Fix spurious underflow exceptions for Bessel functions for ldbl-128 / ldbl-128ibm (bug 14155).

ChangeLog

@@ -1,3 +1,16 @@
+2013-03-16  Joseph Myers  <joseph@codesourcery.com>
+
+	[BZ #14155]
+	* sysdeps/ieee754/ldbl-128/e_j0l.c (__ieee754_j0l): Do not compute
+	1 / x and functions P and Q for arguments above 0x1p256L.
+	(__ieee754_y0l): Likewise.
+	* sysdeps/ieee754/ldbl-128/e_j1l.c (__ieee754_j1l): Likewise.
+	(__ieee754_y1l): Likewise.
+	* math/libm-test.inc (j0_test): Do not allow spurious underflows.
+	(j1_test): Likewise.
+	(y0_test): Likewise.
+	(y1_test): Likewise.
+
 2013-03-16  Thomas Schwinge  <thomas@codesourcery.com>
 
 	* math/test-snan.c (TEST_FUNC): Add and use minus_sNaN_var

math/libm-test.inc

@@ -6243,8 +6243,7 @@ j0_test (void)
   TEST_f_f (j0, 0x1.d7ce3ap+107L, 2.775523647291230802651040996274861694514e-17L);
 
 #ifndef TEST_FLOAT
-  /* Bug 14155: spurious exception may occur.  */
+  TEST_f_f (j0, -0x1.001000001p+593L, -3.927269966354206207832593635798954916263e-90L);
-  TEST_f_f (j0, -0x1.001000001p+593L, -3.927269966354206207832593635798954916263e-90L, UNDERFLOW_EXCEPTION_OK);
 #endif
 
   END (j0);
@@ -6285,8 +6284,7 @@ j1_test (void)
   TEST_f_f (j1, 0x1.3ffp+74L, 1.818984347516051243459364437186082741567e-12L);
 
 #ifndef TEST_FLOAT
-  /* Bug 14155: spurious exception may occur.  */
+  TEST_f_f (j1, 0x1.ff00000000002p+840L, 1.846591691699331493194965158699937660696e-127L);
-  TEST_f_f (j1, 0x1.ff00000000002p+840L, 1.846591691699331493194965158699937660696e-127L, UNDERFLOW_EXCEPTION_OK);
 #endif
 
   END (j1);
@@ -10457,8 +10455,7 @@ y0_test (void)
   TEST_f_f (y0, 0x1.3ffp+74L, 1.818984347516051243459467456433028748678e-12L);
 
 #ifndef TEST_FLOAT
-  /* Bug 14155: spurious exception may occur.  */
+  TEST_f_f (y0, 0x1.ff00000000002p+840L, 1.846591691699331493194965158699937660696e-127L);
-  TEST_f_f (y0, 0x1.ff00000000002p+840L, 1.846591691699331493194965158699937660696e-127L, UNDERFLOW_EXCEPTION_OK);
 #endif
 
   TEST_f_f (y0, 0x1p-10L, -4.4865150767109739412411806297168793661098L);
@@ -10511,8 +10508,7 @@ y1_test (void)
   TEST_f_f (y1, 0x1.27e204p+99L, -8.881610148467797208469612080785210013461e-16L);
 
 #ifndef TEST_FLOAT
-  /* Bug 14155: spurious exception may occur.  */
+  TEST_f_f (y1, 0x1.001000001p+593L, 3.927269966354206207832593635798954916263e-90L);
-  TEST_f_f (y1, 0x1.001000001p+593L, 3.927269966354206207832593635798954916263e-90L, UNDERFLOW_EXCEPTION_OK);
 #endif
 
