Optimize util for calculation year, month, day in Date (#2397)

Author: MaxGraey

Diff for: std/assembly/date.ts

@@ -6,7 +6,12 @@ import { Date as Date_binding } from "./bindings/dom";
   MILLIS_PER_DAY    = 1000 * 60 * 60 * 24,
   MILLIS_PER_HOUR   = 1000 * 60 * 60,
   MILLIS_PER_MINUTE = 1000 * 60,
-  MILLIS_PER_SECOND = 1000;
+  MILLIS_PER_SECOND = 1000,
+
+  YEARS_PER_EPOCH = 400,
+  DAYS_PER_EPOCH = 146097,
+  EPOCH_OFFSET = 719468, // Jan 1, 1970
+  MILLIS_LIMIT = 8640000000000000;
 
 // ymdFromEpochDays returns values via globals to avoid allocations
 // @ts-ignore: decorator
@@ -94,7 +99,7 @@ export class Date {
     // instead throwing exception.
     if (invalidDate(epochMillis)) throw new RangeError(E_INVALIDDATE);
 
-    this.year = ymdFromEpochDays(i32(floorDiv(epochMillis, MILLIS_PER_DAY)));
+    this.year = dateFromEpoch(epochMillis);
     this.month = _month;
     this.day = _day;
   }
@@ -107,7 +112,7 @@ export class Date {
     if (invalidDate(time)) throw new RangeError(E_INVALIDDATE);
 
     this.epochMillis = time;
-    this.year = ymdFromEpochDays(i32(floorDiv(time, MILLIS_PER_DAY)));
+    this.year = dateFromEpoch(time);
     this.month = _month;
     this.day = _day;
 
@@ -306,7 +311,7 @@ function epochMillis(
 
 // @ts-ignore: decorator
 @inline function floorDiv<T extends number>(a: T, b: T): T {
-  return (a >= 0 ? a : a - b + 1) / b as T;
+  return (a - (a < 0 ? b - 1 : 0)) / b as T;
 }
 
 // @ts-ignore: decorator
@@ -317,41 +322,42 @@ function epochMillis(
 
 function invalidDate(millis: i64): bool {
   // @ts-ignore
-  return (millis < -8640000000000000) | (millis > 8640000000000000);
+  return (millis < -MILLIS_LIMIT) | (millis > MILLIS_LIMIT);
 }
 
-// see: http://howardhinnant.github.io/date_algorithms.html#civil_from_days
-function ymdFromEpochDays(z: i32): i32 {
-  z += 719468;
-  var era = <u32>floorDiv(z, 146097);
-  var doe = <u32>z - era * 146097; // [0, 146096]
-  var yoe = (doe - doe / 1460 + doe / 36524 - doe / 146096) / 365; // [0, 399]
-  var year = yoe + era * 400;
-  var doy = doe - (365 * yoe + yoe / 4 - yoe / 100); // [0, 365]
-  var mo = (5 * doy + 2) / 153; // [0, 11]
-  _day = doy - (153 * mo + 2) / 5 + 1; // [1, 31]
-  mo += mo < 10 ? 3 : -9; // [1, 12]
-  _month = mo;
-  year += u32(mo <= 2);
+// Based on "Euclidean Affine Functions and Applications to Calendar Algorithms"
+// Paper: https://arxiv.org/pdf/2102.06959.pdf
+function dateFromEpoch(ms: i64): i32 {
+  var da = (<i32>floorDiv(ms, MILLIS_PER_DAY) * 4 + EPOCH_OFFSET * 4) | 3;
+  var q0 = floorDiv(da, DAYS_PER_EPOCH); // [0, 146096]
+  var r1 = <u32>da - q0 * DAYS_PER_EPOCH;
+  var u1 = u64(r1 | 3) * 2939745;
+  var dm1 = <u32>u1 / 11758980;
+  var n1 = 2141 * dm1 + 197913;
+  var year = 100 * q0 + i32(u1 >>> 32);
+  var mo = n1 >>> 16;
+  _day = (n1 & 0xFFFF) / 2141 + 1; // [1, 31]
+  if (dm1 >= 306) { mo -= 12; ++year; }
+  _month = mo; // [1, 12]
   return year;
 }
 
 // http://howardhinnant.github.io/date_algorithms.html#days_from_civil
 function daysSinceEpoch(y: i32, m: i32, d: i32): i32 {
   y -= i32(m <= 2);
-  var era = <u32>floorDiv(y, 400);
-  var yoe = <u32>y - era * 400; // [0, 399]
+  var era = <u32>floorDiv(y, YEARS_PER_EPOCH);
+  var yoe = <u32>y - era * YEARS_PER_EPOCH; // [0, 399]
   var doy = <u32>(153 * (m + (m > 2 ? -3 : 9)) + 2) / 5 + d - 1; // [0, 365]
   var doe = yoe * 365 + yoe / 4 - yoe / 100 + doy; // [0, 146096]
-  return era * 146097 + doe - 719468;
+  return era * 146097 + doe - EPOCH_OFFSET;
 }
 
 // TomohikoSakamoto algorithm from https://en.wikipedia.org/wiki/Determination_of_the_day_of_the_week
 function dayOfWeek(year: i32, month: i32, day: i32): i32 {
   const tab = memory.data<u8>([0, 3, 2, 5, 0, 3, 5, 1, 4, 6, 2, 4]);
 
   year -= i32(month < 3);
-  year += floorDiv(year, 4) - floorDiv(year, 100) + floorDiv(year, 400);
+  year += floorDiv(year, 4) - floorDiv(year, 100) + floorDiv(year, YEARS_PER_EPOCH);
   month = <i32>load<u8>(tab + month - 1);
   return euclidRem(year + month + day, 7);
 }