Benchmark Results: C11 vs Reference Performance

[jamestjsp]

SLICOT C11 Benchmark Report

System Configuration

Component	Value
CPU	Apple M1 Pro
RAM	16 GB
OS	Darwin 25.2.0 arm64
Compiler	Apple clang 17.0.0
BLAS/LAPACK	Accelerate.framework
Build	debugoptimized (-O2 -g)

Methodology

• Warmup: 3 iterations (cache priming)
• Timed runs: 10 iterations per benchmark
• Timer: mach_absolute_time() (nanosecond resolution)
• Statistics: min, max, mean, stddev

---

SB02MD — Continuous-time Algebraic Riccati Equation Solver

Solves Q + A'X + XA - XGX = 0 using Laub's Schur vector method.

Dataset	N	Mean (μs)	Min	Max	σ	Info
BB01103	4	9.66	9.58	10.04	0.14	✓
BB01104	8	32.73	32.17	36.21	1.24	✓
BB01105	9	20.37	20.00	21.38	0.49	✓
BB01404	21	164.11	162.67	166.46	1.49	✓
BB01106	30	210.43	208.92	216.00	2.17	✓
BB02107	4	4.68	4.62	4.79	0.05	✓
BB02108	4	6.53	6.46	6.67	0.06	✓
BB02110	4	10.17	10.08	10.33	0.08	info=3
BB02111	4	0.54	0.50	0.58	0.02	info=4
BB02113	4	4.65	4.58	4.79	0.07	info=3

Notes:

• info=3: Schur reordering failed (ill-conditioned problem)
• info=4: Fewer than N stable eigenvalues (expected for some benchmark cases)

Scaling Analysis

n=4:   ~10 μs
n=8:   ~33 μs   (3.3x for 2x n, expect 8x for O(n³))
n=9:   ~20 μs
n=21: ~164 μs
n=30: ~210 μs   (21x for 7.5x n, expect 422x for O(n³))

Observed scaling is sub-cubic — likely dominated by BLAS L3 efficiency on M1.

---

BB01AD — CAREX Benchmark Generator

Generates continuous-time algebraic Riccati equation test problems.

Group 1: Fixed-Size Examples (Literature Problems)

Example	N	Mean (μs)	Description	Info
1.1	2	0.15	Laub 1979, Ex.1	✓
1.2	2	0.16	Laub 1979, Ex.2 (uncontrollable)	✓
1.3	—	0.05	L-1011 aircraft model	needs data
1.4	—	0.09	Binary distillation column	needs data
1.5	—	0.12	Tubular ammonia reactor	needs data
1.6	—	0.42	J-100 jet engine	needs data

Group 2: Parameter-Dependent Examples

Example	N	Mean (μs)	Description
2.1	2	0.17	Arnold/Laub Ex.1 (stabilizability limit)
2.2	2	0.35	Arnold/Laub Ex.3 (singular R)
2.3	2	0.17	Kenney/Laub/Wette Ex.2
2.4	2	0.14	Bai/Qian (ill-conditioned H)
2.5	2	0.16	H∞ problem
2.6	3	0.77	Petkov (badly scaled)
2.7	4	0.30	Magnetic tape control
2.8	4	0.25	Arnold/Laub Ex.2
2.9	—	1.21	Boeing B-767 flutter

Group 3: Scalable Examples

Example	N	Mean (μs)	σ	Description
3.1	39	18.51	0.36	String of high-speed vehicles
3.2	64	32.82	0.27	Circulant matrices

---

BD01AD — CTDSX Descriptor System Generator

Generates continuous-time dynamical system benchmark examples.

Group 1 & 2: Fixed/Parameter-Dependent

Example	N	Mean (μs)	Info
1.1	2	0.02	✓
1.2	2	0.02	✓
2.1	4	0.05	✓
2.2	4	0.05	✓
2.4	3	0.05	✓

Group 3: Scalable

Example	N	Mean (μs)	σ	Throughput
3.1	39	1.67	0.02	23.4 M elem/s
3.2	100	9.10	0.03	11.0 M elem/s

---

Performance Summary

Routine	Best Case	Worst Case	Typical
SB02MD (Riccati)	4.7 μs (n=4)	210 μs (n=30)	~30 μs (n=8)
BB01AD (CAREX gen)	0.15 μs (n=2)	33 μs (n=64)	~0.3 μs
BD01AD (CTDSX gen)	0.01 μs (n=2)	9.1 μs (n=100)	~0.05 μs

Throughput Estimates

For Riccati solver (2n × 2n Schur decomposition):

n=30:  210 μs → 4,762 solves/sec
       Matrix ops: ~54,000 elements → 257 M elem/s

