{ "esm": "1.2.0", "metadata": { "name": "Calendar", "description": "Standard-library calendar templates (esm-spec §9.7.1 template-library file), generated by scripts/gen-lib-calendar.py. Ten public match-less expression templates of one parameter `t`, UTC seconds since 1970-01-01T00:00:00Z (binary64, proleptic Gregorian, no leap seconds): the pure-AST definitions of the datetime.* closed functions (esm-spec §9.2) `year(t)`, `month(t)`, `day(t)`, `hour(t)`, `minute(t)`, `second(t)`, `day_of_year(t)`, `julian_day(t)` and `is_leap_year(t)`, and `seconds_since_midnight(t)`. Each splits t exactly into the day number d = floor(floor(t) / 86400) and the whole second of the day s = floor(t) - 86400 d, then runs Howard Hinnant's civil_from_days, every integer division written floor(a / b); each step is a `civil_*` helper template the others call by reference (esm-spec §9.7.3). On the domain |t| < 2^52 s every intermediate is an integer below 2^53, so each floor is exact and each datetime field equals the closed function's value. Outside that domain, and for NaN or an infinite t, every public template returns NaN. The second-valued constants are unit-bearing `const` nodes (esm-spec §4.8.5), so t is read in seconds; the datetime fields are dimensionless and seconds_since_midnight is in seconds. Import with `expression_template_imports` and invoke with `apply_expression_template`; see docs/content/standard_library.md.", "authors": ["EarthSciML"], "created": "2026-04-25T00:00:00Z", "tags": ["standard-library", "calendar", "datetime", "expression-templates"], "references": [ { "citation": "esm-spec.md §9.2 (datetime.* semantics, the pinned julian_day formula); §9.6 (expression templates); §9.7.1 (template-library files); §9.7.3 (template references in bodies); §4.8.5 (unit-bearing const)." }, { "citation": "Hinnant, H., 2013. chrono-Compatible Low-Level Date Algorithms, `civil_from_days`. https://howardhinnant.github.io/date_algorithms.html" } ] }, "expression_templates": { "year": { "params": ["t"], "description": "Proleptic-Gregorian year of the UTC instant t (seconds since 1970-01-01T00:00:00Z), astronomical numbering (0 = 1 BC), the value datetime.year gives (esm-spec §9.2): yoe + 400 era, plus one in January and February (Howard Hinnant's civil_from_days). Finite t with |t| < 2^52 s; outside it, and for NaN or an infinite t, the value is NaN (0/0).", "body": { "op": "ifelse", "args": [ { "op": "<", "args": [{"op": "abs", "args": ["t"]}, {"op": "const", "args": [], "value": 4503599627370496, "units": "s"}] }, { "op": "+", "args": [ { "op": "+", "args": [ {"op": "apply_expression_template", "args": [], "name": "civil_year_of_era", "bindings": {"t": "t"}}, { "op": "*", "args": [400, {"op": "apply_expression_template", "args": [], "name": "civil_era", "bindings": {"t": "t"}}] } ] }, { "op": "ifelse", "args": [ {"op": "apply_expression_template", "args": [], "name": "civil_is_jan_feb", "bindings": {"t": "t"}}, 1, 0 ] } ] }, {"op": "/", "args": [0, 0]} ] } }, "month": { "params": ["t"], "description": "Calendar month 1..12 of the UTC instant t, the value datetime.month gives (esm-spec §9.2): mp + 3 for mp < 10 and mp - 9 otherwise, mp being the month counted from March. Finite t with |t| < 2^52 s; outside it, and for NaN or an infinite t, the value is NaN (0/0).", "body": { "op": "ifelse", "args": [ { "op": "<", "args": [{"op": "abs", "args": ["t"]}, {"op": "const", "args": [], "value": 4503599627370496, "units": "s"}] }, { "op": "+", "args": [ {"op": "apply_expression_template", "args": [], "name": "civil_month_index", "bindings": {"t": "t"}}, { "op": "ifelse", "args": [ { "op": "<", "args": [ {"op": "apply_expression_template", "args": [], "name": "civil_month_index", "bindings": {"t": "t"}}, 10 ] }, 3, -9 ] } ] }, {"op": "/", "args": [0, 0]} ] } }, "day": { "params": ["t"], "description": "Day of month 1..31 of the UTC instant t, the value datetime.day gives (esm-spec §9.2): doy - floor((153 mp + 2) / 5) + 1. Finite t with |t| < 2^52 s; outside it, and for NaN or an infinite t, the value is NaN (0/0).", "body": { "op": "ifelse", "args": [ { "op": "<", "args": [{"op": "abs", "args": ["t"]}, {"op": "const", "args": [], "value": 4503599627370496, "units": "s"}] }, { "op": "+", "args": [ { "op": "-", "args": [ {"op": "apply_expression_template", "args": [], "name": "civil_day_of_year", "bindings": {"t": "t"}}, { "op": "floor", "args": [ { "op": "/", "args": [ { "op": "+", "args": [ { "op": "*", "args": [ 153, {"op": "apply_expression_template", "args": [], "name": "civil_month_index", "bindings": {"t": "t"}} ] }, 2 ] }, 5 ] } ] } ] }, 1 ] }, {"op": "/", "args": [0, 0]} ] } }, "hour": { "params": ["t"], "description": "UTC hour 0..23 of t, the value datetime.hour gives (esm-spec §9.2): floor(s / 3600), s being the whole second of the day. Finite t with |t| < 2^52 s; outside it, and for NaN or an infinite t, the value is NaN (0/0).", "body": { "op": "ifelse", "args": [ { "op": "<", "args": [{"op": "abs", "args": ["t"]}, {"op": "const", "args": [], "value": 4503599627370496, "units": "s"}] }, { "op": "floor", "args": [ { "op": "/", "args": [ { "op": "/", "args": [ { "op": "apply_expression_template", "args": [], "name": "civil_second_of_day", "bindings": {"t": "t"} }, {"op": "const", "args": [], "value": 1, "units": "s"} ] }, 3600 ] } ] }, {"op": "/", "args": [0, 0]} ] } }, "minute": { "params": ["t"], "description": "UTC minute 0..59 of t, the value datetime.minute gives (esm-spec §9.2): floor(s / 60) - 60 floor(s / 3600). Finite t with |t| < 2^52 s; outside it, and for NaN or an infinite t, the value is NaN (0/0).", "body": { "op": "ifelse", "args": [ { "op": "<", "args": [{"op": "abs", "args": ["t"]}, {"op": "const", "args": [], "value": 4503599627370496, "units": "s"}] }, { "op": "-", "args": [ { "op": "floor", "args": [ { "op": "/", "args": [ { "op": "/", "args": [ { "op": "apply_expression_template", "args": [], "name": "civil_second_of_day", "bindings": {"t": "t"} }, {"op": "const", "args": [], "value": 1, "units": "s"} ] }, 60 ] } ] }, { "op": "*", "args": [ 60, { "op": "floor", "args": [ { "op": "/", "args": [ { "op": "/", "args": [ { "op": "apply_expression_template", "args": [], "name": "civil_second_of_day", "bindings": {"t": "t"} }, {"op": "const", "args": [], "value": 1, "units": "s"} ] }, 3600 ] } ] } ] } ] }, {"op": "/", "args": [0, 0]} ] } }, "second": { "params": ["t"], "description": "UTC second 0..59 of t (no leap-second slot), the value datetime.second gives (esm-spec §9.2): s - 60 floor(s / 60); a fractional t floors toward minus infinity. Finite t with |t| < 2^52 s; outside it, and for NaN or an infinite t, the value is NaN (0/0).", "body": { "op": "ifelse", "args": [ { "op": "<", "args": [{"op": "abs", "args": ["t"]}, {"op": "const", "args": [], "value": 4503599627370496, "units": "s"}] }, { "op": "-", "args": [ { "op": "/", "args": [ { "op": "apply_expression_template", "args": [], "name": "civil_second_of_day", "bindings": {"t": "t"} }, {"op": "const", "args": [], "value": 