Skip to content

Commit e8c418c

Browse files
xwuxwu
committed
[SR-14974] Fix 'Decimal.ulp' to reflect spacing between consecutive values.
1 parent 405aaec commit e8c418c

File tree

4 files changed

+199
-96
lines changed

4 files changed

+199
-96
lines changed

‎Darwin/Foundation-swiftoverlay-Tests/TestDecimal.swift‎

Lines changed: 34 additions & 18 deletions
Original file line numberDiff line numberDiff line change
@@ -208,21 +208,6 @@ class TestDecimal : XCTestCase {
208208
XCTAssertEqual(11, sm5)
209209
XCTAssertEqual(12, sm6)
210210
XCTAssertEqual(13, sm7)
211-
212-
let ulp = explicit.ulp
213-
XCTAssertEqual(0x7f, ulp.exponent)
214-
XCTAssertEqual(1, ulp._length)
215-
XCTAssertEqual(0, ulp._isNegative)
216-
XCTAssertEqual(1, ulp._isCompact)
217-
XCTAssertEqual(0, ulp._reserved)
218-
XCTAssertEqual(1, ulp._mantissa.0)
219-
XCTAssertEqual(0, ulp._mantissa.1)
220-
XCTAssertEqual(0, ulp._mantissa.2)
221-
XCTAssertEqual(0, ulp._mantissa.3)
222-
XCTAssertEqual(0, ulp._mantissa.4)
223-
XCTAssertEqual(0, ulp._mantissa.5)
224-
XCTAssertEqual(0, ulp._mantissa.6)
225-
XCTAssertEqual(0, ulp._mantissa.7)
226211
}
227212

228213
func test_Maths() {
@@ -287,8 +272,6 @@ class TestDecimal : XCTestCase {
287272
XCTAssertTrue(Decimal(2) < Decimal(3))
288273
XCTAssertTrue(Decimal(3) > Decimal(2))
289274
XCTAssertEqual(Decimal(-9), Decimal(1) - Decimal(10))
290-
XCTAssertEqual(Decimal(3), Decimal(2).nextUp)
291-
XCTAssertEqual(Decimal(2), Decimal(3).nextDown)
292275
XCTAssertEqual(Decimal(1.234), abs(Decimal(1.234)))
293276
XCTAssertEqual(Decimal(1.234), abs(Decimal(-1.234)))
294277
if #available(macOS 10.15, iOS 13, tvOS 13, watchOS 6, *) {
@@ -608,8 +591,41 @@ class TestDecimal : XCTestCase {
608591
}
609592

610593
func test_ULP() {
611-
let x = 0.1 as Decimal
594+
var x = 0.1 as Decimal
612595
XCTAssertFalse(x.ulp > x)
596+
597+
x = .nan
598+
XCTAssertTrue(x.ulp.isNaN)
599+
XCTAssertTrue(x.nextDown.isNaN)
600+
XCTAssertTrue(x.nextUp.isNaN)
601+
602+
x = .greatestFiniteMagnitude
603+
XCTAssertEqual(x.ulp, Decimal(string: "1e127")!)
604+
XCTAssertEqual(x.nextDown, x - Decimal(string: "1e127")!)
605+
XCTAssertTrue(x.nextUp.isNaN)
606+
607+
x = 1
608+
XCTAssertEqual(x.ulp, Decimal(string: "1e-38")!)
609+
XCTAssertEqual(x.nextDown, x - Decimal(string: "1e-38")!)
610+
XCTAssertEqual(x.nextUp, x + Decimal(string: "1e-38")!)
611+
612+
x = .leastNonzeroMagnitude
613+
// XCTAssertEqual(x.ulp, x) // SR-6671
614+
// XCTAssertEqual(x.nextDown, 0) // SR-6671
615+
// XCTAssertEqual(x.nextUp, x + x) // SR-6671
616+
XCTAssertNotEqual(x.ulp, 0)
617+
XCTAssertNotEqual(x.nextDown, x)
618+
XCTAssertNotEqual(x.nextUp, x)
619+
620+
x = 0
621+
XCTAssertEqual(x.ulp, Decimal(string: "1e-128")!)
622+
XCTAssertEqual(x.nextDown, -Decimal(string: "1e-128")!)
623+
XCTAssertEqual(x.nextUp, Decimal(string: "1e-128")!)
624+
625+
x = -1
626+
XCTAssertEqual(x.ulp, (1 as Decimal).ulp)
627+
XCTAssertEqual(x.nextDown, -((1 as Decimal).nextUp))
628+
XCTAssertEqual(x.nextUp, -((1 as Decimal).nextDown))
613629
}
614630

