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Diffstat (limited to 'Source/Basetypes/BigFloat.cs')
| -rw-r--r-- | Source/Basetypes/BigFloat.cs | 509 |
1 files changed, 509 insertions, 0 deletions
diff --git a/Source/Basetypes/BigFloat.cs b/Source/Basetypes/BigFloat.cs new file mode 100644 index 00000000..cb248340 --- /dev/null +++ b/Source/Basetypes/BigFloat.cs @@ -0,0 +1,509 @@ +//----------------------------------------------------------------------------- +// +// Copyright (C) Microsoft Corporation. All Rights Reserved. +// +//----------------------------------------------------------------------------- + +using System; +using System.Collections.Generic; +using System.Linq; +using System.Text; +using System.Diagnostics.Contracts; +using System.Diagnostics; + +namespace Microsoft.Basetypes +{ + using BIM = System.Numerics.BigInteger; + + /// <summary> + /// A representation of a 32-bit floating point value + /// Note that this value has a 1-bit sign, 8-bit exponent, and 24-bit significand + /// </summary> + public struct BigFloat + { + //Please note that this code outline is copy-pasted from BigDec.cs + + // the internal representation + [Rep] + internal readonly BIM significand; //Note that the significand arrangement matches standard fp arrangement (most significant bit is farthest left) + [Rep] + internal readonly int significandSize; + [Rep] + internal readonly BIM exponent; //The value of the exponent is always positive as per fp representation requirements + [Rep] + internal readonly int exponentSize; //The bit size of the exponent + [Rep] + internal readonly String value; //Only used with second syntax + [Rep] + internal readonly bool isNeg; + + public BIM Significand { + get { + return significand; + } + } + + public BIM Exponent { + get { + return exponent; + } + } + + public int SignificandSize { + get { + return significandSize; + } + } + + public int ExponentSize { + get { + return exponentSize; + } + } + + public bool IsNegative { + get { + return this.isNeg; + } + } + + public String Value { + get { + return value; + } + } + + public static BigFloat ZERO = new BigFloat(false, BIM.Zero, BIM.Zero, 24, 8); //Does not include negative zero + + private static readonly BIM two = new BIM(2); + private static readonly BIM one = new BIM(1); + private static BIM two_n(int n) { + BIM toReturn = one; + for (int i = 0; i < n; i++) + toReturn = toReturn * two; + return toReturn; + } + + + //////////////////////////////////////////////////////////////////////////// + // Constructors + + //Please note that these constructors will be called throughout boogie + //For a complete summary of where this class has been added, simply view constructor references + + [Pure] + public static BigFloat FromInt(int v) { + return new BigFloat(v.ToString(), 24, 8); + } + + public static BigFloat FromInt(int v, int significandSize, int exponentSize) + { + return new BigFloat(v.ToString(), significandSize, exponentSize); + } + + public static BigFloat FromBigInt(BIM v) { + return new BigFloat(v.ToString(), 24, 8); + } + + public static BigFloat FromBigInt(BIM v, int significandSize, int exponentSize) + { + return new BigFloat(v.ToString(), significandSize, exponentSize); + } + + public static BigFloat FromBigDec(BigDec v) + { + return new BigFloat(v.ToDecimalString(), 24, 8); + } + + public static BigFloat FromBigDec(BigDec v, int significandSize, int exponentSize) + { + return new BigFloat(v.ToDecimalString(), significandSize, exponentSize); + } + + [Pure] + public static BigFloat FromString(String s) { + /* + * String must be either of the format *e*f*e* + * or of the special value formats: 0NaN*e* 0nan*e* 0+oo*e* 0-oo*e* + * Where * indicates an integer value (digit) + */ + BIM sig, exp; + int sigSize, expSize; + bool isNeg; + + if (s.IndexOf('f') == -1) { + String val = s; + sigSize = int.Parse(s.Substring(4, s.IndexOf('e')-4)); + expSize = int.Parse(s.Substring(s.IndexOf('e') + 1)); + if (sigSize <= 0 || expSize <= 0) + throw new FormatException("Significand and Exponent sizes must be greater than 0"); + return new BigFloat(val, sigSize, expSize); + } + + sig = BIM.Parse(s.Substring(0, s.IndexOf('e'))); + exp = BIM.Parse(s.Substring(s.IndexOf('e') + 1, s.IndexOf('f') - s.IndexOf('e') - 1)); + sigSize = int.Parse(s.Substring(s.IndexOf('f') + 1, s.IndexOf('e', s.IndexOf('e') + 1) - s.IndexOf('f') - 1)); + expSize = int.Parse(s.Substring(s.IndexOf('e', s.IndexOf('e') + 1) + 1)); + isNeg = s[0] == '-'; //We do this so that -0 is parsed correctly + + if (sigSize <= 0 || expSize <= 0) + throw new FormatException("Significand and Exponent sizes must be greater than 0"); + + sigSize = sigSize - 1; //Get rid of sign bit + sig = BIM.Abs(sig); //sig must be positive + //Uncomment if you want to shift the exponent for the user (i.e. 0e-1f24e8 --> 0e126f24e8) + //exp = exp + BIM.Pow(new BIM(2), expSize-1) - BIM.One; + + if (exp < 0 || exp >= BIM.Pow(new BIM(2), expSize)) + throw new FormatException("The given exponent " + exp + " cannot fit in the bit size " + expSize); + + if (sig >= BIM.Pow(new BIM(2), sigSize)) + throw new FormatException("The given significand " + sig + " cannot fit in the bit size " + (sigSize+1)); + + return new BigFloat(isNeg, sig, exp, sigSize, expSize); + } + + public BigFloat(bool isNeg, BIM significand, BIM exponent, int significandSize, int exponentSize) { + this.exponentSize = exponentSize; + this.exponent = exponent; + this.significand = significand; + this.significandSize = significandSize+1; + this.isNeg = isNeg; + this.value = ""; + } + + public BigFloat(String value, int significandSize, int exponentSize) { + this.exponentSize = exponentSize; + this.significandSize = significandSize; + this.exponent = BIM.Zero; + this.significand = BIM.Zero; + this.value = value; + if (value.Equals("nan")) + this.value = "NaN"; + this.isNeg = value[0] == '-'; + } + + private BIM maxsignificand() + { + BIM result = one; + for (int i = 0; i < significandSize; i++) + result = result * two; + return result - one; + } + private int maxExponent() { return (int)Math.Pow(2, exponentSize) - 1; } + + + + //////////////////////////////////////////////////////////////////////////// + // Basic object operations + + [Pure] + [Reads(ReadsAttribute.Reads.Nothing)] + public override bool Equals(object obj) { + if (obj == null) + return false; + if (!(obj is BigFloat)) + return false; + + return (this == (BigFloat)obj); + } + + [Pure] + public override int GetHashCode() { + return significand.GetHashCode() * 13 + Exponent.GetHashCode(); + } + + [Pure] + public override string/*!*/ ToString() { + Contract.Ensures(Contract.Result<string>() != null); + return value=="" ? String.Format("{0}x2^{1}", significand.ToString(), Exponent.ToString()) : value; + } + + + //////////////////////////////////////////////////////////////////////////// + // Conversion operations + + /// <summary> + /// NOTE: THIS METHOD MAY NOT WORK AS EXPECTED!!! + /// Converts the given decimal value (provided as a string) to the nearest floating point approximation + /// the returned fp assumes the given significand and exponent size + /// </summary> + /// <param name="value"></param> + /// <param name="significandSize"></param> + /// <param name="exponentSize"></param> + /// <returns></returns> + public static BigFloat Round(String value, int exponentSize, int significandSize) + { + int i = value.IndexOf('.'); + if (i == -1) + return Round(BIM.Parse(value), BIM.Zero, exponentSize, significandSize); + return Round(i == 0 ? BIM.Zero : BIM.Parse(value.Substring(0, i)), BIM.Parse(value.Substring(i + 1, value.Length - i - 