numerical.h File Reference

Numerical Library. More...

#include <stdbool.h>

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Data Structures
struct	_numerical_state
struct	_sum_helper_t
	this represents a partial Neumaier sum More...

Macros
#define	ValueSumHelper(a)   (a.crt + a.sum)
#define	CmpSumHelpers(a, b)

Typedefs
typedef uint64_t	seed_type
	Numerical seed type.
typedef struct _numerical_state	numerical_state_t

Functions
void	numerical_init (void)
double	NeumaierSum (unsigned cnt, double addendums[cnt])
struct _sum_helper_t	PartialNeumaierSum (struct _sum_helper_t sh, double addendum)

Detailed Description

Numerical Library.

Piece-Wise Deterministic Random Number Generators.

Copyright

Copyright (C) 2008-2019 HPDCS Group https://hpdcs.github.io

This file is part of ROOT-Sim (ROme OpTimistic Simulator).

ROOT-Sim 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; only version 3 of the License applies.

ROOT-Sim 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 ROOT-Sim; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA

Author

Alessandro Pellegrini

Date

March 16, 2011

Definition in file numerical.h.

Macro Definition Documentation

#define CmpSumHelpers	(		a,
			b
	)

Value:

({\
    double __a_s = a.sum + a.crt;\
    double __b_s = b.sum + b.crt;\
    (__a_s > __b_s) - (__b_s > __a_s);\
})

Definition at line 65 of file numerical.h.

Typedef Documentation

typedef struct _numerical_state numerical_state_t

This structure keeps track of the per-LP members required to rollback the internal state of the simulation library.

Function Documentation

double NeumaierSum	(	unsigned	cnt,
		double	addendums[cnt]
	)

Calculates a sum within double variables with bounded approximation error

This implements a variant of the Kahan summation algorithm: https://en.wikipedia.org/wiki/Kahan_summation_algorithm This is used in the topology module to calculate minimum costs and weighted probabilities since the classic iterated floating point sum may result in unbounded errors originated from the limited precision of the underlying floating point representation.

Author

Andrea Piccione

Parameters

cnt	the number of addendums to sum
addendums	a pointer to a sequence of cnt doubles

Returns

the sum between the addendums with bounded error

Definition at line 432 of file numerical.c.

struct _sum_helper_t PartialNeumaierSum	(	struct _sum_helper_t	sh,
		double	addendum
	)

Calculates a partial sum within double variables with bounded approximation error

This has similar utilization to <NeumaierSum>() with the difference that this can be used to calculate partial sums, adding doubles one by one.

Author

Andrea Piccione

Parameters

sh	a struct _sum_helper_t holding the partial result typically from a previous sum
addendum	the double floating point value to add

Returns

a struct _sum_helper_t holding the sum between sh and addendum

Definition at line 463 of file numerical.c.