615631
func test_unconditionallyBridgeFromObjectiveC() {

‎Darwin/Foundation-swiftoverlay/Decimal.swift‎

Lines changed: 64 additions & 2 deletions
Original file line numberDiff line numberDiff line change
@@ -324,6 +324,57 @@ extension Decimal : Strideable {
324324
}
325325
}
326326

327+
extension Decimal {
328+
// (Used by `_powersOfTen` and `ulp`; note that the representation isn't compact.)
329+
fileprivate init(_length: UInt32, _mantissa: (UInt16, UInt16, UInt16, UInt16, UInt16, UInt16, UInt16, UInt16)) {
330+
self.init(_exponent: 0, _length: _length, _isNegative: 0, _isCompact: 0,
331+
_reserved: 0, _mantissa: _mantissa)
332+
}
333+
}
334+
335+
private let _powersOfTen = [
336+
/*^00*/ 1 as Decimal,
337+
/*^01*/ Decimal(_length: 1, _mantissa: (0x000a,0,0,0,0,0,0,0)),
338+
/*^02*/ Decimal(_length: 1, _mantissa: (0x0064,0,0,0,0,0,0,0)),
339+
/*^03*/ Decimal(_length: 1, _mantissa: (0x03e8,0,0,0,0,0,0,0)),
340+
/*^04*/ Decimal(_length: 1, _mantissa: (0x2710,0,0,0,0,0,0,0)),
341+
/*^05*/ Decimal(_length: 2, _mantissa: (0x86a0, 0x0001,0,0,0,0,0,0)),
342+
/*^06*/ Decimal(_length: 2, _mantissa: (0x4240, 0x000f,0,0,0,0,0,0)),
343+
/*^07*/ Decimal(_length: 2, _mantissa: (0x9680, 0x0098,0,0,0,0,0,0)),
344+
/*^08*/ Decimal(_length: 2, _mantissa: (0xe100, 0x05f5,0,0,0,0,0,0)),
345+
/*^09*/ Decimal(_length: 2, _mantissa: (0xca00, 0x3b9a,0,0,0,0,0,0)),
346+
/*^10*/ Decimal(_length: 3, _mantissa: (0xe400, 0x540b, 0x0002,0,0,0,0,0)),
347+
/*^11*/ Decimal(_length: 3, _mantissa: (0xe800, 0x4876, 0x0017,0,0,0,0,0)),
348+
/*^12*/ Decimal(_length: 3, _mantissa: (0x1000, 0xd4a5, 0x00e8,0,0,0,0,0)),
349+
/*^13*/ Decimal(_length: 3, _mantissa: (0xa000, 0x4e72, 0x0918,0,0,0,0,0)),
350+
/*^14*/ Decimal(_length: 3, _mantissa: (0x4000, 0x107a, 0x5af3,0,0,0,0,0)),
351+
/*^15*/ Decimal(_length: 4, _mantissa: (0x8000, 0xa4c6, 0x8d7e, 0x0003,0,0,0,0)),
352+
/*^16*/ Decimal(_length: 4, _mantissa: (0x0000, 0x6fc1, 0x86f2, 0x0023,0,0,0,0)),
353+
/*^17*/ Decimal(_length: 4, _mantissa: (0x0000, 0x5d8a, 0x4578, 0x0163,0,0,0,0)),
354+
/*^18*/ Decimal(_length: 4, _mantissa: (0x0000, 0xa764, 0xb6b3, 0x0de0,0,0,0,0)),
355+
/*^19*/ Decimal(_length: 4, _mantissa: (0x0000, 0x89e8, 0x2304, 0x8ac7,0,0,0,0)),
