Fix atan / atan2 missing underflows (bug 15319).

This patch fixes bug 15319, missing underflows from atan / atan2 when
the result of atan is very close to its small argument (or that of
atan2 is very close to the ratio of its arguments, which may be an
exact division).

The usual approach of doing an underflowing computation if the
computed result is subnormal is followed.  For 32-bit x86, there are
extra complications: the inline __ieee754_atan2 in bits/mathinline.h
needs to be disabled for float and double because other libm functions
using it generally rely on getting proper underflow exceptions from
it, while the out-of-line functions have to remove excess range and
precision from the underflowing result so as to return an exact 0 in
the case where errno should be set for underflow to 0.  (The failures
I saw without that are similar to those Carlos reported for other
functions, where I haven't seen a response to
<https://sourceware.org/ml/libc-alpha/2015-01/msg00485.html>
confirming if my diagnosis is correct.  Arguably all libm functions
with float and double returns should remove excess range and
precision, but that's a separate matter.)

The x86_64 long double case reported in a comment in bug 15319 is not
a bug (it's an argument of LDBL_MIN, and x86_64 is an after-rounding
architecture so the correct IEEE result is not to raise underflow in
the given rounding mode, in addition to treating the result as an
exact LDBL_MIN being within the newly clarified documentation of
accuracy goals).  I'm presuming that the fpatan instruction can be
trusted to raise appropriate exceptions when the (long double) result
underflows (after rounding) and so no changes are needed for x86 /
x86_64 long double functions here; empirically this is the case for
the cases covered in the testsuite, on my system.

Tested for x86_64, x86, powerpc and mips64.  Only 32-bit x86 needs
ulps updates (for the changes to inlines meaning some functions no
longer get excess precision from their __ieee754_atan2* calls).

	[BZ #15319]
	* sysdeps/i386/fpu/e_atan2.S (dbl_min): New object.
	(MO): New macro.
	(__ieee754_atan2): For results with small absolute value, force
	underflow exception and remove excess range and precision from
	return value.
	* sysdeps/i386/fpu/e_atan2f.S (flt_min): New object.
	(MO): New macro.
	(__ieee754_atan2f): For results with small absolute value, force
	underflow exception and remove excess range and precision from
	return value.
	* sysdeps/i386/fpu/s_atan.S (dbl_min): New object.
	(MO): New macro.
	(__atan): For results with small absolute value, force underflow
	exception and remove excess range and precision from return value.
	* sysdeps/i386/fpu/s_atanf.S (flt_min): New object.
	(MO): New macro.
	(__atanf): For results with small absolute value, force underflow
	exception and remove excess range and precision from return value.
	* sysdeps/ieee754/dbl-64/e_atan2.c: Include <float.h> and
	<math.h>.
	(__ieee754_atan2): Force underflow exception for results with
	small absolute value.
	* sysdeps/ieee754/dbl-64/s_atan.c: Include <float.h> and
	<math_private.h>.
	(atan): Force underflow exception for results with small absolute
	value.
	* sysdeps/ieee754/flt-32/s_atanf.c: Include <float.h>.
	(__atanf): Force underflow exception for results with small
	absolute value.
	* sysdeps/ieee754/ldbl-128/s_atanl.c: Include <float.h> and
	<math.h>.
	(__atanl): Force underflow exception for results with small
	absolute value.
	* sysdeps/ieee754/ldbl-128ibm/s_atanl.c: Include <float.h>.
	(__atanl): Force underflow exception for results with small
	absolute value.
	* sysdeps/x86/fpu/bits/mathinline.h
	[!__SSE2_MATH__ && !__x86_64__ && __LIBC_INTERNAL_MATH_INLINES]
	(__ieee754_atan2): Only define inline for long double.
	* sysdeps/x86_64/fpu/multiarch/e_atan2.c
	[HAVE_FMA4_SUPPORT || HAVE_AVX_SUPPORT]: Include <math.h>.
	* math/auto-libm-test-in: Do not mark underflow exceptions as
	possibly missing for bug 15319.  Add more tests of atan2.
	* math/auto-libm-test-out: Regenerated.
	* math/libm-test.inc (casin_test_data): Do not mark underflow
	exceptions as possibly missing for bug 15319.
	(casinh_test_data): Likewise.
	* sysdeps/i386/fpu/libm-test-ulps: Update.

