Fix ctan, ctanh overflow (bug 11521).

7 files changed, 252 insertions, 70 deletions

diff --git a/math/libm-test.inc b/math/libm-test.inc
index 0533483749..a551b9f3f4 100644
--- a/math/libm-test.inc
+++ b/math/libm-test.inc
@@ -2840,6 +2840,36 @@ ctan_test (void)
   TEST_c_c (ctan, 0.75L, 1.25L, 0.160807785916206426725166058173438663L, 0.975363285031235646193581759755216379L);
   TEST_c_c (ctan, -2, -3, 0.376402564150424829275122113032269084e-2L, -1.00323862735360980144635859782192726L);
 
+  TEST_c_c (ctan, 1, 45, 1.490158918874345552942703234806348520895e-39L, 1.000000000000000000000000000000000000001L);
+  TEST_c_c (ctan, 1, 47, 2.729321264492904590777293425576722354636e-41L, 1.0);
+
+#ifndef TEST_FLOAT
+  TEST_c_c (ctan, 1, 355, 8.140551093483276762350406321792653551513e-309L, 1.0);
+  TEST_c_c (ctan, 1, 365, 1.677892637497921890115075995898773550884e-317L, 1.0);
+#endif
+
+#if defined TEST_LDOUBLE && LDBL_MAX_EXP >= 16384
+  TEST_c_c (ctan, 1, 5680, 4.725214596136812019616700920476949798307e-4934L, 1.0);
+  TEST_c_c (ctan, 1, 5690, 9.739393181626937151720816611272607059057e-4943L, 1.0);
+#endif
+
+  TEST_c_c (ctan, 0x3.243f6cp-1, 0, -2.287733242885645987394874673945769518150e7L, 0.0);
+
+  TEST_c_c (ctan, 0x1p127, 1, 0.2446359391192790896381501310437708987204L, 0.9101334047676183761532873794426475906201L);
+
+#ifndef TEST_FLOAT
+  TEST_c_c (ctan, 0x1p1023, 1, -0.2254627924997545057926782581695274244229L, 0.8786063118883068695462540226219865087189L);
+#endif
+
+#if defined TEST_LDOUBLE && LDBL_MAX_EXP >= 16384
+  TEST_c_c (ctan, 0x1p16383L, 1, 0.1608598776370396607204448234354670036772L, 0.8133818522051542536316746743877629761488L);
+#endif
+
+  TEST_c_c (ctan, 50000, 50000, plus_zero, 1.0);
+  TEST_c_c (ctan, 50000, -50000, plus_zero, -1.0);
+  TEST_c_c (ctan, -50000, 50000, minus_zero, 1.0);
+  TEST_c_c (ctan, -50000, -50000, minus_zero, -1.0);
+
   END (ctan, complex);
 }
 
@@ -2899,6 +2929,36 @@ ctanh_test (void)
   TEST_c_c (ctanh, 0.75L, 1.25L, 1.37260757053378320258048606571226857L, 0.385795952609750664177596760720790220L);
   TEST_c_c (ctanh, -2, -3, -0.965385879022133124278480269394560686L, 0.988437503832249372031403430350121098e-2L);
 
+  TEST_c_c (ctanh, 45, 1, 1.000000000000000000000000000000000000001L, 1.490158918874345552942703234806348520895e-39L);
+  TEST_c_c (ctanh, 47, 1, 1.0, 2.729321264492904590777293425576722354636e-41L);
+
+#ifndef TEST_FLOAT
+  TEST_c_c (ctanh, 355, 1, 1.0, 8.140551093483276762350406321792653551513e-309L);
+  TEST_c_c (ctanh, 365, 1, 1.0, 1.677892637497921890115075995898773550884e-317L);
+#endif
+
+#if defined TEST_LDOUBLE && LDBL_MAX_EXP >= 16384
+  TEST_c_c (ctanh, 5680, 1, 1.0, 4.725214596136812019616700920476949798307e-4934L);
+  TEST_c_c (ctanh, 5690, 1, 1.0, 9.739393181626937151720816611272607059057e-4943L);
+#endif
+
+  TEST_c_c (ctanh, 0, 0x3.243f6cp-1, 0.0, -2.287733242885645987394874673945769518150e7L);
+
+  TEST_c_c (ctanh, 1, 0x1p127, 0.9101334047676183761532873794426475906201L, 0.2446359391192790896381501310437708987204L);
+
+#ifndef TEST_FLOAT
+  TEST_c_c (ctanh, 1, 0x1p1023, 0.8786063118883068695462540226219865087189L, -0.2254627924997545057926782581695274244229L);
+#endif
+
+#if defined TEST_LDOUBLE && LDBL_MAX_EXP >= 16384
+  TEST_c_c (ctanh, 1, 0x1p16383L, 0.8133818522051542536316746743877629761488L, 0.1608598776370396607204448234354670036772L);
+#endif
+
+  TEST_c_c (ctanh, 50000, 50000, 1.0, plus_zero);
+  TEST_c_c (ctanh, 50000, -50000, 1.0, minus_zero);
+  TEST_c_c (ctanh, -50000, 50000, -1.0, plus_zero);
+  TEST_c_c (ctanh, -50000, -50000, -1.0, minus_zero);
+
   END (ctanh, complex);
 }
 
diff --git a/math/s_ctan.c b/math/s_ctan.c
index c838fadebb..78117b3103 100644
--- a/math/s_ctan.c
+++ b/math/s_ctan.c
@@ -1,5 +1,5 @@
 /* Complex tangent function for double.
-   Copyright (C) 1997, 2005, 2011 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.
 
