Change date AOs to accept mathematical values

spec/abstractops.html

@@ -31,6 +31,109 @@ <h1>
     </emu-alg>
   </emu-clause>
 
+  <emu-clause id="sec-isodatetoepochdays" type="abstract operation">
+    <h1>
+      ISODateToEpochDays (
+        _year_: an integer,
+        _month_: an integer,
+        _date_: an integer,
+      ): an integer
+    </h1>
+    <dl class="header">
+      <dt>description</dt>
+      <dd>It calculates a number of days.</dd>
+    </dl>
+    <emu-alg>
+      1. Let _resolvedYear_ be _year_ + floor(_month_ / 12).
+      1. Let _resolvedMonth_ be _month_ modulo 12.
+      1. Find a time _t_ such that EpochTimeToEpochYear(_t_) is _resolvedYear_, EpochTimeToMonthInYear(_t_) is _resolvedMonth_, and EpochTimeToDate(_t_) is 1.
+      1. Return EpochTimeToDayNumber(_t_) + _date_ - 1.
+    </emu-alg>
+    <emu-note type="editor"> This operation corresponds to ECMA-262 operation MakeDay(_year_, _month_, _date_). It calculates the result in mathematical values instead of Number values. These two operations would be unified when https://github.com/tc39/ecma262/issues/1087 is fixed.</emu-note>
+  </emu-clause>
+
+  <emu-clause id="sec-epochdaystoepochms" type="abstract operation">
+    <h1>
+      EpochDaysToEpochMs (
+        _day_: an integer,
+        _time_: an integer,
+      ): an integer
+    </h1>
+    <dl class="header">
+      <dt>description</dt>
+      <dd>It calculates a number of milliseconds.</dd>
+    </dl>
+    <emu-alg>
+      1. Return _day_ × ℝ(msPerDay) + _time_.
+    </emu-alg>
+    <emu-note type="editor"> This operation corresponds to ECMA-262 operation MakeDate(_date_, _time_). It calculates the result in mathematical values instead of Number values. These two operations would be unified when https://github.com/tc39/ecma262/issues/1087 is fixed.</emu-note>
+  </emu-clause>
+
+  <emu-clause id="sec-date-equations">
+    <h1>Date Equations</h1>
+    <p>A given time _t_ belongs to day number</p>
+    <emu-eqn id="eqn-EpochTimeToDayNumber" aoid="EpochTimeToDayNumber">EpochTimeToDayNumber(_t_) = floor(_t_ / ℝ(msPerDay))</emu-eqn>
+    <p>Number of days in year are given by:</p>
+    <emu-eqn id="eqn-mathematicaldaysinyear" aoid="MathematicalDaysInYear">
+      MathematicalDaysInYear(_y_)
+        = 365 if ((_y_) modulo 4) ≠ 0
+        = 366 if ((_y_) modulo 4) = 0 and ((_y_) modulo 100) ≠ 0
+        = 365 if ((_y_) modulo 100) = 0 and ((_y_) modulo 400) ≠ 0
+        = 366 if ((_y_) modulo 400) = 0
+    </emu-eqn>
+    <p>The day number of the first day of year _y_ is given by:</p>
+    <emu-eqn id="eqn-epochdaynumberforyear" aoid="EpochDayNumberForYear">EpochDayNumberForYear(_y_) = 365 × (_y_ - 1970) + floor((_y_ - 1969) / 4) - floor((_y_ - 1901) / 100) + floor((_y_ - 1601) / 400)</emu-eqn>
+    <p>The time of the start of a year is:</p>
