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[PowerPC64] Correct IBM long double frexpl
- From: Alan Modra <amodra at gmail dot com>
- To: libc-alpha at sourceware dot org
- Date: Tue, 25 Mar 2014 13:01:18 +1030
- Subject: [PowerPC64] Correct IBM long double frexpl
- Authentication-results: sourceware.org; auth=none
Besides fixing the bugzilla, this also fixes corner-cases where the high
and low double differ greatly in magnitude, and handles a denormal
input without resorting to a fp rescale.
[BZ #16740]
* sysdeps/ieee754/ldbl-128ibm/s_frexpl.c (__frexpl): Rewrite.
* math/libm-test.inc (frexp_test_data): Add tests.
diff --git a/math/libm-test.inc b/math/libm-test.inc
index e97b18a..01e09d2 100644
--- a/math/libm-test.inc
+++ b/math/libm-test.inc
@@ -7202,6 +7202,15 @@ static const struct test_f_f1_data frexp_test_data[] =
TEST_fI_f1 (frexp, 12.8L, 0.8L, 4, NO_INEXACT_EXCEPTION),
TEST_fI_f1 (frexp, -27.34L, -0.854375L, 5, NO_INEXACT_EXCEPTION),
+
+#if defined TEST_LDOUBLE && LDBL_MANT_DIG >= 106
+ TEST_fI_f1 (frexp, 1.0L-0x1p-106L, 1.0L-0x1p-106L, 0, NO_INEXACT_EXCEPTION),
+ TEST_fI_f1 (frexp, 1.0L, 0.5L, 1, NO_INEXACT_EXCEPTION),
+ TEST_fI_f1 (frexp, 1.0L+0x1p-105L, 0.5L+0x1p-106L, 1, NO_INEXACT_EXCEPTION),
+ TEST_fI_f1 (frexp, -1.0L+0x1p-106L, -1.0L+0x1p-106L, 0, NO_INEXACT_EXCEPTION),
+ TEST_fI_f1 (frexp, -1.0L, -0.5L, 1, NO_INEXACT_EXCEPTION),
+ TEST_fI_f1 (frexp, -1.0L-0x1p-105L, -0.5L-0x1p-106L, 1, NO_INEXACT_EXCEPTION),
+#endif
};
static void
diff --git a/sysdeps/ieee754/ldbl-128ibm/s_frexpl.c b/sysdeps/ieee754/ldbl-128ibm/s_frexpl.c
index 7e40663..a644f92 100644
--- a/sysdeps/ieee754/ldbl-128ibm/s_frexpl.c
+++ b/sysdeps/ieee754/ldbl-128ibm/s_frexpl.c
@@ -31,57 +31,115 @@ static char rcsid[] = "$NetBSD: $";
#include <math_private.h>
#include <math_ldbl_opt.h>
-static const long double
-two107 = 162259276829213363391578010288128.0; /* 0x4670000000000000, 0 */
-
long double __frexpl(long double x, int *eptr)
{
- uint64_t hx, lx, ix, ixl;
- int64_t explo;
- double xhi, xlo;
+ uint64_t hx, lx, ix, ixl;
+ int64_t explo, expon;
+ double xhi, xlo;
+
+ ldbl_unpack (x, &xhi, &xlo);
+ EXTRACT_WORDS64 (hx, xhi);
+ EXTRACT_WORDS64 (lx, xlo);
+ ixl = 0x7fffffffffffffffULL & lx;
+ ix = 0x7fffffffffffffffULL & hx;
+ expon = 0;
+ if (ix >= 0x7ff0000000000000ULL || ix == 0)
+ {
+ /* 0,inf,nan. */
+ *eptr = expon;
+ return x;
+ }
+ expon = ix >> 52;
+ if (expon == 0)
+ {
+ /* Denormal high double, the low double must be 0.0. */
+ int cnt;
+
+ /* Normalize. */
+ if (sizeof (ix) == sizeof (long))
+ cnt = __builtin_clzl (ix);
+ else if ((ix >> 32) != 0)
+ cnt = __builtin_clzl ((long) (ix >> 32));
+ else
+ cnt = __builtin_clzl ((long) ix) + 32;
+ cnt = cnt - 12;
+ expon -= cnt;
+ ix <<= cnt + 1;
+ }
+ expon -= 1022;
+ ix &= 0x000fffffffffffffULL;
+ hx &= 0x8000000000000000ULL;
+ hx |= (1022LL << 52) | ix;