356+
/*^20*/ Decimal(_length: 5, _mantissa: (0x0000, 0x6310, 0x5e2d, 0x6bc7, 0x0005,0,0,0)),
357+
/*^21*/ Decimal(_length: 5, _mantissa: (0x0000, 0xdea0, 0xadc5, 0x35c9, 0x0036,0,0,0)),
358+
/*^22*/ Decimal(_length: 5, _mantissa: (0x0000, 0xb240, 0xc9ba, 0x19e0, 0x021e,0,0,0)),
359+
/*^23*/ Decimal(_length: 5, _mantissa: (0x0000, 0xf680, 0xe14a, 0x02c7, 0x152d,0,0,0)),
360+
/*^24*/ Decimal(_length: 5, _mantissa: (0x0000, 0xa100, 0xcced, 0x1bce, 0xd3c2,0,0,0)),
361+
/*^25*/ Decimal(_length: 6, _mantissa: (0x0000, 0x4a00, 0x0148, 0x1614, 0x4595, 0x0008,0,0)),
362+
/*^26*/ Decimal(_length: 6, _mantissa: (0x0000, 0xe400, 0x0cd2, 0xdcc8, 0xb7d2, 0x0052,0,0)),
363+
/*^27*/ Decimal(_length: 6, _mantissa: (0x0000, 0xe800, 0x803c, 0x9fd0, 0x2e3c, 0x033b,0,0)),
364+
/*^28*/ Decimal(_length: 6, _mantissa: (0x0000, 0x1000, 0x0261, 0x3e25, 0xce5e, 0x204f,0,0)),
365+
/*^29*/ Decimal(_length: 7, _mantissa: (0x0000, 0xa000, 0x17ca, 0x6d72, 0x0fae, 0x431e, 0x0001,0)),
366+
/*^30*/ Decimal(_length: 7, _mantissa: (0x0000, 0x4000, 0xedea, 0x4674, 0x9cd0, 0x9f2c, 0x000c,0)),
367+
/*^31*/ Decimal(_length: 7, _mantissa: (0x0000, 0x8000, 0x4b26, 0xc091, 0x2022, 0x37be, 0x007e,0)),
368+
/*^32*/ Decimal(_length: 7, _mantissa: (0x0000, 0x0000, 0xef81, 0x85ac, 0x415b, 0x2d6d, 0x04ee,0)),
369+
/*^33*/ Decimal(_length: 7, _mantissa: (0x0000, 0x0000, 0x5b0a, 0x38c1, 0x8d93, 0xc644, 0x314d,0)),
370+
/*^34*/ Decimal(_length: 8, _mantissa: (0x0000, 0x0000, 0x8e64, 0x378d, 0x87c0, 0xbead, 0xed09, 0x0001)),
371+
/*^35*/ Decimal(_length: 8, _mantissa: (0x0000, 0x0000, 0x8fe8, 0x2b87, 0x4d82, 0x72c7, 0x4261, 0x0013)),
372+
/*^36*/ Decimal(_length: 8, _mantissa: (0x0000, 0x0000, 0x9f10, 0xb34b, 0x0715, 0x7bc9, 0x97ce, 0x00c0)),
373+
/*^37*/ Decimal(_length: 8, _mantissa: (0x0000, 0x0000, 0x36a0, 0x00f4, 0x46d9, 0xd5da, 0xee10, 0x0785)),
374+
/*^38*/ Decimal(_length: 8, _mantissa: (0x0000, 0x0000, 0x2240, 0x098a, 0xc47a, 0x5a86, 0x4ca8, 0x4b3b))
375+
/*^39 is on 9 shorts.*/
376+
]
377+
327378
// The methods in this extension exist to match the protocol requirements of
328379
// FloatingPoint, even if we can't conform directly.
329380
//
@@ -550,9 +601,20 @@ extension Decimal {
550601
}
551602

