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+/* Manipulation of the bit representation of 'long double' quantities.
+ Copyright (C) 2006-2017 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ The GNU C Library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with the GNU C Library; if not, see
+ <http://www.gnu.org/licenses/>. */
+
+#ifndef _MATH_LDBL_H_
+#define _MATH_LDBL_H_ 1
+
+#include <ieee754.h>
+#include <stdint.h>
+
+/* To suit our callers we return *hi64 and *lo64 as if they came from
+ an ieee854 112 bit mantissa, that is, 48 bits in *hi64 (plus one
+ implicit bit) and 64 bits in *lo64. */
+
+static inline void
+ldbl_extract_mantissa (int64_t *hi64, uint64_t *lo64, int *exp, long double x)
+{
+ /* We have 105 bits of mantissa plus one implicit digit. Since
+ 106 bits are representable we use the first implicit digit for
+ the number before the decimal point and the second implicit bit
+ as bit 53 of the mantissa. */
+ uint64_t hi, lo;
+ union ibm_extended_long_double u;
+
+ u.ld = x;
+ *exp = u.d[0].ieee.exponent - IEEE754_DOUBLE_BIAS;
+
+ lo = ((uint64_t) u.d[1].ieee.mantissa0 << 32) | u.d[1].ieee.mantissa1;
+ hi = ((uint64_t) u.d[0].ieee.mantissa0 << 32) | u.d[0].ieee.mantissa1;
+
+ if (u.d[0].ieee.exponent != 0)
+ {
+ int ediff;
+
+ /* If not a denormal or zero then we have an implicit 53rd bit. */
+ hi |= (uint64_t) 1 << 52;
+
+ if (u.d[1].ieee.exponent != 0)
+ lo |= (uint64_t) 1 << 52;
+ else
+ /* A denormal is to be interpreted as having a biased exponent
+ of 1. */
+ lo = lo << 1;
+
+ /* We are going to shift 4 bits out of hi later, because we only
+ want 48 bits in *hi64. That means we want 60 bits in lo, but
+ we currently only have 53. Shift the value up. */
+ lo = lo << 7;
+
+ /* The lower double is normalized separately from the upper.
+ We may need to adjust the lower mantissa to reflect this.
+ The difference between the exponents can be larger than 53
+ when the low double is much less than 1ULP of the upper
+ (in which case there are significant bits, all 0's or all
+ 1's, between the two significands). The difference between
+ the exponents can be less than 53 when the upper double
+ exponent is nearing its minimum value (in which case the low
+ double is denormal ie. has an exponent of zero). */
+ ediff = u.d[0].ieee.exponent - u.d[1].ieee.exponent - 53;
+ if (ediff > 0)
+ {
+ if (ediff < 64)
+ lo = lo >> ediff;
+ else
+ lo = 0;
+ }
+ else if (ediff < 0)
+ lo = lo << -ediff;
+
+ if (u.d[0].ieee.negative != u.d[1].ieee.negative
+ && lo != 0)
+ {
+ hi--;
+ lo = ((uint64_t) 1 << 60) - lo;
+ if (hi < (uint64_t) 1 << 52)
+ {
+ /* We have a borrow from the hidden bit, so shift left 1. */
+ hi = (hi << 1) | (lo >> 59);
+ lo = (((uint64_t) 1 << 60) - 1) & (lo << 1);
+ *exp = *exp - 1;
+ }
+ }
+ }
+ else
+ /* If the larger magnitude double is denormal then the smaller
+ one must be zero. */
+ hi = hi << 1;
+
+ *lo64 = (hi << 60) | lo;
+ *hi64 = hi >> 4;
+}
+
+static inline long double
+ldbl_insert_mantissa (int sign, int exp, int64_t hi64, uint64_t lo64)
+{
+ union ibm_extended_long_double u;
+ int expnt2;
+ uint64_t hi, lo;
+
+ u.d[0].ieee.negative = sign;
+ u.d[1].ieee.negative = sign;
+ u.d[0].ieee.exponent = exp + IEEE754_DOUBLE_BIAS;
+ u.d[1].ieee.exponent = 0;
+ expnt2 = exp - 53 + IEEE754_DOUBLE_BIAS;
+
+ /* Expect 113 bits (112 bits + hidden) right justified in two longs.
+ The low order 53 bits (52 + hidden) go into the lower double */
+ lo = (lo64 >> 7) & (((uint64_t) 1 << 53) - 1);
+ /* The high order 53 bits (52 + hidden) go into the upper double */
+ hi = lo64 >> 60;
+ hi |= hi64 << 4;
+
+ if (lo != 0)
+ {
+ int lzcount;
+
+ /* hidden bit of low double controls rounding of the high double.