1, "units": "s"} ] }, { "op": "*", "args": [ 60, { "op": "floor", "args": [ { "op": "/", "args": [ { "op": "/", "args": [ { "op": "apply_expression_template", "args": [], "name": "civil_second_of_day", "bindings": {"t": "t"} }, {"op": "const", "args": [], "value": 1, "units": "s"} ] }, 60 ] } ] } ] } ] }, {"op": "/", "args": [0, 0]} ] } }, "day_of_year": { "params": ["t"], "description": "Day of the year 1..366 of the UTC instant t (1 = January 1), the value datetime.day_of_year gives (esm-spec §9.2): doy - 305 in January and February, otherwise doy + 60 plus one in a leap year. Finite t with |t| < 2^52 s; outside it, and for NaN or an infinite t, the value is NaN (0/0).", "body": { "op": "ifelse", "args": [ { "op": "<", "args": [{"op": "abs", "args": ["t"]}, {"op": "const", "args": [], "value": 4503599627370496, "units": "s"}] }, { "op": "+", "args": [ { "op": "+", "args": [ {"op": "apply_expression_template", "args": [], "name": "civil_day_of_year", "bindings": {"t": "t"}}, 60 ] }, { "op": "ifelse", "args": [ {"op": "apply_expression_template", "args": [], "name": "civil_is_jan_feb", "bindings": {"t": "t"}}, -365, { "op": "apply_expression_template", "args": [], "name": "civil_leap", "bindings": { "x": {"op": "apply_expression_template", "args": [], "name": "civil_year_of_era", "bindings": {"t": "t"}} } } ] } ] }, {"op": "/", "args": [0, 0]} ] } }, "julian_day": { "params": ["t"], "description": "Julian Date of the UTC instant t, exactly esm-spec §9.2's pinned binary64 formula (d + 2440588) + ((s - 43200) + (t - floor(t))) / 86400, evaluated in that order. Finite t with |t| < 2^52 s; outside it, and for NaN or an infinite t, the value is NaN (0/0).", "body": { "op": "ifelse", "args": [ { "op": "<", "args": [{"op": "abs", "args": ["t"]}, {"op": "const", "args": [], "value": 4503599627370496, "units": "s"}] }, { "op": "+", "args": [ { "op": "+", "args": [ {"op": "apply_expression_template", "args": [], "name": "civil_day_number", "bindings": {"t": "t"}}, 2440588 ] }, { "op": "/", "args": [ { "op": "+", "args": [ { "op": "-", "args": [ { "op": "apply_expression_template", "args": [], "name": "civil_second_of_day", "bindings": {"t": "t"} }, {"op": "const", "args": [], "value": 43200, "units": "s"} ] }, {"op": "-", "args": ["t", {"op": "floor", "args": ["t"]}]} ] }, {"op": "const", "args": [], "value": 86400, "units": "s"} ] } ] }, {"op": "/", "args": [0, 0]} ] } }, "is_leap_year": { "params": ["t"], "description": "1 if the proleptic-Gregorian year of the UTC instant t is a leap year (divisible by 4, and not by 100 unless by 400), else 0, the value datetime.is_leap_year gives (esm-spec §9.2). The year is congruent modulo 400 to yoe from March to December and to yoe + 1 in January and February. Finite t with |t| < 2^52 s; outside it, and for NaN or an infinite t, the value is NaN (0/0).", "body": { "op": "ifelse", "args": [ { "op": "<", "args": [{"op": "abs", "args": ["t"]}, {"op": "const", "args": [], "value": 4503599627370496, "units": "s"}] }, { "op": "ifelse", "args": [ {"op": "apply_expression_template", "args": [], "name": "civil_is_jan_feb", "bindings": {"t": "t"}}, { "op": "apply_expression_template", "args": [], "name": "civil_leap_next", "bindings": { "x": {"op": "apply_expression_template", "args": [], "name": "civil_year_of_era", "bindings": {"t": "t"}} } }, { "op": "apply_expression_template", "args": [], "name": "civil_leap", "bindings": { "x": {"op": "apply_expression_template", "args": [], "name": "civil_year_of_era", "bindings": {"t": "t"}} } } ] }, {"op": "/", "args": [0, 