552603
public var ulp: Decimal {
553-
if !self.isFinite { return Decimal.nan }
604+
guard isFinite else { return .nan }
605+
606+
let exponent: Int32
607+
if isZero {
608+
exponent = .min
609+
} else {
610+
let significand = Decimal(_length: _length, _mantissa: _mantissa)
611+
let maxPowerOfTen = _powersOfTen.count
612+
let powerOfTen = _powersOfTen.firstIndex { $0 > significand } ?? maxPowerOfTen
613+
exponent = _exponent &- Int32(maxPowerOfTen &- powerOfTen)
614+
}
615+
554616
return Decimal(
555-
_exponent: _exponent, _length: 1, _isNegative: 0, _isCompact: 1,
617+
_exponent: max(exponent, -128), _length: 1, _isNegative: 0, _isCompact: 1,
556618
_reserved: 0, _mantissa: (0x0001, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000))
557619
}
558620

‎Sources/Foundation/Decimal.swift‎

Lines changed: 67 additions & 58 deletions
Original file line numberDiff line numberDiff line change
@@ -492,6 +492,57 @@ extension Decimal : Strideable {
492492
}
493493
}
494494

495+
extension Decimal {
496+
// (Used by `_powersOfTen` and `ulp`; note that the representation isn't compact.)
497+
fileprivate init(_length: UInt32, _mantissa: (UInt16, UInt16, UInt16, UInt16, UInt16, UInt16, UInt16, UInt16)) {
498+
self.init(_exponent: 0, _length: _length, _isNegative: 0, _isCompact: 0,
499+
_reserved: 0, _mantissa: _mantissa)
500+
}
501+
}
502+
503+
private let _powersOfTen = [
504+
/*^00*/ 1 as Decimal,
505+
/*^01*/ Decimal(_length: 1, _mantissa: (0x000a,0,0,0,0,0,0,0)),
506+
/*^02*/ Decimal(_length: 1, _mantissa: (0x0064,0,0,0,0,0,0,0)),
507+
/*^03*/ Decimal(_length: 1, _mantissa: (0x03e8,0,0,0,0,0,0,0)),
508+
/*^04*/ Decimal(_length: 1, _mantissa: (0x2710,0,0,0,0,0,0,0)),
509+
/*^05*/ Decimal(_length: 2, _mantissa: (0x86a0, 0x0001,0,0,0,0,0,0)),
510+
/*^06*/ Decimal(_length: 2, _mantissa: (0x4240, 0x000f,0,0,0,0,0,0)),
511+
/*^07*/ Decimal(_length: 2, _mantissa: (0x9680, 0x0098,0,0,0,0,0,0)),
512+
/*^08*/ Decimal(_length: 2, _mantissa: (0xe100, 0x05f5,0,0,0,0,0,0)),
513+
/*^09*/ Decimal(_length: 2, _mantissa: (0xca00, 0x3b9a,0,0,0,0,0,0)),
514+
/*^10*/ Decimal(_length: 3, _mantissa: (0xe400, 0x540b, 0x0002,0,0,0,0,0)),
515+
/*^11*/ Decimal(_length: 3, _mantissa: (0xe800, 0x4876, 0x0017,0,0,0,0,0)),
516+
/*^12*/ Decimal(_length: 3, _mantissa: (0x1000, 0xd4a5, 0x00e8,0,0,0,0,0)),
517+
/*^13*/ Decimal(_length: 3, _mantissa: (0xa000, 0x4e72, 0x0918,0,0,0,0,0)),
518+
/*^14*/ Decimal(_length: 3, _mantissa: (0x4000, 0x107a, 0x5af3,0,0,0,0,0)),
519+
/*^15*/ Decimal(_length: 4, _mantissa: (0x8000, 0xa4c6, 0x8d7e, 0x0003,0,0,0,0)),
