calculate date_from_iso_days using neri_schneider algorithm

[dkuku]

This is a faster implementation than the erlang one. The reference implementation is mit licensed I adjusted it for elixir needs using windsurf with claude opus.
2x speedup comparing to the version from last week.

Benchmark suite executing with the following configuration:
warmup: 2 s
time: 5 s
memory time: 5 s
reduction time: 0 ns
parallel: 1
inputs: none specified
Estimated total run time: 24 s
Excluding outliers: false

Benchmarking elixir ...
Benchmarking neri-scheneider ...
Calculating statistics...
Formatting results...

Name                      ips        average  deviation         median         99th %
neri-scheneider      400.85 K        2.49 μs   ±281.71%        2.32 μs        3.41 μs
elixir               174.93 K        5.72 μs   ±147.04%        5.50 μs        9.25 μs

Comparison:
neri-scheneider      400.85 K
elixir               174.93 K - 2.29x slower +3.22 μs

Memory usage statistics:

Name               Memory usage
neri-scheneider         4.73 KB
elixir                 11.84 KB - 2.50x memory usage +7.10 KB

**All measurements for memory usage were the same**

Profiling neri-scheneider with fprof...
Reading trace data...

End of trace!
Processing data...
Creating output...
Done!

                                                                   CNT    ACC (ms)    OWN (ms)
Total                                                              297       0.565       0.565
:fprof.apply_start_stop/4                                            0       0.565       0.009
anonymous fn/2 in Benchee.Profile.run/4                              1       0.556       0.004
Benchee.Benchmark.Runner.run_once/2                                  1       0.427       0.004
Benchee.Benchmark.Runner.collect_return_value/2                      1       0.418       0.005
anonymous fn/1 in :elixir_compiler_59.__FILE__/1                     1       0.407       0.001
Enum.map/2                                                           1       0.406       0.001
Enum."-map/2-lists^map/1-1-"/2                                     102       0.405       0.304
Benchee.Benchmark.BenchmarkConfig.from/1                             1       0.125       0.003
XCalendar.ISO.date_from_iso_days/1                                 101       0.101       0.101
Kernel.struct!/2                                                     1       0.097       0.004
Benchee.Benchmark.BenchmarkConfig.__struct__/1                       1       0.092       0.001
Enum.reduce/3                                                        1       0.091       0.002
:maps.fold/3                                                         1       0.089       0.004
:maps.fold_1/4                                                      14       0.080       0.040
anonymous fn/4 in Enum.reduce/3                                     13       0.027       0.014
Map.take/2                                                           1       0.025       0.002
Map.take/3                                                          14       0.023       0.020
:maps.try_next/2                                                    13       0.013       0.013
anonymous fn/2 in Benchee.Benchmark.BenchmarkConfig.__struct        13       0.013       0.013
Benchee.Benchmark.Hooks.run_before_scenario/2                        1       0.004       0.002
Benchee.Benchmark.Hooks.run_before_function/2                        4       0.004       0.004
Benchee.Benchmark.Hooks.run_before_each/2                            1       0.004       0.002
:maps.next/1                                                         1       0.003       0.002
:maps.from_list/1                                                    1       0.003       0.003
:maps.iterator/1                                                     1       0.002       0.001
:maps.iterator/2                                                     1       0.001       0.001
:erts_internal.map_next/3                                            1       0.001       0.001
Kernel.validate_struct!/3                                            1       0.001       0.001
Benchee.Benchmark.Runner.main_function/2                             1       0.001       0.001
Benchee.Benchmark.Hooks.run_after_scenario/2                         1       0.001       0.001
Benchee.Benchmark.Hooks.run_after_each/3                             1       0.001       0.001
:undefined                                                           0       0.000       0.000
:suspend                                                             1       0.000       0.000

Profiling elixir with fprof...
Reading trace data...
..
End of trace!
Processing data...
Creating output...
Done!

