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.

8 files changed, 353 insertions, 248 deletions

diff --git a/sysdeps/i386/fpu/fenv_private.h b/sysdeps/i386/fpu/fenv_private.h
index 3998387c57..e20e1f1662 100644
--- a/sysdeps/i386/fpu/fenv_private.h
+++ b/sysdeps/i386/fpu/fenv_private.h
@@ -482,6 +482,7 @@ libc_feupdateenv_387_ctx (struct rm_ctx *ctx)
 #else
 # define libc_feholdexcept_setround_ctx	libc_feholdexcept_setround_387_ctx
 # define libc_feupdateenv_ctx		libc_feupdateenv_387_ctx
+# define libc_feholdsetround_ctx	libc_feholdsetround_387_ctx
 # define libc_feresetround_ctx		libc_feresetround_387_ctx
 #endif /* __SSE2_MATH__ */
 
diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps
index 7cf958608d..be0e7c3668 100644
--- a/sysdeps/i386/fpu/libm-test-ulps
+++ b/sysdeps/i386/fpu/libm-test-ulps
@@ -1931,4 +1931,28 @@ ifloat: 3
 ildouble: 4
 ldouble: 4
 
+Function: "yn_downward":
+double: 2
+float: 2
+idouble: 2
+ifloat: 2
+ildouble: 5
+ldouble: 5
+
+Function: "yn_towardzero":
+double: 2
+float: 3
+idouble: 2
+ifloat: 3
+ildouble: 5
+ldouble: 5
+
+Function: "yn_upward":
+double: 2
+float: 3
+idouble: 2
+ifloat: 3
+ildouble: 4
+ldouble: 4
+
 # end of automatic generation
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)
diff --git a/sysdeps/ieee754/flt-32/e_jnf.c b/sysdeps/ieee754/flt-32/e_jnf.c
index 5984d94a3c..86085cc635 100644
--- a/sysdeps/ieee754/flt-32/e_jnf.c
+++ b/sysdeps/ieee754/flt-32/e_jnf.c
@@ -14,6 +14,7 @@
  */
 
 #include <errno.h>
+#include <float.h>
 #include <math.h>
 #include <math_private.h>
 
@@ -169,6 +170,8 @@ strong_alias (__ieee754_jnf, __jnf_finite)
 float
 __ieee754_ynf(int n, float x)
 {
+    float ret;
+    {
 	int32_t i,hx,ix;
 	u_int32_t ib;
 	int32_t sign;
@@ -187,7 +190,11 @@ __ieee754_ynf(int n, float x)
 		sign = 1 - ((n&1)<<1);
 	}
 	if(n==0) return(__ieee754_y0f(x));
-	if(n==1) return(sign*__ieee754_y1f(x));
+	SET_RESTORE_ROUNDF (FE_TONEAREST);
+	if(n==1) {
+	    ret = sign*__ieee754_y1f(x);
+	    goto out;
+	}
 	if(__builtin_expect(ix==0x7f800000, 0)) return zero;
 
 	a = __ieee754_y0f(x);
@@ -203,6 +210,11 @@ __ieee754_ynf(int n, float x)
 	/* If B is +-Inf, set up errno accordingly.  */
 	if (! __finitef (b))
 	  __set_errno (ERANGE);
-	if(sign>0) return b; else return -b;
+	if(sign>0) ret = b; else ret = -b;
+    }
+ out:
+    if (__isinff (ret))
+	ret = __copysignf (FLT_MAX, ret) * FLT_MAX;
+    return ret;
 }
 strong_alias (__ieee754_ynf, __ynf_finite)
diff --git a/sysdeps/ieee754/ldbl-128/e_jnl.c b/sysdeps/ieee754/ldbl-128/e_jnl.c
index c2a49235c3..4e32d38581 100644
--- a/sysdeps/ieee754/ldbl-128/e_jnl.c
+++ b/sysdeps/ieee754/ldbl-128/e_jnl.c
@@ -57,6 +57,7 @@
  */
 