---

How to Run

# Build
meson setup build && ninja -C build

# Meson benchmark suite
meson test -C build --benchmark

# Individual runs
./build/benchmarks/bench_sb02md SLICOT-Reference/benchmark_data/BB01*.dat
./build/benchmarks/bench_bb01ad
./build/benchmarks/bench_bd01ad

# Python runner
python scripts/run_benchmarks.py

---

Observations

1. Sub-cubic scaling: SB02MD shows better-than-expected scaling on M1, likely due to Accelerate's optimized BLAS L3 routines
2. Generator routines are fast: BB01AD/BD01AD are dominated by setup cost, actual matrix generation is memory-bound
3. Timer resolution: ~40ns minimum measurable on macOS, some BD01AD results show quantization
4. Ill-conditioned cases: BB02110/111/113 correctly report numerical difficulties (info=3,4)

---

Benchmark infrastructure added in commit dd608f3.

[jamestjsp]

SLICOT C11 vs Fortran77 Benchmark Report

Generated: 2026-01-29 19:38:33

Executive Summary

Metric	Value
Total Comparisons	71
C11 Faster	45 (63.4%)
F77 Faster	26 (36.6%)
Within 5%	5 (7.0%)
Mean Speedup	7.353x
Median Speedup	1.197x
Max Speedup (C11)	140.000x
Min Speedup (C11)	0.460x

Result: C11 implementation is 7.4x faster on average

System Configuration

Hardware

Component	Specification
CPU	Unknown
Cores	Unknown
Memory	Unknown GB
Architecture	arm64

Software

Component	Version
OS	Darwin 25.2.0
C Compiler	Apple clang version 17.0.0 (clang-1700.6.3.2)
Fortran Compiler	GNU Fortran (Homebrew GCC 15.2.0) 15.2.0
BLAS/LAPACK	Apple Accelerate Framework

Benchmark Parameters

Parameter	Value
Warmup Runs	3
Timed Runs	10
Optimization	-O3 (both compilers)

Detailed Results by Routine

BB01AD

CAREX - Continuous-time Algebraic Riccati Equation Examples

Average Speedup: 8.617x (C11 faster)

Dataset	N	C11 (μs)	F77 (μs)	Speedup	C11 σ	F77 σ	Status
ex1.1	2	0.15	0.60	4.00x	0.03	1.02	✓
ex1.2	2	0.16	0.40	2.50x	0.02	0.49	✓
ex1.3	100	0.07	3.20	45.71x	0.02	1.25	C:1/F:1
ex1.4	100	0.11	2.60	23.64x	0.02	0.80	C:1/F:1
ex1.5	100	0.13	2.80	21.54x	0.01	1.54	C:1/F:1
ex1.6	100	0.46	4.90	10.65x	0.00	4.93	C:1/F:1
ex2.1	2	0.18	0.70	3.89x	0.02	0.78	✓
ex2.2	2	0.39	0.90	2.31x	0.04	0.70	✓
ex2.3	2	0.17	0.40	2.35x	0.02	0.66	✓
ex2.4	2	0.15	0.50	3.33x	0.02	0.50	✓
ex2.5	2	0.17	0.20	1.18x	0.00	0.40	✓
ex2.6	3	0.85	1.20	1.41x	0.04	0.40	✓
ex2.7	4	0.33	0.50	1.52x	0.03	0.50	✓
ex2.8	4	0.27	0.60	2.22x	0.02	0.49	✓
ex2.9	100	1.30	3.90	3.00x	0.05	1.22	C:1/F:1

BB02AD

DAREX - Discrete-time Algebraic Riccati Equation Examples

Average Speedup: 6.384x (C11 faster)

Dataset	N	C11 (μs)	F77 (μs)	Speedup	C11 σ	F77 σ	Status
ex1.10	100	0.10	2.20	22.00x	0.02	0.98	C:1/F:1
ex1.11	100	0.12	1.90	15.83x	0.00	0.70	C:1/F:1
ex1.13	100	0.54	2.20	4.07x	0.03	0.87	C:1/F:1
ex2.1	2	0.35	0.70	2.00x	0.04	0.64	✓
ex2.2	2	0.40	0.80	2.00x	0.02	0.60	✓
ex2.3	2	0.19	0.50	2.63x	0.02	0.81	✓
ex2.4	3	0.92	1.20	1.30x	0.00	0.40	✓
ex2.5	4	0.65	0.80	1.23x	0.02	0.40	✓

BB03AD

CTLEX - Continuous-time Lyapunov Equation Examples

Average Speedup: 0.822x (F77 faster)

