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authorZack Weinberg <zackw@panix.com>2017-06-08 15:39:03 -0400
committerZack Weinberg <zackw@panix.com>2017-06-08 15:39:03 -0400
commit5046dbb4a7eba5eccfd258f92f4735c9ffc8d069 (patch)
tree4470480d904b65cf14ca524f96f79eca818c3eaf /REORG.TODO/sysdeps/ieee754/ldbl-128ibm/math_ldbl.h
parent199fc19d3aaaf57944ef036e15904febe877fc93 (diff)
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Prepare for radical source tree reorganization. zack/build-layout-experiment
All top-level files and directories are moved into a temporary storage
directory, REORG.TODO, except for files that will certainly still
exist in their current form at top level when we're done (COPYING,
COPYING.LIB, LICENSES, NEWS, README), all old ChangeLog files (which
are moved to the new directory OldChangeLogs, instead), and the
generated file INSTALL (which is just deleted; in the new order, there
will be no generated files checked into version control).
Diffstat (limited to 'REORG.TODO/sysdeps/ieee754/ldbl-128ibm/math_ldbl.h')
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--- /dev/null
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@@ -0,0 +1,290 @@
+/* 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 */