//-----------------------------------------------------------------------------
//
// 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;
///
/// 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
///
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() != null);
return value=="" ? String.Format("{0}x2^{1}", significand.ToString(), Exponent.ToString()) : value;
}
////////////////////////////////////////////////////////////////////////////
// Conversion operations
///
/// 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
///
///
///
///
///
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);
}
///
/// 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
///
///
///
///
///
///
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).
///
/// 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.
///
/// The Floor (rounded towards negative infinity)
/// Ceiling (rounded towards positive infinity)
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() != 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;
}
}
}