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[SR-14384][SR-14974] Fix Decimal.ulp, nextUp, nextDown #3070

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Merged
merged 4 commits into from
Sep 8, 2021
Merged

[SR-14384][SR-14974] Fix Decimal.ulp, nextUp, nextDown #3070

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405aaec
Use 'Decimal.ulp' to compute 'nextUp' and 'nextDown'.
xwu Aug 29, 2021
e8c418c
[SR-14974] Fix 'Decimal.ulp' to reflect spacing between consecutive v…
xwu Aug 29, 2021
aed94d4
Fix a subtle bug in Decimal.ulp and adjust tests.
xwu Sep 5, 2021
376c6b2
Fix implementation of Decimal.nextUp.
xwu Sep 7, 2021
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52 changes: 34 additions & 18 deletions Darwin/Foundation-swiftoverlay-Tests/TestDecimal.swift
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Original file line number Diff line number Diff line change
Expand Up @@ -208,21 +208,6 @@ class TestDecimal : XCTestCase {
XCTAssertEqual(11, sm5)
XCTAssertEqual(12, sm6)
XCTAssertEqual(13, sm7)

let ulp = explicit.ulp
XCTAssertEqual(0x7f, ulp.exponent)
XCTAssertEqual(1, ulp._length)
XCTAssertEqual(0, ulp._isNegative)
XCTAssertEqual(1, ulp._isCompact)
XCTAssertEqual(0, ulp._reserved)
XCTAssertEqual(1, ulp._mantissa.0)
XCTAssertEqual(0, ulp._mantissa.1)
XCTAssertEqual(0, ulp._mantissa.2)
XCTAssertEqual(0, ulp._mantissa.3)
XCTAssertEqual(0, ulp._mantissa.4)
XCTAssertEqual(0, ulp._mantissa.5)
XCTAssertEqual(0, ulp._mantissa.6)
XCTAssertEqual(0, ulp._mantissa.7)
}

func test_Maths() {
Expand Down Expand Up @@ -287,8 +272,6 @@ class TestDecimal : XCTestCase {
XCTAssertTrue(Decimal(2) < Decimal(3))
XCTAssertTrue(Decimal(3) > Decimal(2))
XCTAssertEqual(Decimal(-9), Decimal(1) - Decimal(10))
XCTAssertEqual(Decimal(3), Decimal(2).nextUp)
XCTAssertEqual(Decimal(2), Decimal(3).nextDown)
XCTAssertEqual(Decimal(1.234), abs(Decimal(1.234)))
XCTAssertEqual(Decimal(1.234), abs(Decimal(-1.234)))
if #available(macOS 10.15, iOS 13, tvOS 13, watchOS 6, *) {
Expand Down Expand Up @@ -608,8 +591,41 @@ class TestDecimal : XCTestCase {
}

func test_ULP() {
let x = 0.1 as Decimal
var x = 0.1 as Decimal
XCTAssertFalse(x.ulp > x)

x = .nan
XCTAssertTrue(x.ulp.isNaN)
XCTAssertTrue(x.nextDown.isNaN)
XCTAssertTrue(x.nextUp.isNaN)

x = .greatestFiniteMagnitude
XCTAssertEqual(x.ulp, Decimal(string: "1e127")!)
XCTAssertEqual(x.nextDown, x - Decimal(string: "1e127")!)
XCTAssertTrue(x.nextUp.isNaN)

x = 1
XCTAssertEqual(x.ulp, Decimal(string: "1e-38")!)
XCTAssertEqual(x.nextDown, x - Decimal(string: "1e-38")!)
XCTAssertEqual(x.nextUp, x + Decimal(string: "1e-38")!)

x = .leastNonzeroMagnitude
// XCTAssertEqual(x.ulp, x) // SR-6671
// XCTAssertEqual(x.nextDown, 0) // SR-6671
// XCTAssertEqual(x.nextUp, x + x) // SR-6671
XCTAssertNotEqual(x.ulp, 0)
XCTAssertNotEqual(x.nextDown, x)
XCTAssertNotEqual(x.nextUp, x)

x = 0
XCTAssertEqual(x.ulp, Decimal(string: "1e-128")!)
XCTAssertEqual(x.nextDown, -Decimal(string: "1e-128")!)
XCTAssertEqual(x.nextUp, Decimal(string: "1e-128")!)

