Fix ctan, ctanh overflow for ldbl-128ibm (bug 11521).

4 files changed, 138 insertions, 33 deletions

diff --git a/sysdeps/ieee754/ldbl-128ibm/e_sinhl.c b/sysdeps/ieee754/ldbl-128ibm/e_sinhl.c
index 4bae85a5a4..4e8481c419 100644
--- a/sysdeps/ieee754/ldbl-128ibm/e_sinhl.c
+++ b/sysdeps/ieee754/ldbl-128ibm/e_sinhl.c
@@ -54,7 +54,8 @@ __ieee754_sinhl(long double x)
 		if(shuge+x>one) return x;/* sinhl(tiny) = tiny with inexact */
 	    t = __expm1l(fabsl(x));
 	    if(ix<0x3ff0000000000000LL) return h*(2.0*t-t*t/(t+one));
-	    return h*(t+t/(t+one));
+	    w = t/(t+one);
+	    return h*(t+w);
 	}
 
     /* |x| in [40, log(maxdouble)] return 0.5*exp(|x|) */
diff --git a/sysdeps/ieee754/ldbl-128ibm/s_ctanhl.c b/sysdeps/ieee754/ldbl-128ibm/s_ctanhl.c
index e4126395bd..2ab80a2246 100644
--- a/sysdeps/ieee754/ldbl-128ibm/s_ctanhl.c
+++ b/sysdeps/ieee754/ldbl-128ibm/s_ctanhl.c
@@ -1,5 +1,5 @@
 /* Complex hyperbole tangent for long double.  IBM extended format version.
-   Copyright (C) 1997,2005,2006 Free Software Foundation, Inc.
+   Copyright (C) 1997-2012 Free Software Foundation, Inc.
    This file is part of the GNU C Library.
    Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
 
@@ -19,6 +19,7 @@
 
 #include <complex.h>
 #include <fenv.h>
+#include <float.h>
 #include <math.h>
 #include <math_ldbl_opt.h>
 
@@ -54,24 +55,44 @@ __ctanhl (__complex__ long double x)
     }
   else
     {
-      long double sin2ix, cos2ix;
+      long double sinix, cosix;
       long double den;
+      const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l / 2);
 
-      __sincosl (2.0 * __imag__ x, &sin2ix, &cos2ix);
+      /* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y))
+        = (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2).  */
 
-      den = (__ieee754_coshl (2.0 * __real__ x) + cos2ix);
+      __sincosl (__imag__ x, &sinix, &cosix);
 
-      if (den == 0.0L)
+      if (fabsl (__real__ x) > t)
 	{
-	  __complex__ long double ez = __cexpl (x);
-	  __complex__ long double emz = __cexpl (-x);
-
-	  res = (ez - emz) / (ez + emz);
+	  /* Avoid intermediate overflow when the imaginary part of
+	     the result may be subnormal.  Ignoring negligible terms,
+	     the real part is +/- 1, the imaginary part is
+	     sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x).  */
+	  long double exp_2t = __ieee754_expl (2 * t);
+	  __real__ res = __copysignl (1.0, __real__ x);
+	  __imag__ res = 4 * sinix * cosix;
+	  __real__ x = fabsl (__real__ x);
+	  __real__ x -= t;
+	  __imag__ res /= exp_2t;
+	  if (__real__ x > t)
+	    {
+	      /* Underflow (original real part of x has absolute value
+		 > 2t).  */
+	      __imag__ res /= exp_2t;
+	    }
+	  else
+	    __imag__ res /= __ieee754_expl (2 * __real__ x);
 	}
       else
 	{
-	  __real__ res = __ieee754_sinhl (2.0 * __real__ x) / den;
-	  __imag__ res = sin2ix / den;
+	  long double sinhrx = __ieee754_sinhl (__real__ x);
+	  long double coshrx = __ieee754_coshl (__real__ x);
+
+	  den = sinhrx * sinhrx + cosix * cosix;
+	  __real__ res = sinhrx * coshrx / den;
+	  __imag__ res = sinix * cosix / den;
 	}
       /* __gcc_qmul does not respect -0.0 so we need the following fixup.  */
       if ((__real__ res == 0.0) && (__real__ x == 0.0))
diff --git a/sysdeps/ieee754/ldbl-128ibm/s_ctanl.c b/sysdeps/ieee754/ldbl-128ibm/s_ctanl.c
index 0b1bc4f70e..9d89bbe311 100644
--- a/sysdeps/ieee754/ldbl-128ibm/s_ctanl.c
+++ b/sysdeps/ieee754/ldbl-128ibm/s_ctanl.c
@@ -1,5 +1,5 @@
 /* Complex tangent function for long double.  IBM extended format version.
-   Copyright (C) 1997,2005,2006 Free Software Foundation, Inc.
+   Copyright (C) 1997-2012 Free Software Foundation, Inc.
    This file is part of the GNU C Library.
    Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
 
