diff libquadmath/math/casinhq_kernel.c @ 145:1830386684a0

gcc-9.2.0
author anatofuz
date Thu, 13 Feb 2020 11:34:05 +0900
parents
children
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--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/libquadmath/math/casinhq_kernel.c	Thu Feb 13 11:34:05 2020 +0900
@@ -0,0 +1,202 @@
+/* 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) 1997-2018 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 "quadmath-imp.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.  */
+
+__complex128
+__quadmath_kernel_casinhq (__complex128 x, int adj)
+{
+  __complex128 res;
+  __float128 rx, ix;
+  __complex128 y;
+
+  /* Avoid cancellation by reducing to the first quadrant.  */
+  rx = fabsq (__real__ x);
+  ix = fabsq (__imag__ x);
+
+  if (rx >= 1 / FLT128_EPSILON || ix >= 1 / FLT128_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)
+	{
+	  __float128 t = __real__ y;
+	  __real__ y = copysignq (__imag__ y, __imag__ x);
+	  __imag__ y = t;
+	}
+
+      res = clogq (y);
+      __real__ res += (__float128) M_LN2q;
+    }
+  else if (rx >= 0.5Q && ix < FLT128_EPSILON / 8)
+    {
+      __float128 s = hypotq (1, rx);
+
+      __real__ res = logq (rx + s);
+      if (adj)
+	__imag__ res = atan2q (s, __imag__ x);
+      else
+	__imag__ res = atan2q (ix, s);
+    }
+  else if (rx < FLT128_EPSILON / 8 && ix >= 1.5Q)
+    {
+      __float128 s = sqrtq ((ix + 1) * (ix - 1));
+
+      __real__ res = logq (ix + s);
+      if (adj)
+	__imag__ res = atan2q (rx, copysignq (s, __imag__ x));
+      else
+	__imag__ res = atan2q (s, rx);
+    }
+  else if (ix > 1 && ix < 1.5Q && rx < 0.5Q)
+    {
+      if (rx < FLT128_EPSILON * FLT128_EPSILON)
+	{
+	  __float128 ix2m1 = (ix + 1) * (ix - 1);
+	  __float128 s = sqrtq (ix2m1);
+
+	  __real__ res = log1pq (2 * (ix2m1 + ix * s)) / 2;
+	  if (adj)
+	    __imag__ res = atan2q (rx, copysignq (s, __imag__ x));
+	  else
+	    __imag__ res = atan2q (s, rx);
+	}
+      else
+	{
+	  __float128 ix2m1 = (ix + 1) * (ix - 1);
+	  __float128 rx2 = rx * rx;
+	  __float128 f = rx2 * (2 + rx2 + 2 * ix * ix);
+	  __float128 d = sqrtq (ix2m1 * ix2m1 + f);
+	  __float128 dp = d + ix2m1;
+	  __float128 dm = f / dp;
+	  __float128 r1 = sqrtq ((dm + rx2) / 2);
+	  __float128 r2 = rx * ix / r1;
+
+	  __real__ res = log1pq (rx2 + dp + 2 * (rx * r1 + ix * r2)) / 2;
+	  if (adj)
+	    __imag__ res = atan2q (rx + r1, copysignq (ix + r2, __imag__ x));
+	  else
+	    __imag__ res = atan2q (ix + r2, rx + r1);
+	}
+    }
+  else if (ix == 1 && rx < 0.5Q)
+    {
+      if (rx < FLT128_EPSILON / 8)
+	{
+	  __real__ res = log1pq (2 * (rx + sqrtq (rx))) / 2;
+	  if (adj)
+	    __imag__ res = atan2q (sqrtq (rx), copysignq (1, __imag__ x));
+	  else
+	    __imag__ res = atan2q (1, sqrtq (rx));
+	}
+      else
+	{
+	  __float128 d = rx * sqrtq (4 + rx * rx);
+	  __float128 s1 = sqrtq ((d + rx * rx) / 2);
+	  __float128 s2 = sqrtq ((d - rx * rx) / 2);
+
+	  __real__ res = log1pq (rx * rx + d + 2 * (rx * s1 + s2)) / 2;
+	  if (adj)
+	    __imag__ res = atan2q (rx + s1, copysignq (1 + s2, __imag__ x));
+	  else
+	    __imag__ res = atan2q (1 + s2, rx + s1);
+	}
+    }
+  else if (ix < 1 && rx < 0.5Q)
+    {
+      if (ix >= FLT128_EPSILON)
+	{
+	  if (rx < FLT128_EPSILON * FLT128_EPSILON)
+	    {
+	      __float128 onemix2 = (1 + ix) * (1 - ix);
+	      __float128 s = sqrtq (onemix2);
+
+	      __real__ res = log1pq (2 * rx / s) / 2;
+	      if (adj)
+		__imag__ res = atan2q (s, __imag__ x);
+	      else
+		__imag__ res = atan2q (ix, s);
+	    }
+	  else
+	    {
+	      __float128 onemix2 = (1 + ix) * (1 - ix);
+	      __float128 rx2 = rx * rx;
+	      __float128 f = rx2 * (2 + rx2 + 2 * ix * ix);
+	      __float128 d = sqrtq (onemix2 * onemix2 + f);
+	      __float128 dp = d + onemix2;
+	      __float128 dm = f / dp;
+	      __float128 r1 = sqrtq ((dp + rx2) / 2);
+	      __float128 r2 = rx * ix / r1;
+
+	      __real__ res = log1pq (rx2 + dm + 2 * (rx * r1 + ix * r2)) / 2;
+	      if (adj)
+		__imag__ res = atan2q (rx + r1, copysignq (ix + r2,
+							     __imag__ x));
+	      else
+		__imag__ res = atan2q (ix + r2, rx + r1);
+	    }
+	}
+      else
+	{
+	  __float128 s = hypotq (1, rx);
+
+	  __real__ res = log1pq (2 * rx * (rx + s)) / 2;
+	  if (adj)
+	    __imag__ res = atan2q (s, __imag__ x);
+	  else
+	    __imag__ res = atan2q (ix, s);
+	}
+      math_check_force_underflow_nonneg (__real__ res);
+    }
+  else
+    {
+      __real__ y = (rx - ix) * (rx + ix) + 1;
+      __imag__ y = 2 * rx * ix;
+
+      y = csqrtq (y);
+
+      __real__ y += rx;
+      __imag__ y += ix;
+
+      if (adj)
+	{
+	  __float128 t = __real__ y;
+	  __real__ y = copysignq (__imag__ y, __imag__ x);
+	  __imag__ y = t;
+	}
+
+      res = clogq (y);
+    }
+
+  /* Give results the correct sign for the original argument.  */
+  __real__ res = copysignq (__real__ res, __real__ x);
+  __imag__ res = copysignq (__imag__ res, (adj ? 1 : __imag__ x));
+
+  return res;
+}