EAF

This repository contains the supplementary material to:

Neri C, Schneider L. "Euclidean affine functions and their application to calendar algorithms". Softw Pract Exper. 2022;1-34. doi: 10.1002/spe.3172.

In particular, it contains instructions on how to build the code and the article's errata.

This work has been presented at C++ Now 2023 and C++ on Sea 2023.

Table of Contents

Building with CMake

• Command line
• Visual Studio IDE

Executables
Dependencies
Assembly snippets shown in the paper
Other implementations
Errata

Building with CMake

A list of CMakePresets is available. For instance, on Linux the preset gcc.debug.make builds in debug mode using gcc and make. On Windows msvc.debug.ninja builds in debug mode using msvc and ninja. In general, preset names have the form compiler.mode.builder where

• compiler is one of clang (Linux), clang-cl (Windows), gcc (Linux) or msvc (Windows);
• mode is one of debug, release or release-symbols;
• builder is one of make (Linux) or ninja.

Tip: cmake --list-presets shows the complete list available presets.

To build everything, on the top level directory, run:

$ cmake --preset <preset-name>
$ cmake --build build/<preset-name>

Visual Studio IDE

Make sure you have the cmake tools installed and, optionally, clang tools if you wish to build with clang-cl. Simply open the top level folder and select one of the available presets.

Executables

They are created in the build/<preset-name>/bin directory and the instructions below assumes this is the current working directory.

Name	Description
algorithm_NN_32	Paper's algorithm number NN for 32-bits
algorithm_NN_64	Paper's algorithm number NN for 64-bits
algorithm_tests	Tests all third party algorithms.
eaf_tests	Exhaustive tests for all 32-bits algorithms in the paper
example_NN	Paper's example number NN
fast_eaf	Calculates fast EAF coefficients
figure_NN	Algorithm of figure NN
info	Display range limits of all algorithms in the paper
to_date	Benchmark of to_date functions
to_rata_die	Benchmark of to_rata_date functions

Algorithms that calculate date from rata die (algorithm_NN_{32|64} for NN ∈ {01, 03, 05} and figure_12) take rata die at command line. For instance:

$ ./algorithm_03_32 738734
rata die = 738734
date     = 2022 10 1

Algorithms that calculate rata die from date (algorithm_NN_{32|64} for NN ∈ {02, 04, 06} and figure_13) take year month day at command line. For instance:

$ ./algorithm_04_32 2022 10 1
rata die = 738734
date     = 2022 10 1

Examples, tests, benchmarks and info do not take compulsory arguments at command line. For instance:

$ ./example_10
Testing:
 (5 * N_Y + 461) / 153 == (2141 * N_Y + 197913) /2^16,
  for all N_Y in [0, 734[.

Using signed integers...
  Pass.

Using unsigned integers...
  Pass.

fast_eaf takes rounding a b d k at command line. For instance (see Example 10):

$ ./fast_eaf down 5 461 153 16
a'          = 2141
b'          = 197913
d'          = 65536
k           = 16
upper bound = 734

Tests (algorithm_tests and eaf_tests) uses Google Test and allows this library's usual options (e.g., --help). The implementations of our own algorithms are exhaustively tested on their whole range of validity (spanning millions of years). Implementations of competitor algorithms are tested on a range spanning 800 years centered at 1 January 1970.

to_date and to_rata_die use Google Benchmark and allow this library's usual options (e.g., --help).

Dependencies

The following third part libraries are automatically downloaded at the time of the first build:

1. Google Benchmark;
2. Google Test;
3. Boost Multiprecision.

Assembly snippets shown in the paper

Here is a list of Compiler Explorer links for each assembly snippet shown in the paper:

• Figure 5: https://godbolt.org/z/zT4xdzTox
• Figure 6: https://godbolt.org/z/zY87WGz3v
• Figure 7:
  • Assembly generation: https://godbolt.org/z/YdfMjGvMd
  • Left timeline: https://godbolt.org/z/j9PWvP4qG
  • Right timeline: https://godbolt.org/z/3EvPodxo8
• Figure 8:
  • Assembly generation: https://godbolt.org/z/KvqqYd71Y
  • Left timeline: https://godbolt.org/z/WKEn75qfY
  • Right timeline: https://godbolt.org/z/sfMcc6z9j
• Figure 9:
  • Assembly generation: https://godbolt.org/z/94TYPd1Tn
  • Left timeline: https://godbolt.org/z/WYbz1xY8a
  • Right timeline: https://godbolt.org/z/e8Kjbsfd7
• Figure 10: https://godbolt.org/z/coM5esxP4

Other implementations

Language	Author	Link
C# (part of .NET7)	Sergei Pavlov	PR72712 and PR73277
Rust	Nuutti Kotivuori	https://github.com/nakedible/datealgo-rs
SPARK/Ada	Jorge Luis Sacchini	04e48784 and e24cb651

Errata

Page numbers below refer to the PDF file.

• Page 2, footnote. "2937 and 2821 BC.¹" should read "2937 and 2821 BC. (See Richards.¹)"
• Page 3, line 43. "does not involve strength reduction." should read "since it involves more than strength reduction."
• Page 11, caption of Figure 4. "On the right, the Gregorian calendar" should read "On the right, the proleptic Gregorian calendar".
• Page 14, line 16. "b' = 2928" should read "b' = -2928".
• Page 18, line 5. "x86_64, the mov instruction" should read "the x86_64's mov instruction".
• Page 22, line 29. "n = q∙q + r" should read "n = d∙q + r".
• Page 23, caption of Figure 12. "at least" should read "at least, Nᵤ∈[-12687428, 11248737]. (The range of validity is much larger though.)"
• Page 25, line 15. " f(g(q)) ≥ f(g(q) - 1)" should read " f(g(q) - 1) ≥ f(g(q))".
• Page 26, line 20. "q + 1f(f*(q + 1)) ≤ f(n)" should read "q + 1 = f(f*(q + 1)) ≤ f(n)".
• Page 28, line 23. "sometimes it is Theorem 3" should read "sometimes it is Theorem 2".
• Page 28, line 25. "Q(N)" should read "Q(n)".
• Page 29, line 11. "obtained in in Cavagnino and Werbrouck" should read "obtained in Cavagnino and Werbrouck".
• Page 29, line 20. "2ᵏ - 2ᵏ/%d + d" should read "2ᵏ - 2ᵏ%d + d".