Fix our <complex.h> support.
We build libm with -fvisibility=hidden, so we weren't exporting any
of the <complex.h> functions.
We also weren't building many of the functions anyway.
We were also missing the complex inverse trigonometric functions.
And because we didn't even have perfunctory "call each function once"
tests, we didn't notice that we weren't exporting any symbols, so this
patch adds at least that level of testing.
Change-Id: Ibcf2843f507126c51d134cc5fc8d67747e033a0d
diff --git a/libm/upstream-freebsd/lib/msun/src/catrigf.c b/libm/upstream-freebsd/lib/msun/src/catrigf.c
new file mode 100644
index 0000000..08ebef7
--- /dev/null
+++ b/libm/upstream-freebsd/lib/msun/src/catrigf.c
@@ -0,0 +1,393 @@
+/*-
+ * Copyright (c) 2012 Stephen Montgomery-Smith <stephen@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 "math.h"
+#include "math_private.h"
+
+#undef isinf
+#define isinf(x) (fabsf(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_signbitf(x))
+
+static const float
+A_crossover = 10,
+B_crossover = 0.6417,
+FOUR_SQRT_MIN = 0x1p-61,
+QUARTER_SQRT_MAX = 0x1p61,
+m_e = 2.7182818285e0, /* 0xadf854.0p-22 */
+m_ln2 = 6.9314718056e-1, /* 0xb17218.0p-24 */
+pio2_hi = 1.5707962513e0, /* 0xc90fda.0p-23 */
+RECIP_EPSILON = 1 / FLT_EPSILON,
+SQRT_3_EPSILON = 5.9801995673e-4, /* 0x9cc471.0p-34 */
+SQRT_6_EPSILON = 8.4572793338e-4, /* 0xddb3d7.0p-34 */
+SQRT_MIN = 0x1p-63;
+
+static const volatile float
+pio2_lo = 7.5497899549e-8, /* 0xa22169.0p-47 */
+tiny = 0x1p-100;
+
+static float complex clog_for_large_values(float complex z);
+
+static inline float
+f(float a, float b, float 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(float x, float y, float *rx, int *B_is_usable, float *B,
+ float *sqrt_A2my2, float *new_y)
+{
+ float R, S, A;
+ float Am1, Amy;
+
+ R = hypotf(x, y + 1);
+ S = hypotf(x, y - 1);
+
+ A = (R + S) / 2;
+ if (A < 1)
+ A = 1;
+
+ if (A < A_crossover) {
+ if (y == 1 && x < FLT_EPSILON * FLT_EPSILON / 128) {
+ *rx = sqrtf(x);
+ } else if (x >= FLT_EPSILON * fabsf(y - 1)) {
+ Am1 = f(x, 1 + y, R) + f(x, 1 - y, S);
+ *rx = log1pf(Am1 + sqrtf(Am1 * (A + 1)));
+ } else if (y < 1) {
+ *rx = x / sqrtf((1 - y) * (1 + y));
+ } else {
+ *rx = log1pf((y - 1) + sqrtf((y - 1) * (y + 1)));
+ }
+ } else {
+ *rx = logf(A + sqrtf(A * A - 1));
+ }
+
+ *new_y = y;
+
+ if (y < FOUR_SQRT_MIN) {
+ *B_is_usable = 0;
+ *sqrt_A2my2 = A * (2 / FLT_EPSILON);
+ *new_y = y * (2 / FLT_EPSILON);
+ return;
+ }
+
+ *B = y / A;
+ *B_is_usable = 1;
+
+ if (*B > B_crossover) {
+ *B_is_usable = 0;
+ if (y == 1 && x < FLT_EPSILON / 128) {
