Esempio n. 1
0
 /// <summary>
 /// Multiplies two numbers and assigns the result to res.
 /// </summary>
 /// <param name="res">a pre-existing BigFloat to take the result</param>
 /// <param name="n1">the first number</param>
 /// <param name="n2">the second number</param>
 /// <returns>a handle to res</returns>
 public static BigFloat Mul(BigFloat res, BigFloat n1, BigFloat n2)
 {
     res.Assign(n1);
     res.Mul(n2);
     return res;
 }
Esempio n. 2
0
        /// <summary>
        /// Multiplication (this = this * n2)
        /// </summary>
        /// <param name="n2">The number to multiply this by</param>
        public void Mul(BigFloat n2)
        {
            if (SpecialValueMulTest(n2)) return;

            //Anything times 0 = 0
            if (n2.mantissa.IsZero())
            {
                mantissa.Assign(n2.mantissa);
                exponent = 0;
                return;
            }

            mantissa.MulHi(n2.mantissa);
            int shift = mantissa.Normalise();
            exponent = exponent + n2.exponent + 1 - shift;
        }
Esempio n. 3
0
        /// <summary>
        /// Division-based reciprocal, fastest for small precisions up to 15,000 bits.
        /// </summary>
        /// <returns>The reciprocal 1/this</returns>
        public BigFloat Reciprocal()
        {
            if (mantissa.Precision.NumBits >= 8192) return ReciprocalNewton();

            BigFloat reciprocal = new BigFloat(1u, mantissa.Precision);
            reciprocal.Div(this);
            return reciprocal;
        }
Esempio n. 4
0
        //******************** Mathematical Constants *******************

        /// <summary>
        /// Gets pi to the indicated precision
        /// </summary>
        /// <param name="precision">The precision to perform the calculation to</param>
        /// <returns>pi (the ratio of the area of a circle to its diameter)</returns>
        public static BigFloat GetPi(PrecisionSpec precision)
        {
            if (pi == null || precision.NumBits <= pi.mantissa.Precision.NumBits)
            {
                CalculatePi(precision.NumBits);
            }

            BigFloat ret = new BigFloat (precision);
            ret.Assign(pi);

            return ret;
        }
Esempio n. 5
0
        //******************** Arithmetic Functions ********************

        /// <summary>
        /// Addition (this = this + n2)
        /// </summary>
        /// <param name="n2">The number to add</param>
        public void Add(BigFloat n2)
        {
            if (SpecialValueAddTest(n2)) return;

            if (scratch.Precision.NumBits != n2.mantissa.Precision.NumBits)
            {
                scratch = new BigInt(n2.mantissa.Precision);
            }

            if (exponent <= n2.exponent)
            {
                int diff = n2.exponent - exponent;
                exponent = n2.exponent;

                if (diff != 0)
                {
                    mantissa.RSH(diff);
                }

                uint carry = mantissa.Add(n2.mantissa);

                if (carry != 0)
                {
                    mantissa.RSH(1);
                    mantissa.SetBit(mantissa.Precision.NumBits - 1);
                    exponent++;
                }

                exponent -= mantissa.Normalise();
            }
            else
            {
                int diff = exponent - n2.exponent;

                scratch.Assign(n2.mantissa);
                scratch.RSH(diff);

                uint carry = scratch.Add(mantissa);

                if (carry != 0)
                {
                    scratch.RSH(1);
                    scratch.SetBit(mantissa.Precision.NumBits - 1);
                    exponent++;
                }

                mantissa.Assign(scratch);

                exponent -= mantissa.Normalise();
            }
        }
Esempio n. 6
0
        /// <summary>
        /// Calculates the odd reciprocals of the natural numbers (for atan series)
        /// </summary>
        /// <param name="numBits"></param>
        /// <param name="terms"></param>
        private static void CalculateReciprocals(int numBits, int terms)
        {
            int bits = numBits + 32;
            PrecisionSpec extendedPres = new PrecisionSpec(bits, PrecisionSpec.BaseType.BIN);
            PrecisionSpec normalPres = new PrecisionSpec(numBits, PrecisionSpec.BaseType.BIN);