1)), exponentSize, significandSize); + } + + /// <summary> + /// NOTE: THIS METHOD MAY NOT WORK AS EXPECTED!!!! + /// Converts value.dec_value to a the closest float approximation with the given significandSize, exponentSize + /// Returns the result of this calculation + /// </summary> + /// <param name="value"></param> + /// <param name="power"></param> + /// <param name="significandSize"></param> + /// <param name="exponentSize"></param> + /// <returns></returns> + public static BigFloat Round(BIM value, BIM dec_value, int exponentSize, int significandSize) + { + int exp = 0; + BIM one = new BIM(1); + BIM ten = new BIM(10); + BIM dec_max = new BIM(0); //represents the order of magnitude of dec_value for carrying during calculations + + //First, determine the exponent + while (value > one) { //Divide by two, increment exponent by 1 + if (!(value % two).IsZero) { //Add "1.0" to the decimal + dec_max = new BIM(10); + while (dec_max < dec_value) + dec_max = dec_max * ten; + dec_value = dec_value + dec_max; + } + value = value / two; + if (!(dec_value % ten).IsZero) + dec_value = dec_value * ten; //Creates excess zeroes to avoid losing data during division + dec_value = dec_value / two; + exp++; + } + if (value.IsZero && !dec_value.IsZero) { + dec_max = new BIM(10); + while (dec_max < dec_value) + dec_max = dec_max * ten; + while (value.IsZero) {//Multiply by two, decrement exponent by 1 + dec_value = dec_value * two; + if (dec_value >= dec_max) { + dec_value = dec_value - dec_max; + value = value + one; + } + exp--; + } + } + + //Second, calculate the significand + value = new BIM(0); //remove implicit bit + dec_max = new BIM(10); + while (dec_max < dec_value) + dec_max = dec_max * ten; + for (int i = significandSize; i > 0 && !dec_value.IsZero; i--) { //Multiply by two until the significand is fully calculated + dec_value = dec_value * two; + if (dec_value >= dec_max) { + dec_value = dec_value - dec_max; + value = value + two_n(i); //Note that i is decrementing so that the most significant bit is left-most in the representation + } + } + + return new BigFloat(false, BIM.Zero, BIM.Parse(value.ToString()), exponentSize, significandSize); //Sign not actually checked... + } + + // ``floor`` rounds towards negative infinity (like SMT-LIBv2's to_int). + /// <summary> + /// NOTE: This may give wrong results, it hasn't been tested extensively + /// If you're getting weird bugs, you may want to check this function out... + /// Computes the floor and ceiling of this BigFloat. Note the choice of rounding towards negative + /// infinity rather than zero for floor is because SMT-LIBv2's to_int function floors this way. + /// </summary> + /// <param name="floor">The Floor (rounded towards negative infinity)</param> + /// <param name="ceiling">Ceiling (rounded towards positive infinity)</param> + public void FloorCeiling(out BIM floor, out BIM ceiling) + { + BIM two = new BIM(2); + + BIM sig = Significand + BIM.Pow(two, SignificandSize); //Add hidden bit + BIM exp = Exponent - BIM.Pow(two, ExponentSize-1) + 1; + + while (exp > BIM.Zero) { + exp--; + sig = sig << 1; + } + + sig = sig >> SignificandSize; + + if (isNeg) { + ceiling = -sig + 1; + floor = -sig; + } + else { + ceiling = sig + 1; + floor = sig; + } + } + + [Pure] + public String ToDecimalString(int maxDigits) { + //TODO: fix for fp functionality + { + throw new NotImplementedException(); + } + } + + public String ToBVString(){ + if (this.IsSpecialType) { + return "_ " + this.value + " " + this.exponentSize + " " + this.significandSize; + } + else if (this.Value == "") { + return "fp (_ bv" + (this.isNeg ? "1" : "0") + " 1) (_ bv" + this.exponent + " " + this.exponentSize + ") (_ bv" + this.significand + " " + (this.significandSize-1) + ")"; + } + else { + return "(_ to_fp " + this.exponentSize + " " + this.significandSize + ") (_ bv" + this.value + " " + (this.exponentSize + this.significandSize).ToString() + ")"; + } + } + + [Pure] + public string ToDecimalString() { + Contract.Ensures(Contract.Result<string>() != null); + return value=="" ? String.Format("{0}x2^{1}", significand.ToString(), Exponent.ToString()) : value; + } + + [Pure] + public static string Zeros(int n) { + //TODO: fix for fp functionality + Contract.Requires(0 <= n); + if (n <= 10) { + var tenZeros = "0000000000"; + return tenZeros.Substring(0, n); + } else { + var d = n / 2; + var s = Zeros(d); + if (n % 2 == 0) { + return s + s; + } else { + return s + s + "0"; + } + } + } + + + //////////////////////////////////////////////////////////////////////////// + // Basic arithmetic operations + + [Pure] + public BigFloat Abs { + get { + return new BigFloat(true, Exponent, Significand, ExponentSize, SignificandSize); + } + } + + [Pure] + public BigFloat Negate { + get { + if (value != "") + return value[0] == '-' ? new BigFloat(value.Remove(0, 1), ExponentSize, significandSize) : new BigFloat("-" + value, ExponentSize, significandSize); + return new BigFloat(!isNeg, Exponent, Significand, ExponentSize, SignificandSize); + } + } + + [Pure] + public static BigFloat operator -(BigFloat x) { + return x.Negate; + } + + [Pure] + public static BigFloat operator +(BigFloat x, BigFloat y) { + //TODO: Modify for correct fp functionality + Contract.Requires(x.ExponentSize == y.ExponentSize); + Contract.Requires(x.significandSize == y.significandSize); + BIM m1 = x.significand; + BIM e1 = x.Exponent; + BIM m2 = y.significand; + BIM e2 = y.Exponent; + m1 = m1 + two_n(x.significandSize + 1); //Add implicit bit + m2 = m2 + two_n(y.significandSize + 1); + if (e2 > e1) { + m1 = y.significand; + e1 = y.Exponent; + m2 = x.significand; + e2 = x.Exponent; + } + + while (e2 < e1) { + m2 = m2 / two; + e2 = e2 + one; + } + + return new BigFloat(false, e1, m1 + m2, x.significandSize, x.ExponentSize); + } + + [Pure] + public static BigFloat operator -(BigFloat x, BigFloat y) { + return x + y.Negate; + } + + [Pure] + public static BigFloat operator *(BigFloat x, BigFloat y) { + Contract.Requires(x.ExponentSize == y.ExponentSize); + Contract.Requires(x.significandSize == y.significandSize); + return new BigFloat(x.isNeg ^ y.isNeg, x.Exponent + y.Exponent, x.significand * y.significand, x.significandSize, x.ExponentSize); + } + + + //////////////////////////////////////////////////////////////////////////// + // Some basic comparison operations + + public bool IsSpecialType { + get { + if (value == "") + return false; + return (value.Equals("NaN") || value.Equals("+oo") || value.Equals("-oo") || value.Equals("zero") || value.Equals("-zero")); + } + } + + public bool IsPositive { + get { + return !IsNegative; + } + } + + public bool IsZero { + get { + return significand.Equals(BigNum.ZERO) && Exponent == BIM.Zero; + } + } + + [Pure] + public int CompareTo(BigFloat that) { + if (this.exponent > that.exponent) + return 1; + if (this.exponent < that.exponent) + return -1; + if (this.significand == that.significand) + return 0; + return this.significand > that.significand ? 1 : -1; + } + + [Pure] + public static bool operator ==(BigFloat x, BigFloat y) { + return x.CompareTo(y) == 0; + } + + [Pure] + public static bool operator !=(BigFloat x, BigFloat y) { + return x.CompareTo(y) != 0; + } + + [Pure] + public static bool operator <(BigFloat x, BigFloat y) { + return x.CompareTo(y) < 0; + } + + [Pure] + public static bool operator >(BigFloat x, BigFloat y) { + return x.CompareTo(y) > 0; + } + + [Pure] + public static bool operator <=(BigFloat x, BigFloat y) { + return x.CompareTo(y) <= 0; + } + + [Pure] + public static bool operator >=(BigFloat x, BigFloat y) { + return x.CompareTo(y) >= 0; + } + } +} |