civil_from_days

std.elementwise.civil_from_days · Level L4

The year, month and day of a date given as days since 1970-01-01, by Howard Hinnant's algorithm: floor divisions by the 400-year era, the year of the era, and a year that starts in March.

era = ⌊(days + 719468)/146097⌋, …

Signature

civil_from_days(days: i64[n]) → i64[n, 3]

Structure

The function as NOVA stores it: one box per input, operation and output, and arrows that carry values. A double border marks another library function this one runs — called once, or by Scan once per element; select it to open that function.

daysi64[n]719468146097AddzFloorDivera400Multiplyera_daysMultiplyera4001460Subtractdoe36524146096FloorDivq1460FloorDivq36524FloorDivq146096Subtractt1Addt2365Subtractt34FloorDivyoe100FloorDivl4Multiplyyoe365FloorDivl100Addy0Adds1Subtracts2Subtractdoy52Multiplydoy5Adddoy5_2153FloorDivmpAddmp212Multiplymp1531Modm0Addmp153_2AddmFloorDivmonth_start14Reshapem_cSubtractd0Subtractt14AdddFloorDivjan_febReshaped_cAddyReshapey_cConcatymdymdi64[n, 3]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference date.fromordinal(719163 + days) → (year, month, day) in exact rational arithmetic, on all 40 test cases.
  • All 462 int64 results are exact: the error is zero.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the int64 nearest the exact value)
100%
bit-equal to the NumPy formula in int64
100%
largest error, in units in the last place
0

Note

The reference is Python's own datetime, a different implementation, over every date from 0001-01-01 to 9999-12-31.

Identity

Calls
—
Called by
—
sha256:89a37d5a4b6cd51eed616c0a2ef1528e3f63651cb05b99f1fb598e9b17be16f4

The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.

Control handle

Symbol
Ω:std.elementwise.civil_from_days · Ω:civil_from_days
Pins
sha256:fffbb886c874a8a0dfca075f475ab230ba966d84a7474741276ba6a2b99b6888this graph alone
Evidence
sha256:87840a81c400f5357671bd4a51959d64669155dec8488c2f644eb3193c9a349ethe hash of its verification record
Needs
no capability: a pure function

Through NOVA’s control layer, the symbol launches this function only while the program still matches what it pins: a change to this graph, or to any graph it reaches, needs a migration first.