Switch to FreeBSD catrigl.c for complex arc trig functions.
Bug: N/A
Test: ran tests
Change-Id: I9efbc23bc101fcf04a01334748461f5467dcf85e
diff --git a/libm/upstream-freebsd/lib/msun/src/catrigl.c b/libm/upstream-freebsd/lib/msun/src/catrigl.c
new file mode 100644
index 0000000..960c1ca
--- /dev/null
+++ b/libm/upstream-freebsd/lib/msun/src/catrigl.c
@@ -0,0 +1,417 @@
+/*-
+ * 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: head/lib/msun/src/catrigl.c 323003 2017-08-29 22:32:29Z rlibby $");
+
+#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 __unused = 1 + tiny; } while(0)
+#undef signbit
+#define signbit(x) (__builtin_signbitl(x))
+
+#if LDBL_MAX_EXP != 0x4000
+#error "Unsupported long double format"
+#endif
+
+static const long double
+A_crossover = 10,
+B_crossover = 0.6417,
+FOUR_SQRT_MIN = 0x1p-8189L,
+HALF_MAX = 0x1p16383L,
+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 > HALF_MAX)
+ 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)));
+}