Add casinl() cacosl() catanl() casinhl() cacoshl() catanhl() APIs to msun

to improve C11 conformance.

PR:		216850 216851 216852 216856 216857 216858
Submitted by:	mmokhi
Reported by:	sgk@troutmask.apl.washington.edu
Reviewed by:	bde, mat, theraven
Approved by:	bde (src committer), mat (mentor)
Differential Revision:	https://reviews.freebsd.org/D9491

3 files changed, 423 insertions, 1 deletions

diff --git a/lib/msun/Makefile b/lib/msun/Makefile
index 69011345a0d6..b2502742ac83 100644
--- a/lib/msun/Makefile
+++ b/lib/msun/Makefile
@@ -107,7 +107,7 @@ COMMON_SRCS+=	e_acoshl.c e_acosl.c e_asinl.c e_atan2l.c e_atanhl.c \
 .endif
 
 # C99 complex functions
-COMMON_SRCS+=	catrig.c catrigf.c \
+COMMON_SRCS+=	catrig.c catrigf.c catrigl.c \
 	s_ccosh.c s_ccoshf.c s_cexp.c s_cexpf.c \
 	s_cimag.c s_cimagf.c s_cimagl.c \
 	s_conj.c s_conjf.c s_conjl.c \
diff --git a/lib/msun/Symbol.map b/lib/msun/Symbol.map
index d5b7f4699f10..5ba7c49c1413 100644
--- a/lib/msun/Symbol.map
+++ b/lib/msun/Symbol.map
@@ -285,3 +285,13 @@ FBSD_1.3 {
 FBSD_1.4 {
 	lgammal_r;
 };
+
+/* First added in 12.0-CURRENT */
+FBSD_1.5 {
+	cacoshl;
+	cacosl;
+	casinhl;
+	casinl;
+	catanl;
+	catanhl;
+};
diff --git a/lib/msun/src/catrigl.c b/lib/msun/src/catrigl.c
new file mode 100644
index 000000000000..f71a3118de7e
--- /dev/null
+++ b/lib/msun/src/catrigl.c
@@ -0,0 +1,412 @@
+/*-
+ * Copyright (c) 2012 Stephen Montgomery-Smith <stephen@FreeBSD.ORG>
+ * Copyright (c) 2017 Mahdi Mokhtari <mmokhi@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.
+ */
+
+/*
+ * The algorithm is very close to that in "Implementing the complex arcsine
+ * and arccosine functions using exception handling" by T. E. Hull, Thomas F.
+ * Fairgrieve, and Ping Tak Peter Tang, published in ACM Transactions on
+ * Mathematical Software, Volume 23 Issue 3, 1997, Pages 299-335,
+ * http://dl.acm.org/citation.cfm?id=275324.
+ *
+ * See catrig.c for complete comments.
+ *
+ * XXX comments were removed automatically, and even short ones on the right
+ * of statements were removed (all of them), contrary to normal style.  Only
+ * a few comments on the right of declarations remain.