520+
/*^16*/ Decimal(_length: 4, _mantissa: (0x0000, 0x6fc1, 0x86f2, 0x0023,0,0,0,0)),
521+
/*^17*/ Decimal(_length: 4, _mantissa: (0x0000, 0x5d8a, 0x4578, 0x0163,0,0,0,0)),
522+
/*^18*/ Decimal(_length: 4, _mantissa: (0x0000, 0xa764, 0xb6b3, 0x0de0,0,0,0,0)),
523+
/*^19*/ Decimal(_length: 4, _mantissa: (0x0000, 0x89e8, 0x2304, 0x8ac7,0,0,0,0)),
524+
/*^20*/ Decimal(_length: 5, _mantissa: (0x0000, 0x6310, 0x5e2d, 0x6bc7, 0x0005,0,0,0)),
525+
/*^21*/ Decimal(_length: 5, _mantissa: (0x0000, 0xdea0, 0xadc5, 0x35c9, 0x0036,0,0,0)),
526+
/*^22*/ Decimal(_length: 5, _mantissa: (0x0000, 0xb240, 0xc9ba, 0x19e0, 0x021e,0,0,0)),
527+
/*^23*/ Decimal(_length: 5, _mantissa: (0x0000, 0xf680, 0xe14a, 0x02c7, 0x152d,0,0,0)),
528+
/*^24*/ Decimal(_length: 5, _mantissa: (0x0000, 0xa100, 0xcced, 0x1bce, 0xd3c2,0,0,0)),
529+
/*^25*/ Decimal(_length: 6, _mantissa: (0x0000, 0x4a00, 0x0148, 0x1614, 0x4595, 0x0008,0,0)),
530+
/*^26*/ Decimal(_length: 6, _mantissa: (0x0000, 0xe400, 0x0cd2, 0xdcc8, 0xb7d2, 0x0052,0,0)),
531+
/*^27*/ Decimal(_length: 6, _mantissa: (0x0000, 0xe800, 0x803c, 0x9fd0, 0x2e3c, 0x033b,0,0)),
532+
/*^28*/ Decimal(_length: 6, _mantissa: (0x0000, 0x1000, 0x0261, 0x3e25, 0xce5e, 0x204f,0,0)),
533+
/*^29*/ Decimal(_length: 7, _mantissa: (0x0000, 0xa000, 0x17ca, 0x6d72, 0x0fae, 0x431e, 0x0001,0)),
534+
/*^30*/ Decimal(_length: 7, _mantissa: (0x0000, 0x4000, 0xedea, 0x4674, 0x9cd0, 0x9f2c, 0x000c,0)),
535+
/*^31*/ Decimal(_length: 7, _mantissa: (0x0000, 0x8000, 0x4b26, 0xc091, 0x2022, 0x37be, 0x007e,0)),
536+
/*^32*/ Decimal(_length: 7, _mantissa: (0x0000, 0x0000, 0xef81, 0x85ac, 0x415b, 0x2d6d, 0x04ee,0)),
537+
/*^33*/ Decimal(_length: 7, _mantissa: (0x0000, 0x0000, 0x5b0a, 0x38c1, 0x8d93, 0xc644, 0x314d,0)),
538+
/*^34*/ Decimal(_length: 8, _mantissa: (0x0000, 0x0000, 0x8e64, 0x378d, 0x87c0, 0xbead, 0xed09, 0x0001)),
539+
/*^35*/ Decimal(_length: 8, _mantissa: (0x0000, 0x0000, 0x8fe8, 0x2b87, 0x4d82, 0x72c7, 0x4261, 0x0013)),
540+
/*^36*/ Decimal(_length: 8, _mantissa: (0x0000, 0x0000, 0x9f10, 0xb34b, 0x0715, 0x7bc9, 0x97ce, 0x00c0)),
541+
/*^37*/ Decimal(_length: 8, _mantissa: (0x0000, 0x0000, 0x36a0, 0x00f4, 0x46d9, 0xd5da, 0xee10, 0x0785)),
542+
/*^38*/ Decimal(_length: 8, _mantissa: (0x0000, 0x0000, 0x2240, 0x098a, 0xc47a, 0x5a86, 0x4ca8, 0x4b3b))
543+
/*^39 is on 9 shorts.*/
544+
]
545+
495546
// The methods in this extension exist to match the protocol requirements of
496547
// FloatingPoint, even if we can't conform directly.
497548
//
@@ -718,9 +769,20 @@ extension Decimal {
718769
}
719770

