Fix ctan, ctanh of subnormals in round-upwards mode (bug 14328).

IBM long double fixes and POWER ulps update.

3 files changed, 324 insertions, 23 deletions

diff --git a/sysdeps/ieee754/ldbl-128ibm/s_ctanhl.c b/sysdeps/ieee754/ldbl-128ibm/s_ctanhl.c
index 2ab80a2246..e11ce56781 100644
--- a/sysdeps/ieee754/ldbl-128ibm/s_ctanhl.c
+++ b/sysdeps/ieee754/ldbl-128ibm/s_ctanhl.c
@@ -25,6 +25,8 @@
 
 #include <math_private.h>
 
+/* IBM long double GCC builtin sets LDBL_EPSILON == LDBL_DENORM_MIN  */
+static const long double ldbl_eps =  0x1p-106L;
 
 __complex__ long double
 __ctanhl (__complex__ long double x)
@@ -35,8 +37,8 @@ __ctanhl (__complex__ long double x)
     {
       if (__isinfl (__real__ x))
 	{
-	  __real__ res = __copysignl (1.0, __real__ x);
-	  __imag__ res = __copysignl (0.0, __imag__ x);
+	  __real__ res = __copysignl (1.0L, __real__ x);
+	  __imag__ res = __copysignl (0.0L, __imag__ x);
 	}
       else if (__imag__ x == 0.0)
 	{
@@ -57,7 +59,7 @@ __ctanhl (__complex__ long double x)
     {
       long double sinix, cosix;
       long double den;
-      const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l / 2);
+      const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l / 2.0L);
 
       /* 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).  */
@@ -71,7 +73,7 @@ __ctanhl (__complex__ long double x)
 	     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);
+	  __real__ res = __copysignl (1.0L, __real__ x);
 	  __imag__ res = 4 * sinix * cosix;
 	  __real__ x = fabsl (__real__ x);
 	  __real__ x -= t;
@@ -83,22 +85,34 @@ __ctanhl (__complex__ long double x)
 	      __imag__ res /= exp_2t;
 	    }
 	  else
-	    __imag__ res /= __ieee754_expl (2 * __real__ x);
+	    __imag__ res /= __ieee754_expl (2.0L * __real__ x);
 	}
       else
 	{
-	  long double sinhrx = __ieee754_sinhl (__real__ x);
-	  long double coshrx = __ieee754_coshl (__real__ x);
+	  long double sinhrx, coshrx;
+	  if (fabs (__real__ x) > LDBL_MIN)
+	    {
+	      sinhrx = __ieee754_sinhl (__real__ x);
+	      coshrx = __ieee754_coshl (__real__ x);
+	    }
+	  else
+	    {
+	      sinhrx = __real__ x;
+	      coshrx = 1.0L;
+	    }
 
-	  den = sinhrx * sinhrx + cosix * cosix;
-	  __real__ res = sinhrx * coshrx / den;
-	  __imag__ res = sinix * cosix / den;
+	  if (fabsl (sinhrx) > fabsl (cosix) * ldbl_eps)
+	    den = sinhrx * sinhrx + cosix * cosix;
+	  else
+	    den = 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))
+      if ((__real__ res == 0.0L) && (__real__ x == 0.0L))
         __real__ res = __real__ x;
 
-      if ((__real__ res == 0.0) && (__imag__ x == 0.0))
+      if ((__real__ res == 0.0L) && (__imag__ x == 0.0L))
         __imag__ res = __imag__ x;
     }
 
diff --git a/sysdeps/ieee754/ldbl-128ibm/s_ctanl.c b/sysdeps/ieee754/ldbl-128ibm/s_ctanl.c
index 9d89bbe311..34a370a308 100644
--- a/sysdeps/ieee754/ldbl-128ibm/s_ctanl.c
+++ b/sysdeps/ieee754/ldbl-128ibm/s_ctanl.c
@@ -25,6 +25,8 @@
 
 #include <math_private.h>
 
+/* IBM long double GCC builtin sets LDBL_EPSILON == LDBL_DENORM_MIN  */
+static const long double ldbl_eps = 0x1p-106L;
 
 __complex__ long double
 __ctanl (__complex__ long double x)
@@ -55,7 +57,7 @@ __ctanl (__complex__ long double x)
     {
       long double sinrx, cosrx;
       long double den;
-      const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l / 2);
+      const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l / 2.0L);
 
       /* 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). */
@@ -70,7 +72,7 @@ __ctanl (__complex__ long double x)
 	    sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y).  */
 	  long double exp_2t = __ieee754_expl (2 * t);
 