x = -1
XCTAssertEqual(x.ulp, (1 as Decimal).ulp)
XCTAssertEqual(x.nextDown, -((1 as Decimal).nextUp))
XCTAssertEqual(x.nextUp, -((1 as Decimal).nextDown))
}

func test_unconditionallyBridgeFromObjectiveC() {
Expand Down
74 changes: 66 additions & 8 deletions Darwin/Foundation-swiftoverlay/Decimal.swift
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Original file line number Diff line number Diff line change
Expand Up @@ -324,6 +324,57 @@ extension Decimal : Strideable {
}
}

extension Decimal {
// (Used by `_powersOfTen` and `ulp`; note that the representation isn't compact.)
fileprivate init(_length: UInt32, _mantissa: (UInt16, UInt16, UInt16, UInt16, UInt16, UInt16, UInt16, UInt16)) {
self.init(_exponent: 0, _length: _length, _isNegative: 0, _isCompact: 0,
_reserved: 0, _mantissa: _mantissa)
}
}

private let _powersOfTen = [
/*^00*/ 1 as Decimal,
/*^01*/ Decimal(_length: 1, _mantissa: (0x000a,0,0,0,0,0,0,0)),
/*^02*/ Decimal(_length: 1, _mantissa: (0x0064,0,0,0,0,0,0,0)),
/*^03*/ Decimal(_length: 1, _mantissa: (0x03e8,0,0,0,0,0,0,0)),
/*^04*/ Decimal(_length: 1, _mantissa: (0x2710,0,0,0,0,0,0,0)),
/*^05*/ Decimal(_length: 2, _mantissa: (0x86a0, 0x0001,0,0,0,0,0,0)),
/*^06*/ Decimal(_length: 2, _mantissa: (0x4240, 0x000f,0,0,0,0,0,0)),
/*^07*/ Decimal(_length: 2, _mantissa: (0x9680, 0x0098,0,0,0,0,0,0)),
/*^08*/ Decimal(_length: 2, _mantissa: (0xe100, 0x05f5,0,0,0,0,0,0)),
/*^09*/ Decimal(_length: 2, _mantissa: (0xca00, 0x3b9a,0,0,0,0,0,0)),
/*^10*/ Decimal(_length: 3, _mantissa: (0xe400, 0x540b, 0x0002,0,0,0,0,0)),
/*^11*/ Decimal(_length: 3, _mantissa: (0xe800, 0x4876, 0x0017,0,0,0,0,0)),
/*^12*/ Decimal(_length: 3, _mantissa: (0x1000, 0xd4a5, 0x00e8,0,0,0,0,0)),
/*^13*/ Decimal(_length: 3, _mantissa: (0xa000, 0x4e72, 0x0918,0,0,0,0,0)),
/*^14*/ Decimal(_length: 3, _mantissa: (0x4000, 0x107a, 0x5af3,0,0,0,0,0)),
/*^15*/ Decimal(_length: 4, _mantissa: (0x8000, 0xa4c6, 0x8d7e, 0x0003,0,0,0,0)),
/*^16*/ Decimal(_length: 4, _mantissa: (0x0000, 0x6fc1, 0x86f2, 0x0023,0,0,0,0)),
/*^17*/ Decimal(_length: 4, _mantissa: (0x0000, 0x5d8a, 0x4578, 0x0163,0,0,0,0)),
/*^18*/ Decimal(_length: 4, _mantissa: (0x0000, 0xa764, 0xb6b3, 0x0de0,0,0,0,0)),
/*^19*/ Decimal(_length: 4, _mantissa: (0x0000, 0x89e8, 0x2304, 0x8ac7,0,0,0,0)),
/*^20*/ Decimal(_length: 5, _mantissa: (0x0000, 0x6310, 0x5e2d, 0x6bc7, 0x0005,0,0,0)),
/*^21*/ Decimal(_length: 5, _mantissa: (0x0000, 0xdea0, 0xadc5, 0x35c9, 0x0036,0,0,0)),
/*^22*/ Decimal(_length: 5, _mantissa: (0x0000, 0xb240, 0xc9ba, 0x19e0, 0x021e,0,0,0)),
/*^23*/ Decimal(_length: 5, _mantissa: (0x0000, 0xf680, 0xe14a, 0x02c7, 0x152d,0,0,0)),
/*^24*/ Decimal(_length: 5, _mantissa: (0x0000, 0xa100, 0xcced, 0x1bce, 0xd3c2,0,0,0)),