+ If hidden is '1' and either the explicit mantissa is non-zero
+ or hi is odd, then round up hi and adjust lo (2nd mantissa)
+ plus change the sign of the low double to compensate. */
+ if ((lo & ((uint64_t) 1 << 52)) != 0
+ && ((hi & 1) != 0 || (lo & (((uint64_t) 1 << 52) - 1)) != 0))
+ {
+ hi++;
+ if ((hi & ((uint64_t) 1 << 53)) != 0)
+ {
+ hi = hi >> 1;
+ u.d[0].ieee.exponent++;
+ }
+ u.d[1].ieee.negative = !sign;
+ lo = ((uint64_t) 1 << 53) - lo;
+ }
+
+ /* Normalize the low double. Shift the mantissa left until
+ the hidden bit is '1' and adjust the exponent accordingly. */
+
+ if (sizeof (lo) == sizeof (long))
+ lzcount = __builtin_clzl (lo);
+ else if ((lo >> 32) != 0)
+ lzcount = __builtin_clzl ((long) (lo >> 32));
+ else
+ lzcount = __builtin_clzl ((long) lo) + 32;
+ lzcount = lzcount - (64 - 53);
+ lo <<= lzcount;
+ expnt2 -= lzcount;
+
+ if (expnt2 >= 1)
+ /* Not denormal. */
+ u.d[1].ieee.exponent = expnt2;
+ else
+ {
+ /* Is denormal. Note that biased exponent of 0 is treated
+ as if it was 1, hence the extra shift. */
+ if (expnt2 > -53)
+ lo >>= 1 - expnt2;
+ else
+ lo = 0;
+ }
+ }
+ else
+ u.d[1].ieee.negative = 0;
+
+ u.d[1].ieee.mantissa1 = lo;
+ u.d[1].ieee.mantissa0 = lo >> 32;
+ u.d[0].ieee.mantissa1 = hi;
+ u.d[0].ieee.mantissa0 = hi >> 32;
+ return u.ld;
+}
+
+/* Handy utility functions to pack/unpack/cononicalize and find the nearbyint
+ of long double implemented as double double. */
+static inline long double
+default_ldbl_pack (double a, double aa)
+{
+ union ibm_extended_long_double u;
+ u.d[0].d = a;
+ u.d[1].d = aa;
+ return u.ld;
+}
+
+static inline void
+default_ldbl_unpack (long double l, double *a, double *aa)
+{
+ union ibm_extended_long_double u;
+ u.ld = l;
+ *a = u.d[0].d;
+ *aa = u.d[1].d;
+}
+
+#ifndef ldbl_pack
+# define ldbl_pack default_ldbl_pack
+#endif
+#ifndef ldbl_unpack
+# define ldbl_unpack default_ldbl_unpack
+#endif
+
+/* Extract high double. */
+#define ldbl_high(x) ((double) x)
+
+/* Convert a finite long double to canonical form.
+ Does not handle +/-Inf properly. */
+static inline void
+ldbl_canonicalize (double *a, double *aa)
+{
+ double xh, xl;
+
+ xh = *a + *aa;
+ xl = (*a - xh) + *aa;
+ *a = xh;
+ *aa = xl;
+}
+
+/* Simple inline nearbyint (double) function.
+ Only works in the default rounding mode
+ but is useful in long double rounding functions. */
+static inline double
+ldbl_nearbyint (double a)
+{
+ double two52 = 0x1p52;
+
+ if (__glibc_likely ((__builtin_fabs (a) < two52)))
+ {
+ if (__glibc_likely ((a > 0.0)))
+ {
+ a += two52;
+ a -= two52;
+ }
+ else if (__glibc_likely ((a < 0.0)))
+ {
+ a = two52 - a;
+ a = -(a - two52);
+ }
+ }
+ return a;
+}
+
+/* Canonicalize a result from an integer rounding function, in any
+ rounding mode. *A and *AA are finite and integers, with *A being
+ nonzero; if the result is not already canonical, *AA is plus or
+ minus a power of 2 that does not exceed the least set bit in
+ *A. */
+static inline void
+ldbl_canonicalize_int (double *a, double *aa)
+{
+ /* Previously we used EXTRACT_WORDS64 from math_private.h, but in order
+ to avoid including internal headers we duplicate that code here. */
+ uint64_t ax, aax;
+ union { double value; uint64_t word; } extractor;
+ extractor.value = *a;
+ ax = extractor.word;
+ extractor.value = *aa;
+ aax = extractor.word;
+
+ int expdiff = ((ax >> 52) & 0x7ff) - ((aax >> 52) & 0x7ff);
+ if (expdiff <= 53)
+ {
+ if (expdiff == 53)
+ {
+ /* Half way between two double values; noncanonical iff the
+ low bit of A's mantissa is 1. */
+ if ((ax & 1) != 0)
+ {
+ *a += 2 * *aa;
+ *aa = -*aa;
+ }
+ }
+ else
+ {
+ /* The sum can be represented in a single double. */
+ *a += *aa;
+ *aa = 0;
+ }
+ }
+}
+
+#endif /* math_ldbl.h */
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