numerics.cpp File Reference

#include <cmath>
#include <cstdlib>
#include <iostream>
#include <numbers>
#include <numeric>
#include "nest_types.h"
#include "numerics.h"

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Functions
long	ld_round (double x)
	Round to nearest int, rounding midpoints upwards.
double	dround (double x)
	Round to nearest int, rounding midpoints upwards.
double	dtruncate (double x)
	Return integer part of argument.
bool	is_integer (double n)
	Returns true if n is integer up to rounding error.
long	mod_inverse (long a, long m)
	Returns inverse of integer a modulo m.
size_t	first_index (long period, long phase0, long step, long phase)
	Return first matching index for entry in container with double periodicity.

Function Documentation

dround()

double dround

(

double

x

)

Round to nearest int, rounding midpoints upwards.

Returns

Result as double

Note

[-1/2, 1/2) -> 0 and in general [ (2n-1)/2, (2n+1)/2 ) -> n

See also

ld_round

Referenced by nest::Time::set_resolution().

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dtruncate()

double dtruncate

(

double

x

)

Return integer part of argument.

first_index()

size_t first_index	(	long	period,
		long	phase0,
		long	step,
		long	phase
	)

Return first matching index for entry in container with double periodicity.

Consider

• a container of arbitrary length containing elements (e.g. GIDs) which map to certain values, e.g., VP(GID), with a given period, e.g., the number of virtual processes
• that the phase (e.g., the VP number) of the first entry in the container is phase0
• that we slice the container with a given step, causing a double periodicity
• that we want to know the index of the first element in the container with a given phase, e.g., the first element on a given VP

If such an index x exists, it is given by

x = phase0 + k' mod lcm(period, step) k' = min_k ( phase0 + k step = phase mod period )

As an example, consider

idx 0 1 2 3 4 5 6 7 8 9 10 11 | 12 13 14 15 16 17 18 gid 1 2 3 4 5 6 7 8 9 10 11 12 | 13 14 15 16 17 18 19 vp 1 2 3 0 1 2 3 0 1 2 3 0 | 1 2 3 0 1 2 3

• * * * | * * * 1 0 3 2 |

Here, idx is a linear index into the container, gid neuron ids which map to the given vp numbers. The container is sliced with step=3, i.e., starting with the first element we take every third, as marked by the asterisks. The question is then at which index we find the first entry belonging to vp 0, 1, 2, or 3. The numbers in the bottom row show for clarity on which VP we find the respective asterisks. The | symbol marks where the pattern repeats itself.

phase0 in this example is 1, i.e., the VP of the first element in the container.

Note

This function returns that index. It is the responsibility of the caller to check if the returned index is within the bounds of the actual container—the algorithm assumes an infinite container.

The function returns invalid_index if no solution exists.

See comments in the function definition for implementation details.

References mod_inverse().

Referenced by nest::NodeCollectionComposite::specific_local_begin_().

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is_integer()

bool is_integer

(

double

n

)

Returns true if n is integer up to rounding error.

Returns

bool

Referenced by nest::SimulationManager::set_status().

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ld_round()

long ld_round

(

double

x

)

Round to nearest int, rounding midpoints upwards.

Returns

Result as long

Note

[-1/2, 1/2) -> 0 and in general [ (2n-1)/2, (2n+1)/2 ) -> n

See also

dround

Referenced by nest::Time::delay_ms_to_steps().

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mod_inverse()

long mod_inverse	(	long	a,
		long	m
	)

Returns inverse of integer a modulo m.

For integer a > 0, m ≥ 2, find x so that ( a * x ) mod m = 1.

Referenced by first_index().

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