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From: Michal Nazarewicz on 13 Aug 2010 08:10
The put_dec() and family of functions were based on a code
optimised for processors with 8-bit ALU but since we don't
need to limit ourselves to such small ALUs, the code was
optimised and used capacities of an 16-bit ALU anyway.

This patch goes further and uses the full capacity of the
processor's ALU.

On 64-bit machines, the number is repeatedly divided by
100,000 to split it into 5-decimal-digit which are converted
using the obvious base conversion algorithm expect division by
ten is replaced with multiplication and shifts.

On 32-bit machines, no division is performed at all and in
particular, no 64-bit division is performed. This can speed
up conversion a few times and up to 10 times!

Signed-off-by: Michal Nazarewicz <mina86(a)mina86.com>
Signed-off-by: Douglas W. Jones <jones(a)cs.uiowa.edu>
Cc: Denis Vlasenko <vda.linux(a)googlemail.com>
---
lib/vsprintf.c | 293 ++++++++++++++++++++++++++++++++++++++------------------
1 files changed, 201 insertions(+), 92 deletions(-)

> On Wednesday 11 August 2010 23:58, Michal Nazarewicz wrote:
>> +static noinline_for_stack
>> +char *put_dec(char *buf, unsigned long long n)
>> +{
>> + uint32_t d3, d2, d1, q;
>> +
>> + if (n < 10) {
>> + *buf++ = '0' + (unsigned)n;
>> + return buf;
>> + }

Denys Vlasenko <vda.linux(a)googlemail.com> writes:
> I looked at it and discovered that 0 is already special-cased
> at put_dec() callsite. You can drop the above if() block
> (or better comment it out, explaining that caller does it),
> and while at it, improve special-case code in number():
> replace
>
> /* generate full string in tmp[], in reverse order */
> i = 0;
> if (num == 0)
> tmp[i++] = '0';
>
> with
>
> if (num <= 7)
> tmp[i++] = '0' + num;
>
> (7, not 9, because it can be an octal conversion).

Well spotted! I've used:

> + if (num < spec.base) {
> + tmp[i++] = (digits[(unsigned)num] | locase);

and also documented that put_dec() won't work with zero.

>> + q = q / 10000;
>> + buf = put_dec_full4(buf, q % 10000);
>
> Bug. You need to use temporary variable to store q / 10000 result.

Fixed.


Delta betwenn v3 and v4:
> diff --git a/lib/vsprintf.c b/lib/vsprintf.c
> index ce55ddc..dd2a189 100644
> --- a/lib/vsprintf.c
> +++ b/lib/vsprintf.c
> @@ -373,7 +373,14 @@ static noinline_for_stack char *put_dec_trunc5(char *buf, unsigned q)
> return buf;
> }
>
> -/* No inlining helps gcc to use registers better */
> +/*
> + * This function formats all integers correctly, however on 32-bit
> + * processors function below is used (not this one) which handles only
> + * NON-ZERO integers. So be advised never to call this function with
> + * num == 0.
> + *
> + * No inlining helps gcc to use registers better
> + */
> static noinline_for_stack
> char *put_dec(char *buf, unsigned long long num)
> {
> @@ -440,25 +447,25 @@ char *put_dec_8bit(char *buf, unsigned q)
> * permission from the author). This performs no 64-bit division and
> * hence should be faster on 32-bit machines then the version of the
> * function above.
> + *
> + * This function formats correctly all NON-ZERO integers. Passing
> + * zero makes daemons come out of your closet. This is OK, since
> + * number(), which calls this function, has a special case for zero
> + * anyways.
> */
> static noinline_for_stack
> char *put_dec(char *buf, unsigned long long n)
> {
> uint32_t d3, d2, d1, q;
>
> - if (n < 10) {
> - *buf++ = '0' + (unsigned)n;
> - return buf;
> - }
> -
> d1 = (n >> 16) & 0xFFFF;
> d2 = (n >> 32) & 0xFFFF;
> d3 = (n >> 48) & 0xFFFF;
>
> q = 656 * d3 + 7296 * d2 + 5536 * d1 + (n & 0xFFFF);
>
> - q = q / 10000;
> buf = put_dec_full4(buf, q % 10000);
> + q = q / 10000;
>
> d1 = q + 7671 * d3 + 9496 * d2 + 6 * d1;
> q = d1 / 10000;
> @@ -554,22 +561,23 @@ char *number(char *buf, char *end, unsigned long long num,
> spec.field_width--;
> }
> }
> - if (need_pfx) {
> - spec.field_width--;
> - if (spec.base == 16)
> - spec.field_width--;
> - }
> + if (need_pfx)
> + /*
> + * This substract 1 for base 8 and 2 for base 16; base
> + * 10 never gets here.
> + */
> + spec.field_width -= spec.base / 8;
>
> /* generate full string in tmp[], in reverse order */
> i = 0;
> - if (num == 0)
> - tmp[i++] = '0';
> + if (num < spec.base) {
> + tmp[i++] = (digits[(unsigned)num] | locase);
> /* Generic code, for any base:
> else do {
> tmp[i++] = (digits[do_div(num,base)] | locase);
> } while (num != 0);
> */
> - else if (spec.base != 10) { /* 8 or 16 */
> + } else if (spec.base != 10) { /* 8 or 16 */
> int mask = spec.base - 1;
> int shift = 3;
>

