2013-01-07  Joseph Myers  <joseph@codesourcery.com>

	[BZ #14996]
	* math/s_casinh.c: Include <float.h>.
	(__casinh): Do not do computation with squaring and square root
	for large arguments.
	* math/s_casinhf.c: Include <float.h>.
	(__casinhf): Do not do computation with squaring and square root
	for large arguments.
	* math/s_casinhl.c: Include <float.h>.
	[LDBL_MANT_DIG == 106] (LDBL_EPSILON): Undefine and redefine.
	(__casinhl): Do not do computation with squaring and square root
	for large arguments.
	* math/libm-test.inc (casin_test): Add more tests.
	(casinh_test): Likewise.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.

Index: glibc-2.11.3/math/libm-test.inc
===================================================================
--- glibc-2.11.3.orig/math/libm-test.inc
+++ glibc-2.11.3/math/libm-test.inc
@@ -1366,6 +1366,14 @@ casin_test (void)
   TEST_c_c (casin, -1.0L, -0x1p5000L, -7.079811261048172892385615158694057552948e-1506L, -3.466429049980286492395577839412341016946e3L);
 #endif
 
+  TEST_c_c (casin, 0x1.fp127L, 0x1.fp127L, 7.853981633974483096156608458198757210493e-1L, 8.973081118419833726837456344608533993585e1L);
+#ifndef TEST_FLOAT
+  TEST_c_c (casin, 0x1.fp1023L, 0x1.fp1023L, 7.853981633974483096156608458198757210493e-1L, 7.107906849659093345062145442726115449315e2L);
+#endif
+#if defined TEST_LDOUBLE && LDBL_MAX_EXP >= 16384
+  TEST_c_c (casin, 0x1.fp16383L, 0x1.fp16383L, 7.853981633974483096156608458198757210493e-1L, 1.135753137836666928715489992987020363057e4L);
+#endif
+
   TEST_c_c (casin, 0.75L, 1.25L, 0.453276177638793913448921196101971749L, 1.13239363160530819522266333696834467L);
   TEST_c_c (casin, -2, -3, -0.57065278432109940071028387968566963L, -1.9833870299165354323470769028940395L);
 
@@ -1485,6 +1493,14 @@ casinh_test (void)
   TEST_c_c (casinh, -1.0L, -0x1p5000L, -3.466429049980286492395577839412341016946e3L, -1.570796326794896619231321691639751442099L);
 #endif
 
+  TEST_c_c (casinh, 0x1.fp127L, 0x1.fp127L, 8.973081118419833726837456344608533993585e1L, 7.853981633974483096156608458198757210493e-1L);
+#ifndef TEST_FLOAT
+  TEST_c_c (casinh, 0x1.fp1023L, 0x1.fp1023L, 7.107906849659093345062145442726115449315e2L, 7.853981633974483096156608458198757210493e-1L);
+#endif
+#if defined TEST_LDOUBLE && LDBL_MAX_EXP >= 16384
+  TEST_c_c (casinh, 0x1.fp16383L, 0x1.fp16383L, 1.135753137836666928715489992987020363057e4L, 7.853981633974483096156608458198757210493e-1L);
+#endif
+
   TEST_c_c (casinh, 0.75L, 1.25L, 1.03171853444778027336364058631006594L, 0.911738290968487636358489564316731207L);
   TEST_c_c (casinh, -2, -3, -1.9686379257930962917886650952454982L, -0.96465850440760279204541105949953237L);
 
Index: glibc-2.11.3/math/s_casinh.c
===================================================================
--- glibc-2.11.3.orig/math/s_casinh.c
+++ glibc-2.11.3/math/s_casinh.c
@@ -20,7 +20,7 @@
 
 #include <complex.h>
 #include <math.h>
-
+#include <float.h>
 
 __complex__ double
 __casinh (__complex__ double x)
@@ -69,15 +69,29 @@ __casinh (__complex__ double x)
       rx = fabs (__real__ x);
       ix = fabs (__imag__ x);
 
-      __real__ y = (rx - ix) * (rx + ix) + 1.0;
-      __imag__ y = 2.0 * rx * ix;
+      if (rx >= 1.0 / DBL_EPSILON || ix >= 1.0 / DBL_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;
+	  res = __clog (y);
+	  __real__ res += M_LN2;
+	}
+      else
+	{
+	  __real__ y = (rx - ix) * (rx + ix) + 1.0;
+	  __imag__ y = 2.0 * rx * ix;
 
-      y = __csqrt (y);
+	  y = __csqrt (y);
 
-      __real__ y += rx;
-      __imag__ y += ix;
+	  __real__ y += rx;
+	  __imag__ y += ix;
 
-      res = __clog (y);
+	  res = __clog (y);
+	}
 
       /* Give results the correct sign for the original argument.  */
       __real__ res = __copysign (__real__ res, __real__ x);
Index: glibc-2.11.3/math/s_casinhf.c
===================================================================
--- glibc-2.11.3.orig/math/s_casinhf.c
+++ glibc-2.11.3/math/s_casinhf.c
@@ -20,7 +20,7 @@
 
 #include <complex.h>
 #include <math.h>
-
+#include <float.h>
 
 __complex__ float
 __casinhf (__complex__ float x)
@@ -69,15 +69,29 @@ __casinhf (__complex__ float x)
       rx = fabsf (__real__ x);
       ix = fabsf (__imag__ x);
 
-      __real__ y = (rx - ix) * (rx + ix) + 1.0;
-      __imag__ y = 2.0 * rx * ix;
+      if (rx >= 1.0f / FLT_EPSILON || ix >= 1.0f / FLT_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;
+	  res = __clogf (y);
+	  __real__ res += (float) M_LN2;
+	}
+      else
+	{
+	  __real__ y = (rx - ix) * (rx + ix) + 1.0;
+	  __imag__ y = 2.0 * rx * ix;
 
