Correct tinyness handling in long-double and float y0/y1.

	With help from Joseph Myers.
	* sysdeps/ieee754/flt-32/e_j0f.c (__ieee754_y0f): Adjust tinyness
	cutoff to 2**-13.
	* sysdeps/ieee754/flt-32/e_j1f.c (__ieee754_y1f): Adjust tinyness
	cutoff to 2**-25.
	* sysdeps/ieee754/ldbl-128/e_j0l.c (U0): New constant.
	( __ieee754_y0l): Avoid arithmetic underflow when 'x' is very
	small.
	* sysdeps/ieee754/ldbl-128/e_j1l.c (__ieee754_y1l): Likewise.
	* math/libm-test.inc (y0_test): New tests.
	(y1_test): New tests.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Update.
	* sysdeps/sparc/fpu/libm-test-ulps: Update.

7 files changed, 113 insertions, 3 deletions

diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps
index 239da44a79..8da973a2f6 100644
--- a/sysdeps/i386/fpu/libm-test-ulps
+++ b/sysdeps/i386/fpu/libm-test-ulps
@@ -3015,6 +3015,28 @@ ldouble: 1
 Test "y0 (0x1.ff00000000002p+840) == 1.846591691699331493194965158699937660696e-127":
 double: 1
 idouble: 1
+Test "y0 (0x1p-10) == -4.4865150767109739412411806297168793661098":
+ildouble: 1
+ldouble: 1
+Test "y0 (0x1p-30) == -1.3311940304267782826037118027401817264906e+1":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "y0 (0x1p-40) == -1.7724652307320814696990854700366226762563e+1":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+Test "y0 (0x1p-60) == -2.6550076313426878432849115782108205929120e+1":
+double: 1
+idouble: 1
+Test "y0 (0x1p-70) == -3.0962788316479910300778244424468159753887e+1":
+double: 1
+idouble: 1
+Test "y0 (0x1p-80) == -3.5375500319532942168707373066828113573541e+1":
+double: 1
+idouble: 1
 Test "y0 (1.0) == 0.0882569642156769579829267660235151628":
 double: 2
 float: 1
@@ -3056,6 +3078,9 @@ idouble: 1
 ifloat: 2
 ildouble: 1
 ldouble: 1
+Test "y1 (0x1p-10) == -6.5190099301063115047395187618929589514382e+02":
+float: 1
+ifloat: 1
 Test "y1 (1.0) == -0.781212821300288716547150000047964821":
 double: 1
 idouble: 1
diff --git a/sysdeps/ieee754/flt-32/e_j0f.c b/sysdeps/ieee754/flt-32/e_j0f.c
index 0729cd04e0..c4cabd584a 100644
--- a/sysdeps/ieee754/flt-32/e_j0f.c
+++ b/sysdeps/ieee754/flt-32/e_j0f.c
@@ -138,7 +138,7 @@ __ieee754_y0f(float x)
 		}
 		return z;
 	}
-	if(ix<=0x32000000) {	/* x < 2**-27 */
+	if(ix<=0x39800000) {	/* x < 2**-13 */
 	    return(u00 + tpi*__ieee754_logf(x));
 	}
 	z = x*x;
diff --git a/sysdeps/ieee754/flt-32/e_j1f.c b/sysdeps/ieee754/flt-32/e_j1f.c
index 30b7d8e250..cb9f97fa28 100644
--- a/sysdeps/ieee754/flt-32/e_j1f.c
+++ b/sysdeps/ieee754/flt-32/e_j1f.c
@@ -133,7 +133,7 @@ __ieee754_y1f(float x)
 		}
 		return z;
 	}
-	if(__builtin_expect(ix<=0x24800000, 0)) {    /* x < 2**-54 */
+	if(__builtin_expect(ix<=0x33000000, 0)) {    /* x < 2**-25 */
 	    return(-tpi/x);
 	}
 	z = x*x;
diff --git a/sysdeps/ieee754/ldbl-128/e_j0l.c b/sysdeps/ieee754/ldbl-128/e_j0l.c
index 112a8f3f9c..1b18289588 100644
--- a/sysdeps/ieee754/ldbl-128/e_j0l.c
+++ b/sysdeps/ieee754/ldbl-128/e_j0l.c
@@ -809,6 +809,7 @@ static long double Y0_2D[NY0_2D + 1] = {
  /* 1.000000000000000000000000000000000000000E0 */
 };
 
+static const long double U0 = -7.3804295108687225274343927948483016310862e-02L;
 