-	  __imag__ res = __copysignl (1.0, __imag__ x);
+	  __imag__ res = __copysignl (1.0L, __imag__ x);
 	  __real__ res = 4 * sinrx * cosrx;
 	  __imag__ x = fabsl (__imag__ x);
 	  __imag__ x -= t;
@@ -82,23 +84,35 @@ __ctanl (__complex__ long double x)
 	      __real__ res /= exp_2t;
 	    }
 	  else
-	    __real__ res /= __ieee754_expl (2 * __imag__ x);
+	    __real__ res /= __ieee754_expl (2.0L * __imag__ x);
 	}
       else
 	{
-	  long double sinhix = __ieee754_sinhl (__imag__ x);
-	  long double coshix = __ieee754_coshl (__imag__ x);
+	  long double sinhix, coshix;
+	  if (fabsl (__imag__ x) > LDBL_MIN)
+	    {
+	      sinhix = __ieee754_sinhl (__imag__ x);
+	      coshix = __ieee754_coshl (__imag__ x);
+	    }
+	  else
+	    {
+	      sinhix = __imag__ x;
+	      coshix = 1.0L;
+	    }
 
-	  den = cosrx * cosrx + sinhix * sinhix;
-	  __real__ res = sinrx * cosrx / den;
-	  __imag__ res = sinhix * coshix / den;
+	  if (fabsl (sinhix) > fabsl (cosrx) * ldbl_eps)
+	    den = cosrx * cosrx + sinhix * sinhix;
+	  else
+	    den = cosrx * cosrx;
+	  __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))
+      if ((__real__ res == 0.0L) && (__real__ x == 0.0L))
         __real__ res = __real__ x;
 
-      if ((__real__ res == 0.0) && (__imag__ x == 0.0))
+      if ((__real__ res == 0.0L) && (__imag__ x == 0.0L))
         __imag__ res = __imag__ x;
     }
 
diff --git a/sysdeps/powerpc/fpu/libm-test-ulps b/sysdeps/powerpc/fpu/libm-test-ulps
index 66576a52a5..ffb8e3a952 100644
--- a/sysdeps/powerpc/fpu/libm-test-ulps
+++ b/sysdeps/powerpc/fpu/libm-test-ulps
@@ -1336,33 +1336,120 @@ ldouble: 1
 Test "Real part of: ctan (0x1p1023 + 1 i) == -0.2254627924997545057926782581695274244229 + 0.8786063118883068695462540226219865087189 i":
 double: 1
 idouble: 1
+Test "Imaginary part of: ctan (0x1p1023 + 1 i) == -0.2254627924997545057926782581695274244229 + 0.8786063118883068695462540226219865087189 i":
+ildouble: 1
+ldouble: 1
 Test "Real part of: ctan (0x1p127 + 1 i) == 0.2446359391192790896381501310437708987204 + 0.9101334047676183761532873794426475906201 i":
 float: 1
 ifloat: 1
+ildouble: 1
+ldouble: 1
 Test "Imaginary part of: ctan (0x1p127 + 1 i) == 0.2446359391192790896381501310437708987204 + 0.9101334047676183761532873794426475906201 i":
 double: 1
 float: 1
 idouble: 1
 ifloat: 1
+ildouble: 2
+ldouble: 2
 Test "Real part of: ctan (0x3.243f6cp-1 + 0 i) == -2.287733242885645987394874673945769518150e7 + 0.0 i":
 float: 1
 ifloat: 1
+ildouble: 2
+ldouble: 2
 Test "Real part of: ctan (1 + 47 i) == 2.729321264492904590777293425576722354636e-41 + 1.0 i":
 ildouble: 2
 ldouble: 2
 