/*^25*/ Decimal(_length: 6, _mantissa: (0x0000, 0x4a00, 0x0148, 0x1614, 0x4595, 0x0008,0,0)),
/*^26*/ Decimal(_length: 6, _mantissa: (0x0000, 0xe400, 0x0cd2, 0xdcc8, 0xb7d2, 0x0052,0,0)),
/*^27*/ Decimal(_length: 6, _mantissa: (0x0000, 0xe800, 0x803c, 0x9fd0, 0x2e3c, 0x033b,0,0)),
/*^28*/ Decimal(_length: 6, _mantissa: (0x0000, 0x1000, 0x0261, 0x3e25, 0xce5e, 0x204f,0,0)),
/*^29*/ Decimal(_length: 7, _mantissa: (0x0000, 0xa000, 0x17ca, 0x6d72, 0x0fae, 0x431e, 0x0001,0)),
/*^30*/ Decimal(_length: 7, _mantissa: (0x0000, 0x4000, 0xedea, 0x4674, 0x9cd0, 0x9f2c, 0x000c,0)),
/*^31*/ Decimal(_length: 7, _mantissa: (0x0000, 0x8000, 0x4b26, 0xc091, 0x2022, 0x37be, 0x007e,0)),
/*^32*/ Decimal(_length: 7, _mantissa: (0x0000, 0x0000, 0xef81, 0x85ac, 0x415b, 0x2d6d, 0x04ee,0)),
/*^33*/ Decimal(_length: 7, _mantissa: (0x0000, 0x0000, 0x5b0a, 0x38c1, 0x8d93, 0xc644, 0x314d,0)),
/*^34*/ Decimal(_length: 8, _mantissa: (0x0000, 0x0000, 0x8e64, 0x378d, 0x87c0, 0xbead, 0xed09, 0x0001)),
/*^35*/ Decimal(_length: 8, _mantissa: (0x0000, 0x0000, 0x8fe8, 0x2b87, 0x4d82, 0x72c7, 0x4261, 0x0013)),
/*^36*/ Decimal(_length: 8, _mantissa: (0x0000, 0x0000, 0x9f10, 0xb34b, 0x0715, 0x7bc9, 0x97ce, 0x00c0)),
/*^37*/ Decimal(_length: 8, _mantissa: (0x0000, 0x0000, 0x36a0, 0x00f4, 0x46d9, 0xd5da, 0xee10, 0x0785)),
/*^38*/ Decimal(_length: 8, _mantissa: (0x0000, 0x0000, 0x2240, 0x098a, 0xc47a, 0x5a86, 0x4ca8, 0x4b3b))
/*^39 is on 9 shorts.*/
]

// The methods in this extension exist to match the protocol requirements of
// FloatingPoint, even if we can't conform directly.
//
Expand Down Expand Up @@ -550,22 +601,29 @@ extension Decimal {
}

public var ulp: Decimal {
if !self.isFinite { return Decimal.nan }
guard isFinite else { return .nan }

let exponent: Int32
if isZero {
exponent = .min
} else {
let significand = Decimal(_length: _length, _mantissa: _mantissa)
let maxPowerOfTen = _powersOfTen.count
let powerOfTen = _powersOfTen.firstIndex { $0 > significand } ?? maxPowerOfTen
exponent = _exponent &- Int32(maxPowerOfTen &- powerOfTen)
}

return Decimal(
_exponent: _exponent, _length: 1, _isNegative: 0, _isCompact: 1,
_exponent: max(exponent, -128), _length: 1, _isNegative: 0, _isCompact: 1,
_reserved: 0, _mantissa: (0x0001, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000))
}

public var nextUp: Decimal {
return self + Decimal(
_exponent: _exponent, _length: 1, _isNegative: 0, _isCompact: 1,
_reserved: 0, _mantissa: (0x0001, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000))
return self + ulp
}

public var nextDown: Decimal {
return self - Decimal(
_exponent: _exponent, _length: 1, _isNegative: 0, _isCompact: 1,
_reserved: 0, _mantissa: (0x0001, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000))
return -(-self).nextUp
}

