feat: backend agnostic numerical conversion

[oameye]

resolves #154

[github-actions]

Benchmark Results

Details

Benchmark suite	Current: 62a66e0	Previous: 3b4b786	Ratio
Accumulation/Many-mode H/foldl M=16	10900 ns	10639 ns	1.02
Accumulation/Many-mode H/foldl M=24	24085 ns	24345 ns	0.99
Accumulation/Many-mode H/foldl M=8	2823.1111111111113 ns	2727.3333333333335 ns	1.04
Accumulation/Many-mode H/sum M=16	1694.2 ns	1704.1 ns	0.99
Accumulation/Many-mode H/sum M=24	2298.6666666666665 ns	2265.222222222222 ns	1.01
Accumulation/Many-mode H/sum M=8	710.3458646616541 ns	708.1363636363636 ns	1.00
Accumulation/Same-site/foldl	6163.6 ns	6313.6 ns	0.98
Accumulation/Same-site/sum	2170.777777777778 ns	2259.777777777778 ns	0.96
Commutator/Nested JC/depth=1	1681.2 ns	1683.2 ns	1.00
Commutator/Nested JC/depth=2	18765 ns	18324 ns	1.02
Commutator/Nested JC/depth=3	68207 ns	67676 ns	1.01
Commutator/Nested JC/depth=4	170137 ns	170367 ns	1.00
Commutator/Nested JC/depth=5	378346 ns	376862 ns	1.00
Commutator/Schrieffer-Wolff/[S, V]	203229 ns	205001 ns	0.99
Commutator/Schrieffer-Wolff/[S, [S, H0]]	373087 ns	383264 ns	0.97
Indexing/Diagonal collapse/[H_Dicke, S_j]	43030 ns	42960 ns	1.00
Indexing/Diagonal collapse/[H_JC, σ_j]	61625 ns	62306 ns	0.99
Indexing/Simplify/double-sum spin-spin	15830 ns	16832 ns	0.94
Indexing/Simplify/indexed JC H	1507.8 ns	1177.2 ns	1.28
Indexing/Sum construction/double Σ_ij(J_ij*S_i*S_j)	8379 ns	8696.333333333334 ns	0.96
Indexing/Sum construction/single Σ_i(σ_i*σ_j)	11913 ns	11411 ns	1.04
Normal Order/Fock (c*c')^n/n=2	602.0055248618785 ns	613.4715909090909 ns	0.98
Normal Order/Fock (c*c')^n/n=3	871.0877192982456 ns	882.5813953488372 ns	0.99
Normal Order/Fock (c*c')^n/n=4	1197.2 ns	1172.1 ns	1.02
Normal Order/Fock (c*c')^n/n=5	1582.9 ns	1570.9 ns	1.01
Normal Order/Ground state/3-level rewrite	797.8636363636364 ns	823.7402597402597 ns	0.97
Normal Order/Multi-mode/2-mode 6-op chain	977.7058823529412 ns	962.7 ns	1.02
Simplify/Jaynes-Cummings/H	1093.1 ns	1091 ns	1.00
Simplify/Jaynes-Cummings/H²	2527 ns	2466.8888888888887 ns	1.02
Simplify/Two cavities/H	1148.1 ns	1139.1 ns	1.01
Simplify/Two cavities/H²	4590.142857142857 ns	4554.285714285715 ns	1.01
Simplify/Λ-system/H	1377.5 ns	1384.6 ns	0.99
Simplify/Λ-system/H²	2356.5555555555557 ns	2375.5555555555557 ns	0.99

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

[codecov]

Codecov Report

❌ Patch coverage is 94.98208% with 28 lines in your changes missing coverage. Please review.
✅ Project coverage is 94.94%. Comparing base (3b4b786) to head (62a66e0).

Files with missing lines	Patch %	Lines
ext/SecondQuantizedAlgebraQuantumToolboxExt.jl	84.61%	20 Missing ⚠️
ext/SecondQuantizedAlgebraQuantumOpticsBaseExt.jl	96.00%	3 Missing ⚠️
src/numeric/api.jl	93.61%	3 Missing ⚠️
src/numeric/backend.jl	89.47%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #200      +/-   ##
==========================================
+ Coverage   94.57%   94.94%   +0.36%     
==========================================
  Files          27       33       +6     
  Lines        3024     3185     +161     
==========================================
+ Hits         2860     3024     +164     
+ Misses        164      161       -3     

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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.