feat: backend agnostic numerical conversion

[oameye]

resolves #154

[github-actions]

Benchmark Results

Details

Benchmark suite	Current: 9ca58bd	Previous: 3b4b786	Ratio
Accumulation/Many-mode H/foldl M=16	11907 ns	10639 ns	1.12
Accumulation/Many-mode H/foldl M=24	26990 ns	24345 ns	1.11
Accumulation/Many-mode H/foldl M=8	2955.625 ns	2727.3333333333335 ns	1.08
Accumulation/Many-mode H/sum M=16	1902.888888888889 ns	1704.1 ns	1.12
Accumulation/Many-mode H/sum M=24	2629.4444444444443 ns	2265.222222222222 ns	1.16
Accumulation/Many-mode H/sum M=8	762.5825242718447 ns	708.1363636363636 ns	1.08
Accumulation/Same-site/foldl	6489.6 ns	6313.6 ns	1.03
Accumulation/Same-site/sum	2212.222222222222 ns	2259.777777777778 ns	0.98
Commutator/Nested JC/depth=1	1779.6 ns	1683.2 ns	1.06
Commutator/Nested JC/depth=2	17666 ns	18324 ns	0.96
Commutator/Nested JC/depth=3	64074 ns	67676 ns	0.95
Commutator/Nested JC/depth=4	161359 ns	170367 ns	0.95
Commutator/Nested JC/depth=5	354515 ns	376862 ns	0.94
Commutator/Schrieffer-Wolff/[S, V]	184033 ns	205001 ns	0.90
Commutator/Schrieffer-Wolff/[S, [S, H0]]	337269 ns	383264 ns	0.88
Indexing/Diagonal collapse/[H_Dicke, S_j]	43995 ns	42960 ns	1.02
Indexing/Diagonal collapse/[H_JC, σ_j]	57936 ns	62306 ns	0.93
Indexing/Simplify/double-sum spin-spin	14442 ns	16832 ns	0.86
Indexing/Simplify/indexed JC H	1275.8 ns	1177.2 ns	1.08
Indexing/Sum construction/double Σ_ij(J_ij*S_i*S_j)	8052 ns	8696.333333333334 ns	0.93
Indexing/Sum construction/single Σ_i(σ_i*σ_j)	9985 ns	11411 ns	0.88
Normal Order/Fock (c*c')^n/n=2	673.0059171597633 ns	613.4715909090909 ns	1.10
Normal Order/Fock (c*c')^n/n=3	950.4 ns	882.5813953488372 ns	1.08
Normal Order/Fock (c*c')^n/n=4	1274.9 ns	1172.1 ns	1.09
Normal Order/Fock (c*c')^n/n=5	1707.6 ns	1570.9 ns	1.09
Normal Order/Ground state/3-level rewrite	862.6363636363636 ns	823.7402597402597 ns	1.05
Normal Order/Multi-mode/2-mode 6-op chain	1059.5 ns	962.7 ns	1.10
Simplify/Jaynes-Cummings/H	1173.7 ns	1091 ns	1.08
Simplify/Jaynes-Cummings/H²	2705.1111111111113 ns	2466.8888888888887 ns	1.10
Simplify/Two cavities/H	1226.8 ns	1139.1 ns	1.08
Simplify/Two cavities/H²	5089.166666666667 ns	4554.285714285715 ns	1.12
Simplify/Λ-system/H	1492.2 ns	1384.6 ns	1.08
Simplify/Λ-system/H²	2568.222222222222 ns	2375.5555555555557 ns	1.08

This comment was automatically generated by workflow using github-action-benchmark.

[codecov]

Codecov Report

❌ Patch coverage is 95.51971% with 25 lines in your changes missing coverage. Please review.
✅ Project coverage is 95.10%. Comparing base (3b4b786) to head (9ca58bd).

Files with missing lines	Patch %	Lines
ext/SecondQuantizedAlgebraQuantumToolboxExt.jl	86.15%	18 Missing ⚠️
ext/SecondQuantizedAlgebraQuantumOpticsBaseExt.jl	96.00%	3 Missing ⚠️
src/numeric/api.jl	93.61%	3 Missing ⚠️
src/numeric/backend.jl	94.73%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #200      +/-   ##
==========================================
+ Coverage   94.57%   95.10%   +0.52%     
==========================================
  Files          27       33       +6     
  Lines        3024     3185     +161     
==========================================
+ Hits         2860     3029     +169     
+ Misses        164      156       -8     

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[github-actions]

⚠️ Performance Alert ⚠️

Possible performance regression was detected for benchmark 'Benchmark Results'.
Benchmark result of this commit is worse than the previous benchmark result exceeding threshold 1.30.

Benchmark suite	Current: 823d4e5	Previous: 3b4b786	Ratio
Accumulation/Same-site/sum	3061 ns	2259.777777777778 ns	1.35

This comment was automatically generated by workflow using github-action-benchmark.