@@ -20,9 +20,8 @@
 #include <complex.h>
 #include <fenv.h>
 #include <math.h>
-
 #include <math_private.h>
-
+#include <float.h>
 
 __complex__ double
 __ctan (__complex__ double x)
@@ -51,24 +50,45 @@ __ctan (__complex__ double x)
     }
   else
     {
-      double sin2rx, cos2rx;
+      double sinrx, cosrx;
       double den;
+      const int t = (int) ((DBL_MAX_EXP - 1) * M_LN2 / 2);
 
-      __sincos (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_cosh (2.0 * __imag__ x);
+      __sincos (__real__ x, &sinrx, &cosrx);
 
-      if (den == 0.0)
+      if (fabs (__imag__ x) > t)
 	{
-	  __complex__ double ez = __cexp (1.0i * x);
-	  __complex__ double emz = __cexp (-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).  */
+	  double exp_2t = __ieee754_exp (2 * t);
 
-	  res = (ez - emz) / (ez + emz) * -1.0i;
+	  __imag__ res = __copysign (1.0, __imag__ x);
+	  __real__ res = 4 * sinrx * cosrx;
+	  __imag__ x = fabs (__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_exp (2 * __imag__ x);
 	}
       else
 	{
-	  __real__ res = sin2rx / den;
-	  __imag__ res = __ieee754_sinh (2.0 * __imag__ x) / den;
+	  double sinhix = __ieee754_sinh (__imag__ x);
+	  double coshix = __ieee754_cosh (__imag__ x);
+
+	  den = cosrx * cosrx + sinhix * sinhix;
+	  __real__ res = sinrx * cosrx / den;
+	  __imag__ res = sinhix * coshix / den;
 	}
     }
 
diff --git a/math/s_ctanf.c b/math/s_ctanf.c
index 5f7f28ad07..4cba559a44 100644
--- a/math/s_ctanf.c
+++ b/math/s_ctanf.c
@@ -1,5 +1,5 @@
 /* Complex tangent function for float.
-   Copyright (C) 1997, 2005, 2011 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.
 
@@ -21,7 +21,7 @@
 #include <fenv.h>
 #include <math.h>
 #include <math_private.h>
-
+#include <float.h>
 
 __complex__ float
 __ctanf (__complex__ float x)
@@ -50,25 +50,45 @@ __ctanf (__complex__ float x)
     }
   else
     {
-      float sin2rx, cos2rx;
+      float sinrx, cosrx;
       float den;
+      const int t = (int) ((FLT_MAX_EXP - 1) * M_LN2 / 2);
 
-      __sincosf (2.0 * __real__ x, &sin2rx, &cos2rx);
-
-      den = cos2rx + __ieee754_coshf (2.0 * __imag__ x);
+      /* 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). */
 
+      __sincosf (__real__ x, &sinrx, &cosrx);
 
-      if (den == 0.0)
+      if (fabsf (__imag__ x) > t)
 	{
-	  __complex__ float ez = __cexpf (1.0i * x);
-	  __complex__ float emz = __cexpf (-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).  */
+	  float exp_2t = __ieee754_expf (2 * t);
 
-	  res = (ez - emz) / (ez + emz) * -1.0i;
+	  __imag__ res = __copysignf (1.0, __imag__ x);
+	  __real__ res = 4 * sinrx * cosrx;
+	  __imag__ x = fabsf (__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_expf (2 * __imag__ x);
 	}
       else
 	{
-	  __real__ res = sin2rx / den;
-	  __imag__ res = __ieee754_sinhf (2.0 * __imag__ x) / den;
+	  float sinhix = __ieee754_sinhf (__imag__ x);
+	  float coshix = __ieee754_coshf (__imag__ x);
+
+	  den = cosrx * cosrx + sinhix * sinhix;
+	  __real__ res = sinrx * cosrx / den;
+	  __imag__ res = sinhix * coshix / den;
 	}
     }
 
diff --git a/math/s_ctanh.c b/math/s_ctanh.c
index 9cecb8bdb7..201871e7ec 100644
--- a/math/s_ctanh.c
+++ b/math/s_ctanh.c
@@ -1,5 +1,5 @@
 /* Complex hyperbole tangent for double.
-   Copyright (C) 1997, 2005, 2011 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.
 
