Correct IBM long double frexpl.
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] [BZ #16619] * sysdeps/ieee754/ldbl-128ibm/s_frexpl.c (__frexpl): Rewrite. * math/libm-test.inc (frexp_test_data): Add tests.
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@ -1,3 +1,10 @@
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2014-04-16 Alan Modra <amodra@gmail.com>
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[BZ #16740]
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[BZ #16619]
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* sysdeps/ieee754/ldbl-128ibm/s_frexpl.c (__frexpl): Rewrite.
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* math/libm-test.inc (frexp_test_data): Add tests.
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2014-04-15 Siddhesh Poyarekar <siddhesh@redhat.com>
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2014-04-15 Siddhesh Poyarekar <siddhesh@redhat.com>
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* benchtests/Makefile: Depend on libraries in build directory.
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* benchtests/Makefile: Depend on libraries in build directory.
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@ -7186,6 +7186,15 @@ static const struct test_f_f1_data frexp_test_data[] =
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TEST_fI_f1 (frexp, 12.8L, 0.8L, 4, NO_INEXACT_EXCEPTION),
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TEST_fI_f1 (frexp, 12.8L, 0.8L, 4, NO_INEXACT_EXCEPTION),
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TEST_fI_f1 (frexp, -27.34L, -0.854375L, 5, NO_INEXACT_EXCEPTION),
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TEST_fI_f1 (frexp, -27.34L, -0.854375L, 5, NO_INEXACT_EXCEPTION),
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#if defined TEST_LDOUBLE && LDBL_MANT_DIG >= 106
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TEST_fI_f1 (frexp, 1.0L-0x1p-106L, 1.0L-0x1p-106L, 0, NO_INEXACT_EXCEPTION),
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TEST_fI_f1 (frexp, 1.0L, 0.5L, 1, NO_INEXACT_EXCEPTION),
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TEST_fI_f1 (frexp, 1.0L+0x1p-105L, 0.5L+0x1p-106L, 1, NO_INEXACT_EXCEPTION),
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TEST_fI_f1 (frexp, -1.0L+0x1p-106L, -1.0L+0x1p-106L, 0, NO_INEXACT_EXCEPTION),
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TEST_fI_f1 (frexp, -1.0L, -0.5L, 1, NO_INEXACT_EXCEPTION),
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TEST_fI_f1 (frexp, -1.0L-0x1p-105L, -0.5L-0x1p-106L, 1, NO_INEXACT_EXCEPTION),
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#endif
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};
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};
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static void
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static void
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@ -31,57 +31,115 @@ static char rcsid[] = "$NetBSD: $";
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#include <math_private.h>
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#include <math_private.h>
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#include <math_ldbl_opt.h>
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#include <math_ldbl_opt.h>
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static const long double
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two107 = 162259276829213363391578010288128.0; /* 0x4670000000000000, 0 */
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long double __frexpl(long double x, int *eptr)
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long double __frexpl(long double x, int *eptr)
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{
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{
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uint64_t hx, lx, ix, ixl;
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uint64_t hx, lx, ix, ixl;
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int64_t explo;
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int64_t explo, expon;
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double xhi, xlo;
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double xhi, xlo;
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ldbl_unpack (x, &xhi, &xlo);
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ldbl_unpack (x, &xhi, &xlo);
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EXTRACT_WORDS64 (hx, xhi);
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EXTRACT_WORDS64 (hx, xhi);
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EXTRACT_WORDS64 (lx, xlo);
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EXTRACT_WORDS64 (lx, xlo);
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ixl = 0x7fffffffffffffffULL&lx;
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ixl = 0x7fffffffffffffffULL & lx;
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ix = 0x7fffffffffffffffULL&hx;
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ix = 0x7fffffffffffffffULL & hx;
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*eptr = 0;
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expon = 0;
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if(ix>=0x7ff0000000000000ULL||ix==0) return x; /* 0,inf,nan */
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if (ix >= 0x7ff0000000000000ULL || ix == 0)
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if (ix<0x0010000000000000ULL) { /* subnormal */
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{
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x *= two107;
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/* 0,inf,nan. */
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xhi = ldbl_high (x);
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*eptr = expon;
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EXTRACT_WORDS64 (hx, xhi);
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return x;
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ix = hx&0x7fffffffffffffffULL;
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}
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*eptr = -107;
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expon = ix >> 52;
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if (expon == 0)
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{
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/* Denormal high double, the low double must be 0.0. */
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int cnt;
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/* Normalize. */
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if (sizeof (ix) == sizeof (long))
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cnt = __builtin_clzl (ix);
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else if ((ix >> 32) != 0)
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cnt = __builtin_clzl ((long) (ix >> 32));
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else
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cnt = __builtin_clzl ((long) ix) + 32;
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cnt = cnt - 12;
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expon -= cnt;
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ix <<= cnt + 1;
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}
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expon -= 1022;
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ix &= 0x000fffffffffffffULL;