            System.Collections.Generic.List<BigFloat> list = new System.Collections.Generic.List<BigFloat>(terms);

            for (int i = 0; i < terms; i++)
            {
                BigFloat term = new BigFloat(i*2 + 1, extendedPres);
                list.Add(new BigFloat(term.Reciprocal(), normalPres));
            }

            reciprocals = list.ToArray();
        }
Esempio n. 7
0
 /// <summary>
 /// Copy Constructor - constructs a new BigFloat with the specified precision, copying the old one.
 /// 
 /// The value is rounded towards zero in the case where precision is decreased. The Round() function
 /// should be used beforehand if a correctly rounded result is required.
 /// </summary>
 /// <param name="value"></param>
 /// <param name="mantissaPrec"></param>
 public BigFloat(BigFloat value, PrecisionSpec mantissaPrec)
 {
     Init(mantissaPrec);
     exponent = value.exponent;
     if (mantissa.AssignHigh(value.mantissa)) exponent++;
 }
Esempio n. 8
0
        private bool SpecialValueDivTest(BigFloat n2)
        {
            if (IsSpecialValue || n2.IsSpecialValue)
            {
                SpecialValueType s1 = SpecialValue;
                SpecialValueType s2 = n2.SpecialValue;

                if (s1 == SpecialValueType.NAN) return true;
                if (s2 == SpecialValueType.NAN)
                {
                    //Set NaN and return.
                    SetNaN();
                    return true;
                }

                if ((s1 == SpecialValueType.INF_PLUS || s1 == SpecialValueType.INF_MINUS))
                {
                    if (s2 == SpecialValueType.INF_PLUS || s2 == SpecialValueType.INF_MINUS)
                    {
                        //Set NaN and return.
                        SetNaN();
                        return true;
                    }

                    if (n2.Sign)
                    {
                        if (s1 == SpecialValueType.INF_PLUS)
                        {
                            SetInfMinus();
                            return true;
                        }

                        SetInfPlus();
                        return true;
                    }

                    //Keep inf
                    return true;
                }

                if (s2 == SpecialValueType.ZERO)
                {
                    if (s1 == SpecialValueType.ZERO)
                    {
                        SetNaN();
                        return true;
                    }

                    if (Sign)
                    {
                        SetInfMinus();
                        return true;
                    }

                    SetInfPlus();
                    return true;
                }
            }

            return false;
        }
Esempio n. 9
0
        /// <summary>
        /// The binary logarithm, log2(x) - for precisions above 1000 bits, use Log() and convert the base.
        /// </summary>
        private void Log2()
        {
            if (scratch.Precision.NumBits != mantissa.Precision.NumBits)
            {
                scratch = new BigInt(mantissa.Precision);
            }

            int bits = mantissa.Precision.NumBits;
            BigFloat temp = new BigFloat(this);
            BigFloat result = new BigFloat(exponent, mantissa.Precision);
            BigFloat pow2 = new BigFloat(1, mantissa.Precision);
            temp.exponent = 0;
            int bitsCalculated = 0;

            while (bitsCalculated < bits)
            {
                int i;
                for (i = 0; (temp.exponent == 0); i++)
                {
                    temp.mantissa.SquareHiFast(scratch);
                    int shift = temp.mantissa.Normalise();
                    temp.exponent += 1 - shift;
                    if (i + bitsCalculated >= bits) break;
                }

                pow2.MulPow2(-i);
                result.Add(pow2);
                temp.exponent = 0;
                bitsCalculated += i;
            }

            this.Assign(result);
        }
Esempio n. 10
0
        private bool SpecialValueAddTest(BigFloat n2)
        {
            if (IsSpecialValue || n2.IsSpecialValue)
            {
                SpecialValueType s1 = SpecialValue;
                SpecialValueType s2 = n2.SpecialValue;

                if (s1 == SpecialValueType.NAN) return true;
                if (s2 == SpecialValueType.NAN)
                {
                    //Set NaN and return.
                    SetNaN();
                    return true;
                }

                if (s1 == SpecialValueType.INF_PLUS)
                {
                    //INF+ + INF- = NAN
                    if (s2 == SpecialValueType.INF_MINUS)
                    {
                        SetNaN();
                        return true;
                    }