diff --git a/lib/vsprintf.c b/lib/vsprintf.c
index b8a2f54..dd2a189 100644
--- a/lib/vsprintf.c
+++ b/lib/vsprintf.c
@@ -278,109 +278,217 @@ int skip_atoi(const char **s)
return i;
}

-/* Decimal conversion is by far the most typical, and is used
+
+#if BITS_PER_LONG > 32 /* machine is at least 64-bit */ \
+ || ULLONG_MAX > 18446744073709551615ULL /* long long is more than 64-bit */
+
+/*
+ * 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].
+ */
+static noinline_for_stack char *put_dec_full5(char *buf, unsigned q)
+{
+ unsigned r;

-/* 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. */
-static noinline_for_stack
-char *put_dec_trunc(char *buf, unsigned q)
+ /*
+ * '(x * 0xcccd) >> 19' is an approximation of 'x / 10' that
+ * gives correct results for all x < 81920 unless we use full
+ * 64-bit intermidiate result in which case it gives correct
+ * results for x < 262149. Because of this, we cast 0xcccd to
+ * (uint64_t). Thanks to this we can produce full 5 digits
+ * without any branches.
+ */
+
+ r = (q * (uint64_t)0xcccd) >> 19;
+ *buf++ = (q - 10 * r) + '0';
+
+ /*
+ * Other, possible ways to approx. divide by 10
+ * -- bigger loose most significant bits and are worse --
+ * (x * 0xcccd) >> 19 x < 81920 (x < 262149 when 64-bit used)
+ * (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
+ * -- smaller are useless --
+ * See <http://www.cs.uiowa.edu/~jones/bcd/divide.html>.
+ */
+
+ q = (r * 0x199a) >> 16;
+ *buf++ = (r - 10 * q) + '0';
+
+ r = (q * 0xcd) >> 11;
+ *buf++ = (q - 10 * r) + '0';
+
+ q = (r * 0xcd) >> 11;
+ *buf++ = (r - 10 * q) + '0';
+
+ *buf++ = q + '0';
+
+ return buf;
+}
+
+/* Same as above but do not pad with zeros. */
+static noinline_for_stack char *put_dec_trunc5(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;
+
+ /*
+ * If q is 5-digit just use the put_dec_full5() instead of
+ * cascading if()s.
+ */
+ if (q > 9999)
+ return put_dec_full5(buf, q);
+
+ r = (q * 0x199a) >> 16;
+ *buf++ = (q - 10 * r) + '0';
+
+ if (r) {
+ q = (r * 0xcd) >> 11;
+ *buf++ = (r - 10 * q) + '0';
+
+ if (q) {
+ r = (q * 0xcd) >> 11;
+ *buf++ = (q - 10 * r) + '0';
+
+ if (r)
+ *buf++ = r + '0';
}
}

return buf;
}
-/* Same with if's removed. Always emits five digits */
+
+/*
+ * This function formats all integers correctly, however on 32-bit
+ * processors function below is used (not this one) which handles only
+ * NON-ZERO integers. So be advised never to call this function with
+ * num == 0.
+ *
+ * No inlining helps gcc to use registers better
+ */
static noinline_for_stack
-char *put_dec_full(char *buf, unsigned q)
+char *put_dec(char *buf, unsigned long long num)
{
- /* 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);
+ while (num >= 100000)
+ buf = put_dec_full5(buf, do_div(num, 100000));
+ return put_dec_trunc5(buf, num);
+}