- ldbl_unpack (x, &xhi, &xlo);
- EXTRACT_WORDS64 (hx, xhi);
- EXTRACT_WORDS64 (lx, xlo);
- ixl = 0x7fffffffffffffffULL&lx;
- ix = 0x7fffffffffffffffULL&hx;
- *eptr = 0;
- if(ix>=0x7ff0000000000000ULL||ix==0) return x; /* 0,inf,nan */
- if (ix<0x0010000000000000ULL) { /* subnormal */
- x *= two107;
- xhi = ldbl_high (x);
- EXTRACT_WORDS64 (hx, xhi);
- ix = hx&0x7fffffffffffffffULL;
- *eptr = -107;
+ if (ixl != 0)
+ {
+ /* If the high double is an exact power of two and the low
+ double has the opposite sign, then the exponent calculated
+ from the high double is one too big. */
+ if (ix == 0
+ && (int64_t) (hx ^ lx) < 0)
+ {
+ hx += 1L << 52;
+ expon -= 1;
}
- *eptr += (ix>>52)-1022;
- if (ixl != 0ULL) {
- explo = (ixl>>52) - (ix>>52) + 0x3fe;
- if ((ixl&0x7ff0000000000000ULL) == 0LL) {
- /* the lower double is a denormal so we need to correct its
- mantissa and perhaps its exponent. */
- int cnt;
+ explo = ixl >> 52;
+ if (explo == 0)
+ {
+ /* The low double started out as a denormal. Normalize its
+ mantissa and adjust the exponent. */
+ int cnt;
- if (sizeof (ixl) == sizeof (long))
- cnt = __builtin_clzl (ixl);
- else if ((ixl >> 32) != 0)
- cnt = __builtin_clzl ((long) (ixl >> 32));
- else
- cnt = __builtin_clzl ((long) ixl) + 32;
- cnt = cnt - 12;
- lx = (lx&0x8000000000000000ULL) | ((explo-cnt)<<52)
- | ((ixl<<(cnt+1))&0x000fffffffffffffULL);
- } else
- lx = (lx&0x800fffffffffffffULL) | (explo<<52);
- } else
- lx = 0ULL;
+ if (sizeof (ixl) == sizeof (long))
+ cnt = __builtin_clzl (ixl);
+ else if ((ixl >> 32) != 0)
+ cnt = __builtin_clzl ((long) (ixl >> 32));
+ else
+ cnt = __builtin_clzl ((long) ixl) + 32;
+ cnt = cnt - 12;
+ explo -= cnt;
+ ixl <<= cnt + 1;
+ }
+
+ /* With variable precision we can't assume much about the
+ magnitude of the returned low double. It may even be a
+ denormal. */
+ explo -= expon;
+ ixl &= 0x000fffffffffffffULL;
+ lx &= 0x8000000000000000ULL;
+ if (explo <= 0)
+ {
+ /* Handle denormal low double. */
+ if (explo > -52)
+ {
+ ixl |= 1LL << 52;
+ ixl >>= 1 - explo;
+ }
+ else
+ {
+ ixl = 0;
+ lx = 0;
+ if ((hx & 0x7ff0000000000000ULL) == (1023LL << 52))
+ {
+ /* Oops, the adjustment we made above for values a
+ little smaller than powers of two turned out to
+ be wrong since the returned low double will be
+ zero. This can happen if the input was
+ something weird like 0x1p1000 - 0x1p-1000. */
+ hx -= 1L << 52;
+ expon += 1;
+ }
+ }
+ explo = 0;
+ }
+ lx |= (explo << 52) | ixl;
+ }
- hx = (hx&0x800fffffffffffffULL) | 0x3fe0000000000000ULL;
- INSERT_WORDS64 (xhi, hx);
- INSERT_WORDS64 (xlo, lx);
- x = ldbl_pack (xhi, xlo);
- return x;
+ INSERT_WORDS64 (xhi, hx);
+ INSERT_WORDS64 (xlo, lx);
+ x = ldbl_pack (xhi, xlo);
+ *eptr = expon;
+ return x;
}
#ifdef IS_IN_libm
long_double_symbol (libm, __frexpl, frexpl);
--
Alan Modra
Australia Development Lab, IBM