+    <emu-eqn id="eqn-epochtimeforyear" aoid="EpochTimeForYear">EpochTimeForYear(_y_) = ℝ(msPerDay) × EpochDayNumberForYear(_y_)</emu-eqn>
+    <p>Epoch year from time _t_ is given by:</p>
+    <emu-eqn id="eqn-epochtimetoepochyear" aoid="EpochTimeToEpochYear">EpochTimeToEpochYear(_t_) = the largest integral Number _y_ (closest to +∞) such that EpochTimeForYear(_y_) ≤ _t_</emu-eqn>
+    <p>The following function returns 1 for a time within leap year otherwise it returns 0:</p>
+    <emu-eqn id="eqn-mathematicalinleapyear" aoid="MathematicalInLeapYear">
+      MathematicalInLeapYear(_t_)
+        = 0 if MathematicalDaysInYear(EpochTimeToEpochYear(_t_)) is 365
+        = 1 if MathematicalDaysInYear(EpochTimeToEpochYear(_t_)) is 366
+    </emu-eqn>
+    <p>The month number for a time _t_ is given by:</p>
+    <emu-eqn id="eqn-epochtimetomonthinyear" aoid="EpochTimeToMonthInYear">
+      EpochTimeToMonthInYear(_t_)
+        = 0 if 0 ≤ EpochTimeToDayInYear(_t_) &lt; 31
+        = 1 if 31 ≤ EpochTimeToDayInYear(_t_) &lt; 59 + MathematicalInLeapYear(_t_)
+        = 2 if 59 + MathematicalInLeapYear(_t_) ≤ EpochTimeToDayInYear(_t_) &lt; 90 + MathematicalInLeapYear(_t_)
+        = 3 if 90 + MathematicalInLeapYear(_t_) ≤ EpochTimeToDayInYear(_t_) &lt; 120 + MathematicalInLeapYear(_t_)
+        = 4 if 120 + MathematicalInLeapYear(_t_) ≤ EpochTimeToDayInYear(_t_) &lt; 151 + MathematicalInLeapYear(_t_)
+        = 5 if 151 + MathematicalInLeapYear(_t_) ≤ EpochTimeToDayInYear(_t_) &lt; 181 + MathematicalInLeapYear(_t_)
+        = 6 if 181 + MathematicalInLeapYear(_t_) ≤ EpochTimeToDayInYear(_t_) &lt; 212 + MathematicalInLeapYear(_t_)
+        = 7 if 212 + MathematicalInLeapYear(_t_) ≤ EpochTimeToDayInYear(_t_) &lt; 243 + MathematicalInLeapYear(_t_)
+        = 8 if 243 + MathematicalInLeapYear(_t_) ≤ EpochTimeToDayInYear(_t_) &lt; 273 + MathematicalInLeapYear(_t_)
+        = 9 if 273 + MathematicalInLeapYear(_t_) ≤ EpochTimeToDayInYear(_t_) &lt; 304 + MathematicalInLeapYear(_t_)
+        = 10 if 304 + MathematicalInLeapYear(_t_) ≤ EpochTimeToDayInYear(_t_) &lt; 334 + MathematicalInLeapYear(_t_)
+        = 11 if 334 + MathematicalInLeapYear(_t_) ≤ EpochTimeToDayInYear(_t_) &lt; 365 + MathematicalInLeapYear(_t_)
+    </emu-eqn>
+    <p>where</p>
+    <emu-eqn id="eqn-epochtimetodayinyear" aoid="EpochTimeToDayInYear">EpochTimeToDayInYear(_t_) = EpochTimeToDayNumber(_t_) - EpochDayNumberForYear(EpochTimeToEpochYear(_t_))</emu-eqn>
+    <p>A month value of 0 specifies January; 1 specifies February; 2 specifies March; 3 specifies April; 4 specifies May; 5 specifies June; 6 specifies July; 7 specifies August; 8 specifies September; 9 specifies October; 10 specifies November; and 11 specifies December. Note that <emu-eqn>EpochTimeToMonthInYear(0) = 0</emu-eqn>, corresponding to Thursday, 1 January 1970.</p>
