[PATCH 4/6] Implement a general log2 facility in the kernel

David Howells
2006-09-13T13:03:12Z

From: David Howells <dhowells@redhat.com>

This facility provides three entry points:

log2() Log base 2 of u32
ll_log2() Log base 2 of u64
long_log2() Log base 2 of unsigned long

These facilities can either be used inside functions on dynamic data:

int do_something(long q)
{
...;
y = log2(x)
...;
}

Or can be used to statically initialise global variables with constant values:

unsigned n = log2(27);

When performing static initialisation, the compiler will report "error:
initializer element is not constant" if asked to take a log of zero or of
something not reducible to a constant. They treat negative numbers as
unsigned.

When not dealing with a constant, they fall back to using fls() which permits
them to use arch-specific log calculation instructions - such as BSR on
x86/x86_64 or SCAN on FRV - if available.

Signed-Off-By: David Howells <dhowells@redhat.com>
---

fs/ext2/super.c | 2 -
fs/ext3/super.c | 2 -
include/asm-frv/bitops.h | 44 +++++++++++
include/linux/kernel.h | 9 --
include/linux/log2.h | 179 ++++++++++++++++++++++++++++++++++++++++++++++
5 files changed, 224 insertions(+), 12 deletions(-)

diff --git a/fs/ext2/super.c b/fs/ext2/super.c
index 681dea8..a4573b6 100644
--- a/fs/ext2/super.c
+++ b/fs/ext2/super.c
@@ -548,8 +548,6 @@ static int ext2_check_descriptors (struc
return 1;
}

-#define log2(n) ffz(~(n))
-
/*
* Maximal file size. There is a direct, and {,double-,triple-}indirect
* block limit, and also a limit of (2^32 - 1) 512-byte sectors in i_blocks.
diff --git a/fs/ext3/super.c b/fs/ext3/super.c
index 813d589..af1424d 100644
--- a/fs/ext3/super.c
+++ b/fs/ext3/super.c
@@ -1294,8 +1294,6 @@ #endif
sb->s_flags = s_flags; /* Restore MS_RDONLY status */
}

-#define log2(n) ffz(~(n))
-
/*
* Maximal file size. There is a direct, and {,double-,triple-}indirect
* block limit, and also a limit of (2^32 - 1) 512-byte sectors in i_blocks.
diff --git a/include/asm-frv/bitops.h b/include/asm-frv/bitops.h
index 1f70d47..41a5866 100644
--- a/include/asm-frv/bitops.h
+++ b/include/asm-frv/bitops.h
@@ -256,6 +256,50 @@ int __ffs(unsigned long x)
return 31 - bit;
}

+/*
+ * special slimline version of fls() for calculating log2()
+ * - note: no protection against n == 0
+ */
+#define ARCH_HAS_LOG2
+static inline __attribute__((const))
+int __log2(u32 n)
+{
+ int bit;
+ asm("scan %1,gr0,%0" : "=r"(bit) : "r"(n));
+ return 31 - bit;
+}
+
+/*
+ * special slimline version of fls64() for calculating ll_log2()
+ * - note: no protection against n == 0
+ */
+#define ARCH_HAS_LL_LOG2
+static inline __attribute__((const))
+int __ll_log2(u64 n)
+{
+ union {
+ u64 ll;
+ struct { u32 h, l; };
+ } _;
+ int bit, x, y;
+
+ _.ll = n;
+
+ asm(" subcc %3,gr0,gr0,icc0 \n"
+ " ckeq icc0,cc4 \n"
+ " cscan.p %3,gr0,%0 ,cc4,0 \n"
+ " setlos #63,%1 \n"
+ " cscan.p %4,gr0,%0 ,cc4,1 \n"
+ " setlos #31,%2 \n"
+ " csub.p %1,%0,%0 ,cc4,0 \n"
+ " csub %2,%0,%0 ,cc4,1 \n"
+ : "=&r"(bit), "=r"(x), "=r"(y)
+ : "0r"(_.h), "r"(_.l)
+ : "icc0", "cc4"
+ );
+ return bit;
+}
+
#include <asm-generic/bitops/sched.h>
#include <asm-generic/bitops/hweight.h>

diff --git a/include/linux/kernel.h b/include/linux/kernel.h
index 851aa1b..e8c6c66 100644
--- a/include/linux/kernel.h
+++ b/include/linux/kernel.h
@@ -13,6 +13,7 @@ #include <linux/stddef.h>
#include <linux/types.h>
#include <linux/compiler.h>
#include <linux/bitops.h>
+#include <linux/log2.h>
#include <asm/byteorder.h>
#include <asm/bug.h>