   TEST_f_f (y1, 0x1p-10L, -6.5190099301063115047395187618929589514382e+02L);

sysdeps/ieee754/ldbl-128/e_j0l.c

@@ -700,6 +700,25 @@ __ieee754_j0l (long double x)
       return p;
     }
 
+  /* X = x - pi/4
+     cos(X) = cos(x) cos(pi/4) + sin(x) sin(pi/4)
+     = 1/sqrt(2) * (cos(x) + sin(x))
+     sin(X) = sin(x) cos(pi/4) - cos(x) sin(pi/4)
+     = 1/sqrt(2) * (sin(x) - cos(x))
+     sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
+     cf. Fdlibm.  */
+  __sincosl (xx, &s, &c);
+  ss = s - c;
+  cc = s + c;
+  z = -__cosl (xx + xx);
+  if ((s * c) < 0)
+    cc = z / ss;
+  else
+    ss = z / cc;
+
+  if (xx > 0x1p256L)
+    return ONEOSQPI * cc / __ieee754_sqrtl (xx);
+
   xinv = 1.0L / xx;
   z = xinv * xinv;
   if (xinv <= 0.25)
@@ -761,21 +780,6 @@ __ieee754_j0l (long double x)
   p = 1.0L + z * p;
   q = z * xinv * q;
   q = q - 0.125L * xinv;
-  /* X = x - pi/4
-     cos(X) = cos(x) cos(pi/4) + sin(x) sin(pi/4)
-     = 1/sqrt(2) * (cos(x) + sin(x))
-     sin(X) = sin(x) cos(pi/4) - cos(x) sin(pi/4)
-     = 1/sqrt(2) * (sin(x) - cos(x))
-     sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
-     cf. Fdlibm.  */
-  __sincosl (xx, &s, &c);
-  ss = s - c;
-  cc = s + c;
-  z = -__cosl (xx + xx);
-  if ((s * c) < 0)
-    cc = z / ss;
-  else
-    ss = z / cc;
   z = ONEOSQPI * (p * cc - q * ss) / __ieee754_sqrtl (xx);
   return z;
 }
@@ -843,6 +847,25 @@ long double
       return p;
     }
 
+  /* X = x - pi/4
+     cos(X) = cos(x) cos(pi/4) + sin(x) sin(pi/4)
+     = 1/sqrt(2) * (cos(x) + sin(x))
+     sin(X) = sin(x) cos(pi/4) - cos(x) sin(pi/4)
+     = 1/sqrt(2) * (sin(x) - cos(x))
+     sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
+     cf. Fdlibm.  */
+  __sincosl (x, &s, &c);
+  ss = s - c;
+  cc = s + c;
+  z = -__cosl (x + x);
+  if ((s * c) < 0)
+    cc = z / ss;
+  else
+    ss = z / cc;
+
+  if (xx > 0x1p256L)
+    return ONEOSQPI * ss / __ieee754_sqrtl (x);
+
   xinv = 1.0L / xx;
   z = xinv * xinv;
   if (xinv <= 0.25)
@@ -904,21 +927,6 @@ long double
   p = 1.0L + z * p;
   q = z * xinv * q;
   q = q - 0.125L * xinv;
-  /* X = x - pi/4
-     cos(X) = cos(x) cos(pi/4) + sin(x) sin(pi/4)
-     = 1/sqrt(2) * (cos(x) + sin(x))
-     sin(X) = sin(x) cos(pi/4) - cos(x) sin(pi/4)
-     = 1/sqrt(2) * (sin(x) - cos(x))
-     sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
-     cf. Fdlibm.  */
-  __sincosl (x, &s, &c);
-  ss = s - c;
-  cc = s + c;
-  z = -__cosl (x + x);
-  if ((s * c) < 0)
-    cc = z / ss;
-  else
-    ss = z / cc;
   z = ONEOSQPI * (p * ss + q * cc) / __ieee754_sqrtl (x);
   return z;
 }