@@ -21,6 +21,7 @@
 #include <fenv.h>
 #include <math.h>
 #include <math_ldbl_opt.h>
+#include <float.h>
 
 #include <math_private.h>
 
@@ -46,34 +47,53 @@ __ctanl (__complex__ long double x)
 	  __real__ res = __nanl ("");
 	  __imag__ res = __nanl ("");
 
-#ifdef FE_INVALID
-	  if (__isinfl (__real__ x))
+	  if (__isinf_nsl (__real__ x))
 	    feraiseexcept (FE_INVALID);
-#endif
 	}
     }
   else
     {
-      long double sin2rx, cos2rx;
+      long double sinrx, cosrx;
       long double den;
+      const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l / 2);
 
-      __sincosl (2.0 * __real__ x, &sin2rx, &cos2rx);
+      /* tan(x+iy) = (sin(2x) + i*sinh(2y))/(cos(2x) + cosh(2y))
+        = (sin(x)*cos(x) + i*sinh(y)*cosh(y)/(cos(x)^2 + sinh(y)^2). */
 
-      den = cos2rx + __ieee754_coshl (2.0 * __imag__ x);
+      __sincosl (__real__ x, &sinrx, &cosrx);
 
-
-      if (den == 0.0)
+      if (fabsl (__imag__ x) > t)
 	{
-	  __complex__ long double ez = __cexpl (1.0i * x);
-	  __complex__ long double emz = __cexpl (-1.0i * x);
+	  /* Avoid intermediate overflow when the real part of the
+	    result may be subnormal.  Ignoring negligible terms, the
+	    imaginary part is +/- 1, the real part is
+	    sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y).  */
+	  long double exp_2t = __ieee754_expl (2 * t);
 
-	  res = (ez - emz) / (ez + emz) * -1.0i;
+	  __imag__ res = __copysignl (1.0, __imag__ x);
+	  __real__ res = 4 * sinrx * cosrx;
+	  __imag__ x = fabsl (__imag__ x);
+	  __imag__ x -= t;
+	  __real__ res /= exp_2t;
+	  if (__imag__ x > t)
+	    {
+	      /* Underflow (original imaginary part of x has absolute
+		 value > 2t).  */
+	      __real__ res /= exp_2t;
+	    }
+	  else
+	    __real__ res /= __ieee754_expl (2 * __imag__ x);
 	}
       else
 	{
-	  __real__ res = sin2rx / den;
-	  __imag__ res = __ieee754_sinhl (2.0 * __imag__ x) / den;
+	  long double sinhix = __ieee754_sinhl (__imag__ x);
+	  long double coshix = __ieee754_coshl (__imag__ x);
+
+	  den = cosrx * cosrx + sinhix * sinhix;
+	  __real__ res = sinrx * cosrx / den;
+	  __imag__ res = sinhix * coshix / den;
 	}
+
       /* __gcc_qmul does not respect -0.0 so we need the following fixup.  */
       if ((__real__ res == 0.0) && (__real__ x == 0.0))
         __real__ res = __real__ x;
diff --git a/sysdeps/powerpc/fpu/libm-test-ulps b/sysdeps/powerpc/fpu/libm-test-ulps
index c555297db5..43fa64289d 100644
--- a/sysdeps/powerpc/fpu/libm-test-ulps
+++ b/sysdeps/powerpc/fpu/libm-test-ulps
@@ -1051,16 +1051,44 @@ ifloat: 2
 
