# Re: [PATCH 1/1] vsprintf: optimize decimal conversion (again)

From: Denys Vlasenko
Date: Mon Mar 26 2012 - 20:27:01 EST

On Monday 26 March 2012 22:13, Andrew Morton wrote:
> On Mon, 26 Mar 2012 21:56:38 +0200
> Denys Vlasenko <vda.linux@xxxxxxxxxxxxxx> wrote:
>
> > >> +#if BITS_PER_LONG != 32 || (~(0ULL)>>1) != ((1ULL<<63)-1)
> > >
> > > What's this for?
> >
> > The second check should be just BITS_PER_LONG_LONG != 64,
> > but we don't have BITS_PER_LONG_LONG.
>
> So let's add BITS_PER_LONG_LONG rather than hacking around its absence!

Sure!

Here is a new version. I also plugged a hole in num_to_str() -
it was assuming it's safe to call put_dec() for num=0.
(We never tripped over it before because the single caller
of num_to_str() takes care of that case).

Signed-off-by and CC are also updated.
--
vda

commit 469bfce8d60d1069424aacc83fef50f9da5701bf
Author: Denys Vlasenko <vda.linux@xxxxxxxxxxxxxx>
Date: Tue Mar 27 02:18:46 2012 +0200

vsprintf: optimize decimal conversion (again)

This patch is based upon an original from Michal Nazarewicz.

Previous code was using optimizations which were developed
to work well even on narrow-word CPUs (by today's standards).
But Linux runs only on 32-bit and wider CPUs. We can use that.

First: using 32x32->64 multiply and trivial 32-bit shift,
we can correctly divide by 10 much larger numbers, and thus
we can print groups of 9 digits instead of groups of 5 digits.

Next: there are two algorithms to print larger numbers.
One is generic: divide by 1000000000 and repeatedly print
groups of (up to) 9 digits. It's conceptually simple,
but requires an (unsigned long long) / 1000000000 division.

Second algorithm splits 64-bit unsigned long long into 16-bit chunks,
manipulates them cleverly and generates groups of 4 decimal digits.
It so happens that it does NOT require long long division.

If long is > 32 bits, division of 64-bit values is relatively easy,
and we will use the first algorithm.
If long long is > 64 bits (strange architecture with VERY large long long),
second algorithm can't be used, and we again use the first one.

Else (if long is 32 bits and long long is 64 bits) we use second one.

And third: there is a simple optimization which takes fast path
not only for zero as was done before, but for all one-digit numbers.

In all tested cases new code is faster than old one, in many cases by 30%,
in few cases by more than 50% (for example, on x86-32, conversion of 12345678).
Code growth is ~0 in 32-bit case and ~130 bytes in 64-bit case.

Signed-off-by: Michal Nazarewicz <mina86@xxxxxxxxxx>
Signed-off-by: Denys Vlasenko <vda.linux@xxxxxxxxxxxxxx>
Cc: Douglas W Jones <jones@xxxxxxxxxxxx>

diff --git a/include/asm-generic/bitsperlong.h b/include/asm-generic/bitsperlong.h
index 4ae54e0..a7b0914 100644
--- a/include/asm-generic/bitsperlong.h
+++ b/include/asm-generic/bitsperlong.h
@@ -28,5 +28,9 @@
#error Inconsistent word size. Check asm/bitsperlong.h
#endif

+#ifndef BITS_PER_LONG_LONG
+#define BITS_PER_LONG_LONG 64
+#endif
+
#endif /* __KERNEL__ */
#endif /* __ASM_GENERIC_BITS_PER_LONG */
diff --git a/lib/vsprintf.c b/lib/vsprintf.c
index abbabec..877a503 100644
--- a/lib/vsprintf.c
+++ b/lib/vsprintf.c
@@ -112,106 +112,191 @@ int skip_atoi(const char **s)
/* Decimal conversion is by far the most typical, and is used
* for /proc and /sys data. This directly impacts e.g. top performance
* with many processes running. We optimize it for speed
- * using code from
- * http://www.cs.uiowa.edu/~jones/bcd/decimal.html
- * (with permission from the author, Douglas W. Jones). */
+ * using ideas described at <http://www.cs.uiowa.edu/~jones/bcd/divide.html>
+ * (with permission from the author, Douglas W. Jones).
+ */