 #include <errno.h>
+#include <float.h>
 #include <math.h>
 #include <math_private.h>
 
@@ -300,7 +301,7 @@ __ieee754_ynl (int n, long double x)
   u_int32_t se;
   int32_t i, ix;
   int32_t sign;
-  long double a, b, temp;
+  long double a, b, temp, ret;
   ieee854_long_double_shape_type u;
 
   u.value = x;
@@ -328,70 +329,80 @@ __ieee754_ynl (int n, long double x)
     }
   if (n == 0)
     return (__ieee754_y0l (x));
-  if (n == 1)
-    return (sign * __ieee754_y1l (x));
-  if (ix >= 0x7fff0000)
-    return zero;
-  if (ix >= 0x412D0000)
-    {				/* x > 2**302 */
+  {
+    SET_RESTORE_ROUNDL (FE_TONEAREST);
+    if (n == 1)
+      {
+	ret = sign * __ieee754_y1l (x);
+	goto out;
+      }
+    if (ix >= 0x7fff0000)
+      return zero;
+    if (ix >= 0x412D0000)
+      {				/* x > 2**302 */
 
-      /* ??? See comment above on the possible futility of this.  */
+	/* ??? See comment above on the possible futility of this.  */
 
-      /* (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
-       */
-      long double s;
-      long double c;
-      __sincosl (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_sqrtl (x);
-    }
-  else
-    {
-      a = __ieee754_y0l (x);
-      b = __ieee754_y1l (x);
-      /* quit if b is -inf */
-      u.value = b;
-      se = u.parts32.w0 & 0xffff0000;
-      for (i = 1; i < n && se != 0xffff0000; i++)
-	{
-	  temp = b;
-	  b = ((long double) (i + i) / x) * b - a;
-	  u.value = b;
-	  se = u.parts32.w0 & 0xffff0000;
-	  a = temp;
-	}
-    }
-  /* If B is +-Inf, set up errno accordingly.  */
-  if (! __finitel (b))
-    __set_errno (ERANGE);
-  if (sign > 0)
-    return b;
-  else
-    return -b;
+	/* (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
+	 */
+	long double s;
+	long double c;
+	__sincosl (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_sqrtl (x);
+      }
+    else
+      {
+	a = __ieee754_y0l (x);
+	b = __ieee754_y1l (x);
+	/* quit if b is -inf */
+	u.value = b;
+	se = u.parts32.w0 & 0xffff0000;
+	for (i = 1; i < n && se != 0xffff0000; i++)
+	  {
+	    temp = b;
+	    b = ((long double) (i + i) / x) * b - a;
+	    u.value = b;
+	    se = u.parts32.w0 & 0xffff0000;
+	    a = temp;
+	  }
+      }
+    /* If B is +-Inf, set up errno accordingly.  */
+    if (! __finitel (b))
+      __set_errno (ERANGE);
+    if (sign > 0)
+      ret = b;
+    else
+      ret = -b;
+  }
+ out:
+  if (__isinfl (ret))
+    ret = __copysignl (LDBL_MAX, ret) * LDBL_MAX;
+  return ret;
 }
 strong_alias (__ieee754_ynl, __ynl_finite)
diff --git a/sysdeps/ieee754/ldbl-128ibm/e_jnl.c b/sysdeps/ieee754/ldbl-128ibm/e_jnl.c
index 6761a0d26f..589f1f822a 100644
--- a/sysdeps/ieee754/ldbl-128ibm/e_jnl.c
+++ b/sysdeps/ieee754/ldbl-128ibm/e_jnl.c
@@ -57,6 +57,7 @@
  */
 
 #include <errno.h>
+#include <float.h>
 #include <math.h>
 #include <math_private.h>
 