 # ctan
 Test "Real part of: ctan (-2 - 3 i) == 0.376402564150424829275122113032269084e-2 - 1.00323862735360980144635859782192726 i":
+float: 1
+ifloat: 1
 double: 1
 idouble: 1
+ldouble: 1
+ildouble: 1
+Test "Real part of: ctan (1 + 47 i) == 2.729321264492904590777293425576722354636e-41 + 1.0 i":
+ldouble: 2
+ildouble: 2
 Test "Imaginary part of: ctan (-2 - 3 i) == 0.376402564150424829275122113032269084e-2 - 1.00323862735360980144635859782192726 i":
+double: 1
+idouble: 1
 ildouble: 1
 ldouble: 1
+Test "Real part of: ctan (0.75 + 1.25 i) == 0.160807785916206426725166058173438663 + 0.975363285031235646193581759755216379 i":
+float: 1
+ifloat: 1
 Test "Imaginary part of: ctan (0.75 + 1.25 i) == 0.160807785916206426725166058173438663 + 0.975363285031235646193581759755216379 i":
+float: 1
+ifloat: 1
 double: 1
 idouble: 1
 ildouble: 1
 ldouble: 1
+Test "Real part of: ctan (0x1p1023 + 1 i) == -0.2254627924997545057926782581695274244229 + 0.8786063118883068695462540226219865087189 i":
+double: 1
+idouble: 1
+Test "Real part of: ctan (0x1p127 + 1 i) == 0.2446359391192790896381501310437708987204 + 0.9101334047676183761532873794426475906201 i":
+float: 1
+ifloat: 1
+Test "Imaginary part of: ctan (0x1p127 + 1 i) == 0.2446359391192790896381501310437708987204 + 0.9101334047676183761532873794426475906201 i":
+float: 1
+ifloat: 1
+double: 1
+idouble: 1
+Test "Real part of: ctan (0x3.243f6cp-1 + 0 i) == -2.287733242885645987394874673945769518150e7 + 0.0 i":
+float: 1
+ifloat: 1
 
 # ctanh
 Test "Real part of: ctanh (-2 - 3 i) == -0.965385879022133124278480269394560686 + 0.988437503832249372031403430350121098e-2 i":
@@ -1068,14 +1096,43 @@ double: 1
 float: 2
 idouble: 1
 ifloat: 2
+Test "Imaginary part of: ctanh (-2 - 3 i) == -0.965385879022133124278480269394560686 + 0.988437503832249372031403430350121098e-2 i":
+double: 1
+idouble: 1
 Test "Imaginary part of: ctanh (0 + pi/4 i) == 0.0 + 1.0 i":
 float: 1
 ifloat: 1
+double: 1
+idouble: 1
 Test "Real part of: ctanh (0.75 + 1.25 i) == 1.37260757053378320258048606571226857 + 0.385795952609750664177596760720790220 i":
 double: 1
 idouble: 1
 ildouble: 1
-ldouble: 1
+ldouble: 3
+ildouble: 3
+Test "Imaginary part of: ctanh (0.75 + 1.25 i) == 1.37260757053378320258048606571226857 + 0.385795952609750664177596760720790220 i":
+float: 1
+ifloat: 1
+ldouble: 2
+ildouble: 2
+Test "Imaginary part of: ctanh (47 + 1 i) == 1.0 + 2.729321264492904590777293425576722354636e-41 i":
+ldouble: 2
+ildouble: 2
+Test "Imaginary part of: ctanh (0 + 0x3.243f6cp-1 i) == 0.0 - 2.287733242885645987394874673945769518150e7 i":
+float: 1
+ifloat: 1
+Test "Imaginary part of: ctanh (1 + 0x1p1023 i) == 0.8786063118883068695462540226219865087189 - 0.2254627924997545057926782581695274244229 i":
+double: 1
+idouble: 1
+Test "Real part of: ctanh (1 + 0x1p127 i) == 0.9101334047676183761532873794426475906201 + 0.2446359391192790896381501310437708987204 i":
+float: 1
+ifloat: 1
+double: 1
+idouble: 1
+Test "Imaginary part of: ctanh (1 + 0x1p127 i) == 0.9101334047676183761532873794426475906201 + 0.2446359391192790896381501310437708987204 i":
+float: 1
+ifloat: 1
+double: 1
 
 # erf
 Test "erf (1.25) == 0.922900128256458230136523481197281140":
@@ -2309,12 +2366,16 @@ ildouble: 1
 ldouble: 1
 
 Function: Real part of "ctan":
+float: 1
+ifloat: 1
 double: 1
 idouble: 1
-ildouble: 1
-ldouble: 1
+ildouble: 2
+ldouble: 2
 
 Function: Imaginary part of "ctan":
+float: 1
+ifloat: 1
 double: 1
 idouble: 1
 ildouble: 1
@@ -2325,14 +2386,16 @@ double: 1
 float: 2
 idouble: 1
 ifloat: 2
-ildouble: 1
-ldouble: 1
+ildouble: 3
+ldouble: 3
 
 Function: Imaginary part of "ctanh":
 float: 1
 ifloat: 1
-ildouble: 1
-ldouble: 1
+double: 1
+idouble: 1
+ildouble: 2
+ldouble: 2
 
 Function: "erf":
 double: 1