-/* Formats correctly any integer in [0,99999].
- * Outputs from one to five digits depending on input.
- * On i386 gcc 4.1.2 -O2: ~250 bytes of code. */
+#if BITS_PER_LONG != 32 || BITS_PER_LONG_LONG != 64
+/* Formats correctly any integer in [0, 999999999] */
static noinline_for_stack
-char *put_dec_trunc(char *buf, unsigned q)
+char *put_dec_full9(char *buf, unsigned q)
{
- unsigned d3, d2, d1, d0;
- d1 = (q>>4) & 0xf;
- d2 = (q>>8) & 0xf;
- d3 = (q>>12);
-
- d0 = 6*(d3 + d2 + d1) + (q & 0xf);
- q = (d0 * 0xcd) >> 11;
- d0 = d0 - 10*q;
- *buf++ = d0 + '0'; /* least significant digit */
- d1 = q + 9*d3 + 5*d2 + d1;
- if (d1 != 0) {
- q = (d1 * 0xcd) >> 11;
- d1 = d1 - 10*q;
- *buf++ = d1 + '0'; /* next digit */
-
- d2 = q + 2*d2;
- if ((d2 != 0) || (d3 != 0)) {
- q = (d2 * 0xd) >> 7;
- d2 = d2 - 10*q;
- *buf++ = d2 + '0'; /* next digit */
-
- d3 = q + 4*d3;
- if (d3 != 0) {
- q = (d3 * 0xcd) >> 11;
- d3 = d3 - 10*q;
- *buf++ = d3 + '0'; /* next digit */
- if (q != 0)
- *buf++ = q + '0'; /* most sign. digit */
- }
- }
- }
-
+ unsigned r;
+
+ /* Possible ways to approx. divide by 10
+ * (x * 0x1999999a) >> 32 x < 1073741829 (multiply must be 64-bit)
+ * (x * 0xcccd) >> 19 x < 81920 (x < 262149 when 64-bit mul)
+ * (x * 0x6667) >> 18 x < 43699
+ * (x * 0x3334) >> 17 x < 16389
+ * (x * 0x199a) >> 16 x < 16389
+ * (x * 0x0ccd) >> 15 x < 16389
+ * (x * 0x0667) >> 14 x < 2739
+ * (x * 0x0334) >> 13 x < 1029
+ * (x * 0x019a) >> 12 x < 1029
+ * (x * 0x00cd) >> 11 x < 1029 shorter code than * 0x67 (on i386)
+ * (x * 0x0067) >> 10 x < 179
+ * (x * 0x0034) >> 9 x < 69 same
+ * (x * 0x001a) >> 8 x < 69 same
+ * (x * 0x000d) >> 7 x < 69 same, shortest code (on i386)
+ * (x * 0x0007) >> 6 x < 19
+ * See <http://www.cs.uiowa.edu/~jones/bcd/divide.html>
+ */
+ r = (q * (uint64_t)0x1999999a) >> 32;
+ *buf++ = (q - 10 * r) + '0'; /* 1 */
+ q = (r * (uint64_t)0x1999999a) >> 32;
+ *buf++ = (r - 10 * q) + '0'; /* 2 */
+ r = (q * (uint64_t)0x1999999a) >> 32;
+ *buf++ = (q - 10 * r) + '0'; /* 3 */
+ q = (r * (uint64_t)0x1999999a) >> 32;
+ *buf++ = (r - 10 * q) + '0'; /* 4 */
+ r = (q * (uint64_t)0x1999999a) >> 32;
+ *buf++ = (q - 10 * r) + '0'; /* 5 */
+ /* Now value is under 10000, can avoid 64-bit multiply */
+ q = (r * 0x199a) >> 16;
+ *buf++ = (r - 10 * q) + '0'; /* 6 */
+ r = (q * 0xcd) >> 11;
+ *buf++ = (q - 10 * r) + '0'; /* 7 */
+ q = (r * 0xcd) >> 11;
+ *buf++ = (r - 10 * q) + '0'; /* 8 */
+ *buf++ = q + '0'; /* 9 */
return buf;
}
-/* Same with if's removed. Always emits five digits */
+#endif
+
+/* Similar to above but do not pad with zeros.
+ * Code can be easily arranged to print 9 digits too, but our callers
+ * always call put_dec_full9() instead when the number has 9 decimal digits.
+ */
static noinline_for_stack
-char *put_dec_full(char *buf, unsigned q)
+char *put_dec_trunc8(char *buf, unsigned r)
{
- /* BTW, if q is in [0,9999], 8-bit ints will be enough, */
- /* but anyway, gcc produces better code with full-sized ints */
- unsigned d3, d2, d1, d0;
- d1 = (q>>4) & 0xf;
- d2 = (q>>8) & 0xf;
- d3 = (q>>12);
+ unsigned q;
+
+ /* Copy of previous function's body with added early returns */
+ q = (r * (uint64_t)0x1999999a) >> 32;
+ *buf++ = (r - 10 * q) + '0'; /* 2 */
+ if (q == 0) return buf;
+ r = (q * (uint64_t)0x1999999a) >> 32;
+ *buf++ = (q - 10 * r) + '0'; /* 3 */
+ if (r == 0) return buf;
+ q = (r * (uint64_t)0x1999999a) >> 32;
+ *buf++ = (r - 10 * q) + '0'; /* 4 */
+ if (q == 0) return buf;
+ r = (q * (uint64_t)0x1999999a) >> 32;
+ *buf++ = (q - 10 * r) + '0'; /* 5 */
+ if (r == 0) return buf;
+ q = (r * 0x199a) >> 16;
+ *buf++ = (r - 10 * q) + '0'; /* 6 */
+ if (q == 0) return buf;
+ r = (q * 0xcd) >> 11;
+ *buf++ = (q - 10 * r) + '0'; /* 7 */
+ if (r == 0) return buf;
+ q = (r * 0xcd) >> 11;
+ *buf++ = (r - 10 * q) + '0'; /* 8 */
+ if (q == 0) return buf;
+ *buf++ = q + '0'; /* 9 */
+ return buf;
+}