+    <p>The date number for a time _t_ is given by:</p>
+    <emu-eqn id="eqn-epochtimetodate" aoid="EpochTimeToDate">
+      EpochTimeToDate(_t_)
+        = EpochTimeToDayInYear(_t_) + 1 if EpochTimeToMonthInYear(_t_) is 0
+        = EpochTimeToDayInYear(_t_) - 30 if EpochTimeToMonthInYear(_t_) is 1
+        = EpochTimeToDayInYear(_t_) - 58 - MathematicalInLeapYear(_t_) if EpochTimeToMonthInYear(_t_) is 2
+        = EpochTimeToDayInYear(_t_) - 89 - MathematicalInLeapYear(_t_) if EpochTimeToMonthInYear(_t_) is 3
+        = EpochTimeToDayInYear(_t_) - 119 - MathematicalInLeapYear(_t_) if EpochTimeToMonthInYear(_t_) is 4
+        = EpochTimeToDayInYear(_t_) - 150 - MathematicalInLeapYear(_t_) if EpochTimeToMonthInYear(_t_) is 5
+        = EpochTimeToDayInYear(_t_) - 180 - MathematicalInLeapYear(_t_) if EpochTimeToMonthInYear(_t_) is 6
+        = EpochTimeToDayInYear(_t_) - 211 - MathematicalInLeapYear(_t_) if EpochTimeToMonthInYear(_t_) is 7
+        = EpochTimeToDayInYear(_t_) - 242 - MathematicalInLeapYear(_t_) if EpochTimeToMonthInYear(_t_) is 8
+        = EpochTimeToDayInYear(_t_) - 272 - MathematicalInLeapYear(_t_) if EpochTimeToMonthInYear(_t_) is 9
+        = EpochTimeToDayInYear(_t_) - 303 - MathematicalInLeapYear(_t_) if EpochTimeToMonthInYear(_t_) is 10
+        = EpochTimeToDayInYear(_t_) - 333 - MathematicalInLeapYear(_t_) if EpochTimeToMonthInYear(_t_) is 11
+    </emu-eqn>
+    <p>The weekday for a particular time _t_ is defined as:</p>
+    <emu-eqn id="eqn-epochtimetoweekday" aoid="EpochTimeToWeekDay">EpochTimeToWeekDay(_t_) =(EpochTimeToDayNumber(_t_) + 4) modulo 7</emu-eqn>
+    <p>A weekday value of 0 specifies Sunday; 1 specifies Monday; 2 specifies Tuesday; 3 specifies Wednesday; 4 specifies Thursday; 5 specifies Friday; and 6 specifies Saturday. Note that <emu-eqn>EpochTimeToWeekDay(0) = 4</emu-eqn>, corresponding to Thursday, 1 January 1970.</p>
+    <emu-note type="editor"> These equations correspond to ECMA-262 equations defined in <emu-xref href="#sec-year-number">Year Number</emu-xref>, <emu-xref href="#sec-month-number">Month Number</emu-xref>, <emu-xref href="#sec-date-number">Date Number</emu-xref>, <emu-xref href="#sec-week-day">Week Day</emu-xref> respectively. These calculate the result in mathematical values instead of Number values. These equations would be unified when https://github.com/tc39/ecma262/issues/1087 is fixed.</emu-note>
+    <emu-note type="editor"> Note that the operation EpochTimeToMonthInYear(_t_) uses 0-based months unlike rest of Temporal since it's intended to be unified with MonthFromTime(_t_) when the above mentioned issue is fixed.</emu-note>
+  </emu-clause>
   <!-- Copied from ECMA-402 GetOptionsObject -->
   <emu-clause id="sec-getoptionsobject" aoid="GetOptionsObject">
     <h1>GetOptionsObject ( _options_ )</h1>