+# ctan_downward
+Test "Real part of: ctan_downward (0x1.921fb54442d18p+0 + 0x1p-1074 i) == 1.633123935319536975596773704152891653086e16 + 1.317719414943508315995636961402669067843e-291 i":
+ildouble: 3
+ldouble: 3
+Test "Real part of: ctan_downward (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i":
+double: 2
+float: 1
+idouble: 2
+ifloat: 1
+ildouble: 4
+ldouble: 4
+Test "Imaginary part of: ctan_downward (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i":
+float: 1
+ifloat: 1
+ildouble: 10
+ldouble: 10
+
+# ctan_tonearest
+Test "Real part of: ctan_tonearest (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i":
+float: 1
+ifloat: 1
+ildouble: 2
+ldouble: 2
+Test "Imaginary part of: ctan_tonearest (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+# ctan_towardzero
+Test "Real part of: ctan_towardzero (0x1.921fb54442d18p+0 + 0x1p-1074 i) == 1.633123935319536975596773704152891653086e16 + 1.317719414943508315995636961402669067843e-291 i":
+ldouble: 4
+ildouble: 4
+Test "Imaginary part of: ctan_towardzero (0x1.921fb54442d18p+0 + 0x1p-1074 i) == 1.633123935319536975596773704152891653086e16 + 1.317719414943508315995636961402669067843e-291 i":
+ildouble: 13
+ldouble: 13
+Test "Real part of: ctan_towardzero (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i":
+float: 1
+ifloat: 1
+ildouble: 2
+ldouble: 2
+Test "Imaginary part of: ctan_towardzero (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i":
+float: 1
+ifloat: 1
+ildouble: 10
+ldouble: 10
+
+# ctan_upward
+Test "Real part of: ctan_upward (0x1.921fb54442d18p+0 + 0x1p-1074 i) == 1.633123935319536975596773704152891653086e16 + 1.317719414943508315995636961402669067843e-291 i":
+double: 1
+idouble: 1
+ildouble: 6
+ldouble: 6
+Test "Imaginary part of: ctan_upward (0x1.921fb54442d18p+0 + 0x1p-1074 i) == 1.633123935319536975596773704152891653086e16 + 1.317719414943508315995636961402669067843e-291 i":
+ildouble: 10
+ldouble: 10
+Test "Real part of: ctan_upward (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i":
+double: 2
+float: 1
+idouble: 2
+ifloat: 1
+ildouble: 6
+ldouble: 6
+Test "Imaginary part of: ctan_upward (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i":
+double: 1
+float: 2
+idouble: 1
+ifloat: 2
+ildouble: 1
+ldouble: 1
+
 # ctanh
 Test "Real part of: ctanh (-2 - 3 i) == -0.965385879022133124278480269394560686 + 0.988437503832249372031403430350121098e-2 i":
 double: 1
 float: 2
 idouble: 1
 ifloat: 2
+idouble: 2
+ildouble: 2
+ldouble: 2
 Test "Imaginary part of: ctanh (-2 - 3 i) == -0.965385879022133124278480269394560686 + 0.988437503832249372031403430350121098e-2 i":
 double: 1
 idouble: 1
+ildouble: 2
+ldouble: 2
 Test "Imaginary part of: ctanh (0 + 0x3.243f6cp-1 i) == 0.0 - 2.287733242885645987394874673945769518150e7 i":
 float: 1
 ifloat: 1
+ildouble: 2
+ldouble: 2
 Test "Imaginary part of: ctanh (0 + pi/4 i) == 0.0 + 1.0 i":
 double: 1
 float: 1
@@ -1378,22 +1465,100 @@ float: 1
 ifloat: 1
 ildouble: 2
 ldouble: 2
+Test "Real part of: ctanh (1 + 0x1p1023 i) == 0.8786063118883068695462540226219865087189 - 0.2254627924997545057926782581695274244229 i":
+ildouble: 1
+ldouble: 1
 Test "Imaginary part of: ctanh (1 + 0x1p1023 i) == 0.8786063118883068695462540226219865087189 - 0.2254627924997545057926782581695274244229 i":
-double: 1
 idouble: 1
+double: 1
 Test "Real part of: ctanh (1 + 0x1p127 i) == 0.9101334047676183761532873794426475906201 + 0.2446359391192790896381501310437708987204 i":
 double: 1
 float: 1
 idouble: 1
 ifloat: 1
+ildouble: 2
+ldouble: 2
 Test "Imaginary part of: ctanh (1 + 0x1p127 i) == 0.9101334047676183761532873794426475906201 + 0.2446359391192790896381501310437708987204 i":
 double: 1
 float: 1
 ifloat: 1
+ildouble: 1
+ldouble: 1
 Test "Imaginary part of: ctanh (47 + 1 i) == 1.0 + 2.729321264492904590777293425576722354636e-41 i":
 ildouble: 2
 ldouble: 2
 