@@ -300,7 +301,7 @@ __ieee754_ynl (int n, long double x)
   uint32_t se, lx;
   int32_t i, ix;
   int32_t sign;
-  long double a, b, temp;
+  long double a, b, temp, ret;
   double xhi;
 
   xhi = ldbl_high (x);
@@ -328,72 +329,82 @@ __ieee754_ynl (int n, long double x)
     }
   if (n == 0)
     return (__ieee754_y0l (x));
-  if (n == 1)
-    return (sign * __ieee754_y1l (x));
-  if (ix >= 0x7ff00000)
-    return zero;
-  if (ix >= 0x52D00000)
-    {				/* x > 2**302 */
+  {
+    SET_RESTORE_ROUNDL (FE_TONEAREST);
+    if (n == 1)
+      {
+	ret = sign * __ieee754_y1l (x);
+	goto out;
+      }
+    if (ix >= 0x7ff00000)
+      return zero;
+    if (ix >= 0x52D00000)
+      {				/* x > 2**302 */
 
-      /* ??? See comment above on the possible futility of this.  */
+	/* ??? See comment above on the possible futility of this.  */
 
-      /* (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
-       */
-      long double s;
-      long double c;
-      __sincosl (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_sqrtl (x);
-    }
-  else
-    {
-      a = __ieee754_y0l (x);
-      b = __ieee754_y1l (x);
-      /* quit if b is -inf */
-      xhi = ldbl_high (b);
-      GET_HIGH_WORD (se, xhi);
-      se &= 0xfff00000;
-      for (i = 1; i < n && se != 0xfff00000; i++)
-	{
-	  temp = b;
-	  b = ((long double) (i + i) / x) * b - a;
-	  xhi = ldbl_high (b);
-	  GET_HIGH_WORD (se, xhi);
-	  se &= 0xfff00000;
-	  a = temp;
-	}
-    }
-  /* If B is +-Inf, set up errno accordingly.  */
-  if (! __finitel (b))
-    __set_errno (ERANGE);
-  if (sign > 0)
-    return b;
-  else
-    return -b;
+	/* (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
+	 */
+	long double s;
+	long double c;
+	__sincosl (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_sqrtl (x);
+      }
+    else
+      {
+	a = __ieee754_y0l (x);
+	b = __ieee754_y1l (x);
+	/* quit if b is -inf */
+	xhi = ldbl_high (b);
+	GET_HIGH_WORD (se, xhi);
+	se &= 0xfff00000;
+	for (i = 1; i < n && se != 0xfff00000; i++)
+	  {
+	    temp = b;
+	    b = ((long double) (i + i) / x) * b - a;
+	    xhi = ldbl_high (b);
+	    GET_HIGH_WORD (se, xhi);
+	    se &= 0xfff00000;
+	    a = temp;
+	  }
+      }
+    /* If B is +-Inf, set up errno accordingly.  */
+    if (! __finitel (b))
+      __set_errno (ERANGE);
+    if (sign > 0)
+      ret = b;
+    else
+      ret = -b;
+  }
+ out:
+  if (__isinfl (ret))
+    ret = __copysignl (LDBL_MAX, ret) * LDBL_MAX;
+  return ret;
 }
 strong_alias (__ieee754_ynl, __ynl_finite)
diff --git a/sysdeps/ieee754/ldbl-96/e_jnl.c b/sysdeps/ieee754/ldbl-96/e_jnl.c
index 11d097c271..95ff24201b 100644
--- a/sysdeps/ieee754/ldbl-96/e_jnl.c
+++ b/sysdeps/ieee754/ldbl-96/e_jnl.c
@@ -57,6 +57,7 @@
  */
 
 #include <errno.h>
+#include <float.h>
 #include <math.h>
 #include <math_private.h>
 
@@ -293,7 +294,7 @@ __ieee754_ynl (int n, long double x)
   u_int32_t se, i0, i1;
   int32_t i, ix;
   int32_t sign;
-  long double a, b, temp;
+  long double a, b, temp, ret;
 
