Add Decimal32, Decimal64, Decimal128 #100729
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| // Licensed to the .NET Foundation under one or more agreements. | ||
| // The .NET Foundation licenses this file to you under the MIT license. | ||
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| using System.Numerics; | ||
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| namespace System | ||
| { | ||
| internal interface IDecimalIeee754ConstructorInfo<TSelf, TSignificand, TValue> | ||
| where TSelf : unmanaged, IDecimalIeee754ConstructorInfo<TSelf, TSignificand, TValue> | ||
| where TSignificand : IBinaryInteger<TSignificand> | ||
| where TValue : IBinaryInteger<TValue> | ||
| { | ||
| static abstract TSignificand MaxSignificand { get; } | ||
| static abstract int MaxDecimalExponent { get; } | ||
| static abstract int MinDecimalExponent { get; } | ||
| static abstract int NumberDigitsPrecision { get; } | ||
| static abstract int Bias { get; } | ||
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| static abstract int CountDigits(TSignificand number); | ||
| static abstract TSignificand Power10(int exponent); | ||
| static abstract int MostSignificantBitNumberOfSignificand { get; } | ||
| static abstract int NumberBitsEncoding { get; } | ||
| static abstract int NumberBitsCombinationField { get; } | ||
| static abstract int NumberBitsExponent { get; } | ||
| static abstract TValue PositiveInfinityBits { get; } | ||
| static abstract TValue NegativeInfinityBits { get; } | ||
| static abstract TValue Zero { get; } | ||
| } | ||
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| internal interface IDecimalIeee754UnpackInfo<TSelf, TSignificand, TValue> | ||
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| where TSelf : unmanaged, IDecimalIeee754UnpackInfo<TSelf, TSignificand, TValue> | ||
| where TSignificand : IBinaryInteger<TSignificand> | ||
| where TValue : IBinaryInteger<TValue> | ||
| { | ||
| static abstract TValue SignMask { get; } | ||
| static abstract int NumberBitsEncoding { get; } | ||
| static abstract int NumberBitsExponent { get; } | ||
| static abstract int NumberDigitsPrecision { get; } | ||
| static abstract int Bias { get; } | ||
| static abstract TSignificand TwoPowerMostSignificantBitNumberOfSignificand { get; } | ||
| static abstract int ConvertToExponent(TValue value); | ||
| static abstract TSignificand ConvertToSignificand(TValue value); | ||
| static abstract TSignificand Power10(int exponent); | ||
| } | ||
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| internal static partial class Number | ||
| { | ||
| internal static TValue CalDecimalIeee754<TDecimal, TSignificand, TValue>(TSignificand significand, int exponent) | ||
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| where TDecimal : unmanaged, IDecimalIeee754ConstructorInfo<TDecimal, TSignificand, TValue> | ||
| where TSignificand : IBinaryInteger<TSignificand> | ||
| where TValue : IBinaryInteger<TValue> | ||
| { | ||
| if (significand == TSignificand.Zero) | ||
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| { | ||
| return TValue.Zero; | ||
| } | ||
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| TSignificand unsignedSignificand = significand > TSignificand.Zero ? significand : -significand; | ||
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| if (unsignedSignificand > TDecimal.MaxSignificand && exponent > TDecimal.MaxDecimalExponent) | ||
| { | ||
| return significand > TSignificand.Zero ? TDecimal.PositiveInfinityBits : TDecimal.NegativeInfinityBits; | ||
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| } | ||
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| TSignificand ten = TSignificand.CreateTruncating(10); | ||
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| if (exponent < TDecimal.MinDecimalExponent) | ||
|
There was a problem hiding this comment. A lot of this logic is complex and doing things that aren't "immediately obvious" if you aren't familiar with the algorithm or format. We need some comments inserted into the code to help explain, overall, what the goal of various blocks of code are. This helps lay out any invariants, any base math that is being done, and lets readers better assert that the code is doing what is intended. This does not need to be "obvious" comments or repeat exactly what the code says. But should instead explain the overarching theme such as is done for https://source.dot.net/#System.Private.CoreLib/src/libraries/Common/src/System/Number.Parsing.Common.cs,116 or https://source.dot.net/#System.Private.CoreLib/src/libraries/System.Private.CoreLib/src/System/Number.Dragon4.cs,86 Something like the Other cases like why converting |
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| { | ||
