/*
* Copyright (C) 2014 Michael Brown <mbrown@fensystems.co.uk>.
*
* 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 any later version.
*
* This program 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
* General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
* 02110-1301, USA.
*
* You can also choose to distribute this program under the terms of
* the Unmodified Binary Distribution Licence (as given in the file
* COPYING.UBDL), provided that you have satisfied its requirements.
*/
FILE_LICENCE ( GPL2_OR_LATER_OR_UBDL );
#include <stdint.h>
#include <stdio.h>
#include <strings.h>
#include <limits.h>
#include <assert.h>
#include <ipxe/isqrt.h>
#include <ipxe/profile.h>
/** @file
*
* Profiling
*
* The profiler computes basic statistics (mean, variance, and
* standard deviation) for the samples which it records. Note that
* these statistics need not be completely accurate; it is sufficient
* to give a rough approximation.
*
* The algorithm for updating the mean and variance estimators is from
* The Art of Computer Programming (via Wikipedia), with adjustments
* to avoid the use of floating-point instructions.
*/
/** Accumulated time excluded from profiling */
unsigned long profile_excluded;
/**
* Format a hex fraction (for debugging)
*
* @v value Value
* @v shift Bit shift
* @ret string Formatted hex fraction
*/
static const char * profile_hex_fraction ( signed long long value,
unsigned int shift ) {
static char buf[23] = "-"; /* -0xXXXXXXXXXXXXXXXX.XX + NUL */
unsigned long long int_part;
uint8_t frac_part;
char *ptr;
if ( value < 0 ) {
value = -value;
ptr = &buf[0];
} else {
ptr = &buf[1];
}
int_part = ( value >> shift );
frac_part = ( value >> ( shift - ( 8 * sizeof ( frac_part ) ) ) );
snprintf ( &buf[1], ( sizeof ( buf ) - 1 ), "%#llx.%02x",
int_part, frac_part );
return ptr;
}
/**
* Calculate bit shift for mean sample value
*
* @v profiler Profiler
* @ret shift Bit shift
*/
static inline unsigned int profile_mean_shift ( struct profiler *profiler ) {
return ( ( ( 8 * sizeof ( profiler->mean ) ) - 1 ) /* MSB */
- 1 /* Leave sign bit unused */
- profiler->mean_msb );
}
/**
* Calculate bit shift for accumulated variance value
*
* @v profiler Profiler
* @ret shift Bit shift
*/
static inline unsigned int profile_accvar_shift ( struct profiler *profiler ) {
return ( ( ( 8 * sizeof ( profiler->accvar ) ) - 1 ) /* MSB */
- 1 /* Leave top bit unused */
- profiler->accvar_msb );
}
/**
* Update profiler with a new sample
*
* @v profiler Profiler
* @v sample Sample value
*/
void profile_update ( struct profiler *profiler, unsigned long sample ) {
unsigned int sample_msb;
unsigned int mean_shift;
unsigned int delta_shift;
signed long pre_delta;
signed long post_delta;
signed long long accvar_delta;
unsigned int accvar_delta_shift;
unsigned int accvar_delta_msb;
unsigned int accvar_shift;
/* Our scaling logic assumes that sample values never overflow
* a signed long (i.e. that the high bit is always zero).
*/
assert ( ( ( signed ) sample ) >= 0 );
/* Update sample count, limiting to avoid signed overflow */
if ( profiler->count < INT_MAX )
profiler->count++;
/* Adjust mean sample value scale if necessary. Skip if
* sample is zero (in which case flsl(sample)-1 would
* underflow): in the case of a zero sample we have no need to
* adjust the scale anyway.
*/
if ( sample ) {
sample_msb = ( flsl ( sample ) - 1 );
if ( profiler->mean_msb < sample_msb ) {
profiler->mean >>= ( sample_msb - profiler->mean_msb );
profiler->mean_msb = sample_msb;
}
}
/* Scale sample to internal units */
mean_shift = profile_mean_shift ( profiler );
sample <<= mean_shift;
/* Update mean */
pre_delta = ( sample - profiler->mean );
profiler->mean += ( pre_delta / ( ( signed ) profiler->count ) );
post_delta = ( sample - profiler->mean );
delta_shift = mean_shift;
DBGC ( profiler, "PROFILER %p sample %#lx mean %s", profiler,
( sample >> mean_shift ),
profile_hex_fraction ( profiler->mean, mean_shift ) );
DBGC ( profiler, " pre %s",
profile_hex_fraction ( pre_delta, delta_shift ) );
DBGC ( profiler, " post %s\n",
profile_hex_fraction ( post_delta, delta_shift ) );
/* Scale both deltas to fit in half of an unsigned long long
* to avoid potential overflow on multiplication. Note that
* shifting a signed quantity is "implementation-defined"
* behaviour in the C standard, but gcc documents that it will
* always perform sign extension.
