Fix yn overflow handling in non-default rounding modes (bug 16561, bug 16562).

This patch fixes bugs 16561 and 16562, bad results of yn in overflow
cases in non-default rounding modes, both because an intermediate
overflow in the recurrence does not get detected if the result is not
an infinity and because an overflowing result may occur in the wrong
sign.  The fix is to set FE_TONEAREST mode internally for the parts of
the function where such overflows can occur (which includes the call
to y1 - where yn is used to compute a Bessel function of order -1,
negating the result of y1 isn't correct for overflowing results in
directed rounding modes) and then compute an overflowing value in the
original rounding mode if the to-nearest result was an infinity.

Tested x86_64 and x86 and ulps updated accordingly.  Also tested for
mips64 and powerpc32 to test the ldbl-128 and ldbl-128ibm changes.

(The tests for these bugs were added in my previous y1 patch, so the
only thing this patch has to do with the testsuite is enable yn
testing in all rounding modes.)

	[BZ #16561]
	[BZ #16562]
	* sysdeps/ieee754/dbl-64/e_jn.c: Include <float.h>.
	(__ieee754_yn): Set FE_TONEAREST mode internally and then
	recompute overflowing results in original rounding mode.
	* sysdeps/ieee754/flt-32/e_jnf.c: Include <float.h>.
	(__ieee754_ynf): Set FE_TONEAREST mode internally and then
	recompute overflowing results in original rounding mode.
	* sysdeps/ieee754/ldbl-128/e_jnl.c: Include <float.h>.
	(__ieee754_ynl): Set FE_TONEAREST mode internally and then
	recompute overflowing results in original rounding mode.
	* sysdeps/ieee754/ldbl-128ibm/e_jnl.c: Include <float.h>.
	(__ieee754_ynl): Set FE_TONEAREST mode internally and then
	recompute overflowing results in original rounding mode.
	* sysdeps/ieee754/ldbl-96/e_jnl.c: Include <float.h>.
	(__ieee754_ynl): Set FE_TONEAREST mode internally and then
	recompute overflowing results in original rounding mode.
	* sysdeps/i386/fpu/fenv_private.h [!__SSE2_MATH__]
	(libc_feholdsetround_ctx): New macro.
	* math/libm-test.inc (yn_test): Use ALL_RM_TEST.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps : Likewise.

1 files changed, 64 insertions, 53 deletions

diff --git a/sysdeps/ieee754/dbl-64/e_jn.c b/sysdeps/ieee754/dbl-64/e_jn.c
index 236878ba1d..bbe04260b8 100644
--- a/sysdeps/ieee754/dbl-64/e_jn.c
+++ b/sysdeps/ieee754/dbl-64/e_jn.c
@@ -37,6 +37,7 @@
  */
 
 #include <errno.h>
+#include <float.h>
 #include <math.h>
 #include <math_private.h>
 
@@ -248,7 +249,7 @@ __ieee754_yn (int n, double x)
 {
   int32_t i, hx, ix, lx;
   int32_t sign;
-  double a, b, temp;
+  double a, b, temp, ret;
 
   EXTRACT_WORDS (hx, lx, x);
   ix = 0x7fffffff & hx;
@@ -268,57 +269,67 @@ __ieee754_yn (int n, double x)
     }
   if (n == 0)
     return (__ieee754_y0 (x));
-  if (n == 1)
-    return (sign * __ieee754_y1 (x));
-  if (__glibc_unlikely (ix == 0x7ff00000))
-    return zero;
-  if (ix >= 0x52D00000)      /* x > 2**302 */
-    { /* (x >> n**2)
-		 *	    Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
-		 *	    Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
-		 *	    Let s=sin(x), c=cos(x),
-		 *		xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
-		 *
-		 *		   n	sin(xn)*sqt2	cos(xn)*sqt2
-		 *		----------------------------------
-		 *		   0	 s-c		 c+s
-		 *		   1	-s-c		-c+s
-		 *		   2	-s+c		-c-s
-		 *		   3	 s+c		 c-s
-		 */
-      double c;
-      double s;
-      __sincos (x, &s, &c);
-      switch (n & 3)
-	{
-	case 0: temp = s - c; break;
-	case 1: temp = -s - c; break;
-	case 2: temp = -s + c; break;
-	case 3: temp = s + c; break;
-	}
-      b = invsqrtpi * temp / __ieee754_sqrt (x);
-    }
-  else
-    {
-      u_int32_t high;
-      a = __ieee754_y0 (x);
-      b = __ieee754_y1 (x);
-      /* quit if b is -inf */
-      GET_HIGH_WORD (high, b);
-      for (i = 1; i < n && high != 0xfff00000; i++)
-	{
-	  temp = b;
-	  b = ((double) (i + i) / x) * b - a;
-	  GET_HIGH_WORD (high, b);
-	  a = temp;
-	}
-      /* If B is +-Inf, set up errno accordingly.  */
-      if (!__finite (b))
-	__set_errno (ERANGE);
-    }
-  if (sign > 0)
-    return b;
-  else
-    return -b;
+  {
+    SET_RESTORE_ROUND (FE_TONEAREST);
+    if (n == 1)
+      {
+	ret = sign * __ieee754_y1 (x);
+	goto out;
+      }
+    if (__glibc_unlikely (ix == 0x7ff00000))
+      return zero;
+    if (ix >= 0x52D00000)      /* x > 2**302 */
+      { /* (x >> n**2)
+	 *	    Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
+	 *	    Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
+	 *	    Let s=sin(x), c=cos(x),
+	 *		xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
+	 *
+	 *		   n	sin(xn)*sqt2	cos(xn)*sqt2
+	 *		----------------------------------
+	 *		   0	 s-c		 c+s
+	 *		   1	-s-c		-c+s
+	 *		   2	-s+c		-c-s
+	 *		   3	 s+c		 c-s
+	 */
+	double c;
+	double s;
+	__sincos (x, &s, &c);
+	switch (n & 3)
+	  {
+	  case 0: temp = s - c; break;
+	  case 1: temp = -s - c; break;
+	  case 2: temp = -s + c; break;
+	  case 3: temp = s + c; break;
+	  }
+	b = invsqrtpi * temp / __ieee754_sqrt (x);
+      }
+    else
+      {
+	u_int32_t high;
+	a = __ieee754_y0 (x);
+	b = __ieee754_y1 (x);
+	/* quit if b is -inf */
+	GET_HIGH_WORD (high, b);
+	for (i = 1; i < n && high != 0xfff00000; i++)
+	  {
+	    temp = b;
+	    b = ((double) (i + i) / x) * b - a;
+	    GET_HIGH_WORD (high, b);
+	    a = temp;
+	  }
+	/* If B is +-Inf, set up errno accordingly.  */
+	if (!__finite (b))
+	  __set_errno (ERANGE);
+      }
+    if (sign > 0)
+      ret = b;
+    else
+      ret = -b;
+  }
+ out:
+  if (__isinf (ret))
+    ret = __copysign (DBL_MAX, ret) * DBL_MAX;
+  return ret;
 }
 strong_alias (__ieee754_yn, __yn_finite)