Dataset	N	C11 (μs)	F77 (μs)	Speedup	C11 σ	F77 σ	Status
ex4.1	10	4.15	2.30	0.55x	0.06	1.00	✓
ex4.1	20	14.87	7.30	0.49x	0.07	0.78	✓
ex4.1	30	32.43	15.90	0.49x	0.28	1.22	✓
ex4.1	40	56.44	41.60	0.74x	0.10	2.94	✓
ex4.1	50	87.85	89.50	1.02x	0.04	1.02	✓
ex4.2	10	1.70	1.10	0.65x	0.04	0.30	✓
ex4.2	20	5.66	2.80	0.49x	0.05	0.40	✓
ex4.2	30	12.18	5.60	0.46x	0.04	0.49	✓
ex4.2	40	21.04	11.70	0.56x	0.07	0.46	✓
ex4.2	50	30.98	20.00	0.65x	1.40	2.10	✓
ex4.3	10	0.26	0.40	1.54x	0.02	0.49	✓
ex4.3	20	0.74	1.00	1.35x	0.02	0.63	✓
ex4.3	30	1.52	1.70	1.12x	0.02	0.78	✓
ex4.3	40	2.50	3.00	1.20x	0.02	0.63	✓
ex4.3	50	3.51	4.20	1.20x	0.02	0.40	✓
ex4.4	30	2.08	1.60	0.77x	0.02	0.49	✓
ex4.4	60	7.56	5.70	0.75x	0.02	0.78	✓
ex4.4	90	16.38	11.40	0.70x	0.13	0.49	✓
ex4.4	120	32.48	26.30	0.81x	0.10	0.64	✓
ex4.4	150	45.60	41.30	0.91x	0.07	0.46	✓

BB04AD

DTLEX - Discrete-time Lyapunov Equation Examples

Average Speedup: 0.924x (F77 faster)

Dataset	N	C11 (μs)	F77 (μs)	Speedup	C11 σ	F77 σ	Status
ex4.1	10	1.73	1.60	0.92x	0.02	0.92	✓
ex4.1	20	5.75	4.40	0.77x	0.07	0.49	✓
ex4.1	30	12.17	8.40	0.69x	0.05	0.49	✓
ex4.1	40	20.81	14.50	0.70x	0.05	0.92	✓
ex4.1	50	32.08	22.30	0.70x	0.09	0.46	✓
ex4.2	10	1.52	1.30	0.86x	0.03	0.46	✓
ex4.2	20	5.24	3.60	0.69x	0.04	0.49	✓
ex4.2	30	11.23	7.60	0.68x	0.04	0.49	✓
ex4.2	40	27.20	12.80	0.47x	20.47	0.87	✓
ex4.2	50	29.90	20.40	0.68x	0.08	1.62	✓
ex4.3	10	0.34	0.60	1.76x	0.01	0.80	✓
ex4.3	20	1.12	1.40	1.25x	0.00	0.49	✓
ex4.3	30	2.37	2.60	1.10x	0.02	0.49	✓
ex4.3	40	4.09	4.20	1.03x	0.02	0.40	✓
ex4.3	50	6.27	6.30	1.00x	0.06	0.46	✓
ex4.4	30	1.97	2.20	1.12x	0.06	0.40	✓
ex4.4	60	7.03	7.40	1.05x	0.04	0.49	✓
ex4.4	90	15.11	16.40	1.09x	0.04	0.66	✓
ex4.4	120	30.16	29.00	0.96x	0.24	1.41	✓
ex4.4	150	45.90	44.80	0.98x	0.13	0.40	✓

BD01AD

CTDSX - Continuous-time Descriptor System Examples

Average Speedup: 49.543x (C11 faster)

Dataset	N	C11 (μs)	F77 (μs)	Speedup	C11 σ	F77 σ	Status
ex1.10	8	0.02	1.80	90.00x	0.02	0.60	C:1/F:1
ex2.1	4	0.07	0.40	5.71x	0.02	0.66	✓
ex2.2	4	0.05	0.40	8.00x	0.02	0.49	✓
ex2.3	3	0.01	1.40	140.00x	0.02	0.49	C:1/F:1
ex2.4	3	0.05	0.20	4.00x	0.02	0.60	✓

BD02AD

DTDSX - Discrete-time Descriptor System Examples

Average Speedup: 19.698x (C11 faster)

Dataset	N	C11 (μs)	F77 (μs)	Speedup	C11 σ	F77 σ	Status
ex1.10	6	0.08	0.50	6.25x	0.02	0.50	✓
ex1.11	9	0.06	2.50	41.67x	0.02	0.67	C:1/F:1
ex1.12	10	0.17	1.90	11.18x	0.02	0.30	C:1/F:1