sysdeps/ieee754/ldbl-128/e_j1l.c

@@ -706,6 +706,29 @@ __ieee754_j1l (long double x)
       return p;
     }
 
+  /* X = x - 3 pi/4
+     cos(X) = cos(x) cos(3 pi/4) + sin(x) sin(3 pi/4)
+     = 1/sqrt(2) * (-cos(x) + sin(x))
+     sin(X) = sin(x) cos(3 pi/4) - cos(x) sin(3 pi/4)
+     = -1/sqrt(2) * (sin(x) + cos(x))
+     cf. Fdlibm.  */
+  __sincosl (xx, &s, &c);
+  ss = -s - c;
+  cc = s - c;
+  z = __cosl (xx + xx);
+  if ((s * c) > 0)
+    cc = z / ss;
+  else
+    ss = z / cc;
+
+  if (xx > 0x1p256L)
+    {
+      z = ONEOSQPI * cc / __ieee754_sqrtl (xx);
+      if (x < 0)
+	z = -z;
+      return z;
+    }
+
   xinv = 1.0L / xx;
   z = xinv * xinv;
   if (xinv <= 0.25)
@@ -767,20 +790,6 @@ __ieee754_j1l (long double x)
   p = 1.0L + z * p;
   q = z * q;
   q = q * xinv + 0.375L * xinv;
-  /* X = x - 3 pi/4
-     cos(X) = cos(x) cos(3 pi/4) + sin(x) sin(3 pi/4)
-     = 1/sqrt(2) * (-cos(x) + sin(x))
-     sin(X) = sin(x) cos(3 pi/4) - cos(x) sin(3 pi/4)
-     = -1/sqrt(2) * (sin(x) + cos(x))
-     cf. Fdlibm.  */
-  __sincosl (xx, &s, &c);
-  ss = -s - c;
-  cc = s - c;
-  z = __cosl (xx + xx);
-  if ((s * c) > 0)
-    cc = z / ss;
-  else
-    ss = z / cc;
   z = ONEOSQPI * (p * cc - q * ss) / __ieee754_sqrtl (xx);
   if (x < 0)
     z = -z;
@@ -850,6 +859,24 @@ __ieee754_y1l (long double x)
       return p;
     }
 
+  /* X = x - 3 pi/4
+     cos(X) = cos(x) cos(3 pi/4) + sin(x) sin(3 pi/4)
+     = 1/sqrt(2) * (-cos(x) + sin(x))
+     sin(X) = sin(x) cos(3 pi/4) - cos(x) sin(3 pi/4)
+     = -1/sqrt(2) * (sin(x) + cos(x))
+     cf. Fdlibm.  */
+  __sincosl (xx, &s, &c);
+  ss = -s - c;
+  cc = s - c;
+  z = __cosl (xx + xx);
+  if ((s * c) > 0)
+    cc = z / ss;
+  else
+    ss = z / cc;
+
+  if (xx > 0x1p256L)
+    return ONEOSQPI * ss / __ieee754_sqrtl (xx);
+
   xinv = 1.0L / xx;
   z = xinv * xinv;
   if (xinv <= 0.25)
@@ -911,20 +938,6 @@ __ieee754_y1l (long double x)
   p = 1.0L + z * p;
   q = z * q;
   q = q * xinv + 0.375L * xinv;
-  /* X = x - 3 pi/4
-     cos(X) = cos(x) cos(3 pi/4) + sin(x) sin(3 pi/4)
-     = 1/sqrt(2) * (-cos(x) + sin(x))
-     sin(X) = sin(x) cos(3 pi/4) - cos(x) sin(3 pi/4)
-     = -1/sqrt(2) * (sin(x) + cos(x))
-     cf. Fdlibm.  */
-  __sincosl (xx, &s, &c);
-  ss = -s - c;
-  cc = s - c;
-  z = __cosl (xx + xx);
-  if ((s * c) > 0)
-    cc = z / ss;
-  else
-    ss = z / cc;
   z = ONEOSQPI * (p * ss + q * cc) / __ieee754_sqrtl (xx);
   return z;
 }