                                                                   CNT    ACC (ms)    OWN (ms)
Total                                                             1409       2.778       2.777
:fprof.apply_start_stop/4                                            0       2.778       0.007
anonymous fn/2 in Benchee.Profile.run/4                              1       2.771       0.003
Benchee.Benchmark.Runner.run_once/2                                  1       2.651       0.004
Benchee.Benchmark.Runner.collect_return_value/2                      1       2.642       0.005
anonymous fn/1 in :elixir_compiler_59.__FILE__/1                     1       2.631       0.001
Enum.map/2                                                           1       2.630       0.001
Enum."-map/2-lists^map/1-1-"/2                                     102       2.629       0.305
Calendar.ISO.date_from_iso_days/1                                  101       2.323       0.404
Calendar.ISO.days_to_year/1                                        101       1.717       0.606
Calendar.ISO.days_to_year_interpolated/5                           101       0.707       0.404
Calendar.ISO.floor_div_positive_divisor/2                          303       0.303       0.303
Calendar.ISO.days_in_previous_years/1                              303       0.303       0.303
Calendar.ISO.leap_year?/1                                          202       0.202       0.202
Benchee.Benchmark.BenchmarkConfig.from/1                             1       0.117       0.003
Calendar.ISO.year_day_to_year_date/1                               101       0.101       0.101
Kernel.struct!/2                                                     1       0.095       0.004
Benchee.Benchmark.BenchmarkConfig.__struct__/1                       1       0.090       0.001
Enum.reduce/3                                                        1       0.089       0.001
:maps.fold/3                                                         1       0.088       0.004
:maps.fold_1/4                                                      14       0.079       0.040
anonymous fn/4 in Enum.reduce/3                                     13       0.026       0.013
Map.take/2                                                           1       0.019       0.001
Map.take/3                                                          14       0.018       0.016
:maps.try_next/2                                                    13       0.013       0.013
anonymous fn/2 in Benchee.Benchmark.BenchmarkConfig.__struct        13       0.013       0.013
Benchee.Benchmark.Hooks.run_before_scenario/2                        1       0.004       0.002
Benchee.Benchmark.Hooks.run_before_function/2                        4       0.004       0.004
Benchee.Benchmark.Hooks.run_before_each/2                            1       0.004       0.002
:maps.next/1                                                         1       0.003       0.002
:maps.iterator/1                                                     1       0.002       0.001
:maps.from_list/1                                                    1       0.002       0.002
:maps.iterator/2                                                     1       0.001       0.001
:erts_internal.map_next/3                                            1       0.001       0.001
Kernel.validate_struct!/3                                            1       0.001       0.001
Benchee.Benchmark.Runner.main_function/2                             1       0.001       0.001
Benchee.Benchmark.Hooks.run_after_scenario/2                         1       0.001       0.001
Benchee.Benchmark.Hooks.run_after_each/3                             1       0.001       0.001
:suspend                                                             2       0.001       0.000
:undefined                                                           0       0.000       0.000

[sabiwara]

Maybe we could mention the name of the algorithm in a comment with a link for future reference?

[leonqadirie]

Was very intrigued, took a look and stumbled across this recent article claiming to surpass Neri-Schneider.

A New Faster Algorithm for Gregorian Date Conversion - also note the mention of an even faster version by now.

It might be of interest, if not, apologies for the noise :)

[dkuku]

Was very intrigued, took a look and stumbled across this recent article claiming to surpass Neri-Schneider.

A New Faster Algorithm for Gregorian Date Conversion - also note the mention of an even faster version by now.

It might be of interest, if not, apologies for the noise :)

Same here: this new algorithm made me curious how we do it. :) The mentioned algorithm from last week is implemented in c and uses compiler tricks that can't be implemented on the beam: like bit shifting a 128bit number by 64bits that is 'free' on modern computers.
There is also an issue with it: it counts backwards from some very big year that you pick, so it is not infinite.
Second problem was that before year 0 I saw off by one errors. Maybe I was doing something wrong, but because the first limitation I decided to leave the idea and pick something else.

[dkuku]

here a benchmark for the function date_to_iso_days:

Benchmark suite executing with the following configuration:
warmup: 2 s
time: 5 s
memory time: 5 s
reduction time: 0 ns
parallel: 1
inputs: none specified
Estimated total run time: 24 s
Excluding outliers: false

Benchmarking elixir ...
Benchmarking neri-scheneider ...
Calculating statistics...
Formatting results...

Name                      ips        average  deviation         median         99th %
neri-scheneider      511.46 K        1.96 μs   ±344.78%        1.85 μs        2.63 μs
elixir               467.63 K        2.14 μs   ±321.91%        2.06 μs        3.25 μs

Comparison:
neri-scheneider      511.46 K
elixir               467.63 K - 1.09x slower +0.183 μs

Memory usage statistics:

Name               Memory usage
neri-scheneider         1.58 KB
elixir                  1.58 KB - 1.00x memory usage +0 KB

**All measurements for memory usage were the same**

Profiling neri-scheneider with fprof...
Reading trace data...
.
End of trace!
Processing data...
Creating output...
Done!

