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authorZack Weinberg <zackw@panix.com>2017-06-08 15:39:03 -0400
committerZack Weinberg <zackw@panix.com>2017-06-08 15:39:03 -0400
commit5046dbb4a7eba5eccfd258f92f4735c9ffc8d069 (patch)
tree4470480d904b65cf14ca524f96f79eca818c3eaf /REORG.TODO/math/k_casinh_template.c
parent199fc19d3aaaf57944ef036e15904febe877fc93 (diff)
downloadglibc-zack/build-layout-experiment.tar.gz
Prepare for radical source tree reorganization.zack/build-layout-experiment
All top-level files and directories are moved into a temporary storage directory, REORG.TODO, except for files that will certainly still exist in their current form at top level when we're done (COPYING, COPYING.LIB, LICENSES, NEWS, README), all old ChangeLog files (which are moved to the new directory OldChangeLogs, instead), and the generated file INSTALL (which is just deleted; in the new order, there will be no generated files checked into version control).
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+/* Return arc hyperbolic sine for a complex float type, with the
+ imaginary part of the result possibly adjusted for use in
+ computing other functions.
+ Copyright (C) 1997-2017 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ The GNU C Library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with the GNU C Library; if not, see
+ <http://www.gnu.org/licenses/>. */
+
+#include <complex.h>
+#include <math.h>
+#include <math_private.h>
+#include <float.h>
+
+/* Return the complex inverse hyperbolic sine of finite nonzero Z,
+ with the imaginary part of the result subtracted from pi/2 if ADJ
+ is nonzero. */
+
+CFLOAT
+M_DECL_FUNC (__kernel_casinh) (CFLOAT x, int adj)
+{
+ CFLOAT res;
+ FLOAT rx, ix;
+ CFLOAT y;
+
+ /* Avoid cancellation by reducing to the first quadrant. */
+ rx = M_FABS (__real__ x);
+ ix = M_FABS (__imag__ x);
+
+ if (rx >= 1 / M_EPSILON || ix >= 1 / M_EPSILON)
+ {
+ /* For large x in the first quadrant, x + csqrt (1 + x * x)
+ is sufficiently close to 2 * x to make no significant
+ difference to the result; avoid possible overflow from
+ the squaring and addition. */
+ __real__ y = rx;
+ __imag__ y = ix;
+
+ if (adj)
+ {
+ FLOAT t = __real__ y;
+ __real__ y = M_COPYSIGN (__imag__ y, __imag__ x);
+ __imag__ y = t;
+ }
+
+ res = M_SUF (__clog) (y);
+ __real__ res += (FLOAT) M_MLIT (M_LN2);
+ }
+ else if (rx >= M_LIT (0.5) && ix < M_EPSILON / 8)
+ {
+ FLOAT s = M_HYPOT (1, rx);
+
+ __real__ res = M_LOG (rx + s);
+ if (adj)
+ __imag__ res = M_ATAN2 (s, __imag__ x);
+ else
+ __imag__ res = M_ATAN2 (ix, s);
+ }
+ else if (rx < M_EPSILON / 8 && ix >= M_LIT (1.5))
+ {
+ FLOAT s = M_SQRT ((ix + 1) * (ix - 1));
+
+ __real__ res = M_LOG (ix + s);
+ if (adj)
+ __imag__ res = M_ATAN2 (rx, M_COPYSIGN (s, __imag__ x));
+ else
+ __imag__ res = M_ATAN2 (s, rx);
+ }
+ else if (ix > 1 && ix < M_LIT (1.5) && rx < M_LIT (0.5))
+ {