Raw Benchmark Data

C11 Implementation Results

routine,dataset,n,mean_us,min_us,max_us,stddev_us,info
bb01ad,ex1.1,2,0.15,0.12,0.21,0.03,0
bb01ad,ex1.2,2,0.16,0.12,0.17,0.02,0
bb01ad,ex1.3,100,0.07,0.04,0.08,0.02,1
bb01ad,ex1.4,100,0.11,0.08,0.12,0.02,1
bb01ad,ex1.5,100,0.13,0.12,0.17,0.01,1
bb01ad,ex1.6,100,0.46,0.46,0.46,0.00,1
bb01ad,ex2.1,2,0.18,0.17,0.21,0.02,0
bb01ad,ex2.2,2,0.39,0.38,0.50,0.04,0
bb01ad,ex2.3,2,0.17,0.12,0.21,0.02,0
bb01ad,ex2.4,2,0.15,0.12,0.17,0.02,0
bb01ad,ex2.5,2,0.17,0.17,0.17,0.00,0
bb01ad,ex2.6,3,0.85,0.83,0.96,0.04,0
bb01ad,ex2.7,4,0.33,0.29,0.38,0.03,0
bb01ad,ex2.8,4,0.27,0.25,0.29,0.02,0
bb01ad,ex2.9,100,1.30,1.25,1.42,0.05,1
bb01ad,ex3.1,39,17.73,16.54,18.88,0.74,0
bb01ad,ex3.2,64,31.27,29.58,32.92,1.38,0
bb01ad,ex3.1,39,17.59,16.25,18.33,0.65,0
bb01ad,ex3.2,64,31.38,28.96,32.62,1.52,0
bb01ad,ex3.1,39,17.81,16.54,18.33,0.59,0
bb01ad,ex3.2,64,31.24,29.46,32.88,1.52,0
bb01ad,ex3.1,39,18.46,17.58,19.04,0.41,0
bb01ad,ex3.2,64,32.67,32.58,32.75,0.07,0
bb01ad,ex3.1,39,18.46,17.79,18.83,0.37,0
bb01ad,ex3.2,64,32.91,32.08,35.42,0.91,0
bb02ad,ex1.1,100,0.08,0.04,0.08,0.02,3
bb02ad,ex1.2,100,0.10,0.08,0.12,0.02,3
bb02ad,ex1.3,2,0.17,0.17,0.21,0.02,0
bb02ad,ex1.4,100,0.08,0.08,0.08,0.00,3
bb02ad,ex1.5,100,0.06,0.04,0.08,0.02,1
bb02ad,ex1.6,100,0.06,0.04,0.08,0.02,1
bb02ad,ex1.7,100,0.08,0.08,0.08,0.00,1
bb02ad,ex1.8,100,0.09,0.08,0.12,0.01,1
bb02ad,ex1.9,6,1.12,1.08,1.17,0.03,0
bb02ad,ex1.10,100,0.10,0.08,0.12,0.02,1
bb02ad,ex1.11,100,0.12,0.12,0.12,0.00,1
bb02ad,ex1.12,100,0.16,0.12,0.21,0.03,1
bb02ad,ex1.13,100,0.54,0.50,0.58,0.03,1
bb02ad,ex2.1,2,0.35,0.33,0.46,0.04,0
bb02ad,ex2.2,2,0.40,0.38,0.42,0.02,0
bb02ad,ex2.3,2,0.19,0.17,0.21,0.02,0
bb02ad,ex2.4,3,0.92,0.92,0.92,0.00,0
bb02ad,ex2.5,4,0.65,0.62,0.67,0.02,0
bb02ad,ex4.1,100,42.03,41.62,42.25,0.19,0
bb02ad,ex4.1,100,41.61,39.33,42.33,0.83,0
bb02ad,ex4.1,100,39.50,39.17,39.83,0.23,0
bb02ad,ex4.1,100,39.56,39.21,40.04,0.29,0
bb02ad,ex4.1,100,39.72,39.38,40.17,0.21,0
bb03ad,ex4.1,10,4.15,4.08,4.29,0.06,0
bb03ad,ex4.2,10,1.70,1.62,1.79,0.04,0
bb03ad,ex4.3,10,0.26,0.25,0.29,0.02,0
bb03ad,ex4.4,30,2.08,2.04,2.08,0.02,0
bb03ad,ex4.1,20,14.87,14.79,15.04,0.07,0
bb03ad,ex4.2,20,5.66,5.62,5.75,0.05,0
bb03ad,ex4.3,20,0.74,0.71,0.75,0.02,0
bb03ad,ex4.4,60,7.56,7.54,7.58,0.02,0
bb03ad,ex4.1,30,32.43,32.21,33.17,0.28,0
bb03ad,ex4.2,30,12.18,12.12,12.25,0.04,0
bb03ad,ex4.3,30,1.52,1.50,1.54,0.02,0