+ */
+
+#include <sys/cdefs.h>
+__FBSDID("$FreeBSD$");
+
+#include <complex.h>
+#include <float.h>
+
+#include "invtrig.h"
+#include "math.h"
+#include "math_private.h"
+
+#undef isinf
+#define isinf(x)	(fabsl(x) == INFINITY)
+#undef isnan
+#define isnan(x)	((x) != (x))
+#define	raise_inexact()	do { volatile float junk = 1 + tiny; } while(0)
+#undef signbit
+#define signbit(x)	(__builtin_signbitl(x))
+
+static const long double
+A_crossover =		10,
+B_crossover =		0.6417,
+FOUR_SQRT_MIN =		0x1p-8189L,
+QUARTER_SQRT_MAX =	0x1p8189L,
+RECIP_EPSILON =		1 / LDBL_EPSILON,
+SQRT_MIN =		0x1p-8191L;
+
+#if LDBL_MANT_DIG == 64
+static const union IEEEl2bits
+um_e =		LD80C(0xadf85458a2bb4a9b,  1, 2.71828182845904523536e+0L),
+um_ln2 =	LD80C(0xb17217f7d1cf79ac, -1, 6.93147180559945309417e-1L);
+#define		m_e	um_e.e
+#define		m_ln2	um_ln2.e
+static const long double
+/* The next 2 literals for non-i386.  Misrounding them on i386 is harmless. */
+SQRT_3_EPSILON = 5.70316273435758915310e-10,	/*  0x9cc470a0490973e8.0p-94 */
+SQRT_6_EPSILON = 8.06549008734932771664e-10;	/*  0xddb3d742c265539e.0p-94 */
+#elif LDBL_MANT_DIG == 113
+static const long double
+m_e =		2.71828182845904523536028747135266250e0L,	/* 0x15bf0a8b1457695355fb8ac404e7a.0p-111 */
+m_ln2 =		6.93147180559945309417232121458176568e-1L,	/* 0x162e42fefa39ef35793c7673007e6.0p-113 */
+SQRT_3_EPSILON = 2.40370335797945490975336727199878124e-17,	/*  0x1bb67ae8584caa73b25742d7078b8.0p-168 */
+SQRT_6_EPSILON = 3.39934988877629587239082586223300391e-17;	/*  0x13988e1409212e7d0321914321a55.0p-167 */
+#else
+#error "Unsupported long double format"
+#endif
+
+static const volatile float
+tiny =			0x1p-100;
+
+static long double complex clog_for_large_values(long double complex z);
+
+static inline long double
+f(long double a, long double b, long double hypot_a_b)
+{
+	if (b < 0)
+		return ((hypot_a_b - b) / 2);
+	if (b == 0)
+		return (a / 2);
+	return (a * a / (hypot_a_b + b) / 2);
+}
+
+static inline void
+do_hard_work(long double x, long double y, long double *rx, int *B_is_usable,
+    long double *B, long double *sqrt_A2my2, long double *new_y)
+{
+	long double R, S, A;
+	long double Am1, Amy;
+
+	R = hypotl(x, y + 1);
+	S = hypotl(x, y - 1);
+
+	A = (R + S) / 2;
+	if (A < 1)
+		A = 1;
+
+	if (A < A_crossover) {
+		if (y == 1 && x < LDBL_EPSILON * LDBL_EPSILON / 128) {
+			*rx = sqrtl(x);
+		} else if (x >= LDBL_EPSILON * fabsl(y - 1)) {
+			Am1 = f(x, 1 + y, R) + f(x, 1 - y, S);
+			*rx = log1pl(Am1 + sqrtl(Am1 * (A + 1)));
+		} else if (y < 1) {
+			*rx = x / sqrtl((1 - y) * (1 + y));
+		} else {
+			*rx = log1pl((y - 1) + sqrtl((y - 1) * (y + 1)));
+		}
+	} else {
+		*rx = logl(A + sqrtl(A * A - 1));
+	}
+
+	*new_y = y;
+
+	if (y < FOUR_SQRT_MIN) {
+		*B_is_usable = 0;
+		*sqrt_A2my2 = A * (2 / LDBL_EPSILON);
+		*new_y = y * (2 / LDBL_EPSILON);
+		return;
+	}
+
+	*B = y / A;
+	*B_is_usable = 1;
+
+	if (*B > B_crossover) {
+		*B_is_usable = 0;