@@ -154,14 +155,6 @@ #endif

unsigned long int_sqrt(unsigned long);

-static inline int __attribute_pure__ long_log2(unsigned long x)
-{
- int r = 0;
- for (x >>= 1; x > 0; x >>= 1)
- r++;
- return r;
-}
-
static inline unsigned long
__attribute_const__ roundup_pow_of_two(unsigned long x)
{
diff --git a/include/linux/log2.h b/include/linux/log2.h
new file mode 100644
index 0000000..9bef055
--- /dev/null
+++ b/include/linux/log2.h
@@ -0,0 +1,179 @@
+/* Log base 2 calculation
+ *
+ * Copyright (C) 2006 Red Hat, Inc. All Rights Reserved.
+ * Written by David Howells (dhowells@redhat.com)
+ *
+ * This program is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU General Public License
+ * as published by the Free Software Foundation; either version
+ * 2 of the License, or (at your option) any later version.
+ */
+
+#ifndef _LINUX_LOG2_H
+#define _LINUX_LOG2_H
+
+#include <linux/types.h>
+#include <linux/bitops.h>
+
+/*
+ * deal with unrepresentable constant logarithms
+ */
+extern __attribute__((const, noreturn))
+int ____log2_NaN(void);
+
+/*
+ * non-constant log of base 2 calculation
+ * - the arch may override these in asm/bitops.h if they can be implemented
+ * more efficiently than using fls() and fls64()
+ */
+#ifndef ARCH_HAS_LOG2
+static inline __attribute__((const))
+int __log2(u32 n)
+{
+ return fls(n) - 1;
+}
+#endif
+
+#ifndef ARCH_HAS_LL_LOG2
+static inline __attribute__((const))
+int __ll_log2(u64 n)
+{
+ return fls64(n) - 1;
+}
+#endif
+
+/*
+ * constant-capable 32-bit log of base 2 calculation
+ * - this can be used to initialise global variables from constant data, hence
+ * the massive ternary operator construction
+ */
+#define log2(n) \
+( \
+ __builtin_constant_p(n) ? ( \
+ n < 1 ? ____log2_NaN() : \
+ n >= (1ULL << 31) ? 31 : \
+ n >= (1ULL << 30) ? 30 : \
+ n >= (1ULL << 29) ? 29 : \
+ n >= (1ULL << 28) ? 28 : \
+ n >= (1ULL << 27) ? 27 : \
+ n >= (1ULL << 26) ? 26 : \
+ n >= (1ULL << 25) ? 25 : \
+ n >= (1ULL << 24) ? 24 : \
+ n >= (1ULL << 23) ? 23 : \
+ n >= (1ULL << 22) ? 22 : \
+ n >= (1ULL << 21) ? 21 : \
+ n >= (1ULL << 20) ? 20 : \
+ n >= (1ULL << 19) ? 19 : \
+ n >= (1ULL << 18) ? 18 : \
+ n >= (1ULL << 17) ? 17 : \
+ n >= (1ULL << 16) ? 16 : \
+ n >= (1ULL << 15) ? 15 : \
+ n >= (1ULL << 14) ? 14 : \
+ n >= (1ULL << 13) ? 13 : \
+ n >= (1ULL << 12) ? 12 : \
+ n >= (1ULL << 11) ? 11 : \
+ n >= (1ULL << 10) ? 10 : \
+ n >= (1ULL << 9) ? 9 : \
+ n >= (1ULL << 8) ? 8 : \
+ n >= (1ULL << 7) ? 7 : \
+ n >= (1ULL << 6) ? 6 : \
+ n >= (1ULL << 5) ? 5 : \
+ n >= (1ULL << 4) ? 4 : \
+ n >= (1ULL << 3) ? 3 : \