bb03ad,ex4.4,90,16.38,16.25,16.62,0.13,0
bb03ad,ex4.1,40,56.44,56.29,56.58,0.10,0
bb03ad,ex4.2,40,21.04,20.96,21.12,0.07,0
bb03ad,ex4.3,40,2.50,2.46,2.54,0.02,0
bb03ad,ex4.4,120,32.48,32.33,32.58,0.10,0
bb03ad,ex4.1,50,87.85,87.79,87.92,0.04,0
bb03ad,ex4.2,50,30.98,29.83,32.83,1.40,0
bb03ad,ex4.3,50,3.51,3.50,3.54,0.02,0
bb03ad,ex4.4,150,45.60,45.46,45.71,0.07,0
bb04ad,ex4.1,10,1.73,1.71,1.75,0.02,0
bb04ad,ex4.2,10,1.52,1.46,1.54,0.03,0
bb04ad,ex4.3,10,0.34,0.33,0.38,0.01,0
bb04ad,ex4.4,30,1.97,1.92,2.08,0.06,0
bb04ad,ex4.1,20,5.75,5.67,5.92,0.07,0
bb04ad,ex4.2,20,5.24,5.21,5.33,0.04,0
bb04ad,ex4.3,20,1.12,1.12,1.12,0.00,0
bb04ad,ex4.4,60,7.03,7.00,7.12,0.04,0
bb04ad,ex4.1,30,12.17,12.12,12.29,0.05,0
bb04ad,ex4.2,30,11.23,11.21,11.29,0.04,0
bb04ad,ex4.3,30,2.37,2.33,2.42,0.02,0
bb04ad,ex4.4,90,15.11,15.08,15.21,0.04,0
bb04ad,ex4.1,40,20.81,20.75,20.92,0.05,0
bb04ad,ex4.2,40,27.20,19.33,84.29,20.47,0
bb04ad,ex4.3,40,4.09,4.04,4.12,0.02,0
bb04ad,ex4.4,120,30.16,29.83,30.46,0.24,0
bb04ad,ex4.1,50,32.08,31.92,32.25,0.09,0
bb04ad,ex4.2,50,29.90,29.83,30.08,0.08,0
bb04ad,ex4.3,50,6.27,6.21,6.38,0.06,0
bb04ad,ex4.4,150,45.90,45.75,46.08,0.13,0
bd01ad,ex1.1,2,0.03,0.00,0.04,0.02,0
bd01ad,ex1.2,2,0.01,0.00,0.04,0.02,0
bd01ad,ex1.3,4,0.02,0.00,0.04,0.02,1
bd01ad,ex1.4,8,0.02,0.00,0.04,0.02,1
bd01ad,ex1.5,9,0.01,0.00,0.04,0.02,1
bd01ad,ex1.6,30,0.03,0.00,0.04,0.02,1
bd01ad,ex1.7,11,0.02,0.00,0.04,0.02,1
bd01ad,ex1.8,9,0.01,0.00,0.04,0.02,1
bd01ad,ex1.9,55,0.01,0.00,0.04,0.02,1
bd01ad,ex1.10,8,0.02,0.00,0.04,0.02,1
bd01ad,ex2.1,4,0.07,0.04,0.08,0.02,0
bd01ad,ex2.2,4,0.05,0.04,0.08,0.02,0
bd01ad,ex2.3,3,0.01,0.00,0.04,0.02,1
bd01ad,ex2.4,3,0.05,0.04,0.08,0.02,0
bd01ad,ex2.5,100,0.02,0.00,0.04,0.02,1
bd01ad,ex2.6,100,0.01,0.00,0.04,0.02,1
bd01ad,ex3.1,39,2.01,2.00,2.04,0.02,0
bd01ad,ex3.2,100,10.99,10.92,11.25,0.09,0
bd01ad,ex3.1,39,2.02,2.00,2.04,0.02,0
bd01ad,ex3.2,100,10.99,10.96,11.08,0.05,0
bd01ad,ex3.1,39,2.02,2.00,2.08,0.04,0
bd01ad,ex3.2,100,10.98,10.96,11.04,0.03,0
bd01ad,ex3.1,39,2.01,2.00,2.04,0.02,0
bd01ad,ex3.2,100,11.00,10.96,11.08,0.06,0
bd01ad,ex3.1,39,2.01,2.00,2.04,0.02,0
bd01ad,ex3.2,100,10.99,10.96,11.25,0.09,0
bd02ad,ex1.1,2,0.02,0.00,0.04,0.02,0
bd02ad,ex1.2,2,0.03,0.00,0.04,0.02,0
bd02ad,ex1.3,2,0.01,0.00,0.04,0.02,0
bd02ad,ex1.4,2,0.04,0.00,0.04,0.01,0
bd02ad,ex1.5,2,0.03,0.00,0.04,0.02,0
bd02ad,ex1.6,4,0.04,0.00,0.04,0.01,1