| while (unsignedSignificand >= ten) | ||
| { | ||
| unsignedSignificand /= ten; | ||
| ++exponent; | ||
| } | ||
| if (exponent < TDecimal.MinDecimalExponent) | ||
| { | ||
| throw new OverflowException(SR.Overflow_Decimal); | ||
| } | ||
| } | ||
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| if (unsignedSignificand > TDecimal.MaxSignificand) | ||
| { | ||
| int numberDigitsRemoving = TDecimal.CountDigits(unsignedSignificand) - TDecimal.NumberDigitsPrecision; | ||
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| if (exponent + numberDigitsRemoving > TDecimal.MaxDecimalExponent) | ||
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| { | ||
| throw new OverflowException(SR.Overflow_Decimal); | ||
| } | ||
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| exponent += numberDigitsRemoving; | ||
| TSignificand two = TSignificand.CreateTruncating(2); | ||
| TSignificand divisor = TDecimal.Power10(numberDigitsRemoving); | ||
| TSignificand quotient = unsignedSignificand / divisor; | ||
| TSignificand remainder = unsignedSignificand % divisor; | ||
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| TSignificand midPoint = divisor / two; | ||
| bool needRouding = remainder > midPoint || (remainder == midPoint && quotient % two == TSignificand.One); | ||
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| if (needRouding && quotient == TDecimal.MaxSignificand && exponent < TDecimal.MaxDecimalExponent) | ||
| { | ||
| unsignedSignificand = TDecimal.Power10(TDecimal.NumberDigitsPrecision - 1); | ||
| exponent++; | ||
| } | ||
| else if (needRouding && quotient < TDecimal.MaxSignificand) | ||
| { | ||
| unsignedSignificand = quotient + TSignificand.One; | ||
| } | ||
| else | ||
| { | ||
| unsignedSignificand = quotient; | ||
| } | ||
| } | ||
| else if (exponent > TDecimal.MaxDecimalExponent) | ||
| { | ||
| int numberZeroDigits = exponent - TDecimal.MaxDecimalExponent; | ||
| int numberSignificandDigits = TDecimal.CountDigits(unsignedSignificand); | ||
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| if (numberSignificandDigits + numberZeroDigits > TDecimal.NumberDigitsPrecision) | ||
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| { | ||
| throw new OverflowException(SR.Overflow_Decimal); | ||
| } | ||
| unsignedSignificand *= TDecimal.Power10(numberZeroDigits); | ||
| exponent -= numberZeroDigits; | ||
| } | ||
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| exponent += TDecimal.Bias; | ||
| bool msbSignificand = (unsignedSignificand & TSignificand.One << TDecimal.MostSignificantBitNumberOfSignificand) != TSignificand.Zero; | ||
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| TValue value = TValue.Zero; | ||
| TValue exponentVal = TValue.CreateTruncating(exponent); | ||
| TValue significandVal = TValue.CreateTruncating(unsignedSignificand); | ||
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| if (significand < TSignificand.Zero) | ||
| { | ||
| value = TValue.One << TDecimal.NumberBitsEncoding - 1; | ||
| } | ||
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| if (msbSignificand) | ||
| { | ||
| value ^= TValue.One << TDecimal.NumberBitsEncoding - 2; | ||
| value ^= TValue.One << TDecimal.NumberBitsEncoding - 3; | ||
| exponentVal <<= TDecimal.NumberBitsEncoding - 4; | ||
| value ^= exponentVal; | ||
| significandVal <<= TDecimal.NumberBitsEncoding - TDecimal.MostSignificantBitNumberOfSignificand; | ||
| significandVal >>= TDecimal.NumberBitsCombinationField; | ||
| value ^= significandVal; | ||
| } | ||
| else | ||
| { | ||
| exponentVal <<= TDecimal.NumberBitsEncoding - TDecimal.NumberBitsExponent - 1; | ||
| value ^= exponentVal; | ||
| value ^= significandVal; | ||
| } | ||
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| return value; | ||
| } | ||
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| internal struct DecimalIeee754<TSignificand> | ||
| where TSignificand : IBinaryInteger<TSignificand> | ||
| { | ||
| public bool Signed { get; } | ||
| public int Exponent { get; } | ||
| public TSignificand Significand { get; } | ||
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| public DecimalIeee754(bool signed, int exponent, TSignificand significand) | ||
| { | ||
| Signed = signed; | ||
| Exponent = exponent; | ||
| Significand = significand; | ||
| } | ||
| } | ||
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| internal static DecimalIeee754<TSignificand> UnpackDecimalIeee754<TDecimal, TSignificand, TValue>(TValue value) | ||
| where TDecimal : unmanaged, IDecimalIeee754UnpackInfo<TDecimal, TSignificand, TValue> | ||
| where TSignificand : IBinaryInteger<TSignificand> | ||
| where TValue : IBinaryInteger<TValue> | ||
| { | ||
| bool signed = (value & TDecimal.SignMask) != TValue.Zero; | ||