+		if (y == 1 && x < LDBL_EPSILON / 128) {
+			*sqrt_A2my2 = sqrtl(x) * sqrtl((A + y) / 2);
+		} else if (x >= LDBL_EPSILON * fabsl(y - 1)) {
+			Amy = f(x, y + 1, R) + f(x, y - 1, S);
+			*sqrt_A2my2 = sqrtl(Amy * (A + y));
+		} else if (y > 1) {
+			*sqrt_A2my2 = x * (4 / LDBL_EPSILON / LDBL_EPSILON) * y /
+			    sqrtl((y + 1) * (y - 1));
+			*new_y = y * (4 / LDBL_EPSILON / LDBL_EPSILON);
+		} else {
+			*sqrt_A2my2 = sqrtl((1 - y) * (1 + y));
+		}
+	}
+}
+
+long double complex
+casinhl(long double complex z)
+{
+	long double x, y, ax, ay, rx, ry, B, sqrt_A2my2, new_y;
+	int B_is_usable;
+	long double complex w;
+
+	x = creall(z);
+	y = cimagl(z);
+	ax = fabsl(x);
+	ay = fabsl(y);
+
+	if (isnan(x) || isnan(y)) {
+		if (isinf(x))
+			return (CMPLXL(x, y + y));
+		if (isinf(y))
+			return (CMPLXL(y, x + x));
+		if (y == 0)
+			return (CMPLXL(x + x, y));
+		return (CMPLXL(x + 0.0L + (y + 0), x + 0.0L + (y + 0)));
+	}
+
+	if (ax > RECIP_EPSILON || ay > RECIP_EPSILON) {
+		if (signbit(x) == 0)
+			w = clog_for_large_values(z) + m_ln2;
+		else
+			w = clog_for_large_values(-z) + m_ln2;
+		return (CMPLXL(copysignl(creall(w), x),
+		    copysignl(cimagl(w), y)));
+	}
+
+	if (x == 0 && y == 0)
+		return (z);
+
+	raise_inexact();
+
+	if (ax < SQRT_6_EPSILON / 4 && ay < SQRT_6_EPSILON / 4)
+		return (z);
+
+	do_hard_work(ax, ay, &rx, &B_is_usable, &B, &sqrt_A2my2, &new_y);
+	if (B_is_usable)
+		ry = asinl(B);
+	else
+		ry = atan2l(new_y, sqrt_A2my2);
+	return (CMPLXL(copysignl(rx, x), copysignl(ry, y)));
+}
+
+long double complex
+casinl(long double complex z)
+{
+	long double complex w;
+
+	w = casinhl(CMPLXL(cimagl(z), creall(z)));
+	return (CMPLXL(cimagl(w), creall(w)));
+}
+
+long double complex
+cacosl(long double complex z)
+{
+	long double x, y, ax, ay, rx, ry, B, sqrt_A2mx2, new_x;
+	int sx, sy;
+	int B_is_usable;
+	long double complex w;
+
+	x = creall(z);
+	y = cimagl(z);
+	sx = signbit(x);
+	sy = signbit(y);
+	ax = fabsl(x);
+	ay = fabsl(y);
+
+	if (isnan(x) || isnan(y)) {
+		if (isinf(x))
+			return (CMPLXL(y + y, -INFINITY));
+		if (isinf(y))
+			return (CMPLXL(x + x, -y));
+		if (x == 0)
+			return (CMPLXL(pio2_hi + pio2_lo, y + y));
+		return (CMPLXL(x + 0.0L + (y + 0), x + 0.0L + (y + 0)));
+	}
+
+	if (ax > RECIP_EPSILON || ay > RECIP_EPSILON) {
+		w = clog_for_large_values(z);
+		rx = fabsl(cimagl(w));
+		ry = creall(w) + m_ln2;
+		if (sy == 0)
+			ry = -ry;
+		return (CMPLXL(rx, ry));
+	}
+
+	if (x == 1 && y == 0)
+		return (CMPLXL(0, -y));
+
+	raise_inexact();
+
+	if (ax < SQRT_6_EPSILON / 4 && ay < SQRT_6_EPSILON / 4)
+		return (CMPLXL(pio2_hi - (x - pio2_lo), -y));
+
+	do_hard_work(ay, ax, &ry, &B_is_usable, &B, &sqrt_A2mx2, &new_x);
+	if (B_is_usable) {
+		if (sx == 0)
+			rx = acosl(B);
+		else
+			rx = acosl(-B);
+	} else {
+		if (sx == 0)
+			rx = atan2l(sqrt_A2mx2, new_x);
+		else
+			rx = atan2l(sqrt_A2mx2, -new_x);
+	}
+	if (sy == 0)
+		ry = -ry;
+	return (CMPLXL(rx, ry));
+}
+
+long double complex