spec/calendar.html

@@ -762,7 +762,7 @@ <h1>
         1. If _month_ is 1, 3, 5, 7, 8, 10, or 12, return 31.
         1. If _month_ is 4, 6, 9, or 11, return 30.
         1. Assert: _month_ is 2.
-        1. Return 28 + ℝ(InLeapYear(TimeFromYear(𝔽(_year_)))).
+        1. Return 28 + MathematicalInLeapYear(EpochTimeForYear(_year_)).
       </emu-alg>
     </emu-clause>
 
@@ -794,11 +794,11 @@ <h1>
           1. Let _dayOfJan1st_ be ToISODayOfWeek(_year_, 1, 1).
           1. If _dayOfJan1st_ is _friday_, then
             1. Return the Year-Week Record { [[Week]]: _maxWeekNumber_, [[Year]]: _year_ - 1 }.
-          1. If _dayOfJan1st_ is _saturday_, and InLeapYear(TimeFromYear(𝔽(_year_ - 1))) is *1*<sub>𝔽</sub>, then
+          1. If _dayOfJan1st_ is _saturday_, and MathematicalInLeapYear(EpochTimeForYear(_year_ - 1)) is 1, then
             1. Return the Year-Week Record { [[Week]]: _maxWeekNumber_. [[Year]]: _year_ - 1 }.
           1. Return the Year-Week Record { [[Week]]: _maxWeekNumber_ - 1, [[Year]]: _year_ - 1 }.
         1. If _week_ is _maxWeekNumber_, then
-          1. Let _daysInYear_ be DaysInYear(𝔽(_year_)).
+          1. Let _daysInYear_ be MathematicalDaysInYear(_year_).
           1. Let _daysLaterInYear_ be _daysInYear_ - _dayOfYear_.
           1. Let _daysAfterThursday_ be _thursday_ - _dayOfWeek_.
           1. If _daysLaterInYear_ &lt; _daysAfterThursday_, then
@@ -955,9 +955,8 @@ <h1>
       </dl>
       <emu-alg>
         1. Assert: IsValidISODate(_year_, _month_, _day_) is *true*.
-        1. Let _epochDays_ be MakeDay(𝔽(year), 𝔽(month - 1), 𝔽(day)).
-        1. Assert: _epochDays_ is finite.
-        1. Return ℝ(DayWithinYear(MakeDate(_epochDays_, *+0*<sub>𝔽</sub>))) + 1.
+        1. Let _epochDays_ be ISODateToEpochDays(year, month - 1, day).
+        1. Return EpochTimeToDayInYear(EpochDaysToEpochMs(_epochDays_, 0)) + 1.
       </emu-alg>
     </emu-clause>
 
@@ -975,11 +974,10 @@ <h1>
       </dl>
       <emu-alg>
         1. Assert: IsValidISODate(_year_, _month_, _day_) is *true*.
-        1. Let _epochDays_ be MakeDay(𝔽(year), 𝔽(month - 1), 𝔽(day)).
-        1. Assert: _epochDays_ is finite.
-        1. Let _dayOfWeek_ be WeekDay(MakeDate(_epochDays_, *+0*<sub>𝔽</sub>)).
-        1. If _dayOfWeek_ = *+0*<sub>𝔽</sub>, return 7.
-        1. Return ℝ(_dayOfWeek_).
+        1. Let _epochDays_ be ISODateToEpochDays(year, month - 1, day).
+        1. Let _dayOfWeek_ be EpochTimeToWeekDay(EpochDaysToEpochMs(_epochDays_, 0)).
+        1. If _dayOfWeek_ = 0, return 7.
+        1. Return _dayOfWeek_.
       </emu-alg>
     </emu-clause>
   </emu-clause>
@@ -1406,7 +1404,7 @@ <h1>Temporal.Calendar.prototype.daysInYear ( _temporalDateLike_ )</h1>
         1. Assert: _calendar_.[[Identifier]] is *"iso8601"*.
         1. If Type(_temporalDateLike_) is not Object or _temporalDateLike_ does not have an [[InitializedTemporalDate]], [[InitializedTemporalDateTime]], or [[InitializedTemporalYearMonth]] internal slot, then
           1. Set _temporalDateLike_ to ? ToTemporalDate(_temporalDateLike_).
-        1. Return DaysInYear(𝔽(_temporalDateLike_.[[ISOYear]])).
+        1. Return 𝔽(MathematicalDaysInYear(_temporalDateLike_.[[ISOYear]])).
       </emu-alg>
     </emu-clause>
 