| TValue g0g1Bits = (value << 1) >> TDecimal.NumberBitsEncoding - 2; | ||
| TSignificand significand; | ||
| int exponent; | ||
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| if (g0g1Bits == TValue.CreateTruncating(3)) | ||
| { | ||
| exponent = TDecimal.ConvertToExponent((value << 3) >> TDecimal.NumberBitsEncoding - TDecimal.NumberBitsExponent); | ||
| significand = TDecimal.ConvertToSignificand((value << TDecimal.NumberBitsEncoding + 3) >> TDecimal.NumberBitsEncoding + 3); | ||
| significand += TDecimal.TwoPowerMostSignificantBitNumberOfSignificand; | ||
| } | ||
| else | ||
| { | ||
| exponent = TDecimal.ConvertToExponent((value << 1) >> TDecimal.NumberBitsEncoding - TDecimal.NumberBitsExponent); | ||
| significand = TDecimal.ConvertToSignificand((value << TDecimal.NumberBitsExponent + 1) >> TDecimal.NumberBitsExponent + 1); | ||
| } | ||
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| return new DecimalIeee754<TSignificand>(signed, exponent - TDecimal.Bias, significand); | ||
| } | ||
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| internal static int CompareDecimalIeee754<TDecimal, TSignificand, TValue>(TValue currentValue, TValue otherValue) | ||
| where TDecimal : unmanaged, IDecimalIeee754UnpackInfo<TDecimal, TSignificand, TValue> | ||
| where TSignificand : IBinaryInteger<TSignificand> | ||
| where TValue : IBinaryInteger<TValue> | ||
| { | ||
| if (currentValue == otherValue) | ||
| { | ||
| return 0; | ||
| } | ||
| DecimalIeee754<TSignificand> current = UnpackDecimalIeee754<TDecimal, TSignificand, TValue>(currentValue); | ||
| DecimalIeee754<TSignificand> other = UnpackDecimalIeee754<TDecimal, TSignificand, TValue>(otherValue); | ||
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| if (current.Signed && !other.Signed) return -1; | ||
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| if (!current.Signed && other.Signed) return 1; | ||
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| if (current.Exponent > other.Exponent) | ||
| { | ||
| return current.Signed ? -InternalUnsignedCompare(current, other) : InternalUnsignedCompare(current, other); | ||
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| } | ||
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| if (current.Exponent < other.Exponent) | ||
| { | ||
| return current.Signed ? InternalUnsignedCompare(other, current) : -InternalUnsignedCompare(current, other); | ||
| } | ||
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| if (current.Significand == other.Significand) return 0; | ||
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| if (current.Significand > other.Significand) | ||
| { | ||
| return current.Signed ? -1 : 1; | ||
| } | ||
| else | ||
| { | ||
| return current.Signed ? 1 : -1; | ||
| } | ||
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| static int InternalUnsignedCompare(DecimalIeee754<TSignificand> biggerExp, DecimalIeee754<TSignificand> smallerExp) | ||
| { | ||
| if (biggerExp.Significand >= smallerExp.Significand) return 1; | ||
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| int diffExponent = biggerExp.Exponent - smallerExp.Exponent; | ||
| if (diffExponent < TDecimal.NumberDigitsPrecision) | ||
| { | ||
| TSignificand factor = TDecimal.Power10(diffExponent); | ||
| TSignificand quotient = smallerExp.Significand / biggerExp.Significand; | ||
| TSignificand remainder = smallerExp.Significand % biggerExp.Significand; | ||
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| if (quotient < factor) return 1; | ||
| if (quotient > factor) return -1; | ||
| if (remainder > TSignificand.Zero) return -1; | ||
| return 0; | ||
| } | ||
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| return 1; | ||
| } | ||
| } | ||
| } | ||
| } | ||
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A comment explaining why these numbers are correct would be beneficial.
There's many resources out there that break down the algorithm for how you get to
767digits for the longest double (or11563forbinary128), as it is:But the algorithm for
decimalisn't as well known (but should overall be similar).There was a problem hiding this comment.
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Hi @tannergooding , I have tried your formula but I can't get the
767result.MaxUnbiasedExponent = 1023, SignificandBits = 52result is
1023 + (−309) + 1= 715.There was a problem hiding this comment.
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Sorry, I did it from memory initially. It should be
(MaxUnbiasedExponent + TrailingSignificandBits - 1)So for
doubleit is1074 + ⌊log10((2^53 – 1) / 2^1074)⌋ + 1. This is because the largest subnormal expands to a value that is 1074 digits in length (which is why in many comments and other places you'll see 1074 and 1075 being used)