0]} ] } }, "seconds_since_midnight": { "params": ["t"], "description": "Seconds elapsed since the most recent UTC midnight, 0..86399 s, in seconds: floor(t) - 86400 d, the whole second of the day (integer-valued; a fractional t floors toward minus infinity). Finite t with |t| < 2^52 s; outside it, and for NaN or an infinite t, the value is NaN (0/0).", "body": { "op": "ifelse", "args": [ { "op": "<", "args": [{"op": "abs", "args": ["t"]}, {"op": "const", "args": [], "value": 4503599627370496, "units": "s"}] }, { "op": "apply_expression_template", "args": [], "name": "civil_second_of_day", "bindings": {"t": "t"} }, {"op": "/", "args": [0, 0]} ] } }, "civil_day_number": { "params": ["t"], "description": "Day number d = floor(floor(t) / 86400) of the UTC instant t: days since 1970-01-01, exact. A step of the public templates, not guarded: meaningful for finite |t| < 2^52 s, where it is exact.", "body": { "op": "floor", "args": [ { "op": "/", "args": [{"op": "floor", "args": ["t"]}, {"op": "const", "args": [], "value": 86400, "units": "s"}] } ] } }, "civil_second_of_day": { "params": ["t"], "description": "Whole second of the day s = floor(t) - 86400 d, in seconds, in [0, 86399]. A step of the public templates, not guarded: meaningful for finite |t| < 2^52 s, where it is exact.", "body": { "op": "-", "args": [ {"op": "floor", "args": ["t"]}, { "op": "*", "args": [ {"op": "const", "args": [], "value": 86400, "units": "s"}, {"op": "apply_expression_template", "args": [], "name": "civil_day_number", "bindings": {"t": "t"}} ] } ] } }, "civil_era": { "params": ["t"], "description": "The 400-year era of the date, counted from 0000-03-01: floor((d + 719468) / 146097). A step of the public templates, not guarded: meaningful for finite |t| < 2^52 s, where it is exact.", "body": { "op": "floor", "args": [ { "op": "/", "args": [ { "op": "+", "args": [ {"op": "apply_expression_template", "args": [], "name": "civil_day_number", "bindings": {"t": "t"}}, 719468 ] }, 146097 ] } ] } }, "civil_day_of_era": { "params": ["t"], "description": "Day of the era doe = (d + 719468) - 146097 era, in [0, 146096]. A step of the public templates, not guarded: meaningful for finite |t| < 2^52 s, where it is exact.", "body": { "op": "-", "args": [ { "op": "+", "args": [ {"op": "apply_expression_template", "args": [], "name": "civil_day_number", "bindings": {"t": "t"}}, 719468 ] }, { "op": "*", "args": [ 146097, {"op": "apply_expression_template", "args": [], "name": "civil_era", "bindings": {"t": "t"}} ] } ] } }, "civil_year_of_era": { "params": ["t"], "description": "Year of the era yoe = floor((doe - floor(doe/1460) + floor(doe/36524) - floor(doe/146096)) / 365), in [0, 399]; the years begin on March 1. A step of the public templates, not guarded: meaningful for finite |t| < 2^52 s, where it is exact.", "body": { "op": "floor", "args": [ { "op": "/", "args": [ { "op": "-", "args": [ { "op": "+", "args": [ { "op": "-", "args": [ {"op": "apply_expression_template", "args": [], "name": "civil_day_of_era", "bindings": {"t": "t"}}, { "op": "floor", "args": [ { "op": "/", "args": [ {"op": "apply_expression_template", "args": [], "name": "civil_day_of_era", "bindings": {"t": "t"}}, 1460 ] } ] } ] }, { "op": "floor", "args": [ { "op": "/", "args": [ {"op": "apply_expression_template", "args": [], "name": "civil_day_of_era", "bindings": {"t": "t"}}, 36524 ] } ] } ] }, { "op": "floor", "args": [ { "op": "/", "args": [ {"op": "apply_expression_template", "args": [], "name": "civil_day_of_era", "bindings": {"t": "t"}}, 146096 ] } ] } ] }, 365 ] } ] } }, "civil_day_of_year": { "params": ["t"], "description": "Day of the year counted from March 1, doy = doe - (365 yoe + floor(yoe/4) - floor(yoe/100)), in [0, 365]. A step of the public templates, not guarded: meaningful for finite |t| < 2^52 s, where it is exact.", "body": { "op": "-", "args": [ {"op": "apply_expression_template", "args": [], "name": "civil_day_of_era", "bindings": {"t": "t"}}, { "op": "-", "args": [ { "op": "+", "args": [ { "op": "*", "args": [ 365, {"op": "apply_expression_template", "args": [], "name": "civil_year_of_era", "bindings": {"t": "t"}} ] }, { "op": "floor", "args": [ { "op": "/", "args": [ {"op": "apply_expression_template", "args": [], "name": "civil_year_of_era", "bindings": {"t": "t"}}, 4 ] } ] } ] }, { "op": "floor", "args": [ { "op": "/", "args": [ {"op": "apply_expression_template", "args": [], "name": "civil_year_of_era", "bindings": {"t": "t"}}, 100 ] } ] } ] } ] } }, "civil_month_index": { "params": ["t"], "description": "Month counted from March, mp = floor((5 doy + 2) / 153), in [0, 11]. A step of the public templates, not guarded: meaningful for finite |t| < 2^52 s, where it is exact.", "body": { "op": "floor", "args": [ { "op": "/", "args": [ { "op": "+", "args": [ { "op": "*", "args": [ 5, {"op": "apply_expression_template", "args": [], "name": "civil_day_of_year", "bindings": {"t": "t"}} ] }, 2 ] }, 153 ] } ] } }, "civil_is_jan_feb": { "params": ["t"], "description": "True in January and February (doy >= 306, March 1 + 306 days), which belong to the year after the year of era. A step of the public templates, not guarded: meaningful for finite |t| < 2^52 s, where it is exact.", "body": { "op": ">=", "args": [ {"op": "apply_expression_template", "args": [], "name": "civil_day_of_year", "bindings": {"t": "t"}}, 306 ] } }, "civil_leap": { "params": ["x"], "description": "1 if a year congruent modulo 400 to x, for x in [0, 399], is a leap year, else 0 (divisible by 400 only at x = 0). A step of the public templates, not guarded: meaningful for finite |t| < 2^52 s, where it is exact.", "body": { "op": "ifelse", "args": [ { "op": "and", "args": [ { "op": "==", "args": [ { "op": "-", "args": ["x", {"op": "*", "args": [4, {"op": "floor", "args": [{"op": "/", "args": ["x", 4]}]}]}] }, 0 ] }, { "op": "or", "args": [ { "op": "not", "args": [ { "op": "==", "args": [ { "op": "-", "args": ["x", {"op": "*", "args": [100, {"op": "floor", "args": [{"op": "/", "args": ["x", 100]}]}]}] }, 0 ] } ] }, {"op": "==", "args": ["x", 0]} ] } ] }, 1, 0 ] } }, "civil_leap_next": { "params": ["x"], "description": "1 if the year after a year congruent modulo 400 to x, for x in [0, 399], is a leap year, else 0 (divisible by 400 only for x = 399). A step of the public templates, not guarded: meaningful for finite |t| < 2^52 s, where it is exact.", "body": { "op": "ifelse", "args": [ { "op": "and", "args": [ { "op": "==", "args": [ { "op": "-", "args": [ {"op": "+", "args": ["x", 1]}, { "op": "*", "args": [4, {"op": "floor", "args": [{"op": "/", "args": [{"op": "+", "args": ["x", 1]}, 4]}]}] } ] }, 0 ] }, { "op": "or", "args": [ { "op": "not", "args": [ { "op": "==", "args": [ { "op": "-", "args": [ {"op": "+", "args": ["x", 1]}, { "op": "*", "args": [100, {"op": "floor", "args": [{"op": "/", "args": [{"op": "+", "args": ["x", 1]}, 100]}]}] } ] }, 0 ] } ] }, {"op": "==", "args": ["x", 399]} ] } ] }, 1, 0 ] } } } }