/// The IEEE 754 "class" of this type.
Expand Down
133 changes: 69 additions & 64 deletions Sources/Foundation/Decimal.swift
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -492,6 +492,57 @@ extension Decimal : Strideable {
}
}

extension Decimal {
// (Used by `_powersOfTen` and `ulp`; note that the representation isn't compact.)
fileprivate init(_length: UInt32, _mantissa: (UInt16, UInt16, UInt16, UInt16, UInt16, UInt16, UInt16, UInt16)) {
self.init(_exponent: 0, _length: _length, _isNegative: 0, _isCompact: 0,
_reserved: 0, _mantissa: _mantissa)
}
}

private let _powersOfTen = [
/*^00*/ 1 as Decimal,
/*^01*/ Decimal(_length: 1, _mantissa: (0x000a,0,0,0,0,0,0,0)),
/*^02*/ Decimal(_length: 1, _mantissa: (0x0064,0,0,0,0,0,0,0)),
/*^03*/ Decimal(_length: 1, _mantissa: (0x03e8,0,0,0,0,0,0,0)),
/*^04*/ Decimal(_length: 1, _mantissa: (0x2710,0,0,0,0,0,0,0)),
/*^05*/ Decimal(_length: 2, _mantissa: (0x86a0, 0x0001,0,0,0,0,0,0)),
/*^06*/ Decimal(_length: 2, _mantissa: (0x4240, 0x000f,0,0,0,0,0,0)),
/*^07*/ Decimal(_length: 2, _mantissa: (0x9680, 0x0098,0,0,0,0,0,0)),
/*^08*/ Decimal(_length: 2, _mantissa: (0xe100, 0x05f5,0,0,0,0,0,0)),
/*^09*/ Decimal(_length: 2, _mantissa: (0xca00, 0x3b9a,0,0,0,0,0,0)),
/*^10*/ Decimal(_length: 3, _mantissa: (0xe400, 0x540b, 0x0002,0,0,0,0,0)),
/*^11*/ Decimal(_length: 3, _mantissa: (0xe800, 0x4876, 0x0017,0,0,0,0,0)),
/*^12*/ Decimal(_length: 3, _mantissa: (0x1000, 0xd4a5, 0x00e8,0,0,0,0,0)),
/*^13*/ Decimal(_length: 3, _mantissa: (0xa000, 0x4e72, 0x0918,0,0,0,0,0)),
/*^14*/ Decimal(_length: 3, _mantissa: (0x4000, 0x107a, 0x5af3,0,0,0,0,0)),
/*^15*/ Decimal(_length: 4, _mantissa: (0x8000, 0xa4c6, 0x8d7e, 0x0003,0,0,0,0)),
/*^16*/ Decimal(_length: 4, _mantissa: (0x0000, 0x6fc1, 0x86f2, 0x0023,0,0,0,0)),
/*^17*/ Decimal(_length: 4, _mantissa: (0x0000, 0x5d8a, 0x4578, 0x0163,0,0,0,0)),
/*^18*/ Decimal(_length: 4, _mantissa: (0x0000, 0xa764, 0xb6b3, 0x0de0,0,0,0,0)),
/*^19*/ Decimal(_length: 4, _mantissa: (0x0000, 0x89e8, 0x2304, 0x8ac7,0,0,0,0)),
/*^20*/ Decimal(_length: 5, _mantissa: (0x0000, 0x6310, 0x5e2d, 0x6bc7, 0x0005,0,0,0)),
/*^21*/ Decimal(_length: 5, _mantissa: (0x0000, 0xdea0, 0xadc5, 0x35c9, 0x0036,0,0,0)),
/*^22*/ Decimal(_length: 5, _mantissa: (0x0000, 0xb240, 0xc9ba, 0x19e0, 0x021e,0,0,0)),
/*^23*/ Decimal(_length: 5, _mantissa: (0x0000, 0xf680, 0xe14a, 0x02c7, 0x152d,0,0,0)),
/*^24*/ Decimal(_length: 5, _mantissa: (0x0000, 0xa100, 0xcced, 0x1bce, 0xd3c2,0,0,0)),
/*^25*/ Decimal(_length: 6, _mantissa: (0x0000, 0x4a00, 0x0148, 0x1614, 0x4595, 0x0008,0,0)),
/*^26*/ Decimal(_length: 6, _mantissa: (0x0000, 0xe400, 0x0cd2, 0xdcc8, 0xb7d2, 0x0052,0,0)),