720771
public var ulp: Decimal {
721-
if !self.isFinite { return Decimal.nan }
772+
guard isFinite else { return .nan }
773+
774+
let exponent: Int32
775+
if isZero {
776+
exponent = .min
777+
} else {
778+
let significand = Decimal(_length: _length, _mantissa: _mantissa)
779+
let maxPowerOfTen = _powersOfTen.count
780+
let powerOfTen = _powersOfTen.firstIndex { $0 > significand } ?? maxPowerOfTen
781+
exponent = _exponent &- Int32(maxPowerOfTen &- powerOfTen)
782+
}
783+
722784
return Decimal(
723-
_exponent: _exponent, _length: 1, _isNegative: 0, _isCompact: 1,
785+
_exponent: max(exponent, -128), _length: 1, _isNegative: 0, _isCompact: 1,
724786
_reserved: 0, _mantissa: (0x0001, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000))
725787
}
726788

@@ -1216,14 +1278,14 @@ fileprivate func integerMultiplyByPowerOf10<T:VariableLengthNumber>(_ result: in
12161278
}
12171279
result = left
12181280

1219-
let maxpow10 = pow10.count - 1
1281+
let maxpow10 = _powersOfTen.count - 1
12201282
var error:NSDecimalNumber.CalculationError = .noError
12211283

12221284
while power > maxpow10 {
12231285
var big = T()
12241286

12251287
power -= maxpow10
1226-
let p10 = pow10[maxpow10]
1288+
let p10 = _powersOfTen[maxpow10]
12271289

12281290
if !isNegative {
12291291
error = integerMultiply(&big,result,p10)
@@ -1245,7 +1307,7 @@ fileprivate func integerMultiplyByPowerOf10<T:VariableLengthNumber>(_ result: in
12451307
var big = T()
12461308

12471309
// Handle the rest of the power (<= maxpow10)
1248-
let p10 = pow10[Int(power)]
1310+
let p10 = _powersOfTen[Int(power)]
12491311

12501312
if !isNegative {
12511313
error = integerMultiply(&big, result, p10)
@@ -1929,15 +1991,6 @@ fileprivate struct WideDecimal : VariableLengthNumber {
19291991
extension Decimal {
19301992
fileprivate static let maxSize: UInt32 = UInt32(NSDecimalMaxSize)
19311993

1932-
fileprivate init(length: UInt32, mantissa: (UInt16, UInt16, UInt16, UInt16, UInt16, UInt16, UInt16, UInt16)) {
1933-
precondition(length <= 15)
1934-
self._mantissa = mantissa
1935-
self.__exponent = 0
1936-
self.__lengthAndFlags = 0
1937-
self.__reserved = 0
1938-
self._length = length
1939-
}
1940-
19411994
fileprivate var isCompact: Bool {
19421995
get {
19431996
return _isCompact != 0
@@ -2196,50 +2249,6 @@ extension Decimal {
21962249
}
21972250
}
21982251