12 files changed, 192 insertions, 25 deletions

diff --git a/sysdeps/i386/fpu/e_atan2.S b/sysdeps/i386/fpu/e_atan2.S
index e76f8e2a78..6f5481fb5c 100644
--- a/sysdeps/i386/fpu/e_atan2.S
+++ b/sysdeps/i386/fpu/e_atan2.S
@@ -7,10 +7,43 @@
 
 RCSID("$NetBSD: e_atan2.S,v 1.4 1995/05/08 23:46:28 jtc Exp $")
 
+	.section .rodata.cst8,"aM",@progbits,8
+
+	.p2align 3
+	.type dbl_min,@object
+dbl_min:	.byte 0, 0, 0, 0, 0, 0, 0x10, 0
+	ASM_SIZE_DIRECTIVE(dbl_min)
+
+#ifdef PIC
+# define MO(op) op##@GOTOFF(%ecx)
+#else
+# define MO(op) op
+#endif
+
+	.text
 ENTRY(__ieee754_atan2)
+#ifdef  PIC
+	LOAD_PIC_REG (cx)
+#endif
 	fldl	 4(%esp)
 	fldl	12(%esp)
 	fpatan
-	ret
+	fldl	MO(dbl_min)
+	fld	%st(1)
+	fabs
+	fucompp
+	fnstsw
+	sahf
+	jnc 1f
+	subl	$8, %esp
+	cfi_adjust_cfa_offset (8)
+	fld	%st(0)
+	fmul	%st(0)
+	fstpl	(%esp)
+	fstpl	(%esp)
+	fldl	(%esp)
+	addl	$8, %esp
+	cfi_adjust_cfa_offset (-8)
+1:	ret
 END (__ieee754_atan2)
 strong_alias (__ieee754_atan2, __atan2_finite)
diff --git a/sysdeps/i386/fpu/e_atan2f.S b/sysdeps/i386/fpu/e_atan2f.S
index 9ffa6373be..ec0eb3fd71 100644
--- a/sysdeps/i386/fpu/e_atan2f.S
+++ b/sysdeps/i386/fpu/e_atan2f.S
@@ -7,10 +7,43 @@
 
 RCSID("$NetBSD: e_atan2f.S,v 1.1 1995/05/08 23:35:10 jtc Exp $")
 
+	.section .rodata.cst4,"aM",@progbits,4
+
+	.p2align 2
+	.type flt_min,@object
+flt_min:	.byte 0, 0, 0x80, 0
+	ASM_SIZE_DIRECTIVE(flt_min)
+
+#ifdef PIC
+# define MO(op) op##@GOTOFF(%ecx)
+#else
+# define MO(op) op
+#endif
+
+	.text
 ENTRY(__ieee754_atan2f)
+#ifdef  PIC
+	LOAD_PIC_REG (cx)
+#endif
 	flds	4(%esp)
 	flds	8(%esp)
 	fpatan
-	ret
+	flds	MO(flt_min)
+	fld	%st(1)
+	fabs
+	fucompp
+	fnstsw
+	sahf
+	jnc 1f
+	subl	$4, %esp
+	cfi_adjust_cfa_offset (4)
+	fld	%st(0)
+	fmul	%st(0)
+	fstps	(%esp)
+	fstps	(%esp)
+	flds	(%esp)
+	addl	$4, %esp
+	cfi_adjust_cfa_offset (-4)
+1:	ret
 END (__ieee754_atan2f)
 strong_alias (__ieee754_atan2f, __atan2f_finite)
diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps
index a408a82615..5e79307f30 100644
--- a/sysdeps/i386/fpu/libm-test-ulps
+++ b/sysdeps/i386/fpu/libm-test-ulps
@@ -324,10 +324,10 @@ ildouble: 2
 ldouble: 2
 