/*^27*/ Decimal(_length: 6, _mantissa: (0x0000, 0xe800, 0x803c, 0x9fd0, 0x2e3c, 0x033b,0,0)),
/*^28*/ Decimal(_length: 6, _mantissa: (0x0000, 0x1000, 0x0261, 0x3e25, 0xce5e, 0x204f,0,0)),
/*^29*/ Decimal(_length: 7, _mantissa: (0x0000, 0xa000, 0x17ca, 0x6d72, 0x0fae, 0x431e, 0x0001,0)),
/*^30*/ Decimal(_length: 7, _mantissa: (0x0000, 0x4000, 0xedea, 0x4674, 0x9cd0, 0x9f2c, 0x000c,0)),
/*^31*/ Decimal(_length: 7, _mantissa: (0x0000, 0x8000, 0x4b26, 0xc091, 0x2022, 0x37be, 0x007e,0)),
/*^32*/ Decimal(_length: 7, _mantissa: (0x0000, 0x0000, 0xef81, 0x85ac, 0x415b, 0x2d6d, 0x04ee,0)),
/*^33*/ Decimal(_length: 7, _mantissa: (0x0000, 0x0000, 0x5b0a, 0x38c1, 0x8d93, 0xc644, 0x314d,0)),
/*^34*/ Decimal(_length: 8, _mantissa: (0x0000, 0x0000, 0x8e64, 0x378d, 0x87c0, 0xbead, 0xed09, 0x0001)),
/*^35*/ Decimal(_length: 8, _mantissa: (0x0000, 0x0000, 0x8fe8, 0x2b87, 0x4d82, 0x72c7, 0x4261, 0x0013)),
/*^36*/ Decimal(_length: 8, _mantissa: (0x0000, 0x0000, 0x9f10, 0xb34b, 0x0715, 0x7bc9, 0x97ce, 0x00c0)),
/*^37*/ Decimal(_length: 8, _mantissa: (0x0000, 0x0000, 0x36a0, 0x00f4, 0x46d9, 0xd5da, 0xee10, 0x0785)),
/*^38*/ Decimal(_length: 8, _mantissa: (0x0000, 0x0000, 0x2240, 0x098a, 0xc47a, 0x5a86, 0x4ca8, 0x4b3b))
/*^39 is on 9 shorts.*/
]

// The methods in this extension exist to match the protocol requirements of
// FloatingPoint, even if we can't conform directly.
//
Expand Down Expand Up @@ -718,22 +769,29 @@ extension Decimal {
}

public var ulp: Decimal {
if !self.isFinite { return Decimal.nan }
guard isFinite else { return .nan }

let exponent: Int32
if isZero {
exponent = .min
} else {
let significand = Decimal(_length: _length, _mantissa: _mantissa)
let maxPowerOfTen = _powersOfTen.count
let powerOfTen = _powersOfTen.firstIndex { $0 > significand } ?? maxPowerOfTen
exponent = _exponent &- Int32(maxPowerOfTen &- powerOfTen)
}

return Decimal(
_exponent: _exponent, _length: 1, _isNegative: 0, _isCompact: 1,
_exponent: max(exponent, -128), _length: 1, _isNegative: 0, _isCompact: 1,
_reserved: 0, _mantissa: (0x0001, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000))
}

public var nextUp: Decimal {
return self + Decimal(
_exponent: _exponent, _length: 1, _isNegative: 0, _isCompact: 1,
_reserved: 0, _mantissa: (0x0001, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000))
return self + ulp
}

public var nextDown: Decimal {
return self - Decimal(
_exponent: _exponent, _length: 1, _isNegative: 0, _isCompact: 1,
_reserved: 0, _mantissa: (0x0001, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000))
return -(-self).nextUp
}