- /*
- * Possible ways to approx. divide by 10
- * gcc -O2 replaces multiply with shifts and adds
- * (x * 0xcd) >> 11: 11001101 - shorter code than * 0x67 (on i386)
- * (x * 0x67) >> 10: 1100111
- * (x * 0x34) >> 9: 110100 - same
- * (x * 0x1a) >> 8: 11010 - same
- * (x * 0x0d) >> 7: 1101 - same, shortest code (on i386)
- */
- d0 = 6*(d3 + d2 + d1) + (q & 0xf);
- q = (d0 * 0xcd) >> 11;
- d0 = d0 - 10*q;
- *buf++ = d0 + '0';
- d1 = q + 9*d3 + 5*d2 + d1;
- q = (d1 * 0xcd) >> 11;
- d1 = d1 - 10*q;
- *buf++ = d1 + '0';
-
- d2 = q + 2*d2;
- q = (d2 * 0xd) >> 7;
- d2 = d2 - 10*q;
- *buf++ = d2 + '0';
-
- d3 = q + 4*d3;
- q = (d3 * 0xcd) >> 11; /* - shorter code */
- /* q = (d3 * 0x67) >> 10; - would also work */
- d3 = d3 - 10*q;
- *buf++ = d3 + '0';
- *buf++ = q + '0';
+/* There are two algorithms to print larger numbers.
+ * One is generic: divide by 1000000000 and repeatedly print
+ * groups of (up to) 9 digits. It's conceptually simple,
+ * but requires a (unsigned long long) / 1000000000 division.
+ *
+ * Second algorithm splits 64-bit unsigned long long into 16-bit chunks,
+ * manipulates them cleverly and generates groups of 4 decimal digits.
+ * It so happens that it does NOT require long long division.
+ *
+ * If long is > 32 bits, division of 64-bit values is relatively easy,
+ * and we will use the first algorithm.
+ * If long long is > 64 bits (strange architecture with VERY large long long),
+ * second algorithm can't be used, and we again use the first one.
+ *
+ * Else (if long is 32 bits and long long is 64 bits) we use second one.
+ */