 Function: Real part of "casin_downward":
-double: 1
-float: 1
-idouble: 1
-ifloat: 1
+double: 2
+float: 2
+idouble: 2
+ifloat: 2
 ildouble: 2
 ldouble: 2
 
@@ -357,9 +357,9 @@ ldouble: 5
 
 Function: Real part of "casin_upward":
 double: 2
-float: 1
+float: 2
 idouble: 2
-ifloat: 1
+ifloat: 2
 ildouble: 2
 ldouble: 2
 
@@ -396,10 +396,10 @@ ildouble: 5
 ldouble: 5
 
 Function: Imaginary part of "casinh_downward":
-double: 1
-float: 1
-idouble: 1
-ifloat: 1
+double: 2
+float: 2
+idouble: 2
+ifloat: 2
 ildouble: 2
 ldouble: 2
 
@@ -429,9 +429,9 @@ ldouble: 5
 
 Function: Imaginary part of "casinh_upward":
 double: 2
-float: 1
+float: 2
 idouble: 2
-ifloat: 1
+ifloat: 2
 ildouble: 2
 ldouble: 2
 
diff --git a/sysdeps/i386/fpu/s_atan.S b/sysdeps/i386/fpu/s_atan.S
index 7502f6d828..c28b73ce75 100644
--- a/sysdeps/i386/fpu/s_atan.S
+++ b/sysdeps/i386/fpu/s_atan.S
@@ -7,10 +7,41 @@
 
 RCSID("$NetBSD: s_atan.S,v 1.4 1995/05/08 23:50:41 jtc Exp $")
 
+	.section .rodata.cst8,"aM",@progbits,8
+
+	.p2align 3
+	.type dbl_min,@object
+dbl_min:	.byte 0, 0, 0, 0, 0, 0, 0x10, 0
+	ASM_SIZE_DIRECTIVE(dbl_min)
+
+#ifdef PIC
+# define MO(op) op##@GOTOFF(%ecx)
+#else
+# define MO(op) op
+#endif
+
+	.text
 ENTRY(__atan)
+#ifdef  PIC
+	LOAD_PIC_REG (cx)
+#endif
 	fldl	4(%esp)
 	fld1
 	fpatan
-	ret
+	fldl	MO(dbl_min)
+	fld	%st(1)
+	fabs
+	fucompp
+	fnstsw
+	sahf
+	jnc 1f
+	subl	$8, %esp
+	cfi_adjust_cfa_offset (8)
+	fld	%st(0)
+	fmul	%st(0)
+	fstpl	(%esp)
+	addl	$8, %esp
+	cfi_adjust_cfa_offset (-8)
+1:	ret
 END (__atan)
 weak_alias (__atan, atan)
diff --git a/sysdeps/i386/fpu/s_atanf.S b/sysdeps/i386/fpu/s_atanf.S
index 70232c8240..da3c2a64b5 100644
--- a/sysdeps/i386/fpu/s_atanf.S
+++ b/sysdeps/i386/fpu/s_atanf.S
@@ -7,10 +7,41 @@
 
 RCSID("$NetBSD: s_atanf.S,v 1.3 1995/05/08 23:51:33 jtc Exp $")
 
