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

and cargl().

Reviewed by:			bde
sparc64 testing resources from:	remko

2 files changed, 213 insertions, 0 deletions

diff --git a/lib/msun/ld128/invtrig.c b/lib/msun/ld128/invtrig.c
new file mode 100644
index 0000000..4ceca8a
--- /dev/null
+++ b/lib/msun/ld128/invtrig.c
@@ -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;
diff --git a/lib/msun/ld128/invtrig.h b/lib/msun/ld128/invtrig.h
new file mode 100644
index 0000000..12f598b
--- /dev/null
+++ b/lib/msun/ld128/invtrig.h
@@ -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])))))))))));
+}