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Diffstat (limited to 'Source/Basetypes/BigFloat.cs')
| -rw-r--r-- | Source/Basetypes/BigFloat.cs | 475 |
1 files changed, 475 insertions, 0 deletions
diff --git a/Source/Basetypes/BigFloat.cs b/Source/Basetypes/BigFloat.cs new file mode 100644 index 00000000..3c4cc40a --- /dev/null +++ b/Source/Basetypes/BigFloat.cs @@ -0,0 +1,475 @@ +//-----------------------------------------------------------------------------
+//
+// 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 BigNum significand; //Note that the significand arrangement matches standard fp arrangement (most significant bit is farthest left)
+ [Rep]
+ internal readonly int significandSize;
+ [Rep]
+ internal readonly BigNum 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 BigNum Significand {
+ get {
+ return significand;
+ }
+ }
+
+ public BigNum 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(int exponentSize, int significandSize) { return new BigFloat(false, BigNum.ZERO, BigNum.ZERO, exponentSize, significandSize); } //Does not include negative zero
+
+ private static readonly BigNum two = new BigNum(2);
+ private static readonly BigNum one = new BigNum(1);
+ private static BigNum two_n(int n) {
+ BigNum 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(), 8, 24);
+ }
+
+ public static BigFloat FromInt(int v, int exponentSize, int significandSize)
+ {
+ return new BigFloat(v.ToString(), exponentSize, significandSize);
+ }
+
+ public static BigFloat FromBigInt(BIM v) {
+ return new BigFloat(v.ToString(), 8, 24);
+ }
+
+ public static BigFloat FromBigInt(BIM v, int exponentSize, int significandSize)
+ {
+ return new BigFloat(v.ToString(), exponentSize, significandSize);
+ }
+
+ public static BigFloat FromBigDec(BigDec v)
+ {
+ return new BigFloat(v.ToDecimalString(), 8, 24);
+ }
+
+ public static BigFloat FromBigDec(BigDec v, int exponentSize, int significandSize)
+ {
+ return new BigFloat(v.ToDecimalString(), exponentSize, significandSize);
+ }
+
+ [Pure]
+ public static BigFloat FromString(String v, int exp, int sig) { //String must be
+ return new BigFloat(v, exp, sig);
+ }
+
+ public BigFloat(bool sign, BigNum exponent, BigNum significand, int exponentSize, int significandSize) {
+ this.exponentSize = exponentSize;
+ this.exponent = exponent;
+ this.significand = significand;
+ this.significandSize = significandSize+1;
+ this.isNeg = sign;
+ this.value = "";
+ }
+
+ public BigFloat(String value, int exponentSize, int significandSize) {
+ this.exponentSize = exponentSize;
+ this.significandSize = significandSize;
+ this.exponent = BigNum.ZERO;
+ this.significand = BigNum.ZERO;
+ this.value = value;
+ this.isNeg = value[0] == '-';
+ }
+
+ private BigNum maxsignificand()
+ {
+ BigNum 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(BigNum.FromString(value), BigNum.ZERO, exponentSize, significandSize);
+ return Round(i == 0 ? BigNum.ZERO : BigNum.FromString(value.Substring(0, i)), BigNum.FromString(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(BigNum value, BigNum dec_value, int exponentSize, int significandSize)
+ {
+ int exp = 0;
+ BigNum one = new BigNum(1);
+ BigNum ten = new BigNum(10);
+ BigNum dec_max = new BigNum(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 BigNum(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 BigNum(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 BigNum(0); //remove implicit bit
+ dec_max = new BigNum(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, BigNum.ZERO, BigNum.FromString(value.ToString()), exponentSize, significandSize); //Sign not actually checked...
+ }
+
+ // ``floor`` rounds towards negative infinity (like SMT-LIBv2's to_int).
+ /// <summary>
+ /// NOTE: THIS PROBABLY WON'T GIVE USEFUL OUTPUT!!!
+ /// 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 BigNum floor, out BigNum ceiling) {
+ //TODO: fix for fp functionality
+ BigNum n = Significand;
+ BigNum e = Exponent;
+ if (n.IsZero) {
+ floor = ceiling = n;
+ } else if (BigNum.ZERO <= e) {
+ // it's an integer
+ for (; BigNum.ZERO < e; e = e - one)
+ {
+ n = n * two;
+ }
+ floor = ceiling = n;
+ } else {
+ // it's a non-zero integer, so the ceiling is one more than the floor
+ for (; BigNum.ZERO < e && !n.IsZero; e = e + one)
+ {
+ n = n / two; // Division rounds towards negative infinity
+ }
+
+ if (!IsNegative) {
+ floor = n;
+ ceiling = n + one;
+ } else {
+ ceiling = n;
+ floor = n - one;
+ }
+ }
+ Debug.Assert(floor <= ceiling, "Invariant was not maintained");
+ }
+
+ [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);
+ BigNum m1 = x.significand;
+ BigNum e1 = x.Exponent;
+ BigNum m2 = y.significand;
+ BigNum 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 == BigNum.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;
+ }
+ }
+}
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