@@ -1444,7 +1442,7 @@ <h1>Temporal.Calendar.prototype.inLeapYear ( _temporalDateLike_ )</h1>
         1. Assert: _calendar_.[[Identifier]] is *"iso8601"*.
         1. If Type(_temporalDateLike_) is not Object or _temporalDateLike_ does not have an [[InitializedTemporalDate]], [[InitializedTemporalDateTime]], or [[InitializedTemporalYearMonth]] internal slot, then
           1. Set _temporalDateLike_ to ? ToTemporalDate(_temporalDateLike_).
-        1. If InLeapYear(TimeFromYear(𝔽(_temporalDateLike_.[[ISOYear]]))) is *1*<sub>𝔽</sub>, return *true*.
+        1. If MathematicalInLeapYear(EpochTimeForYear(_temporalDateLike_.[[ISOYear]])) is 1, return *true*.
         1. Return *false*.
       </emu-alg>
     </emu-clause>

spec/duration.html

@@ -1572,11 +1572,9 @@ <h1>
         If _earlier_ is later than _later_, then the result is negative.</dd>
       </dl>
       <emu-alg>
-        1. Let _epochDays1_ be MakeDay(𝔽(_earlier_.[[ISOYear]]), 𝔽(_earlier_.[[ISOMonth]] - 1), 𝔽(_earlier_.[[ISODay]])).
-        1. Assert: _epochDays1_ is finite.
-        1. Let _epochDays2_ be MakeDay(𝔽(_later_.[[ISOYear]]), 𝔽(_later_.[[ISOMonth]] - 1), 𝔽(_later_.[[ISODay]])).
-        1. Assert: _epochDays2_ is finite.
-        1. Return ℝ(_epochDays2_) - ℝ(_epochDays1_).
+        1. Let _epochDays1_ be ISODateToEpochDays(_earlier_.[[ISOYear]], _earlier_.[[ISOMonth]] - 1, _earlier_.[[ISODay]]).
+        1. Let _epochDays2_ be ISODateToEpochDays(_later_.[[ISOYear]], _later_.[[ISOMonth]] - 1, _later_.[[ISODay]]).
+        1. Return _epochDays2_ - _epochDays1_.
       </emu-alg>
     </emu-clause>
 

spec/intl.html

@@ -2137,7 +2137,7 @@ <h1>Temporal.Calendar.prototype.daysInYear ( _temporalDateLike_ )</h1>
             1. If Type(_temporalDateLike_) is not Object or _temporalDateLike_ does not have an [[InitializedTemporalDate]], [[InitializedTemporalDateTime]], or [[InitializedTemporalYearMonth]] internal slot, then
               1. Set _temporalDateLike_ to ? ToTemporalDate(_temporalDateLike_).
             1. If _calendar_.[[Identifier]] is *"iso8601"*, then
-              1. Return DaysInYear(𝔽(_temporalDateLike_.[[ISOYear]])).
+              1. Return 𝔽(MathematicalDaysInYear(_temporalDateLike_.[[ISOYear]])).
             1. Let _daysInYear_ be ! CalendarDateDaysInYear(_calendar_.[[Identifier]], _temporalDateLike_).
             1. Return 𝔽(_daysInYear_).
           </emu-alg>
@@ -2174,7 +2174,7 @@ <h1>Temporal.Calendar.prototype.inLeapYear ( _temporalDateLike_ )</h1>
             1. If Type(_temporalDateLike_) is not Object or _temporalDateLike_ does not have an [[InitializedTemporalDate]], [[InitializedTemporalDateTime]], or [[InitializedTemporalYearMonth]] internal slot, then
               1. Set _temporalDateLike_ to ? ToTemporalDate(_temporalDateLike_).
             1. If _calendar_.[[Identifier]] is *"iso8601"*, then
-              1. If InLeapYear(TimeFromYear(𝔽(_temporalDateLike_.[[ISOYear]]))) is *1*<sub>𝔽</sub>, then
+              1. If MathematicalInLeapYear(EpochTimeForYear(_temporalDateLike_.[[ISOYear]])) is 1, then
                 1. Let _inLeapYear_ be *true*.
               1. Else,
                 1. Let _inLeapYear_ be *false*.