2199-
fileprivate let pow10 = [
2200-
/*^00*/ Decimal(length: 1, mantissa:( 0x0001,0,0,0,0,0,0,0)),
2201-
/*^01*/ Decimal(length: 1, mantissa:( 0x000a,0,0,0,0,0,0,0)),
2202-
/*^02*/ Decimal(length: 1, mantissa:( 0x0064,0,0,0,0,0,0,0)),
2203-
/*^03*/ Decimal(length: 1, mantissa:( 0x03e8,0,0,0,0,0,0,0)),
2204-
/*^04*/ Decimal(length: 1, mantissa:( 0x2710,0,0,0,0,0,0,0)),
2205-
/*^05*/ Decimal(length: 2, mantissa:( 0x86a0, 0x0001,0,0,0,0,0,0)),
2206-
/*^06*/ Decimal(length: 2, mantissa:( 0x4240, 0x000f,0,0,0,0,0,0)),
2207-
/*^07*/ Decimal(length: 2, mantissa:( 0x9680, 0x0098,0,0,0,0,0,0)),
2208-
/*^08*/ Decimal(length: 2, mantissa:( 0xe100, 0x05f5,0,0,0,0,0,0)),
2209-
/*^09*/ Decimal(length: 2, mantissa:( 0xca00, 0x3b9a,0,0,0,0,0,0)),
2210-
/*^10*/ Decimal(length: 3, mantissa:( 0xe400, 0x540b, 0x0002,0,0,0,0,0)),
2211-
/*^11*/ Decimal(length: 3, mantissa:( 0xe800, 0x4876, 0x0017,0,0,0,0,0)),
2212-
/*^12*/ Decimal(length: 3, mantissa:( 0x1000, 0xd4a5, 0x00e8,0,0,0,0,0)),
2213-
/*^13*/ Decimal(length: 3, mantissa:( 0xa000, 0x4e72, 0x0918,0,0,0,0,0)),
2214-
/*^14*/ Decimal(length: 3, mantissa:( 0x4000, 0x107a, 0x5af3,0,0,0,0,0)),
2215-
/*^15*/ Decimal(length: 4, mantissa:( 0x8000, 0xa4c6, 0x8d7e, 0x0003,0,0,0,0)),
2216-
/*^16*/ Decimal(length: 4, mantissa:( 0x0000, 0x6fc1, 0x86f2, 0x0023,0,0,0,0)),
2217-
/*^17*/ Decimal(length: 4, mantissa:( 0x0000, 0x5d8a, 0x4578, 0x0163,0,0,0,0)),
2218-
/*^18*/ Decimal(length: 4, mantissa:( 0x0000, 0xa764, 0xb6b3, 0x0de0,0,0,0,0)),
2219-
/*^19*/ Decimal(length: 4, mantissa:( 0x0000, 0x89e8, 0x2304, 0x8ac7,0,0,0,0)),
2220-
/*^20*/ Decimal(length: 5, mantissa:( 0x0000, 0x6310, 0x5e2d, 0x6bc7, 0x0005,0,0,0)),
2221-
/*^21*/ Decimal(length: 5, mantissa:( 0x0000, 0xdea0, 0xadc5, 0x35c9, 0x0036,0,0,0)),
2222-
/*^22*/ Decimal(length: 5, mantissa:( 0x0000, 0xb240, 0xc9ba, 0x19e0, 0x021e,0,0,0)),
2223-
/*^23*/ Decimal(length: 5, mantissa:( 0x0000, 0xf680, 0xe14a, 0x02c7, 0x152d,0,0,0)),
2224-
/*^24*/ Decimal(length: 5, mantissa:( 0x0000, 0xa100, 0xcced, 0x1bce, 0xd3c2,0,0,0)),
2225-
/*^25*/ Decimal(length: 6, mantissa:( 0x0000, 0x4a00, 0x0148, 0x1614, 0x4595, 0x0008,0,0)),
2226-
/*^26*/ Decimal(length: 6, mantissa:( 0x0000, 0xe400, 0x0cd2, 0xdcc8, 0xb7d2, 0x0052,0,0)),
2227-
/*^27*/ Decimal(length: 6, mantissa:( 0x0000, 0xe800, 0x803c, 0x9fd0, 0x2e3c, 0x033b,0,0)),
2228-
/*^28*/ Decimal(length: 6, mantissa:( 0x0000, 0x1000, 0x0261, 0x3e25, 0xce5e, 0x204f,0,0)),
2229-
/*^29*/ Decimal(length: 7, mantissa:( 0x0000, 0xa000, 0x17ca, 0x6d72, 0x0fae, 0x431e, 0x0001,0)),
2230-
/*^30*/ Decimal(length: 7, mantissa:( 0x0000, 0x4000, 0xedea, 0x4674, 0x9cd0, 0x9f2c, 0x000c,0)),
2231-
/*^31*/ Decimal(length: 7, mantissa:( 0x0000, 0x8000, 0x4b26, 0xc091, 0x2022, 0x37be, 0x007e,0)),
2232-
/*^32*/ Decimal(length: 7, mantissa:( 0x0000, 0x0000, 0xef81, 0x85ac, 0x415b, 0x2d6d, 0x04ee,0)),
2233-
/*^33*/ Decimal(length: 7, mantissa:( 0x0000, 0x0000, 0x5b0a, 0x38c1, 0x8d93, 0xc644, 0x314d,0)),
2234-
/*^34*/ Decimal(length: 8, mantissa:( 0x0000, 0x0000, 0x8e64, 0x378d, 0x87c0, 0xbead, 0xed09, 0x0001)),
2235-
/*^35*/ Decimal(length: 8, mantissa:( 0x0000, 0x0000, 0x8fe8, 0x2b87, 0x4d82, 0x72c7, 0x4261, 0x0013)),
2236-
/*^36*/ Decimal(length: 8, mantissa:( 0x0000, 0x0000, 0x9f10, 0xb34b, 0x0715, 0x7bc9, 0x97ce, 0x00c0)),
2237-
/*^37*/ Decimal(length: 8, mantissa:( 0x0000, 0x0000, 0x36a0, 0x00f4, 0x46d9, 0xd5da, 0xee10, 0x0785)),
2238-
/*^38*/ Decimal(length: 8, mantissa:( 0x0000, 0x0000, 0x2240, 0x098a, 0xc47a, 0x5a86, 0x4ca8, 0x4b3b))
2239-
/*^39 is on 9 shorts. */
2240-
]
2241-
2242-
22432252
// Could be silently inexact for float and double.
22442253
extension Scanner {
22452254

0 commit comments

Comments
 (0)