+ *sqrt_A2my2 = sqrtf(x) * sqrtf((A + y) / 2);
+ } else if (x >= FLT_EPSILON * fabsf(y - 1)) {
+ Amy = f(x, y + 1, R) + f(x, y - 1, S);
+ *sqrt_A2my2 = sqrtf(Amy * (A + y));
+ } else if (y > 1) {
+ *sqrt_A2my2 = x * (4 / FLT_EPSILON / FLT_EPSILON) * y /
+ sqrtf((y + 1) * (y - 1));
+ *new_y = y * (4 / FLT_EPSILON / FLT_EPSILON);
+ } else {
+ *sqrt_A2my2 = sqrtf((1 - y) * (1 + y));
+ }
+ }
+}
+
+float complex
+casinhf(float complex z)
+{
+ float x, y, ax, ay, rx, ry, B, sqrt_A2my2, new_y;
+ int B_is_usable;
+ float complex w;
+
+ x = crealf(z);
+ y = cimagf(z);
+ ax = fabsf(x);
+ ay = fabsf(y);
+
+ if (isnan(x) || isnan(y)) {
+ if (isinf(x))
+ return (cpackf(x, y + y));
+ if (isinf(y))
+ return (cpackf(y, x + x));
+ if (y == 0)
+ return (cpackf(x + x, y));
+ return (cpackf(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 (cpackf(copysignf(crealf(w), x),
+ copysignf(cimagf(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 = asinf(B);
+ else
+ ry = atan2f(new_y, sqrt_A2my2);
+ return (cpackf(copysignf(rx, x), copysignf(ry, y)));
+}
+
+float complex
+casinf(float complex z)
+{
+ float complex w = casinhf(cpackf(cimagf(z), crealf(z)));
+
+ return (cpackf(cimagf(w), crealf(w)));
+}
+
+float complex
+cacosf(float complex z)
+{
+ float x, y, ax, ay, rx, ry, B, sqrt_A2mx2, new_x;
+ int sx, sy;
+ int B_is_usable;
+ float complex w;
+
+ x = crealf(z);
+ y = cimagf(z);
+ sx = signbit(x);
+ sy = signbit(y);
+ ax = fabsf(x);
+ ay = fabsf(y);
+
+ if (isnan(x) || isnan(y)) {
+ if (isinf(x))
+ return (cpackf(y + y, -INFINITY));
+ if (isinf(y))
+ return (cpackf(x + x, -y));
+ if (x == 0)
+ return (cpackf(pio2_hi + pio2_lo, y + y));
+ return (cpackf(x + 0.0L + (y + 0), x + 0.0L + (y + 0)));
+ }
+
+ if (ax > RECIP_EPSILON || ay > RECIP_EPSILON) {
+ w = clog_for_large_values(z);
+ rx = fabsf(cimagf(w));
+ ry = crealf(w) + m_ln2;
+ if (sy == 0)
+ ry = -ry;
+ return (cpackf(rx, ry));
+ }
+
+ if (x == 1 && y == 0)
+ return (cpackf(0, -y));
+
+ raise_inexact();
+
+ if (ax < SQRT_6_EPSILON / 4 && ay < SQRT_6_EPSILON / 4)
+ return (cpackf(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 = acosf(B);
+ else
+ rx = acosf(-B);
+ } else {
+ if (sx == 0)
+ rx = atan2f(sqrt_A2mx2, new_x);
+ else
+ rx = atan2f(sqrt_A2mx2, -new_x);
+ }
+ if (sy == 0)
+ ry = -ry;
+ return (cpackf(rx, ry));
+}
+
+float complex
+cacoshf(float complex z)
+{
+ float complex w;
+ float rx, ry;
+
+ w = cacosf(z);
+ rx = crealf(w);
+ ry = cimagf(w);
+ if (isnan(rx) && isnan(ry))
+ return (cpackf(ry, rx));
+ if (isnan(rx))
+ return (cpackf(fabsf(ry), rx));