/// The IEEE 754 "class" of this type.
Expand Down Expand Up @@ -1220,14 +1278,14 @@ fileprivate func integerMultiplyByPowerOf10<T:VariableLengthNumber>(_ result: in
}
result = left

let maxpow10 = pow10.count - 1
let maxpow10 = _powersOfTen.count - 1
var error:NSDecimalNumber.CalculationError = .noError

while power > maxpow10 {
var big = T()

power -= maxpow10
let p10 = pow10[maxpow10]
let p10 = _powersOfTen[maxpow10]

if !isNegative {
error = integerMultiply(&big,result,p10)
Expand All @@ -1249,7 +1307,7 @@ fileprivate func integerMultiplyByPowerOf10<T:VariableLengthNumber>(_ result: in
var big = T()

// Handle the rest of the power (<= maxpow10)
let p10 = pow10[Int(power)]
let p10 = _powersOfTen[Int(power)]

if !isNegative {
error = integerMultiply(&big, result, p10)
Expand Down Expand Up @@ -1933,15 +1991,6 @@ fileprivate struct WideDecimal : VariableLengthNumber {
extension Decimal {
fileprivate static let maxSize: UInt32 = UInt32(NSDecimalMaxSize)

fileprivate init(length: UInt32, mantissa: (UInt16, UInt16, UInt16, UInt16, UInt16, UInt16, UInt16, UInt16)) {
precondition(length <= 15)
self._mantissa = mantissa
self.__exponent = 0
self.__lengthAndFlags = 0
self.__reserved = 0
self._length = length
}

fileprivate var isCompact: Bool {
get {
return _isCompact != 0
Expand Down Expand Up @@ -2200,50 +2249,6 @@ extension Decimal {
}
}