spec/plaindate.html

@@ -824,11 +824,9 @@ <h1>
           1. Return ! CreateDateDurationRecord(_years_, _months_, 0, _days_).
         1. Else,
           1. Assert: _largestUnit_ is *"day"* or *"week"*.
-          1. Let _epochDays1_ be MakeDay(𝔽(_y1_), 𝔽(_m1_ - 1), 𝔽(_d1_)).
-          1. Assert: _epochDays1_ is finite.
-          1. Let _epochDays2_ be MakeDay(𝔽(_y2_), 𝔽(_m2_ - 1), 𝔽(_d2_)).
-          1. Assert: _epochDays2_ is finite.
-          1. Let _days_ be ℝ(_epochDays2_) - ℝ(_epochDays1_).
+          1. Let _epochDays1_ be ISODateToEpochDays(_y1_, _m1_ - 1, _d1_).
+          1. Let _epochDays2_ be ISODateToEpochDays(_y2_, _m2_ - 1, _d2_).
+          1. Let _days_ be _epochDays2_ - _epochDays1_.
           1. Let _weeks_ be 0.
           1. If _largestUnit_ is *"week"*, then
             1. Set _weeks_ to truncate(_days_ / 7).
@@ -906,10 +904,9 @@ <h1>BalanceISODate (
         </dd>
       </dl>
       <emu-alg>
-        1. Let _epochDays_ be MakeDay(𝔽(_year_), 𝔽(_month_ - 1), 𝔽(_day_)).
-        1. Assert: _epochDays_ is finite.
-        1. Let _ms_ be MakeDate(_epochDays_, *+0*<sub>𝔽</sub>).
-        1. Return CreateISODateRecord(ℝ(YearFromTime(_ms_)), ℝ(MonthFromTime(_ms_)) + 1, ℝ(DateFromTime(_ms_))).
+        1. Let _epochDays_ be ISODateToEpochDays(_year_, _month_ - 1, _day_).
+        1. Let _ms_ be EpochDaysToEpochMs(_epochDays_, 0).
+        1. Return CreateISODateRecord(EpochTimeToEpochYear(_ms_), EpochTimeToMonthInYear(_ms_) + 1, EpochTimeToDate(_ms_)).
       </emu-alg>
     </emu-clause>
 

spec/timezone.html

@@ -421,9 +421,9 @@ <h1>
         1. Assert: ! IsValidEpochNanoseconds(ℤ(_epochNanoseconds_)) is *true*.
         1. Let _remainderNs_ be _epochNanoseconds_ modulo 10<sup>6</sup>.
         1. Let _epochMilliseconds_ be 𝔽((_epochNanoseconds_ - _remainderNs_) / 10<sup>6</sup>).
-        1. Let _year_ be ℝ(! YearFromTime(_epochMilliseconds_)).
-        1. Let _month_ be ℝ(! MonthFromTime(_epochMilliseconds_)) + 1.
-        1. Let _day_ be ℝ(! DateFromTime(_epochMilliseconds_)).
+        1. Let _year_ be EpochTimeToEpochYear(_epochMilliseconds_).
+        1. Let _month_ be EpochTimeToMonthInYear(_epochMilliseconds_) + 1.
+        1. Let _day_ be EpochTimeToDate(_epochMilliseconds_).
         1. Let _hour_ be ℝ(! HourFromTime(_epochMilliseconds_)).
         1. Let _minute_ be ℝ(! MinFromTime(_epochMilliseconds_)).
         1. Let _second_ be ℝ(! SecFromTime(_epochMilliseconds_)).