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hx &= 0x8000000000000000ULL;
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hx |= (1022LL << 52) | ix;
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if (ixl != 0)
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{
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/* If the high double is an exact power of two and the low
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double has the opposite sign, then the exponent calculated
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from the high double is one too big. */
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if (ix == 0
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&& (int64_t) (hx ^ lx) < 0)
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{
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hx += 1L << 52;
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expon -= 1;
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}
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}
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*eptr += (ix>>52)-1022;
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if (ixl != 0ULL) {
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explo = ixl >> 52;
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explo = (ixl>>52) - (ix>>52) + 0x3fe;
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if (explo == 0)
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if ((ixl&0x7ff0000000000000ULL) == 0LL) {
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{
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/* the lower double is a denormal so we need to correct its
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/* The low double started out as a denormal. Normalize its
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mantissa and perhaps its exponent. */
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mantissa and adjust the exponent. */
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int cnt;
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int cnt;
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if (sizeof (ixl) == sizeof (long))
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if (sizeof (ixl) == sizeof (long))
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cnt = __builtin_clzl (ixl);
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cnt = __builtin_clzl (ixl);
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else if ((ixl >> 32) != 0)
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else if ((ixl >> 32) != 0)
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cnt = __builtin_clzl ((long) (ixl >> 32));
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cnt = __builtin_clzl ((long) (ixl >> 32));
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else
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else
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cnt = __builtin_clzl ((long) ixl) + 32;
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cnt = __builtin_clzl ((long) ixl) + 32;
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cnt = cnt - 12;
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cnt = cnt - 12;
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lx = (lx&0x8000000000000000ULL) | ((explo-cnt)<<52)
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explo -= cnt;
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ixl <<= cnt + 1;
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} else
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}
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lx = (lx&0x800fffffffffffffULL) | (explo<<52);
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} else
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lx = 0ULL;
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hx = (hx&0x800fffffffffffffULL) | 0x3fe0000000000000ULL;
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/* With variable precision we can't assume much about the
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INSERT_WORDS64 (xhi, hx);
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magnitude of the returned low double. It may even be a
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INSERT_WORDS64 (xlo, lx);
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denormal. */
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x = ldbl_pack (xhi, xlo);
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explo -= expon;
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return x;
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ixl &= 0x000fffffffffffffULL;
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lx &= 0x8000000000000000ULL;
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if (explo <= 0)
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{
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/* Handle denormal low double. */
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if (explo > -52)
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{
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ixl |= 1LL << 52;
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ixl >>= 1 - explo;
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}
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else
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{
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ixl = 0;
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lx = 0;
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if ((hx & 0x7ff0000000000000ULL) == (1023LL << 52))
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{
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/* Oops, the adjustment we made above for values a
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little smaller than powers of two turned out to
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be wrong since the returned low double will be
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zero. This can happen if the input was
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something weird like 0x1p1000 - 0x1p-1000. */
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hx -= 1L << 52;
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expon += 1;
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}
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}
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explo = 0;
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}
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lx |= (explo << 52) | ixl;
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}
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INSERT_WORDS64 (xhi, hx);
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INSERT_WORDS64 (xlo, lx);
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x = ldbl_pack (xhi, xlo);
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*eptr = expon;
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return x;
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}
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}
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#ifdef IS_IN_libm
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#ifdef IS_IN_libm
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long_double_symbol (libm, __frexpl, frexpl);
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long_double_symbol (libm, __frexpl, frexpl);
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