@@ -21,7 +21,7 @@
 #include <fenv.h>
 #include <math.h>
 #include <math_private.h>
-
+#include <float.h>
 
 __complex__ double
 __ctanh (__complex__ double x)
@@ -50,24 +50,45 @@ __ctanh (__complex__ double x)
     }
   else
     {
-      double sin2ix, cos2ix;
+      double sinix, cosix;
       double den;
+      const int t = (int) ((DBL_MAX_EXP - 1) * M_LN2 / 2);
 
-      __sincos (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_cosh (2.0 * __real__ x) + cos2ix);
+      __sincos (__imag__ x, &sinix, &cosix);
 
-      if (den == 0.0)
+      if (fabs (__real__ x) > t)
 	{
-	  __complex__ double ez = __cexp (x);
-	  __complex__ double emz = __cexp (-x);
+	  /* 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).  */
+	  double exp_2t = __ieee754_exp (2 * t);
 
-	  res = (ez - emz) / (ez + emz);
+	  __real__ res = __copysign (1.0, __real__ x);
+	  __imag__ res = 4 * sinix * cosix;
+	  __real__ x = fabs (__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_exp (2 * __real__ x);
 	}
       else
 	{
-	  __real__ res = __ieee754_sinh (2.0 * __real__ x) / den;
-	  __imag__ res = sin2ix / den;
+	  double sinhrx = __ieee754_sinh (__real__ x);
+	  double coshrx = __ieee754_cosh (__real__ x);
+
+	  den = sinhrx * sinhrx + cosix * cosix;
+	  __real__ res = sinhrx * coshrx / den;
+	  __imag__ res = sinix * cosix / den;
 	}
     }
 
diff --git a/math/s_ctanhf.c b/math/s_ctanhf.c
index fce5aaf290..e505155774 100644
--- a/math/s_ctanhf.c
+++ b/math/s_ctanhf.c
@@ -1,5 +1,5 @@
 /* Complex hyperbole tangent for float.
-   Copyright (C) 1997, 2005, 2011 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.
 
@@ -21,7 +21,7 @@
 #include <fenv.h>
 #include <math.h>
 #include <math_private.h>
-
+#include <float.h>
 
 __complex__ float
 __ctanhf (__complex__ float x)
@@ -50,24 +50,45 @@ __ctanhf (__complex__ float x)
     }
   else
     {
-      float sin2ix, cos2ix;
+      float sinix, cosix;
       float den;
+      const int t = (int) ((FLT_MAX_EXP - 1) * M_LN2 / 2);
 
-      __sincosf (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_coshf (2.0 * __real__ x) + cos2ix);
+      __sincosf (__imag__ x, &sinix, &cosix);
 
-      if (den == 0.0f)
+      if (fabsf (__real__ x) > t)
 	{
-	  __complex__ float ez = __cexpf (x);
-	  __complex__ float emz = __cexpf (-x);
+	  /* 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).  */
+	  float exp_2t = __ieee754_expf (2 * t);
 
-	  res = (ez - emz) / (ez + emz);
+	  __real__ res = __copysignf (1.0, __real__ x);
+	  __imag__ res = 4 * sinix * cosix;
+	  __real__ x = fabsf (__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_expf (2 * __real__ x);
 	}
       else
 	{
-	  __real__ res = __ieee754_sinhf (2.0 * __real__ x) / den;
-	  __imag__ res = sin2ix / den;
+	  float sinhrx = __ieee754_sinhf (__real__ x);
+	  float coshrx = __ieee754_coshf (__real__ x);
+
+	  den = sinhrx * sinhrx + cosix * cosix;
+	  __real__ res = sinhrx * coshrx / den;
+	  __imag__ res = sinix * cosix / den;
 	}
     }
 
diff --git a/math/s_ctanhl.c b/math/s_ctanhl.c
index d22e13a975..e5d677903f 100644
--- a/math/s_ctanhl.c
+++ b/math/s_ctanhl.c
@@ -1,5 +1,5 @@
 /* Complex hyperbole tangent for long double.
-   Copyright (C) 1997, 2005, 2011 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.
 
@@ -21,7 +21,7 @@
 #include <fenv.h>
 #include <math.h>
 #include <math_private.h>
-
+#include <float.h>
 
 __complex__ long double
 __ctanhl (__complex__ long double x)
@@ -50,24 +50,45 @@ __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);
+	  /* 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);
 
-	  res = (ez - emz) / (ez + emz);
+	  __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;
 	}
     }
 
diff --git a/math/s_ctanl.c b/math/s_ctanl.c
index 112dd723d8..12d700cad9 100644
--- a/math/s_ctanl.c
+++ b/math/s_ctanl.c
@@ -1,5 +1,5 @@
 /* Complex tangent function for long double.
-   Copyright (C) 1997, 2005, 2011 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.
 
@@ -20,9 +20,8 @@
 #include <complex.h>
 #include <fenv.h>
 #include <math.h>
-
 #include <math_private.h>
-
+#include <float.h>
 
 __complex__ long double
 __ctanl (__complex__ long double x)
@@ -51,25 +50,45 @@ __ctanl (__complex__ long double x)
     }
   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);
-
-      den = cos2rx + __ieee754_coshl (2.0 * __imag__ x);
+      /* 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). */
 
+      __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;
 	}
     }