                    return true;
                }

                if (s1 == SpecialValueType.INF_MINUS)
                {
                    //INF+ + INF- = NAN
                    if (s2 == SpecialValueType.INF_PLUS)
                    {
                        SetNaN();
                        return true;
                    }

                    return true;
                }

                if (s2 == SpecialValueType.ZERO)
                {
                    return true;
                }

                if (s1 == SpecialValueType.ZERO)
                {
                    Assign(n2);
                    return true;
                }
            }

            return false;
        }
Esempio n. 11
0
        private bool SpecialValueMulTest(BigFloat n2)
        {
            if (IsSpecialValue || n2.IsSpecialValue)
            {
                SpecialValueType s1 = SpecialValue;
                SpecialValueType s2 = n2.SpecialValue;

                if (s1 == SpecialValueType.NAN) return true;
                if (s2 == SpecialValueType.NAN)
                {
                    //Set NaN and return.
                    SetNaN();
                    return true;
                }

                if (s1 == SpecialValueType.INF_PLUS)
                {
                    //Inf+ * Inf- = Inf-
                    if (s2 == SpecialValueType.INF_MINUS)
                    {
                        Assign(n2);
                        return true;
                    }

                    //Inf+ * 0 = NaN
                    if (s2 == SpecialValueType.ZERO)
                    {
                        //Set NaN and return.
                        SetNaN();
                        return true;
                    }

                    return true;
                }

                if (s1 == SpecialValueType.INF_MINUS)
                {
                    //Inf- * Inf- = Inf+
                    if (s2 == SpecialValueType.INF_MINUS)
                    {
                        Sign = false;
                        return true;
                    }

                    //Inf- * 0 = NaN
                    if (s2 == SpecialValueType.ZERO)
                    {
                        //Set NaN and return.
                        SetNaN();
                        return true;
                    }

                    return true;
                }

                if (s2 == SpecialValueType.ZERO)
                {
                    SetZero();
                    return true;
                }

                if (s1 == SpecialValueType.ZERO)
                {
                    return true;
                }
            }

            return false;
        }
Esempio n. 12
0
        /// <summary>
        /// Returns a base-10 string representing the number.
        /// 
        /// Note: This is inefficient and possibly inaccurate. Please use with enough
        /// rounding digits (set using the RoundingDigits property) to ensure accuracy
        /// </summary>
        public override string ToString()
        {
            if (IsSpecialValue)
            {
                SpecialValueType s = SpecialValue;
                if (s == SpecialValueType.ZERO)
                {
                    return String.Format("0{0}0", System.Globalization.CultureInfo.CurrentCulture.NumberFormat.NumberDecimalSeparator);
                }
                else if (s == SpecialValueType.INF_PLUS)
                {
                    return System.Globalization.CultureInfo.CurrentCulture.NumberFormat.PositiveInfinitySymbol;
                }
                else if (s == SpecialValueType.INF_MINUS)
                {
                    return System.Globalization.CultureInfo.CurrentCulture.NumberFormat.NegativeInfinitySymbol;
                }
                else if (s == SpecialValueType.NAN)
                {
                    return System.Globalization.CultureInfo.CurrentCulture.NumberFormat.NaNSymbol;
                }
                else
                {
                    return "Unrecognised special type";
                }
            }

            if (scratch.Precision.NumBits != mantissa.Precision.NumBits)
            {
                scratch = new BigInt(mantissa.Precision);
            }

            //The mantissa expresses 1.xxxxxxxxxxx
            //The highest possible value for the mantissa without the implicit 1. is 0.9999999...
            scratch.Assign(mantissa);
            //scratch.Round(3);
            scratch.Sign = false;
            BigInt denom = new BigInt("0", mantissa.Precision);
            denom.SetBit(mantissa.Precision.NumBits - 1);

            bool useExponentialNotation = false;
            int halfBits = mantissa.Precision.NumBits / 2;
            if (halfBits > 60) halfBits = 60;
            int precDec = 10;

            if (exponent > 0)
            {
                if (exponent < halfBits)
                {
                    denom.RSH(exponent);
                }
                else
                {
                    useExponentialNotation = true;
                }
            }
            else if (exponent < 0)
            {
                int shift = -(exponent);
                if (shift < precDec)
                {
                    scratch.RSH(shift);
                }
                else
                {
                    useExponentialNotation = true;
                }
            }

            string output;

            if (useExponentialNotation)
            {
                int absExponent = exponent;
                if (absExponent < 0) absExponent = -absExponent;
                int powerOf10 = (int)((double)absExponent * Math.Log10(2.0));