+ n >= (1ULL << 2) ? 2 : \
+ n >= (1ULL << 1) ? 1 : \
+ n >= (1ULL << 0) ? 0 : \
+ ____log2_NaN() \
+ ) : \
+ __log2(n) \
+ )
+
+/*
+ * constant-capable 64-bit log of base 2 calculation
+ * - this can be used to initialise global variables from constant data, hence
+ * the massive ternary operator construction
+ */
+#define ll_log2(n) \
+( \
+ __builtin_constant_p(n) ? ( \
+ n < 1 ? ____log2_NaN() : \
+ n >= (1ULL << 63) ? 63 : \
+ n >= (1ULL << 62) ? 62 : \
+ n >= (1ULL << 61) ? 61 : \
+ n >= (1ULL << 60) ? 60 : \
+ n >= (1ULL << 59) ? 59 : \
+ n >= (1ULL << 58) ? 58 : \
+ n >= (1ULL << 57) ? 57 : \
+ n >= (1ULL << 56) ? 56 : \
+ n >= (1ULL << 55) ? 55 : \
+ n >= (1ULL << 54) ? 54 : \
+ n >= (1ULL << 53) ? 53 : \
+ n >= (1ULL << 52) ? 52 : \
+ n >= (1ULL << 51) ? 51 : \
+ n >= (1ULL << 50) ? 50 : \
+ n >= (1ULL << 49) ? 49 : \
+ n >= (1ULL << 48) ? 48 : \
+ n >= (1ULL << 47) ? 47 : \
+ n >= (1ULL << 46) ? 46 : \
+ n >= (1ULL << 45) ? 45 : \
+ n >= (1ULL << 44) ? 44 : \
+ n >= (1ULL << 43) ? 43 : \
+ n >= (1ULL << 42) ? 42 : \
+ n >= (1ULL << 41) ? 41 : \
+ n >= (1ULL << 40) ? 40 : \
+ n >= (1ULL << 39) ? 39 : \
+ n >= (1ULL << 38) ? 38 : \
+ n >= (1ULL << 37) ? 37 : \
+ n >= (1ULL << 36) ? 36 : \
+ n >= (1ULL << 35) ? 35 : \
+ n >= (1ULL << 34) ? 34 : \
+ n >= (1ULL << 33) ? 33 : \
+ n >= (1ULL << 32) ? 32 : \
+ n >= (1ULL << 31) ? 31 : \
+ n >= (1ULL << 30) ? 30 : \
+ n >= (1ULL << 29) ? 29 : \
+ n >= (1ULL << 28) ? 28 : \
+ n >= (1ULL << 27) ? 27 : \
+ n >= (1ULL << 26) ? 26 : \
+ n >= (1ULL << 25) ? 25 : \
+ n >= (1ULL << 24) ? 24 : \
+ n >= (1ULL << 23) ? 23 : \
+ n >= (1ULL << 22) ? 22 : \
+ n >= (1ULL << 21) ? 21 : \
+ n >= (1ULL << 20) ? 20 : \
+ n >= (1ULL << 19) ? 19 : \
+ n >= (1ULL << 18) ? 18 : \
+ n >= (1ULL << 17) ? 17 : \
+ n >= (1ULL << 16) ? 16 : \
+ n >= (1ULL << 15) ? 15 : \
+ n >= (1ULL << 14) ? 14 : \
+ n >= (1ULL << 13) ? 13 : \
+ n >= (1ULL << 12) ? 12 : \
+ n >= (1ULL << 11) ? 11 : \
+ n >= (1ULL << 10) ? 10 : \
+ n >= (1ULL << 9) ? 9 : \
+ n >= (1ULL << 8) ? 8 : \
+ n >= (1ULL << 7) ? 7 : \
+ n >= (1ULL << 6) ? 6 : \
+ n >= (1ULL << 5) ? 5 : \
+ n >= (1ULL << 4) ? 4 : \
+ n >= (1ULL << 3) ? 3 : \
+ n >= (1ULL << 2) ? 2 : \
+ n >= (1ULL << 1) ? 1 : \
+ n >= (1ULL << 0) ? 0 : \
+ ____log2_NaN() \
+ ) : \
+ __ll_log2(n) \
+ )
+
+/*
+ * constant-capable unsigned long log of base 2 calculation
+ * - this can be used to initialise global variables from constant data
+ */
+#if BITS_PER_LONG == 32
+#define long_log2(n) log2(n)
+#else
+#define long_log2(n) ll_log2(n)
+#endif
+
+#endif /* _LINUX_LOG2_H */