BENCHMARK – FORTVSH

Timing benchmarks comparing the batch (_ALL) Legendre/SSH/VSH routines against naive per-mode loops over the corresponding single-mode routines, evaluated across a grid of NX colatitude/ argument points -- mirroring how a spectral MHD transform would call these routines once per grid point every timestep. Each measurement is auto-calibrated: the full grid sweep is repeated until elapsed wall time crosses MIN_TIME, so timings stay resolvable across the full $\ell_{max}$ sweep used for the manuscript's performance figure, without a hardcoded repeat count. Not part of ctest (opt-in VSH_BUILD_BENCHMARK CMake target instead) since wall-clock timings are machine/compiler-dependent and shouldn't gate a pass/fail build.

Uses

- KINDS
- VSH
- GLOBALS
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Used by

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Graph Key

Nodes of different colours represent the following:

Solid arrows point from a submodule to the (sub)module which it is descended from. Dashed arrows point from a module or program unit to modules which it uses.
Where possible, edges connecting nodes are given different colours to make them easier to distinguish in large graphs.

Variables

Type	Visibility	Attributes		Name		Initial
integer(kind=i4),	private,	parameter	::	LOOP_LMAX_CAP	=	200	Naive-loop measurements are skipped above this Lmax. Each single-mode call (ASSOC_LEGENDRE, SSH, ...) is itself an O(l) recurrence, so one naive-loop grid sweep costs O(NXLMAX^3), not O(NXLMAX^2) like the batch routines -- at LMAX=4000 a single measurement (NREP=1, before MIN_TIME calibration even gets a chance to stop doubling) took multiple hours and never completed. There's no reason to pay that cost anyway: the naive/single-mode routines are only verified-safe to l<=150 (see STABILITY_FINDINGS.md Part 2), so timing them past that range times how fast they compute wrong answers.
real(kind=dp),	private,	parameter	::	MIN_TIME	=	0.2_dp	Minimum elapsed wall time (seconds) a calibration measurement must reach before its repeat count is accepted; below this, repeats double and the measurement is retried.
integer(kind=i4),	private,	parameter	::	NREP_CAP	=	1000000	Safety cap on the repeat-count doubling loop, so a pathologically fast measurement can't spin forever.

Functions

private function WALL_TIME() result(T)

Wall-clock seconds elapsed, via SYSTEM_CLOCK with an INTEGER(i8) count so the calibration loops in every BENCH_* routine below cannot roll the counter over during a long-running sweep.

Arguments

None

Return Value real(kind=dp)

Subroutines

public subroutine BENCH_LEGENDRE(LMAX, NX, OUTUNIT)

Benchmarks ASSOC_LEGENDRE_NORM_ALL (batch) against looped ASSOC_LEGENDRE (single-mode) calls, for $0\le\ell\le\ell_{max},\, 0\le m\le\ell$ , swept over NX points $x\in[-0.9,0.9]$ (one grid sweep per timing, repeated/calibrated per WALL_TIME).

Arguments

Type	Intent		Name
integer(kind=i4),	intent(in)	::	LMAX	Maximum degree benchmarked, $\ell_{max}\ge0$ .
integer(kind=i4),	intent(in)	::	NX	Number of $x$ points swept per timing measurement.
integer(kind=i4),	intent(in)	::	OUTUNIT	Fortran unit number to append one result row to:

public subroutine BENCH_SSH(LMAX, NX, OUTUNIT)

Benchmarks SSH_ALL (batch) against looped SSH (single-mode) calls, for $0\le\ell\le\ell_{max},\,-\ell\le m\le\ell$ , swept over NX colatitude points in $(0,\pi)$ at a fixed longitude.

Arguments

Type	Intent		Name
integer(kind=i4),	intent(in)	::	LMAX	Maximum degree benchmarked, $\ell_{max}\ge0$ .
integer(kind=i4),	intent(in)	::	NX	Number of colatitude points swept per timing measurement.
integer(kind=i4),	intent(in)	::	OUTUNIT	Fortran unit number to append one result row to:

public subroutine BENCH_VSH_POL_DN(LMAX, NX, OUTUNIT)

Benchmarks VSH_POL_DN_ALL (batch) against looped VSH_POL_DN (single-mode) calls, for $0\le\ell\le\ell_{max},\,-\ell\le m\le\ell$ , swept over NX colatitude points.

Arguments

Type	Intent		Name
integer(kind=i4),	intent(in)	::	LMAX	Maximum degree benchmarked, $\ell_{max}\ge0$ .
integer(kind=i4),	intent(in)	::	NX	Number of colatitude points swept per timing measurement.
integer(kind=i4),	intent(in)	::	OUTUNIT	Fortran unit number to append one result row to:

public subroutine BENCH_VSH_POL_UP(LMAX, NX, OUTUNIT)

Benchmarks VSH_POL_UP_ALL (batch) against looped VSH_POL_UP (single-mode) calls, for $0\le\ell\le\ell_{max},\,-\ell\le m\le\ell$ , swept over NX colatitude points.

Arguments

Type	Intent		Name
integer(kind=i4),	intent(in)	::	LMAX	Maximum degree benchmarked, $\ell_{max}\ge0$ .
integer(kind=i4),	intent(in)	::	NX	Number of colatitude points swept per timing measurement.
integer(kind=i4),	intent(in)	::	OUTUNIT	Fortran unit number to append one result row to:

public subroutine BENCH_VSH_TOR(LMAX, NX, OUTUNIT)

Benchmarks VSH_TOR_ALL (batch) against looped VSH_TOR (single-mode) calls, for $0\le\ell\le\ell_{max},\,-\ell\le m\le\ell$ , swept over NX colatitude points.

Arguments

Type	Intent		Name
integer(kind=i4),	intent(in)	::	LMAX	Maximum degree benchmarked, $\ell_{max}\ge0$ .
integer(kind=i4),	intent(in)	::	NX	Number of colatitude points swept per timing measurement.
integer(kind=i4),	intent(in)	::	OUTUNIT	Fortran unit number to append one result row to:

BENCHMARK Module

Contents

Variables

Functions

Subroutines

Uses

Used by

Variables

Functions

private function WALL_TIME() result(T)

Arguments

Return Value real(kind=dp)

Subroutines

public subroutine BENCH_LEGENDRE(LMAX, NX, OUTUNIT)

Arguments

public subroutine BENCH_SSH(LMAX, NX, OUTUNIT)

Arguments

public subroutine BENCH_VSH_POL_DN(LMAX, NX, OUTUNIT)

Arguments

public subroutine BENCH_VSH_POL_UP(LMAX, NX, OUTUNIT)

Arguments

public subroutine BENCH_VSH_TOR(LMAX, NX, OUTUNIT)

Arguments