 /* Bessel function of the second kind, order zero.  */
 
@@ -831,6 +832,8 @@ long double
       return -HUGE_VALL + x;
     }
   xx = fabsl (x);
+  if (xx <= 0x1p-57)
+    return U0 + TWOOPI * __ieee754_logl (x);
   if (xx <= 2.0L)
     {
       /* 0 <= x <= 2 */
diff --git a/sysdeps/ieee754/ldbl-128/e_j1l.c b/sysdeps/ieee754/ldbl-128/e_j1l.c
index 1f62bd0920..f16343b26b 100644
--- a/sysdeps/ieee754/ldbl-128/e_j1l.c
+++ b/sysdeps/ieee754/ldbl-128/e_j1l.c
@@ -838,6 +838,8 @@ __ieee754_y1l (long double x)
       return -HUGE_VALL + x;
     }
   xx = fabsl (x);
+  if (xx <= 0x1p-114)
+    return -TWOOPI / x;
   if (xx <= 2.0L)
     {
       /* 0 <= x <= 2 */
diff --git a/sysdeps/sparc/fpu/libm-test-ulps b/sysdeps/sparc/fpu/libm-test-ulps
index 0f8179f6b4..ec0ad66204 100644
--- a/sysdeps/sparc/fpu/libm-test-ulps
+++ b/sysdeps/sparc/fpu/libm-test-ulps
@@ -1328,8 +1328,8 @@ Test "Imaginary part of: clog10 (0xf2p-10 + 0x3e3p-10 i) == 2.692124017335111295
 double: 1
 idouble: 1
 Test "Imaginary part of: clog10 (0xfd95243681c055c2632286921092p-113 + 0x1bccabcd29ca2152860ec29e34ef7p-113 i) == 2.8774482675253468630312378575186855052697e-66 + 0.4571561610046221605554903008571429975493 i":
-ldouble: 2
 ildouble: 2
+ldouble: 2
 Test "Imaginary part of: clog10 (0xfe961079616p-45 + 0x1bc37e09e6d1p-45 i) == 2.3329549194675052736016290082882121135546e-26 + 0.4561756099441139182878993697611751382976 i":
 double: 1
 idouble: 1
@@ -2861,6 +2861,43 @@ double: 1
 idouble: 1
 ildouble: 1
 ldouble: 1
+Test "y0 (0x1p-10) == -4.4865150767109739412411806297168793661098":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "y0 (0x1p-110) == -4.861363632869203777249475899390797503250e+1":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "y0 (0x1p-20) == -8.8992283012125827603076426611387876938160":
+float: 1
+ifloat: 1
+Test "y0 (0x1p-30) == -1.3311940304267782826037118027401817264906e+1":
+float: 1
+ifloat: 1
+ildouble: 2
+ldouble: 2
+Test "y0 (0x1p-40) == -1.7724652307320814696990854700366226762563e+1":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+Test "y0 (0x1p-50) == -2.2137364310373846564919987139743760738155e+1":
+float: 1
+ifloat: 1
+Test "y0 (0x1p-60) == -2.6550076313426878432849115782108205929120e+1":
+ildouble: 1
+ldouble: 1
+Test "y0 (0x1p-70) == -3.0962788316479910300778244424468159753887e+1":
+double: 1
+idouble: 1
+Test "y0 (0x1p-80) == -3.5375500319532942168707373066828113573541e+1":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
 Test "y0 (1.0) == 0.0882569642156769579829267660235151628":
 double: 2
 float: 1
@@ -2897,6 +2934,14 @@ ldouble: 1
 Test "y1 (0x1.27e204p+99) == -8.881610148467797208469612080785210013461e-16":
 double: 1
 idouble: 1
+Test "y1 (0x1p-10) == -6.5190099301063115047395187618929589514382e+02":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "y1 (0x1p-30) == -6.8356527557643159612937462812258975438856e+08":
+ildouble: 1
+ldouble: 1
 Test "y1 (1.5) == -0.412308626973911295952829820633445323":
 float: 1
 ifloat: 1
diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps
index 9c5157ff7e..4767be94db 100644
--- a/sysdeps/x86_64/fpu/libm-test-ulps
+++ b/sysdeps/x86_64/fpu/libm-test-ulps
@@ -2796,6 +2796,38 @@ ldouble: 1
 Test "y0 (0x1.ff00000000002p+840) == 1.846591691699331493194965158699937660696e-127":
 double: 1
 idouble: 1
+Test "y0 (0x1p-10) == -4.4865150767109739412411806297168793661098":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "y0 (0x1p-110) == -4.861363632869203777249475899390797503250e+1":
+double: 1
+idouble: 1
+Test "y0 (0x1p-20) == -8.8992283012125827603076426611387876938160":
+float: 1
+ifloat: 1
+Test "y0 (0x1p-30) == -1.3311940304267782826037118027401817264906e+1":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "y0 (0x1p-40) == -1.7724652307320814696990854700366226762563e+1":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+Test "y0 (0x1p-50) == -2.2137364310373846564919987139743760738155e+1":
+float: 1
+ifloat: 1
+Test "y0 (0x1p-70) == -3.0962788316479910300778244424468159753887e+1":
+double: 1
+idouble: 1
+Test "y0 (0x1p-80) == -3.5375500319532942168707373066828113573541e+1":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
 Test "y0 (1.0) == 0.0882569642156769579829267660235151628":
 double: 2
 float: 1
@@ -2837,6 +2869,9 @@ idouble: 1
 ifloat: 1
 ildouble: 1
 ldouble: 1
+Test "y1 (0x1p-10) == -6.5190099301063115047395187618929589514382e+02":
+double: 1
+idouble: 1
 Test "y1 (1.5) == -0.412308626973911295952829820633445323":
 float: 1
 ifloat: 1