                //Use 1 extra digit of precision (this is actually 32 bits more, nb)
                BigFloat thisFloat = new BigFloat(this, new PrecisionSpec(mantissa.Precision.NumBits + 1, PrecisionSpec.BaseType.BIN));
                thisFloat.mantissa.Sign = false;

                //Multiplicative correction factor to bring number into range.
                BigFloat one = new BigFloat(1, new PrecisionSpec(mantissa.Precision.NumBits + 1, PrecisionSpec.BaseType.BIN));
                BigFloat ten = new BigFloat(10, new PrecisionSpec(mantissa.Precision.NumBits + 1, PrecisionSpec.BaseType.BIN));
                BigFloat tenRCP = ten.Reciprocal();

                //Accumulator for the power of 10 calculation.
                BigFloat acc = new BigFloat(1, new PrecisionSpec(mantissa.Precision.NumBits + 1, PrecisionSpec.BaseType.BIN));

                BigFloat tenToUse;

                if (exponent > 0)
                {
                    tenToUse = new BigFloat(tenRCP, new PrecisionSpec(mantissa.Precision.NumBits + 1, PrecisionSpec.BaseType.BIN));
                }
                else
                {
                    tenToUse = new BigFloat(ten, new PrecisionSpec(mantissa.Precision.NumBits + 1, PrecisionSpec.BaseType.BIN));
                }

                BigFloat tenToPower = new BigFloat(1, new PrecisionSpec(mantissa.Precision.NumBits + 1, PrecisionSpec.BaseType.BIN));

                int powerTemp = powerOf10;

                //Fast power function
                while (powerTemp != 0)
                {
                    tenToPower.Mul(tenToUse);
                    tenToUse.Assign(tenToPower);

                    if ((powerTemp & 1) != 0)
                    {
                        acc.Mul(tenToPower);
                    }

                    powerTemp >>= 1;
                }

                thisFloat.Mul(acc);

                //If we are out of range, correct.           
                if (thisFloat.GreaterThan(ten))
                {
                    thisFloat.Mul(tenRCP);
                    if (exponent > 0)
                    {
                        powerOf10++;
                    }
                    else
                    {
                        powerOf10--;
                    }
                }
                else if (thisFloat.LessThan(one))
                {
                    thisFloat.Mul(ten);
                    if (exponent > 0)
                    {
                        powerOf10--;
                    }
                    else
                    {
                        powerOf10++;
                    }
                }

                //Restore the precision and the sign.
                BigFloat printable = new BigFloat(thisFloat, mantissa.Precision);
                printable.mantissa.Sign = mantissa.Sign;
                output = printable.ToString();

                if (exponent < 0) powerOf10 = -powerOf10;

                output = String.Format("{0}E{1}", output, powerOf10);
            }
            else
            {
                BigInt bigDigit = BigInt.Div(scratch, denom);
                bigDigit.Sign = false;
                scratch.Sub(BigInt.Mul(denom, bigDigit));

                if (mantissa.Sign)
                {
                    output = String.Format("-{0}.", bigDigit);
                }
                else
                {
                    output = String.Format("{0}.", bigDigit);
                }

                denom = BigInt.Div(denom, 10u);

                while (!denom.IsZero())
                {
                    uint digit = (uint)BigInt.Div(scratch, denom);
                    if (digit == 10) digit--;
                    scratch.Sub(BigInt.Mul(denom, digit));
                    output = String.Format("{0}{1}", output, digit);
                    denom = BigInt.Div(denom, 10u);
                }

                output = RoundString(output, RoundingDigits);
            }

            return output;
        }
Esempio n. 13
0
        //************************** Conversions *************************