fileprivate let pow10 = [
/*^00*/ Decimal(length: 1, mantissa:( 0x0001,0,0,0,0,0,0,0)),
/*^01*/ Decimal(length: 1, mantissa:( 0x000a,0,0,0,0,0,0,0)),
/*^02*/ Decimal(length: 1, mantissa:( 0x0064,0,0,0,0,0,0,0)),
/*^03*/ Decimal(length: 1, mantissa:( 0x03e8,0,0,0,0,0,0,0)),
/*^04*/ Decimal(length: 1, mantissa:( 0x2710,0,0,0,0,0,0,0)),
/*^05*/ Decimal(length: 2, mantissa:( 0x86a0, 0x0001,0,0,0,0,0,0)),
/*^06*/ Decimal(length: 2, mantissa:( 0x4240, 0x000f,0,0,0,0,0,0)),
/*^07*/ Decimal(length: 2, mantissa:( 0x9680, 0x0098,0,0,0,0,0,0)),
/*^08*/ Decimal(length: 2, mantissa:( 0xe100, 0x05f5,0,0,0,0,0,0)),
/*^09*/ Decimal(length: 2, mantissa:( 0xca00, 0x3b9a,0,0,0,0,0,0)),
/*^10*/ Decimal(length: 3, mantissa:( 0xe400, 0x540b, 0x0002,0,0,0,0,0)),
/*^11*/ Decimal(length: 3, mantissa:( 0xe800, 0x4876, 0x0017,0,0,0,0,0)),
/*^12*/ Decimal(length: 3, mantissa:( 0x1000, 0xd4a5, 0x00e8,0,0,0,0,0)),
/*^13*/ Decimal(length: 3, mantissa:( 0xa000, 0x4e72, 0x0918,0,0,0,0,0)),
/*^14*/ Decimal(length: 3, mantissa:( 0x4000, 0x107a, 0x5af3,0,0,0,0,0)),
/*^15*/ Decimal(length: 4, mantissa:( 0x8000, 0xa4c6, 0x8d7e, 0x0003,0,0,0,0)),
/*^16*/ Decimal(length: 4, mantissa:( 0x0000, 0x6fc1, 0x86f2, 0x0023,0,0,0,0)),
/*^17*/ Decimal(length: 4, mantissa:( 0x0000, 0x5d8a, 0x4578, 0x0163,0,0,0,0)),
/*^18*/ Decimal(length: 4, mantissa:( 0x0000, 0xa764, 0xb6b3, 0x0de0,0,0,0,0)),
/*^19*/ Decimal(length: 4, mantissa:( 0x0000, 0x89e8, 0x2304, 0x8ac7,0,0,0,0)),
/*^20*/ Decimal(length: 5, mantissa:( 0x0000, 0x6310, 0x5e2d, 0x6bc7, 0x0005,0,0,0)),
/*^21*/ Decimal(length: 5, mantissa:( 0x0000, 0xdea0, 0xadc5, 0x35c9, 0x0036,0,0,0)),
/*^22*/ Decimal(length: 5, mantissa:( 0x0000, 0xb240, 0xc9ba, 0x19e0, 0x021e,0,0,0)),
/*^23*/ Decimal(length: 5, mantissa:( 0x0000, 0xf680, 0xe14a, 0x02c7, 0x152d,0,0,0)),
/*^24*/ Decimal(length: 5, mantissa:( 0x0000, 0xa100, 0xcced, 0x1bce, 0xd3c2,0,0,0)),
/*^25*/ Decimal(length: 6, mantissa:( 0x0000, 0x4a00, 0x0148, 0x1614, 0x4595, 0x0008,0,0)),
/*^26*/ Decimal(length: 6, mantissa:( 0x0000, 0xe400, 0x0cd2, 0xdcc8, 0xb7d2, 0x0052,0,0)),
/*^27*/ Decimal(length: 6, mantissa:( 0x0000, 0xe800, 0x803c, 0x9fd0, 0x2e3c, 0x033b,0,0)),
/*^28*/ Decimal(length: 6, mantissa:( 0x0000, 0x1000, 0x0261, 0x3e25, 0xce5e, 0x204f,0,0)),
/*^29*/ Decimal(length: 7, mantissa:( 0x0000, 0xa000, 0x17ca, 0x6d72, 0x0fae, 0x431e, 0x0001,0)),
/*^30*/ Decimal(length: 7, mantissa:( 0x0000, 0x4000, 0xedea, 0x4674, 0x9cd0, 0x9f2c, 0x000c,0)),
/*^31*/ Decimal(length: 7, mantissa:( 0x0000, 0x8000, 0x4b26, 0xc091, 0x2022, 0x37be, 0x007e,0)),
/*^32*/ Decimal(length: 7, mantissa:( 0x0000, 0x0000, 0xef81, 0x85ac, 0x415b, 0x2d6d, 0x04ee,0)),
/*^33*/ Decimal(length: 7, mantissa:( 0x0000, 0x0000, 0x5b0a, 0x38c1, 0x8d93, 0xc644, 0x314d,0)),
/*^34*/ Decimal(length: 8, mantissa:( 0x0000, 0x0000, 0x8e64, 0x378d, 0x87c0, 0xbead, 0xed09, 0x0001)),
/*^35*/ Decimal(length: 8, mantissa:( 0x0000, 0x0000, 0x8fe8, 0x2b87, 0x4d82, 0x72c7, 0x4261, 0x0013)),
/*^36*/ Decimal(length: 8, mantissa:( 0x0000, 0x0000, 0x9f10, 0xb34b, 0x0715, 0x7bc9, 0x97ce, 0x00c0)),
/*^37*/ Decimal(length: 8, mantissa:( 0x0000, 0x0000, 0x36a0, 0x00f4, 0x46d9, 0xd5da, 0xee10, 0x0785)),
/*^38*/ Decimal(length: 8, mantissa:( 0x0000, 0x0000, 0x2240, 0x098a, 0xc47a, 0x5a86, 0x4ca8, 0x4b3b))
/*^39 is on 9 shorts. */
]


// Could be silently inexact for float and double.
extension Scanner {

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