                                                                   CNT    ACC (ms)    OWN (ms)
Total                                                              802       1.366       1.366
:fprof.apply_start_stop/4                                            0       1.366       0.009
anonymous fn/2 in Benchee.Profile.run/4                              1       1.357       0.004
Benchee.Benchmark.Runner.run_once/2                                  1       1.235       0.004
Benchee.Benchmark.Runner.collect_return_value/2                      1       1.226       0.005
anonymous fn/1 in :elixir_compiler_2.__FILE__/1                      1       1.215       0.001
Enum.map/2                                                           1       1.214       0.001
Enum."-map/2-lists^map/1-1-"/2                                     102       1.213       0.304
anonymous fn/1 in :elixir_compiler_2.__FILE__/1                    101       0.909       0.101
XCalendar.ISO.date_to_iso_days/3                                   101       0.808       0.202
XCalendar.ISO.ensure_day_in_month!/3                               101       0.606       0.202
XCalendar.ISO.days_in_month/2                                      101       0.404       0.101
XCalendar.ISO.days_in_month_guarded/2                              101       0.303       0.202
Benchee.Benchmark.BenchmarkConfig.from/1                             1       0.118       0.003
XCalendar.ISO.leap_year?/1                                         101       0.101       0.101
Kernel.struct!/2                                                     1       0.095       0.003
Benchee.Benchmark.BenchmarkConfig.__struct__/1                       1       0.091       0.002
Enum.reduce/3                                                        1       0.089       0.001
:maps.fold/3                                                         1       0.088       0.004
:maps.fold_1/4                                                      14       0.079       0.040
anonymous fn/4 in Enum.reduce/3                                     13       0.026       0.013
Map.take/2                                                           1       0.020       0.001
Map.take/3                                                          14       0.019       0.017
:maps.try_next/2                                                    13       0.013       0.013
anonymous fn/2 in Benchee.Benchmark.BenchmarkConfig.__struct        13       0.013       0.013
Benchee.Benchmark.Hooks.run_before_scenario/2                        1       0.004       0.002
Benchee.Benchmark.Hooks.run_before_function/2                        4       0.004       0.004
Benchee.Benchmark.Hooks.run_before_each/2                            1       0.004       0.002
:maps.next/1                                                         1       0.003       0.002
:maps.iterator/1                                                     1       0.002       0.001
:maps.from_list/1                                                    1       0.002       0.002
:maps.iterator/2                                                     1       0.001       0.001
:erts_internal.map_next/3                                            1       0.001       0.001
Kernel.validate_struct!/3                                            1       0.001       0.001
Benchee.Benchmark.Runner.main_function/2                             1       0.001       0.001
Benchee.Benchmark.Hooks.run_after_scenario/2                         1       0.001       0.001
Benchee.Benchmark.Hooks.run_after_each/3                             1       0.001       0.001
:undefined                                                           0       0.000       0.000
:suspend                                                             1       0.000       0.000

Profiling elixir with fprof...
Reading trace data...
.
End of trace!
Processing data...
Creating output...
Done!

                                                                   CNT    ACC (ms)    OWN (ms)
Total                                                             1105       1.969       1.969
:fprof.apply_start_stop/4                                            0       1.969       0.009
anonymous fn/2 in Benchee.Profile.run/4                              1       1.960       0.003
Benchee.Benchmark.Runner.run_once/2                                  1       1.841       0.004
Benchee.Benchmark.Runner.collect_return_value/2                      1       1.832       0.005
anonymous fn/1 in :elixir_compiler_2.__FILE__/1                      1       1.821       0.001
Enum.map/2                                                           1       1.820       0.001
Enum."-map/2-lists^map/1-1-"/2                                     102       1.819       0.304
anonymous fn/1 in :elixir_compiler_2.__FILE__/1                    101       1.515       0.101
Calendar.ISO.date_to_iso_days/3                                    101       1.414       0.505
Calendar.ISO.ensure_day_in_month!/3                                101       0.606       0.202
Calendar.ISO.days_in_month/2                                       101       0.404       0.101
Calendar.ISO.days_in_month_guarded/2                               101       0.303       0.202
Benchee.Benchmark.BenchmarkConfig.from/1                             1       0.116       0.003
Calendar.ISO.leap_year?/1                                          101       0.101       0.101
Calendar.ISO.leap_day_offset/2                                     101       0.101       0.101
Calendar.ISO.days_in_previous_years/1                              101       0.101       0.101
Calendar.ISO.days_before_month/1                                   101       0.101       0.101
Kernel.struct!/2                                                     1       0.094       0.003
Benchee.Benchmark.BenchmarkConfig.__struct__/1                       1       0.090       0.001
Enum.reduce/3                                                        1       0.089       0.001
:maps.fold/3                                                         1       0.088       0.004
:maps.fold_1/4                                                      14       0.079       0.040
anonymous fn/4 in Enum.reduce/3                                     13       0.026       0.013
Map.take/2                                                           1       0.019       0.001
Map.take/3                                                          14       0.018       0.016
:maps.try_next/2                                                    13       0.013       0.013
anonymous fn/2 in Benchee.Benchmark.BenchmarkConfig.__struct        13       0.013       0.013
Benchee.Benchmark.Hooks.run_before_scenario/2                        1       0.004       0.002
Benchee.Benchmark.Hooks.run_before_function/2                        4       0.004       0.004
Benchee.Benchmark.Hooks.run_before_each/2                            1       0.004       0.002
:maps.next/1                                                         1       0.003       0.002
:maps.iterator/1                                                     1       0.002       0.001
:maps.from_list/1                                                    1       0.002       0.002
:maps.iterator/2                                                     1       0.001       0.001
:erts_internal.map_next/3                                            1       0.001       0.001
Kernel.validate_struct!/3                                            1       0.001       0.001
Benchee.Benchmark.Runner.main_function/2                             1       0.001       0.001
Benchee.Benchmark.Hooks.run_after_scenario/2                         1       0.001       0.001
Benchee.Benchmark.Hooks.run_after_each/3                             1       0.001       0.001
:undefined                                                           0       0.000       0.000
:suspend                                                             1       0.000       0.000

[josevalim]

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