 
   GET_LDOUBLE_WORDS (se, i0, i1, x);
@@ -314,69 +315,79 @@ __ieee754_ynl (int n, long double x)
     }
   if (n == 0)
     return (__ieee754_y0l (x));
-  if (n == 1)
-    return (sign * __ieee754_y1l (x));
-  if (__glibc_unlikely (ix == 0x7fff))
-    return zero;
-  if (ix >= 0x412D)
-    {				/* x > 2**302 */
+  {
+    SET_RESTORE_ROUNDL (FE_TONEAREST);
+    if (n == 1)
+      {
+	ret = sign * __ieee754_y1l (x);
+	goto out;
+      }
+    if (__glibc_unlikely (ix == 0x7fff))
+      return zero;
+    if (ix >= 0x412D)
+      {				/* x > 2**302 */
 
-      /* ??? See comment above on the possible futility of this.  */
+	/* ??? See comment above on the possible futility of this.  */
 
-      /* (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
-       */
-      long double s;
-      long double c;
-      __sincosl (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_sqrtl (x);
-    }
-  else
-    {
-      a = __ieee754_y0l (x);
-      b = __ieee754_y1l (x);
-      /* quit if b is -inf */
-      GET_LDOUBLE_WORDS (se, i0, i1, b);
-      /* Use 0xffffffff since GET_LDOUBLE_WORDS sign-extends SE.  */
-      for (i = 1; i < n && se != 0xffffffff; i++)
-	{
-	  temp = b;
-	  b = ((long double) (i + i) / x) * b - a;
-	  GET_LDOUBLE_WORDS (se, i0, i1, b);
-	  a = temp;
-	}
-    }
-  /* If B is +-Inf, set up errno accordingly.  */
-  if (! __finitel (b))
-    __set_errno (ERANGE);
-  if (sign > 0)
-    return b;
-  else
-    return -b;
+	/* (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
+	 */
+	long double s;
+	long double c;
+	__sincosl (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_sqrtl (x);
+      }
+    else
+      {
+	a = __ieee754_y0l (x);
+	b = __ieee754_y1l (x);
+	/* quit if b is -inf */
+	GET_LDOUBLE_WORDS (se, i0, i1, b);
+	/* Use 0xffffffff since GET_LDOUBLE_WORDS sign-extends SE.  */
+	for (i = 1; i < n && se != 0xffffffff; i++)
+	  {
+	    temp = b;
+	    b = ((long double) (i + i) / x) * b - a;
+	    GET_LDOUBLE_WORDS (se, i0, i1, b);
+	    a = temp;
+	  }
+      }
+    /* If B is +-Inf, set up errno accordingly.  */
+    if (! __finitel (b))
+      __set_errno (ERANGE);
+    if (sign > 0)
+      ret = b;
+    else
+      ret = -b;
+  }
+ out:
+  if (__isinfl (ret))
+    ret = __copysignl (LDBL_MAX, ret) * LDBL_MAX;
+  return ret;
 }
 strong_alias (__ieee754_ynl, __ynl_finite)
diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps
index f68650d36d..36e1b76811 100644
--- a/sysdeps/x86_64/fpu/libm-test-ulps
+++ b/sysdeps/x86_64/fpu/libm-test-ulps
@@ -2033,4 +2033,28 @@ ifloat: 3
 ildouble: 4
 ldouble: 4
 
+Function: "yn_downward":
+double: 3
+float: 4
+idouble: 3
+ifloat: 4
+ildouble: 5
+ldouble: 5
+
+Function: "yn_towardzero":
+double: 3
+float: 3
+idouble: 3
+ifloat: 3
+ildouble: 5
+ldouble: 5
+
+Function: "yn_upward":
+double: 4
+float: 5
+idouble: 4
+ifloat: 5
+ildouble: 4
+ldouble: 4
+
 # end of automatic generation