*/
if ( sizeof ( pre_delta ) > ( sizeof ( accvar_delta ) / 2 ) ) {
unsigned int shift = ( 8 * ( sizeof ( pre_delta ) -
( sizeof ( accvar_delta ) / 2 ) ));
pre_delta >>= shift;
post_delta >>= shift;
delta_shift -= shift;
}
/* Update variance, if applicable. Skip if either delta is
* zero (in which case flsl(delta)-1 would underflow): in the
* case of a zero delta there is no change to the accumulated
* variance anyway.
*/
if ( pre_delta && post_delta ) {
/* Calculate variance delta */
accvar_delta = ( ( ( signed long long ) pre_delta ) *
( ( signed long long ) post_delta ) );
accvar_delta_shift = ( 2 * delta_shift );
assert ( accvar_delta > 0 );
/* Calculate variance delta MSB, using flsl() on each
* delta individually to provide an upper bound rather
* than requiring the existence of flsll().
*/
accvar_delta_msb = ( flsll ( accvar_delta ) - 1 );
if ( accvar_delta_msb > accvar_delta_shift ) {
accvar_delta_msb -= accvar_delta_shift;
} else {
accvar_delta_msb = 0;
}
/* Adjust scales as necessary */
if ( profiler->accvar_msb < accvar_delta_msb ) {
/* Rescale accumulated variance */
profiler->accvar >>= ( accvar_delta_msb -
profiler->accvar_msb );
profiler->accvar_msb = accvar_delta_msb;
} else {
/* Rescale variance delta */
accvar_delta >>= ( profiler->accvar_msb -
accvar_delta_msb );
accvar_delta_shift -= ( profiler->accvar_msb -
accvar_delta_msb );
}
/* Scale delta to internal units */
accvar_shift = profile_accvar_shift ( profiler );
accvar_delta <<= ( accvar_shift - accvar_delta_shift );
/* Accumulate variance */
profiler->accvar += accvar_delta;
/* Adjust scale if necessary */
if ( profiler->accvar &
( 1ULL << ( ( 8 * sizeof ( profiler->accvar ) ) - 1 ) ) ) {
profiler->accvar >>= 1;
profiler->accvar_msb++;
accvar_delta >>= 1;
accvar_shift--;
}
DBGC ( profiler, "PROFILER %p accvar %s", profiler,
profile_hex_fraction ( profiler->accvar, accvar_shift ));
DBGC ( profiler, " delta %s\n",
profile_hex_fraction ( accvar_delta, accvar_shift ) );
}
}
/**
* Get mean sample value
*
* @v profiler Profiler
* @ret mean Mean sample value
*/
unsigned long profile_mean ( struct profiler *profiler ) {
unsigned int mean_shift = profile_mean_shift ( profiler );
/* Round to nearest and scale down to original units */
return ( ( profiler->mean + ( 1UL << ( mean_shift - 1 ) ) )
>> mean_shift );
}
/**
* Get sample variance
*
* @v profiler Profiler
* @ret variance Sample variance
*/
unsigned long profile_variance ( struct profiler *profiler ) {
unsigned int accvar_shift = profile_accvar_shift ( profiler );
/* Variance is zero if fewer than two samples exist (avoiding
* division by zero error).
*/
if ( profiler->count < 2 )
return 0;
/* Calculate variance, round to nearest, and scale to original units */
return ( ( ( profiler->accvar / ( profiler->count - 1 ) )
+ ( 1ULL << ( accvar_shift - 1 ) ) ) >> accvar_shift );
}
/**
* Get sample standard deviation
*
* @v profiler Profiler
* @ret stddev Sample standard deviation
*/
unsigned long profile_stddev ( struct profiler *profiler ) {
return isqrt ( profile_variance ( profiler ) );
}