+	.section .rodata.cst4,"aM",@progbits,4
+
+	.p2align 2
+	.type flt_min,@object
+flt_min:	.byte 0, 0, 0x80, 0
+	ASM_SIZE_DIRECTIVE(flt_min)
+
+#ifdef PIC
+# define MO(op) op##@GOTOFF(%ecx)
+#else
+# define MO(op) op
+#endif
+
+	.text
 ENTRY(__atanf)
+#ifdef  PIC
+	LOAD_PIC_REG (cx)
+#endif
 	flds	4(%esp)
 	fld1
 	fpatan
-	ret
+	flds	MO(flt_min)
+	fld	%st(1)
+	fabs
+	fucompp
+	fnstsw
+	sahf
+	jnc 1f
+	subl	$4, %esp
+	cfi_adjust_cfa_offset (4)
+	fld	%st(0)
+	fmul	%st(0)
+	fstps	(%esp)
+	addl	$4, %esp
+	cfi_adjust_cfa_offset (-4)
+1:	ret
 END (__atanf)
 weak_alias (__atanf, atanf)
diff --git a/sysdeps/ieee754/dbl-64/e_atan2.c b/sysdeps/ieee754/dbl-64/e_atan2.c
index 425da22719..a03ce3e4a6 100644
--- a/sysdeps/ieee754/dbl-64/e_atan2.c
+++ b/sysdeps/ieee754/dbl-64/e_atan2.c
@@ -41,6 +41,8 @@
 #include "MathLib.h"
 #include "uatan.tbl"
 #include "atnat2.h"
+#include <float.h>
+#include <math.h>
 #include <math_private.h>
 #include <stap-probe.h>
 
@@ -202,10 +204,18 @@ __ieee754_atan2 (double y, double x)
     {
       if (x > 0)
 	{
+	  double ret;
 	  if ((z = ay / ax) < TWOM1022)
-	    return normalized (ax, ay, y, z);
+	    ret = normalized (ax, ay, y, z);
 	  else
-	    return signArctan2 (y, z);
+	    ret = signArctan2 (y, z);
+	  if (fabs (ret) < DBL_MIN)
+	    {
+	      double vret = ret ? ret : DBL_MIN;
+	      double force_underflow = vret * vret;
+	      math_force_eval (force_underflow);
+	    }
+	  return ret;
 	}
       else
 	{
diff --git a/sysdeps/ieee754/dbl-64/s_atan.c b/sysdeps/ieee754/dbl-64/s_atan.c
index a482badc56..7b598f14a9 100644
--- a/sysdeps/ieee754/dbl-64/s_atan.c
+++ b/sysdeps/ieee754/dbl-64/s_atan.c
@@ -41,7 +41,9 @@
 #include "MathLib.h"
 #include "uatan.tbl"
 #include "atnat.h"
+#include <float.h>
 #include <math.h>
+#include <math_private.h>
 #include <stap-probe.h>
 
 void __mpatan (mp_no *, mp_no *, int);	/* see definition in mpatan.c */
@@ -85,7 +87,14 @@ atan (double x)
       if (u < B)
 	{
 	  if (u < A)
-	    return x;
+	    {
+	      if (u < DBL_MIN)
+		{
+		  double force_underflow = x * x;
+		  math_force_eval (force_underflow);
+		}
+	      return x;
+	    }
 	  else
 	    {			/* A <= u < B */
 	      v = x * x;
diff --git a/sysdeps/ieee754/flt-32/s_atanf.c b/sysdeps/ieee754/flt-32/s_atanf.c
index 02c5e46287..159391894f 100644
--- a/sysdeps/ieee754/flt-32/s_atanf.c
+++ b/sysdeps/ieee754/flt-32/s_atanf.c
@@ -17,6 +17,7 @@
 static char rcsid[] = "$NetBSD: s_atanf.c,v 1.4 1995/05/10 20:46:47 jtc Exp $";
 #endif
 
+#include <float.h>
 #include <math.h>
 #include <math_private.h>
 
@@ -66,6 +67,11 @@ float __atanf(float x)
 	    else     return -atanhi[3]-atanlo[3];
 	} if (ix < 0x3ee00000) {	/* |x| < 0.4375 */
 	    if (ix < 0x31000000) {	/* |x| < 2^-29 */
+		if (fabsf (x) < FLT_MIN)
+		  {
+		    float force_underflow = x * x;
+		    math_force_eval (force_underflow);
+		  }
 		if(huge+x>one) return x;	/* raise inexact */
 	    }
 	    id = -1;
diff --git a/sysdeps/ieee754/ldbl-128/s_atanl.c b/sysdeps/ieee754/ldbl-128/s_atanl.c
index dc5e7ef462..1367b6b15d 100644
--- a/sysdeps/ieee754/ldbl-128/s_atanl.c
+++ b/sysdeps/ieee754/ldbl-128/s_atanl.c
@@ -59,6 +59,8 @@
     <http://www.gnu.org/licenses/>.  */
 