+cacoshl(long double complex z)
+{
+	long double complex w;
+	long double rx, ry;
+
+	w = cacosl(z);
+	rx = creall(w);
+	ry = cimagl(w);
+	if (isnan(rx) && isnan(ry))
+		return (CMPLXL(ry, rx));
+	if (isnan(rx))
+		return (CMPLXL(fabsl(ry), rx));
+	if (isnan(ry))
+		return (CMPLXL(ry, ry));
+	return (CMPLXL(fabsl(ry), copysignl(rx, cimagl(z))));
+}
+
+static long double complex
+clog_for_large_values(long double complex z)
+{
+	long double x, y;
+	long double ax, ay, t;
+
+	x = creall(z);
+	y = cimagl(z);
+	ax = fabsl(x);
+	ay = fabsl(y);
+	if (ax < ay) {
+		t = ax;
+		ax = ay;
+		ay = t;
+	}
+
+	if (ax > LDBL_MAX / 2)
+		return (CMPLXL(logl(hypotl(x / m_e, y / m_e)) + 1,
+		    atan2l(y, x)));
+
+	if (ax > QUARTER_SQRT_MAX || ay < SQRT_MIN)
+		return (CMPLXL(logl(hypotl(x, y)), atan2l(y, x)));
+
+	return (CMPLXL(logl(ax * ax + ay * ay) / 2, atan2l(y, x)));
+}
+
+static inline long double
+sum_squares(long double x, long double y)
+{
+
+	if (y < SQRT_MIN)
+		return (x * x);
+
+	return (x * x + y * y);
+}
+
+static inline long double
+real_part_reciprocal(long double x, long double y)
+{
+	long double scale;
+	uint16_t hx, hy;
+	int16_t ix, iy;
+
+	GET_LDBL_EXPSIGN(hx, x);
+	ix = hx & 0x7fff;
+	GET_LDBL_EXPSIGN(hy, y);
+	iy = hy & 0x7fff;
+#define	BIAS	(LDBL_MAX_EXP - 1)
+#define	CUTOFF	(LDBL_MANT_DIG / 2 + 1)
+	if (ix - iy >= CUTOFF || isinf(x))
+		return (1 / x);
+	if (iy - ix >= CUTOFF)
+		return (x / y / y);
+	if (ix <= BIAS + LDBL_MAX_EXP / 2 - CUTOFF)
+		return (x / (x * x + y * y));
+	scale = 1;
+	SET_LDBL_EXPSIGN(scale, 0x7fff - ix);
+	x *= scale;
+	y *= scale;
+	return (x / (x * x + y * y) * scale);
+}
+
+long double complex
+catanhl(long double complex z)
+{
+	long double x, y, ax, ay, rx, ry;
+
+	x = creall(z);
+	y = cimagl(z);
+	ax = fabsl(x);
+	ay = fabsl(y);
+
+	if (y == 0 && ax <= 1)
+		return (CMPLXL(atanhl(x), y));
+
+	if (x == 0)
+		return (CMPLXL(x, atanl(y)));
+
+	if (isnan(x) || isnan(y)) {
+		if (isinf(x))
+			return (CMPLXL(copysignl(0, x), y + y));
+		if (isinf(y))
+			return (CMPLXL(copysignl(0, x),
+			    copysignl(pio2_hi + pio2_lo, y)));
+		return (CMPLXL(x + 0.0L + (y + 0), x + 0.0L + (y + 0)));
+	}
+
+	if (ax > RECIP_EPSILON || ay > RECIP_EPSILON)
+		return (CMPLXL(real_part_reciprocal(x, y),
+		    copysignl(pio2_hi + pio2_lo, y)));
+
+	if (ax < SQRT_3_EPSILON / 2 && ay < SQRT_3_EPSILON / 2) {
+		raise_inexact();
+		return (z);
+	}
+
+	if (ax == 1 && ay < LDBL_EPSILON)
+		rx = (m_ln2 - logl(ay)) / 2;
+	else
+		rx = log1pl(4 * ax / sum_squares(ax - 1, ay)) / 4;
+
+	if (ax == 1)
+		ry = atan2l(2, -ay) / 2;
+	else if (ay < LDBL_EPSILON)
+		ry = atan2l(2 * ay, (1 - ax) * (1 + ax)) / 2;
+	else
+		ry = atan2l(2 * ay, (1 - ax) * (1 + ax) - ay * ay) / 2;
+
+	return (CMPLXL(copysignl(rx, x), copysignl(ry, y)));
+}
+
+long double complex
+catanl(long double complex z)
+{
+	long double complex w;
+
+	w = catanhl(CMPLXL(cimagl(z), creall(z)));
+	return (CMPLXL(cimagl(w), creall(w)));
+}