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Fix ldbl-128ibm cos range reduction near pi/2 (bug 15359)


Bug 15359 is inaccuracy of ldbl-128ibm cos near pi/2.  As with the
ldbl-128 case, the cause is inaccurate range reduction, and like that
patch <http://sourceware.org/ml/libc-alpha/2013-05/msg00271.html> this
patch uses the full precision of long double for the high and low
parts of pi/2 to fix the inaccuracy.  Tested powerpc to confirm the
large ulps no longer appear.

2013-05-09  Joseph Myers  <joseph@codesourcery.com>

	[BZ #15359]
	* sysdeps/ieee754/ldbl-128ibm/e_rem_pio2l.c (c): Use 106 bits for
	high part of pi/2.
	(__ieee754_rem_pio2l): Update comments.

diff --git a/sysdeps/ieee754/ldbl-128ibm/e_rem_pio2l.c b/sysdeps/ieee754/ldbl-128ibm/e_rem_pio2l.c
index 692ae24..6a72d6a 100644
--- a/sysdeps/ieee754/ldbl-128ibm/e_rem_pio2l.c
+++ b/sysdeps/ieee754/ldbl-128ibm/e_rem_pio2l.c
@@ -185,13 +185,13 @@ static const int32_t two_over_pi[] = {
 };
 
 static const long double c[] = {
-/* 93 bits of pi/2 */
+/* 106 bits of pi/2 */
 #define PI_2_1 c[0]
- 1.57079632679489661923132169155131424e+00L, /* 3fff921fb54442d18469898cc5100000 */
+ 0x1.921fb54442d18469898cc517018p+0L,
 
 /* pi/2 - PI_2_1 */
 #define PI_2_1t c[1]
- 8.84372056613570112025531863263659260e-29L, /* 3fa1c06e0e68948127044533e63a0106 */
+ 0x3.839a252049c1114cf98e804178p-108L,
 };
 
 int32_t __ieee754_rem_pio2l(long double x, long double *y)
@@ -216,7 +216,7 @@ int32_t __ieee754_rem_pio2l(long double x, long double *y)
     {
       if (hx > 0)
 	{
-	  /* 113 + 93 bit PI is ok */
+	  /* 106 + 106 bit PI is ok */
 	  z = x - PI_2_1;
 	  y[0] = z - PI_2_1t;
 	  y[1] = (z - y[0]) - PI_2_1t;
@@ -224,7 +224,7 @@ int32_t __ieee754_rem_pio2l(long double x, long double *y)
 	}
       else
         {
-	  /* 113 + 93 bit PI is ok */
+	  /* 106 + 106 bit PI is ok */
 	  z = x + PI_2_1;
 	  y[0] = z + PI_2_1t;
 	  y[1] = (z - y[0]) + PI_2_1t;

-- 
Joseph S. Myers
joseph@codesourcery.com


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