+ if (isnan(ry))
+ return (cpackf(ry, ry));
+ return (cpackf(fabsf(ry), copysignf(rx, cimagf(z))));
+}
+
+static float complex
+clog_for_large_values(float complex z)
+{
+ float x, y;
+ float ax, ay, t;
+
+ x = crealf(z);
+ y = cimagf(z);
+ ax = fabsf(x);
+ ay = fabsf(y);
+ if (ax < ay) {
+ t = ax;
+ ax = ay;
+ ay = t;
+ }
+
+ if (ax > FLT_MAX / 2)
+ return (cpackf(logf(hypotf(x / m_e, y / m_e)) + 1,
+ atan2f(y, x)));
+
+ if (ax > QUARTER_SQRT_MAX || ay < SQRT_MIN)
+ return (cpackf(logf(hypotf(x, y)), atan2f(y, x)));
+
+ return (cpackf(logf(ax * ax + ay * ay) / 2, atan2f(y, x)));
+}
+
+static inline float
+sum_squares(float x, float y)
+{
+
+ if (y < SQRT_MIN)
+ return (x * x);
+
+ return (x * x + y * y);
+}
+
+static inline float
+real_part_reciprocal(float x, float y)
+{
+ float scale;
+ uint32_t hx, hy;
+ int32_t ix, iy;
+
+ GET_FLOAT_WORD(hx, x);
+ ix = hx & 0x7f800000;
+ GET_FLOAT_WORD(hy, y);
+ iy = hy & 0x7f800000;
+#define BIAS (FLT_MAX_EXP - 1)
+#define CUTOFF (FLT_MANT_DIG / 2 + 1)
+ if (ix - iy >= CUTOFF << 23 || isinf(x))
+ return (1 / x);
+ if (iy - ix >= CUTOFF << 23)
+ return (x / y / y);
+ if (ix <= (BIAS + FLT_MAX_EXP / 2 - CUTOFF) << 23)
+ return (x / (x * x + y * y));
+ SET_FLOAT_WORD(scale, 0x7f800000 - ix);
+ x *= scale;
+ y *= scale;
+ return (x / (x * x + y * y) * scale);
+}
+
+float complex
+catanhf(float complex z)
+{
+ float x, y, ax, ay, rx, ry;
+
+ x = crealf(z);
+ y = cimagf(z);
+ ax = fabsf(x);
+ ay = fabsf(y);
+
+ if (y == 0 && ax <= 1)
+ return (cpackf(atanhf(x), y));
+
+ if (x == 0)
+ return (cpackf(x, atanf(y)));
+
+ if (isnan(x) || isnan(y)) {
+ if (isinf(x))
+ return (cpackf(copysignf(0, x), y + y));
+ if (isinf(y))
+ return (cpackf(copysignf(0, x),
+ copysignf(pio2_hi + pio2_lo, y)));
+ return (cpackf(x + 0.0L + (y + 0), x + 0.0L + (y + 0)));
+ }
+
+ if (ax > RECIP_EPSILON || ay > RECIP_EPSILON)
+ return (cpackf(real_part_reciprocal(x, y),
+ copysignf(pio2_hi + pio2_lo, y)));
+
+ if (ax < SQRT_3_EPSILON / 2 && ay < SQRT_3_EPSILON / 2) {
+ raise_inexact();
+ return (z);
+ }
+
+ if (ax == 1 && ay < FLT_EPSILON)
+ rx = (m_ln2 - logf(ay)) / 2;
+ else
+ rx = log1pf(4 * ax / sum_squares(ax - 1, ay)) / 4;
+
+ if (ax == 1)
+ ry = atan2f(2, -ay) / 2;
+ else if (ay < FLT_EPSILON)
+ ry = atan2f(2 * ay, (1 - ax) * (1 + ax)) / 2;
+ else
+ ry = atan2f(2 * ay, (1 - ax) * (1 + ax) - ay * ay) / 2;
+
+ return (cpackf(copysignf(rx, x), copysignf(ry, y)));
+}
+
+float complex
+catanf(float complex z)
+{
+ float complex w = catanhf(cpackf(cimagf(z), crealf(z)));
+
+ return (cpackf(cimagf(w), crealf(w)));
+}