Go complex numbers: builtin vs library implementation

See proposal: remove complex numbers.

This repository:

1. Implements most complex64 operations with user-defined type Complex64.
2. Measures performance of complex64 VS Complex64.
3. Provides amd64 machine code output for both builtin and Complex64 operations.

Results and conclusions may be extrapolated to complex128.

This is performance comparison of the potential implementation, not a library.

TL;DR

# old is builtin complex64
# new is user-defined Complex64

name       old time/op  new time/op  delta
Logical-4  2.89µs ± 1%  2.77µs ± 8%    ~     (p=0.108 n=9+10)
Add64-4    1.50µs ± 1%  1.51µs ± 1%    ~     (p=0.174 n=9+10)
Sub64-4    1.50µs ± 1%  1.52µs ± 1%  +0.80%  (p=0.000 n=9+10)
Mul64-4    6.50µs ± 2%  6.74µs ± 7%    ~     (p=0.101 n=10+10)
Div64-4    52.6µs ± 0%  47.9µs ± 7%  -8.99%  (p=0.000 n=9+10)

Note: it is strange that Sub/Add/Mul time differs as their machine code is exactly the same on amd64 (see "Machine code comparison").

go test -bench=.
BenchmarkLogicalBuiltin-4   	  500000	      2876 ns/op
BenchmarkLogical-4          	  500000	      2711 ns/op
BenchmarkAdd64Builtin-4     	 1000000	      1539 ns/op
BenchmarkAdd64-4            	 1000000	      1516 ns/op
BenchmarkSub64Builtin-4     	 1000000	      1511 ns/op
BenchmarkSub64-4            	 1000000	      1568 ns/op
BenchmarkMul64Builtin-4     	  200000	      6476 ns/op
BenchmarkMul64-4            	  200000	      6456 ns/op
BenchmarkDiv64Builtin-4     	   30000	     52589 ns/op
BenchmarkDiv64-4            	   30000	     44854 ns/op

Benchmark results.

Results stored in "benchmark-results/". Structure is "benchmark-results/$arch/$machine_id/$version".

Each machine folder can contain some hardware/system info:

• lscpu.txt, the result of lscpu invocation result
• uname.txt, optional uname -a invocation result

For each version that was tested on that machine, there is "v$number" folder, which consist of:

• builtin.out & lib.out - results of the benchmark runs
• benchstat.txt result of benchstat builtin.out lib.out

Run benchmark

Benchstat is required to aggregate benchmark statistics.

See run-benchmarks bash script for detailed instruction.

Machine code comparison

Most code looks the same, but some code compiled to different instruction sequences.

Look inside disasm.go to inspect objdump output.

Edge cases / limitations

Constant semantics

Spec:complex_numbers: complex, imag and real can be a constant value.

If the operands of these functions are all constants, the return value is a constant.

User-defined struct literal is never a constant.

Versions

• 1 : up to 1c7348b2f4683432625a7e1c9c9b434fd48b6ad7 initial implementation
• 2 : from 41112b4215a2d02aca055a751f8e4047168397c5 alternative Eq/Neq/IsZero implementation