- return buf;
+#if BITS_PER_LONG != 32 || BITS_PER_LONG_LONG != 64
+
+/* First algorithm: generic */
+
+static
+char *put_dec(char *buf, unsigned long long n)
+{
+ if (n >= 100*1000*1000) {
+ while (n >= 1000*1000*1000)
+ buf = put_dec_full9(buf, do_div(n, 1000*1000*1000));
+ if (n >= 100*1000*1000)
+ return put_dec_full9(buf, n);
+ }
+ return put_dec_trunc8(buf, n);
}
-/* No inlining helps gcc to use registers better */
+
+#else
+
+/* Second algorithm: valid only for 64-bit long longs */
+
static noinline_for_stack
-char *put_dec(char *buf, unsigned long long num)
+char *put_dec_full4(char *buf, unsigned q)
{
- while (1) {
- unsigned rem;
- if (num < 100000)
- return put_dec_trunc(buf, num);
- rem = do_div(num, 100000);
- buf = put_dec_full(buf, rem);
- }
+ unsigned r;
+ r = (q * 0xcccd) >> 19;
+ *buf++ = (q - 10 * r) + '0';
+ q = (r * 0x199a) >> 16;
+ *buf++ = (r - 10 * q) + '0';
+ r = (q * 0xcd) >> 11;
+ *buf++ = (q - 10 * r) + '0';
+ *buf++ = r + '0';
+ return buf;
}

+/* Based on code by Douglas W. Jones found at
+ * <http://www.cs.uiowa.edu/~jones/bcd/decimal.html#sixtyfour>
+ * (with permission from the author).
+ * Performs no 64-bit division and hence should be fast on 32-bit machines.
+ */
+static
+char *put_dec(char *buf, unsigned long long n)
+{
+ uint32_t d3, d2, d1, q, h;
+
+ if (n < 100*1000*1000)
+ return put_dec_trunc8(buf, n);
+
+ d1 = ((uint32_t)n >> 16); /* implicit "& 0xffff" */
+ h = (n >> 32);
+ d2 = (h ) & 0xffff;
+ d3 = (h >> 16); /* implicit "& 0xffff" */
+
+ q = 656 * d3 + 7296 * d2 + 5536 * d1 + ((uint32_t)n & 0xffff);
+
+ buf = put_dec_full4(buf, q % 10000);
+ q = q / 10000;
+
+ d1 = q + 7671 * d3 + 9496 * d2 + 6 * d1;
+ buf = put_dec_full4(buf, d1 % 10000);
+ q = d1 / 10000;
+
+ d2 = q + 4749 * d3 + 42 * d2;
+ buf = put_dec_full4(buf, d2 % 10000);
+ q = d2 / 10000;
+
+ d3 = q + 281 * d3;
+ if (!d3)
+ goto done;
+ buf = put_dec_full4(buf, d3 % 10000);
+ q = d3 / 10000;
+ if (!q)
+ goto done;
+ buf = put_dec_full4(buf, q);
+ done:
+ while (buf[-1] == '0')
+ --buf;
+
+ return buf;
+}
+
+#endif
+
/*
* Convert passed number to decimal string.
* Returns the length of string. On buffer overflow, returns 0.
@@ -220,16 +305,22 @@ char *put_dec(char *buf, unsigned long long num)
*/
int num_to_str(char *buf, int size, unsigned long long num)
{
- char tmp; /* Enough for 2^64 in decimal */
+ char tmp[sizeof(num) * 3];
int idx, len;

- len = put_dec(tmp, num) - tmp;
+ /* put_dec() may work incorrectly for num = 0 (generate "", not "0") */
+ if (num <= 9) {
+ tmp = '0' + num;
+ len = 1;
+ } else {
+ len = put_dec(tmp, num) - tmp;
+ }

if (len > size)
return 0;
for (idx = 0; idx < len; ++idx)
buf[idx] = tmp[len - idx - 1];
- return len;
+ return len;
}

@@ -312,8 +403,8 @@ char *number(char *buf, char *end, unsigned long long num,

/* generate full string in tmp[], in reverse order */
i = 0;
- if (num == 0)
- tmp[i++] = '0';
+ if (num < spec.base)
+ tmp[i++] = digits[num] | locase;
/* Generic code, for any base:
else do {
tmp[i++] = (digits[do_div(num,base)] | locase);
@@ -607,7 +698,7 @@ char *ip4_string(char *p, const u8 *addr, const char *fmt)
}
for (i = 0; i < 4; i++) {
char temp; /* hold each IP quad in reverse order */
- int digits = put_dec_trunc(temp, addr[index]) - temp;
+ int digits = put_dec_trunc8(temp, addr[index]) - temp;