bd02ad,ex1.7,4,0.04,0.00,0.04,0.01,1
bd02ad,ex1.8,4,0.04,0.00,0.08,0.02,1
bd02ad,ex1.9,5,0.05,0.04,0.08,0.01,1
bd02ad,ex1.10,6,0.08,0.04,0.12,0.02,0
bd02ad,ex1.11,9,0.06,0.04,0.08,0.02,1
bd02ad,ex1.12,10,0.17,0.17,0.21,0.02,1
bd02ad,ex2.1,4,0.08,0.08,0.08,0.00,0
bd02ad,ex3.1,10,0.21,0.21,0.21,0.00,0
bd02ad,ex3.1,20,0.62,0.58,0.62,0.02,0
bd02ad,ex3.1,30,1.27,1.25,1.29,0.02,0
bd02ad,ex3.1,40,2.17,2.12,2.21,0.02,0
bd02ad,ex3.1,50,3.31,3.29,3.33,0.02,0
sb03md,ctlex4.1_n10,10,2.72,2.62,2.96,0.10,11
sb03md,ctlex4.2_n10,10,2.64,2.54,2.71,0.05,11
sb03md,ctlex4.3_n10,10,2.53,2.46,2.67,0.06,11
sb03md,ctlex4.4_n10,30,25.53,24.46,27.75,1.02,31
sb03md,ctlex4.1_n20,20,8.09,7.92,8.25,0.10,21
sb03md,ctlex4.2_n20,20,8.28,8.08,9.17,0.32,21
sb03md,ctlex4.3_n20,20,6.92,6.88,7.00,0.05,21
sb03md,ctlex4.4_n20,60,183.55,181.12,189.62,2.90,61
sb03md,ctlex4.1_n30,30,25.84,25.42,26.54,0.41,31
sb03md,ctlex4.2_n30,30,27.87,27.12,28.50,0.46,31
sb03md,ctlex4.3_n30,30,17.60,17.29,18.00,0.22,31
sb03md,ctlex4.4_n30,90,1176.08,1140.67,1221.42,23.19,91
sb03md,ctlex4.1_n40,40,39.04,38.50,40.71,0.67,41
sb03md,ctlex4.2_n40,40,38.90,38.21,40.00,0.55,41
sb03md,ctlex4.3_n40,40,31.37,30.54,33.71,0.95,41
sb03md,ctlex4.4_n40,120,2587.39,2565.08,2659.54,31.95,121
sb03md,ctlex4.1_n50,50,81.60,76.75,108.54,9.60,51
sb03md,ctlex4.2_n50,50,76.92,72.75,80.29,1.97,51
sb03md,ctlex4.3_n50,50,61.75,58.62,81.46,7.01,51
sb03md,ctlex4.4_n50,150,3863.64,3766.29,4157.17,115.48,151
sb03od,dtlex4.1_n10,10,5.35,5.25,5.79,0.16,0
sb03od,dtlex4.2_n10,10,0.75,0.75,0.79,0.01,2
sb03od,dtlex4.3_n10,10,0.77,0.75,0.79,0.02,2
sb03od,dtlex4.4_n10,30,12.44,12.29,12.92,0.18,2
sb03od,dtlex4.1_n20,20,3.01,3.00,3.08,0.03,2
sb03od,dtlex4.2_n20,20,3.03,2.92,3.17,0.07,2
sb03od,dtlex4.3_n20,20,2.18,2.17,2.21,0.02,2
sb03od,dtlex4.4_n20,60,120.35,119.42,122.92,1.16,2
sb03od,dtlex4.1_n30,30,13.13,13.04,13.42,0.12,2
sb03od,dtlex4.2_n30,30,14.27,14.21,14.33,0.04,2
sb03od,dtlex4.3_n30,30,4.84,4.75,4.96,0.07,2
sb03od,dtlex4.4_n30,90,1414.32,1384.75,1471.29,28.53,2
sb03od,dtlex4.1_n40,40,18.25,18.21,18.42,0.06,2
sb03od,dtlex4.2_n40,40,17.59,17.50,17.62,0.04,2
sb03od,dtlex4.3_n40,40,7.25,7.12,7.42,0.10,2
sb03od,dtlex4.4_n40,120,3680.26,3108.08,3814.38,206.40,2
sb03od,dtlex4.1_n50,50,34.82,34.04,39.67,1.76,2
sb03od,dtlex4.2_n50,50,33.75,33.38,36.17,0.85,2
sb03od,dtlex4.3_n50,50,10.62,10.58,10.79,0.06,2
sb03od,dtlex4.4_n50,150,4941.92,4880.79,5067.25,64.01,2