- /*
- * 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';
+/* This is used by ip4_string(). */
+#define put_dec_8bit put_dec_trunc5
+
+#else /* BITS_PER_LONG <= 32 (ie. 32-bit machine) && long long is 64-bit*/
+
+/*
+ * This is similar to the put_dec_full5() above expect it handles
+ * numbers from 0 to 9999 (ie. at most four digits). It is used by
+ * the put_dec() below which is optimised for 32-bit processors.
+ */
+static noinline_for_stack
+char *put_dec_full4(char *buf, unsigned q)
+{
+ 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;
}
-/* No inlining helps gcc to use registers better */
+
+/*
+ * Similar to above but handles only 8-bit operands and does not pad
+ * with zeros. Used by ip4_string().
+ */
static noinline_for_stack
-char *put_dec(char *buf, unsigned long long num)
+char *put_dec_8bit(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 * 0xcd) >> 11;
+ *buf++ = (q - 10 * r) + '0';
+
+ if (r) {
+ q = (r * 0xd) >> 7;
+ *buf++ = (r - 10 * q) + '0';
+
+ if (q)
+ *buf++ = q + '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). This performs no 64-bit division and
+ * hence should be faster on 32-bit machines then the version of the
+ * function above.
+ *
+ * This function formats correctly all NON-ZERO integers. Passing
+ * zero makes daemons come out of your closet. This is OK, since
+ * number(), which calls this function, has a special case for zero
+ * anyways.
+ */
+static noinline_for_stack
+char *put_dec(char *buf, unsigned long long n)
+{
+ uint32_t d3, d2, d1, q;
+
+ d1 = (n >> 16) & 0xFFFF;
+ d2 = (n >> 32) & 0xFFFF;
+ d3 = (n >> 48) & 0xFFFF;
+
+ q = 656 * d3 + 7296 * d2 + 5536 * d1 + (n & 0xFFFF);
+
+ buf = put_dec_full4(buf, q % 10000);
+ q = q / 10000;
+
+ d1 = q + 7671 * d3 + 9496 * d2 + 6 * d1;
+ q = d1 / 10000;
+ buf = put_dec_full4(buf, d1 % 10000);
+
+ d2 = q + 4749 * d3 + 42 * d2;
+ q = d2 / 10000;
+ buf = put_dec_full4(buf, d2 % 10000);
+
+ d3 = q + 281 * d3;
+ q = d3 / 10000;
+ buf = put_dec_full4(buf, d3 % 10000);
+
+ buf = put_dec_full4(buf, q);
+
+ while (buf[-1] == '0')
+ --buf;
+
+ return buf;
}

+#endif
+
#define ZEROPAD 1 /* pad with zero */
#define SIGN 2 /* unsigned/signed long */
#define PLUS 4 /* show plus */
@@ -453,22 +561,23 @@ char *number(char *buf, char *end, unsigned long long num,
spec.field_width--;
}
}
- if (need_pfx) {
- spec.field_width--;
- if (spec.base == 16)
- spec.field_width--;
- }
+ if (need_pfx)
+ /*
+ * This substract 1 for base 8 and 2 for base 16; base
+ * 10 never gets here.
+ */
+ spec.field_width -= spec.base / 8;

/* generate full string in tmp[], in reverse order */
i = 0;
- if (num == 0)
- tmp[i++] = '0';
+ if (num < spec.base) {
+ tmp[i++] = (digits[(unsigned)num] | locase);
/* Generic code, for any base:
else do {
tmp[i++] = (digits[do_div(num,base)] | locase);
} while (num != 0);
*/
- else if (spec.base != 10) { /* 8 or 16 */
+ } else if (spec.base != 10) { /* 8 or 16 */
int mask = spec.base - 1;
int shift = 3;

@@ -754,7 +863,7 @@ char *ip4_string(char *p, const u8 *addr, const char *fmt)
}
for (i = 0; i < 4; i++) {
char temp[3]; /* hold each IP quad in reverse order */
- int digits = put_dec_trunc(temp, addr[index]) - temp;
+ int digits = put_dec_8bit(temp, addr[index]) - temp;
if (leading_zeros) {
if (digits < 3)
*p++ = '0';
--
1.7.1

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