 
+#include <float.h>
+#include <math.h>
 #include <math_private.h>
 
 /* arctan(k/8), k = 0, ..., 82 */
@@ -200,6 +202,11 @@ __atanl (long double x)
 
   if (k <= 0x3fc50000) /* |x| < 2**-58 */
     {
+      if (fabsl (x) < LDBL_MIN)
+	{
+	  long double force_underflow = x * x;
+	  math_force_eval (force_underflow);
+	}
       /* Raise inexact. */
       if (huge + x > 0.0)
 	return x;
diff --git a/sysdeps/ieee754/ldbl-128ibm/s_atanl.c b/sysdeps/ieee754/ldbl-128ibm/s_atanl.c
index 41dde23998..6ddf4b1c5e 100644
--- a/sysdeps/ieee754/ldbl-128ibm/s_atanl.c
+++ b/sysdeps/ieee754/ldbl-128ibm/s_atanl.c
@@ -59,6 +59,7 @@
     <http://www.gnu.org/licenses/>.  */
 
 
+#include <float.h>
 #include <math.h>
 #include <math_private.h>
 #include <math_ldbl_opt.h>
@@ -198,6 +199,11 @@ __atanl (long double x)
 
   if (k <= 0x3c800000) /* |x| <= 2**-55.  */
     {
+      if (fabsl (x) < LDBL_MIN)
+	{
+	  long double force_underflow = x * x;
+	  math_force_eval (force_underflow);
+	}
       /* Raise inexact.  */
       if (1e300L + x > 0.0)
 	return x;
diff --git a/sysdeps/x86/fpu/bits/mathinline.h b/sysdeps/x86/fpu/bits/mathinline.h
index 6a7489114c..c87300f7b8 100644
--- a/sysdeps/x86/fpu/bits/mathinline.h
+++ b/sysdeps/x86/fpu/bits/mathinline.h
@@ -965,12 +965,12 @@ __NTH (__finite (double __x))
 /* This code is used internally in the GNU libc.  */
 # ifdef __LIBC_INTERNAL_MATH_INLINES
 __inline_mathop (__ieee754_sqrt, "fsqrt")
-__inline_mathcode2 (__ieee754_atan2, __y, __x,
-		    register long double __value;
-		    __asm __volatile__ ("fpatan\n\t"
-					: "=t" (__value)
-					: "0" (__x), "u" (__y) : "st(1)");
-		    return __value;)
+__inline_mathcode2_ (long double, __ieee754_atan2l, __y, __x,
+		     register long double __value;
+		     __asm __volatile__ ("fpatan\n\t"
+					 : "=t" (__value)
+					 : "0" (__x), "u" (__y) : "st(1)");
+		     return __value;)
 # endif
 
 #endif /* !__SSE2_MATH__ && !__x86_64__ */
diff --git a/sysdeps/x86_64/fpu/multiarch/e_atan2.c b/sysdeps/x86_64/fpu/multiarch/e_atan2.c
index 6867c6e64e..547681cb59 100644
--- a/sysdeps/x86_64/fpu/multiarch/e_atan2.c
+++ b/sysdeps/x86_64/fpu/multiarch/e_atan2.c
@@ -1,5 +1,6 @@
 #if defined HAVE_FMA4_SUPPORT || defined HAVE_AVX_SUPPORT
 # include <init-arch.h>
+# include <math.h>
 # include <math_private.h>
 
 extern double __ieee754_atan2_sse2 (double, double);