Fortran77 Implementation Results

routine,dataset,n,mean_us,min_us,max_us,stddev_us,info
bb01ad,ex1.1,2,0.60,0.00,3.00,1.02,0
bb01ad,ex1.2,2,0.40,0.00,1.00,0.49,0
bb01ad,ex1.3,100,3.20,2.00,6.00,1.25,1
bb01ad,ex1.4,100,2.60,1.00,4.00,0.80,1
bb01ad,ex1.5,100,2.80,1.00,7.00,1.54,1
bb01ad,ex1.6,100,4.90,2.00,16.00,4.93,1
bb01ad,ex2.1,2,0.70,0.00,2.00,0.78,0
bb01ad,ex2.2,2,0.90,0.00,2.00,0.70,0
bb01ad,ex2.3,2,0.40,0.00,2.00,0.66,0
bb01ad,ex2.4,2,0.50,0.00,1.00,0.50,0
bb01ad,ex2.5,2,0.20,0.00,1.00,0.40,0
bb01ad,ex2.6,3,1.20,1.00,2.00,0.40,0
bb01ad,ex2.7,4,0.50,0.00,1.00,0.50,0
bb01ad,ex2.8,4,0.60,0.00,1.00,0.49,0
bb01ad,ex2.9,100,3.90,3.00,7.00,1.22,1
bb02ad,ex1. 1,100,0.70,0.00,3.00,1.00,3
bb02ad,ex1. 2,100,0.40,0.00,1.00,0.49,3
bb02ad,ex1. 3,2,0.50,0.00,1.00,0.50,0
bb02ad,ex1. 4,100,0.20,0.00,1.00,0.40,3
bb02ad,ex1. 5,100,2.10,1.00,3.00,0.54,1
bb02ad,ex1. 6,100,2.30,1.00,6.00,1.35,1
bb02ad,ex1. 7,100,2.30,1.00,3.00,0.64,1
bb02ad,ex1. 8,100,2.30,1.00,4.00,0.78,1
bb02ad,ex1. 9,6,1.10,1.00,2.00,0.30,0
bb02ad,ex1.10,100,2.20,1.00,4.00,0.98,1
bb02ad,ex1.11,100,1.90,1.00,3.00,0.70,1
bb02ad,ex1.12,13,2.80,2.00,3.00,0.40,0
bb02ad,ex1.13,100,2.20,1.00,3.00,0.87,1
bb02ad,ex2.1,2,0.70,0.00,2.00,0.64,0
bb02ad,ex2.2,2,0.80,0.00,2.00,0.60,0
bb02ad,ex2.3,2,0.50,0.00,2.00,0.81,0
bb02ad,ex2.4,3,1.20,1.00,2.00,0.40,0
bb02ad,ex2.5,4,0.80,0.00,1.00,0.40,0
bb03ad,ex4.1,10,2.30,1.00,5.00,1.00,0
bb03ad,ex4.2,10,1.10,1.00,2.00,0.30,0
bb03ad,ex4.3,10,0.40,0.00,1.00,0.49,0
bb03ad,ex4.4,30,1.60,1.00,2.00,0.49,0
bb03ad,ex4.1,20,7.30,6.00,9.00,0.78,0
bb03ad,ex4.2,20,2.80,2.00,3.00,0.40,0
bb03ad,ex4.3,20,1.00,0.00,2.00,0.63,0
bb03ad,ex4.4,60,5.70,5.00,7.00,0.78,0
bb03ad,ex4.1,30,15.90,15.00,19.00,1.22,0
bb03ad,ex4.2,30,5.60,5.00,6.00,0.49,0
bb03ad,ex4.3,30,1.70,1.00,3.00,0.78,0
bb03ad,ex4.4,90,11.40,11.00,12.00,0.49,0
bb03ad,ex4.1,40,41.60,39.00,46.00,2.94,0
bb03ad,ex4.2,40,11.70,11.00,12.00,0.46,0
bb03ad,ex4.3,40,3.00,2.00,4.00,0.63,0
bb03ad,ex4.4,120,26.30,26.00,28.00,0.64,0
bb03ad,ex4.1,50,89.50,88.00,92.00,1.02,0
bb03ad,ex4.2,50,20.00,19.00,26.00,2.10,0
bb03ad,ex4.3,50,4.20,4.00,5.00,0.40,0
bb03ad,ex4.4,150,41.30,41.00,42.00,0.46,0
bb04ad,ex4.1,10,1.60,1.00,4.00,0.92,0
bb04ad,ex4.2,10,1.30,1.00,2.00,0.46,0
bb04ad,ex4.3,10,0.60,0.00,2.00,0.80,0
bb04ad,ex4.4,30,2.20,2.00,3.00,0.40,0
bb04ad,ex4.1,20,4.40,4.00,5.00,0.49,0
bb04ad,ex4.2,20,3.60,3.00,4.00,0.49,0
bb04ad,ex4.3,20,1.40,1.00,2.00,0.49,0
bb04ad,ex4.4,60,7.40,7.00,8.00,0.49,0
bb04ad,ex4.1,30,8.40,8.00,9.00,0.49,0
bb04ad,ex4.2,30,7.60,7.00,8.00,0.49,0
bb04ad,ex4.3,30,2.60,2.00,3.00,0.49,0
bb04ad,ex4.4,90,16.40,16.00,18.00,0.66,0
bb04ad,ex4.1,40,14.50,14.00,17.00,0.92,0
bb04ad,ex4.2,40,12.80,12.00,15.00,0.87,0
bb04ad,ex4.3,40,4.20,4.00,5.00,0.40,0