-      y = __csqrtf (y);
+	  y = __csqrtf (y);
 
-      __real__ y += rx;
-      __imag__ y += ix;
+	  __real__ y += rx;
+	  __imag__ y += ix;
 
-      res = __clogf (y);
+	  res = __clogf (y);
+	}
 
       /* Give results the correct sign for the original argument.  */
       __real__ res = __copysignf (__real__ res, __real__ x);
Index: glibc-2.11.3/math/s_casinhl.c
===================================================================
--- glibc-2.11.3.orig/math/s_casinhl.c
+++ glibc-2.11.3/math/s_casinhl.c
@@ -20,7 +20,14 @@
 
 #include <complex.h>
 #include <math.h>
+#include <float.h>
 
+/* To avoid spurious overflows, use this definition to treat IBM long
+   double as approximating an IEEE-style format.  */
+#if LDBL_MANT_DIG == 106
+# undef LDBL_EPSILON
+# define LDBL_EPSILON 0x1p-106L
+#endif
 
 __complex__ long double
 __casinhl (__complex__ long double x)
@@ -69,15 +76,29 @@ __casinhl (__complex__ long double x)
       rx = fabsl (__real__ x);
       ix = fabsl (__imag__ x);
 
-      __real__ y = (rx - ix) * (rx + ix) + 1.0;
-      __imag__ y = 2.0 * rx * ix;
+      if (rx >= 1.0L / LDBL_EPSILON || ix >= 1.0L / LDBL_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;
+	  res = __clogl (y);
+	  __real__ res += M_LN2l;
+	}
+      else
+	{
+	  __real__ y = (rx - ix) * (rx + ix) + 1.0;
+	  __imag__ y = 2.0 * rx * ix;
 
-      y = __csqrtl (y);
+	  y = __csqrtl (y);
 
-      __real__ y += rx;
-      __imag__ y += ix;
+	  __real__ y += rx;
+	  __imag__ y += ix;
 
-      res = __clogl (y);
+	  res = __clogl (y);
+	}
 
       /* Give results the correct sign for the original argument.  */
       __real__ res = __copysignl (__real__ res, __real__ x);
Index: glibc-2.11.3/sysdeps/i386/fpu/libm-test-ulps
===================================================================
--- glibc-2.11.3.orig/sysdeps/i386/fpu/libm-test-ulps
+++ glibc-2.11.3/sysdeps/i386/fpu/libm-test-ulps
@@ -291,6 +291,12 @@ float: 1
 ifloat: 1
 ildouble: 2
 ldouble: 2
+Test "Imaginary part of: casin (0x1.fp1023 + 0x1.fp1023 i) == 7.853981633974483096156608458198757210493e-1 + 7.107906849659093345062145442726115449315e2 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: casin (0x1.fp127 + 0x1.fp127 i) == 7.853981633974483096156608458198757210493e-1 + 8.973081118419833726837456344608533993585e1 i":
+double: 1
+idouble: 1
 Test "Imaginary part of: casin (1.5 + +0 i) == pi/2 + 0.9624236501192068949955178268487368462704 i":
 double: 1
 float: 1
@@ -391,6 +397,12 @@ idouble: 1
 ifloat: 1
 ildouble: 1
 ldouble: 1
+Test "Real part of: casinh (0x1.fp1023 + 0x1.fp1023 i) == 7.107906849659093345062145442726115449315e2 + 7.853981633974483096156608458198757210493e-1 i":
+double: 1
+idouble: 1
+Test "Real part of: casinh (0x1.fp127 + 0x1.fp127 i) == 8.973081118419833726837456344608533993585e1 + 7.853981633974483096156608458198757210493e-1 i":
+double: 1
+idouble: 1
 Test "Real part of: casinh (1.0 + +0 i) == 0.8813735870195430252326093249797923090282 + +0 i":
 double: 1
 float: 1
Index: glibc-2.11.3/sysdeps/x86_64/fpu/libm-test-ulps
===================================================================
--- glibc-2.11.3.orig/sysdeps/x86_64/fpu/libm-test-ulps
+++ glibc-2.11.3/sysdeps/x86_64/fpu/libm-test-ulps
@@ -304,6 +304,12 @@ float: 1
 ifloat: 1
 ildouble: 2
 ldouble: 2
+Test "Imaginary part of: casin (0x1.fp1023 + 0x1.fp1023 i) == 7.853981633974483096156608458198757210493e-1 + 7.107906849659093345062145442726115449315e2 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: casin (0x1.fp127 + 0x1.fp127 i) == 7.853981633974483096156608458198757210493e-1 + 8.973081118419833726837456344608533993585e1 i":
+double: 1
+idouble: 1
 Test "Imaginary part of: casin (1.5 + +0 i) == pi/2 + 0.9624236501192068949955178268487368462704 i":
 double: 1
 float: 1
@@ -449,6 +455,12 @@ double: 1
 idouble: 1
 ildouble: 1
 ldouble: 1
+Test "Real part of: casinh (0x1.fp1023 + 0x1.fp1023 i) == 7.107906849659093345062145442726115449315e2 + 7.853981633974483096156608458198757210493e-1 i":
+double: 1
+idouble: 1
+Test "Real part of: casinh (0x1.fp127 + 0x1.fp127 i) == 8.973081118419833726837456344608533993585e1 + 7.853981633974483096156608458198757210493e-1 i":
+double: 1
+idouble: 1
 Test "Real part of: casinh (1.0 + +0 i) == 0.8813735870195430252326093249797923090282 + +0 i":
 double: 1
 float: 1