+ if (rx < M_EPSILON * M_EPSILON)
+ {
+ FLOAT ix2m1 = (ix + 1) * (ix - 1);
+ FLOAT s = M_SQRT (ix2m1);
+
+ __real__ res = M_LOG1P (2 * (ix2m1 + ix * s)) / 2;
+ if (adj)
+ __imag__ res = M_ATAN2 (rx, M_COPYSIGN (s, __imag__ x));
+ else
+ __imag__ res = M_ATAN2 (s, rx);
+ }
+ else
+ {
+ FLOAT ix2m1 = (ix + 1) * (ix - 1);
+ FLOAT rx2 = rx * rx;
+ FLOAT f = rx2 * (2 + rx2 + 2 * ix * ix);
+ FLOAT d = M_SQRT (ix2m1 * ix2m1 + f);
+ FLOAT dp = d + ix2m1;
+ FLOAT dm = f / dp;
+ FLOAT r1 = M_SQRT ((dm + rx2) / 2);
+ FLOAT r2 = rx * ix / r1;
+
+ __real__ res = M_LOG1P (rx2 + dp + 2 * (rx * r1 + ix * r2)) / 2;
+ if (adj)
+ __imag__ res = M_ATAN2 (rx + r1, M_COPYSIGN (ix + r2, __imag__ x));
+ else
+ __imag__ res = M_ATAN2 (ix + r2, rx + r1);
+ }
+ }
+ else if (ix == 1 && rx < M_LIT (0.5))
+ {
+ if (rx < M_EPSILON / 8)
+ {
+ __real__ res = M_LOG1P (2 * (rx + M_SQRT (rx))) / 2;
+ if (adj)
+ __imag__ res = M_ATAN2 (M_SQRT (rx), M_COPYSIGN (1, __imag__ x));
+ else
+ __imag__ res = M_ATAN2 (1, M_SQRT (rx));
+ }
+ else
+ {
+ FLOAT d = rx * M_SQRT (4 + rx * rx);
+ FLOAT s1 = M_SQRT ((d + rx * rx) / 2);
+ FLOAT s2 = M_SQRT ((d - rx * rx) / 2);
+
+ __real__ res = M_LOG1P (rx * rx + d + 2 * (rx * s1 + s2)) / 2;
+ if (adj)
+ __imag__ res = M_ATAN2 (rx + s1, M_COPYSIGN (1 + s2, __imag__ x));
+ else
+ __imag__ res = M_ATAN2 (1 + s2, rx + s1);
+ }
+ }
+ else if (ix < 1 && rx < M_LIT (0.5))
+ {
+ if (ix >= M_EPSILON)
+ {
+ if (rx < M_EPSILON * M_EPSILON)
+ {
+ FLOAT onemix2 = (1 + ix) * (1 - ix);
+ FLOAT s = M_SQRT (onemix2);
+
+ __real__ res = M_LOG1P (2 * rx / s) / 2;
+ if (adj)
+ __imag__ res = M_ATAN2 (s, __imag__ x);
+ else
+ __imag__ res = M_ATAN2 (ix, s);
+ }
+ else
+ {
+ FLOAT onemix2 = (1 + ix) * (1 - ix);
+ FLOAT rx2 = rx * rx;
+ FLOAT f = rx2 * (2 + rx2 + 2 * ix * ix);
+ FLOAT d = M_SQRT (onemix2 * onemix2 + f);
+ FLOAT dp = d + onemix2;
+ FLOAT dm = f / dp;
+ FLOAT r1 = M_SQRT ((dp + rx2) / 2);
+ FLOAT r2 = rx * ix / r1;
+
+ __real__ res = M_LOG1P (rx2 + dm + 2 * (rx * r1 + ix * r2)) / 2;
+ if (adj)
+ __imag__ res = M_ATAN2 (rx + r1, M_COPYSIGN (ix + r2,
+ __imag__ x));
+ else
+ __imag__ res = M_ATAN2 (ix + r2, rx + r1);
+ }
+ }
+ else
+ {
+ FLOAT s = M_HYPOT (1, rx);
+
+ __real__ res = M_LOG1P (2 * rx * (rx + s)) / 2;
+ if (adj)
+ __imag__ res = M_ATAN2 (s, __imag__ x);
+ else
+ __imag__ res = M_ATAN2 (ix, s);
+ }
+ math_check_force_underflow_nonneg (__real__ res);
+ }
+ else
+ {
+ __real__ y = (rx - ix) * (rx + ix) + 1;
+ __imag__ y = 2 * rx * ix;
+
+ y = M_SUF (__csqrt) (y);
+
+ __real__ y += rx;
+ __imag__ y += ix;
+
+ if (adj)
+ {
+ FLOAT t = __real__ y;
+ __real__ y = M_COPYSIGN (__imag__ y, __imag__ x);
+ __imag__ y = t;
+ }
+
+ res = M_SUF (__clog) (y);
+ }
+
+ /* Give results the correct sign for the original argument. */
+ __real__ res = M_COPYSIGN (__real__ res, __real__ x);
+ __imag__ res = M_COPYSIGN (__imag__ res, (adj ? 1 : __imag__ x));
+
+ return res;
+}