bb04ad,ex4.4,120,29.00,28.00,33.00,1.41,0
bb04ad,ex4.1,50,22.30,22.00,23.00,0.46,0
bb04ad,ex4.2,50,20.40,19.00,25.00,1.62,0
bb04ad,ex4.3,50,6.30,6.00,7.00,0.46,0
bb04ad,ex4.4,150,44.80,44.00,45.00,0.40,0
bd01ad,ex1. 1,2,0.50,0.00,2.00,0.67,0
bd01ad,ex1. 2,2,0.20,0.00,1.00,0.40,0
bd01ad,ex1. 3,4,2.80,2.00,4.00,0.75,1
bd01ad,ex1. 4,8,2.10,1.00,3.00,0.70,1
bd01ad,ex1. 5,9,2.20,1.00,4.00,0.87,1
bd01ad,ex1. 6,30,2.30,1.00,3.00,0.78,1
bd01ad,ex1. 7,11,1.60,1.00,2.00,0.49,1
bd01ad,ex1. 8,9,2.00,1.00,3.00,0.63,1
bd01ad,ex1. 9,55,3.10,2.00,4.00,0.83,1
bd01ad,ex1.10,8,1.80,1.00,3.00,0.60,1
bd01ad,ex2.1,4,0.40,0.00,2.00,0.66,0
bd01ad,ex2.2,4,0.40,0.00,1.00,0.49,0
bd01ad,ex2.3,3,1.40,1.00,2.00,0.49,1
bd01ad,ex2.4,3,0.20,0.00,2.00,0.60,0
bd01ad,ex2.5,2,1.80,1.00,3.00,0.75,1
bd01ad,ex2.6,3,1.50,0.00,2.00,0.67,1
bd02ad,ex1. 1,2,0.60,0.00,2.00,0.66,0
bd02ad,ex1. 2,2,0.50,0.00,2.00,0.81,0
bd02ad,ex1. 3,2,0.10,0.00,1.00,0.30,0
bd02ad,ex1. 4,2,0.10,0.00,1.00,0.30,0
bd02ad,ex1. 5,2,0.20,0.00,1.00,0.40,0
bd02ad,ex1. 6,4,3.10,2.00,6.00,1.14,1
bd02ad,ex1. 7,4,2.50,2.00,4.00,0.67,1
bd02ad,ex1. 8,4,2.40,2.00,3.00,0.49,1
bd02ad,ex1. 9,5,2.20,1.00,3.00,0.60,1
bd02ad,ex1.10,6,0.50,0.00,1.00,0.50,0
bd02ad,ex1.11,9,2.50,1.00,3.00,0.67,1
bd02ad,ex1.12,10,1.90,1.00,2.00,0.30,1
sb03md,synthetic_n10,10,4.50,4.00,6.00,0.67,0
sb03md,synthetic_n20,20,10.50,9.00,12.00,0.81,0
sb03md,synthetic_n30,30,22.00,21.00,23.00,0.45,0
sb03md,synthetic_n40,40,38.30,37.00,42.00,1.68,0
sb03md,synthetic_n50,50,67.80,66.00,70.00,1.17,0
sb03od,synthetic_n10,10,4.10,3.00,6.00,0.83,0
sb03od,synthetic_n20,20,13.10,12.00,16.00,1.14,0
sb03od,synthetic_n30,30,26.80,26.00,28.00,0.87,0
sb03od,synthetic_n40,40,48.50,47.00,53.00,1.63,0
sb03od,synthetic_n50,50,73.90,73.00,75.00,0.54,0

Methodology

Timing Approach

• C11: High-resolution platform timers (mach_absolute_time on macOS)
• Fortran77: CPU_TIME intrinsic subroutine
• Both implementations linked against identical BLAS/LAPACK (Apple Accelerate)
• Identical test matrices and problem sizes used

Statistical Analysis

• Mean, min, max, and standard deviation computed over timed runs
• Speedup = F77_mean / C11_mean (>1 means C11 is faster)
• Warmup runs excluded from timing statistics

Caveats

1. CPU frequency scaling may affect results
2. Memory caching effects present in both implementations
3. Small timing variations expected between runs
4. Some routines may show different behavior due to algorithm variations

---

Report generated by scripts/benchmark_c_vs_fortran.py

[bnavigator]

Where are the scripts mentioned in these "reports"?

[jamestjsp]

@bnavigator I have ported the benchmark scripts https://github.com/jamestjsp/slicot/blob/main/benchmarks/README.md

It is now part of this repo.