*
* See comments in s_atan.c.
* Converted to long double by David Schultz <das@FreeBSD.ORG>.
*/
#include <float.h>
#include "invtrig.h"
#include "math.h"
#include "math_private.h"
static const long double
one = 1.0,
huge = 1.0e300;
long double
atanl(long double x)
{
union IEEEl2bits u;
long double w,s1,s2,z;
int id;
int16_t expsign, expt;
int32_t expman;
u.e = x;
expsign = u.xbits.expsign;
expt = expsign & 0x7fff;
if(expt >= ATAN_CONST) { /* if |x| is large, atan(x)~=pi/2 */
if(expt == BIAS + LDBL_MAX_EXP &&
((u.bits.manh&~LDBL_NBIT)|u.bits.manl)!=0)
return x+x; /* NaN */
if(expsign>0) return atanhi[3]+atanlo[3];
else return -atanhi[3]-atanlo[3];
}
/* Extract the exponent and the first few bits of the mantissa. */
/* XXX There should be a more convenient way to do this. */
expman = (expt << 8) | ((u.bits.manh >> (MANH_SIZE - 9)) & 0xff);
if (expman < ((BIAS - 2) << 8) + 0xc0) { /* |x| < 0.4375 */
if (expt < ATAN_LINEAR) { /* if |x| is small, atanl(x)~=x */
if(huge+x>one) return x; /* raise inexact */
}
id = -1;
} else {
x = fabsl(x);
if (expman < (BIAS << 8) + 0x30) { /* |x| < 1.1875 */
if (expman < ((BIAS - 1) << 8) + 0x60) { /* 7/16 <=|x|<11/16 */
id = 0; x = (2.0*x-one)/(2.0+x);
} else { /* 11/16<=|x|< 19/16 */
id = 1; x = (x-one)/(x+one);
}
} else {
if (expman < ((BIAS + 1) << 8) + 0x38) { /* |x| < 2.4375 */
id = 2; x = (x-1.5)/(one+1.5*x);
} else { /* 2.4375 <= |x| < 2^ATAN_CONST */
id = 3; x = -1.0/x;
}
}}
/* end of argument reduction */
z = x*x;
w = z*z;
/* break sum aT[i]z**(i+1) into odd and even poly */
s1 = z*T_even(w);
s2 = w*T_odd(w);
if (id<0) return x - x*(s1+s2);
else {
z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
return (expsign<0)? -z:z;
}
}

38
lib/msun/src/s_cargl.c Normal file
View File

@ -0,0 +1,38 @@
/*-
* Copyright (c) 2005-2008 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>
long double
cargl(long double complex z)
{
return (atan2l(cimagl(z), creall(z)));
}