+# ctanh_downward
+Test "Imaginary part of: ctanh_downward (0x1p-1074 + 0x1.921fb54442d18p+0 i) == 1.317719414943508315995636961402669067843e-291 + 1.633123935319536975596773704152891653086e16 i":
+ildouble: 3
+ldouble: 3
+Test "Real part of: ctanh_downward (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i":
+float: 1
+ifloat: 1
+ildouble: 10
+ldouble: 10
+Test "Imaginary part of: ctanh_downward (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i":
+double: 2
+float: 1
+idouble: 2
+ifloat: 1
+ildouble: 4
+ldouble: 4
+
+# ctanh_tonearest
+Test "Real part of: ctanh_tonearest (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ctanh_tonearest (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i":
+float: 1
+ifloat: 1
+ildouble: 2
+ldouble: 2
+
+# ctanh_towardzero
+Test "Real part of: ctanh_towardzero (0x1p-1074 + 0x1.921fb54442d18p+0 i) == 1.317719414943508315995636961402669067843e-291 + 1.633123935319536975596773704152891653086e16 i":
+ildouble: 13
+ldouble: 13
+Test "Imaginary part of: ctanh_towardzero (0x1p-1074 + 0x1.921fb54442d18p+0 i) == 1.317719414943508315995636961402669067843e-291 + 1.633123935319536975596773704152891653086e16 i":
+ildouble: 4
+ldouble: 4
+Test "Real part of: ctanh_towardzero (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i":
+float: 1
+ifloat: 1
+ildouble: 10
+ldouble: 10
+Test "Imaginary part of: ctanh_towardzero (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i":
+float: 1
+ifloat: 1
+ildouble: 2
+ldouble: 2
+
+# ctanh_upward
+Test "Real part of: ctanh_upward (0x1p-1074 + 0x1.921fb54442d18p+0 i) == 1.317719414943508315995636961402669067843e-291 + 1.633123935319536975596773704152891653086e16 i":
+ildouble: 10
+ldouble: 10
+Test "Imaginary part of: ctanh_upward (0x1p-1074 + 0x1.921fb54442d18p+0 i) == 1.317719414943508315995636961402669067843e-291 + 1.633123935319536975596773704152891653086e16 i":
+double: 1
+idouble: 1
+ildouble: 6
+ldouble: 6
+Test "Real part of: ctanh_upward (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i":
+double: 1
+float: 2
+idouble: 1
+ifloat: 2
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ctanh_upward (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i":
+double: 2
+float: 1
+idouble: 2
+ifloat: 1
+ildouble: 3
+ldouble: 3
+
 # erf
 Test "erf (1.25) == 0.922900128256458230136523481197281140":
 double: 1
@@ -2714,9 +2879,63 @@ double: 1
 float: 1
 idouble: 1
 ifloat: 1
+ildouble: 2
+ldouble: 2
+
+Function: Real part of "ctan_downward":
+double: 2
+float: 1
+idouble: 2
+ifloat: 1
+ildouble: 4
+ldouble: 4
+
+Function: Imaginary part of "ctan_downward":
+float: 1
+ifloat: 1
+ildouble: 10
+ldouble: 10
+
+Function: Real part of "ctan_tonearest":
+float: 1
+ifloat: 1
+ildouble: 2
+ldouble: 2
+
+Function: Imaginary part of "ctan_tonearest":
+float: 1
+ifloat: 1
 ildouble: 1
 ldouble: 1
 
+Function: Real part of "ctan_towardzero":
+float: 1
+ifloat: 1
+ildouble: 4
+ldouble: 4
+
+Function: Imaginary part of "ctan_towardzero":
+float: 1
+ifloat: 1
+ildouble: 13
+ldouble: 13
+
+Function: Real part of "ctan_upward":
+double: 2
+float: 1
+idouble: 2
+ifloat: 1
+ildouble: 6
+ldouble: 6
+
+Function: Imaginary part of "ctan_upward":
+double: 1
+float: 2
+idouble: 1
+ifloat: 2
+ildouble: 10
+ldouble: 10
+
 Function: Real part of "ctanh":
 double: 1
 float: 2
@@ -2733,6 +2952,60 @@ ifloat: 1
 ildouble: 2
 ldouble: 2
 
+Function: Real part of "ctanh_downward":
+float: 1
+ifloat: 1
+ildouble: 10
+ldouble: 10
+
+Function: Imaginary part of "ctanh_downward":
+double: 2
+float: 1
+idouble: 2
+ifloat: 1
+ildouble: 4
+ldouble: 4
+
+Function: Real part of "ctanh_tonearest":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+Function: Imaginary part of "ctanh_tonearest":
+float: 1
+ifloat: 1
+ildouble: 2
+ldouble: 2
+
+Function: Real part of "ctanh_towardzero":
+float: 1
+ifloat: 1
+ildouble: 13
+ldouble: 13
+
+Function: Imaginary part of "ctanh_towardzero":
+float: 1
+ifloat: 1
+ildouble: 4
+ldouble: 4
+
+Function: Real part of "ctanh_upward":
+double: 1
+float: 2
+idouble: 1
+ifloat: 2
+ildouble: 10
+ldouble: 10
+
+Function: Imaginary part of "ctanh_upward":
+double: 2
+float: 1
+idouble: 2
+ifloat: 1
+ildouble: 6
+ldouble: 6
+
 Function: "erf":
 double: 1
 idouble: 1