[glibc/fw/dl-bind-performance] Introduce divopt.h

[Florian Weimer <fw@sourceware.org>]

https://sourceware.org/git/gitweb.cgi?p=glibc.git;h=0e5a24f5a968c0f791ea5e6625ad41a27c82cce6

commit 0e5a24f5a968c0f791ea5e6625ad41a27c82cce6
Author: Florian Weimer <fweimer@redhat.com>
Date:   Mon Nov 4 18:07:06 2019 +0100

    Introduce divopt.h
    
    Change-Id: I440e41fd50de1cfc036c8557846c0bfc75654e49

Diff:
---
 include/divopt.h | 78 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 78 insertions(+)

diff --git a/include/divopt.h b/include/divopt.h
new file mode 100644
index 0000000000..85eece8fd9
--- /dev/null
+++ b/include/divopt.h
@@ -0,0 +1,78 @@
+/* Optimization of repeated integer division.
+   Copyright (C) 2019 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
+   <https://www.gnu.org/licenses/>.  */
+
+#include <stdint.h>
+#include <sys/param.h>
+
+/* Precompute *MULTIPLIER for dividing by DIVISOR, which must be two
+   or larger, and return the shift count (non-negative and less than
+   32), for use with divopt_32 below.  */
+static int __attribute__ ((used))
+precompute_divopt_32 (uint32_t divisor, uint32_t *multiplier)
+{
+  if (divisor == 1)
+    {
+      *multiplier = 1;
+      return 0;
+    }
+
+  int log2 = 32 - __builtin_clz (divisor);
+
+  /* Handle powers-of-two first, so that we do not need to deal with
+     the clz corner cases below.  */
+  if (powerof2 (divisor))
+    {
+      *multiplier = 1;
+      return log2 - 2;
+    }
+
+  if (log2 != 32)
+    {
+      /* Compute ceil (2**(32 + log2) / divisor).  The
+         most-significant bit is always set and is discarded.  */
+      *multiplier = (((uint64_t) 1 << (32 + log2)) + divisor) / divisor;
+      return log2 - 1;
+    }
+  else
+    {
+      /* Perform a long division of 2**64 + (divisor - 1) by the
+         divisor, encoded in base-2**32, using a 64-by-32 division.
+         Start out with the first two digits, which are (1, 0).  2**32
+         divided by the divisor is 1 because the divisor is larger
+         than 2**31.  This set bit is discarded.  */
+      uint64_t remainder = -divisor;
+
+      /* Combine the remainder of the first division with the third
+         and final base 2**32 digit.  */
+      *multiplier = ((remainder << 32) | (divisor - 1)) / divisor;
+      return 31;
+    }
+}
+
+/* Return the quotient of DIVIDEND devided by the divisor that was
+   used to compute MULTIPLIER and SHIFT via precompute_divopt_32.  */
+static inline uint32_t
+divopt_32 (uint32_t dividend, uint32_t multiplier, int shift)
+{
+  /* Approximation to the quotient.  */
+  uint32_t quotient = ((uint64_t) dividend * multiplier) >> 32;
+  /* Compute (dividend + quotient) / 2 without overflow.  */
+  uint32_t temp = ((dividend - quotient) >> 1) + quotient;
+  /* The result is in the higher-order bits.  */
+  return temp >> shift;
+}