        /// <summary>
        /// Converts a BigFloat to an BigInt with the specified precision
        /// </summary>
        /// <param name="n1">The number to convert</param>
        /// <param name="precision">The precision to convert it with</param>
        /// <param name="round">Do we round the number if we are truncating the mantissa?</param>
        /// <returns></returns>
        public static BigInt ConvertToInt(BigFloat n1, PrecisionSpec precision, bool round)
        {
            BigInt ret = new BigInt(precision);

            int numBits = n1.mantissa.Precision.NumBits;
            int shift = numBits - (n1.exponent + 1);

            BigFloat copy = new BigFloat(n1);
            bool inc = false;

            //Rounding
            if (copy.mantissa.Precision.NumBits > ret.Precision.NumBits)
            {
                inc = true;

                for (int i = copy.exponent + 1; i <= ret.Precision.NumBits; i++)
                {
                    if (copy.mantissa.GetBitFromTop(i) == 0)
                    {
                        inc = false;
                        break;
                    }
                }
            }

            if (shift > 0)
            {
                copy.mantissa.RSH(shift);
            }
            else if (shift < 0)
            {
                copy.mantissa.LSH(-shift);
            }

            ret.Assign(copy.mantissa);

            if (inc) ret.Increment();

            return ret;
        }
Esempio n. 14
0
 /// <summary>
 /// Divides two numbers and assigns the result to res.
 /// </summary>
 /// <param name="res">a pre-existing BigFloat to take the result</param>
 /// <param name="n1">the first number</param>
 /// <param name="n2">the second number</param>
 /// <returns>a handle to res</returns>
 public static BigFloat Div(BigFloat res, BigFloat n1, BigFloat n2)
 {
     res.Assign(n1);
     res.Div(n2);
     return res;
 }
Esempio n. 15
0
        private static void CalculateEOnly(int numBits)
        {
            PrecisionSpec extendedPrecision = new PrecisionSpec(numBits + 1, PrecisionSpec.BaseType.BIN);
            PrecisionSpec normalPrecision = new PrecisionSpec(numBits, PrecisionSpec.BaseType.BIN);

            int iExponent = (int)(Math.Sqrt(numBits));

            BigFloat factorial = new BigFloat(1, extendedPrecision);
            BigFloat constant = new BigFloat(1, extendedPrecision);
            constant.exponent -= iExponent;
            BigFloat numerator = new BigFloat(constant);
            BigFloat reciprocal;

            //Calculate the 2^iExponent th root of e
            BigFloat e = new BigFloat(1, extendedPrecision);

            int i;
            for (i = 1; i < Int32.MaxValue; i++)
            {
                BigFloat number = new BigFloat(i, extendedPrecision);
                factorial.Mul(number);
                reciprocal = factorial.Reciprocal();
                reciprocal.Mul(numerator);

                if (-reciprocal.exponent > numBits) break;

                e.Add(reciprocal);
                numerator.Mul(constant);
                System.GC.Collect();
            }

            for (i = 0; i < iExponent; i++)
            {
                numerator.Assign(e);
                e.Mul(numerator);
            }

            //Set the cached static values.
            eCache = new BigFloat(e, normalPrecision);
            eRCPCache = new BigFloat(e.Reciprocal(), normalPrecision);
        }
Esempio n. 16
0
        /// <summary>
        /// Tried the newton method for logs, but the exponential function is too slow to do it.
        /// </summary>
        private void LogNewton()
        {
            if (mantissa.IsZero() || mantissa.Sign)
            {
                return;
            }

            //Compute ln2.
            if (ln2cache == null || mantissa.Precision.NumBits > ln2cache.mantissa.Precision.NumBits)
            {
                CalculateLog2(mantissa.Precision.NumBits);
            }

            int numBits = mantissa.Precision.NumBits;

            //Use inverse exp function with Newton's method.
            BigFloat xn = new BigFloat(this);
            BigFloat oldExponent = new BigFloat(xn.exponent, mantissa.Precision);
            xn.exponent = 0;
            this.exponent = 0;
            //Hack to subtract 1
            xn.mantissa.ClearBit(numBits - 1);
            //x0 = (x - 1) * log2 - this is a straight line fit between log(1) = 0 and log(2) = ln2
            xn.Mul(ln2cache);
            //x0 = (x - 1) * log2 + C - this corrects for minimum error over the range.
            xn.Add(logNewtonConstant);
            BigFloat term = new BigFloat(mantissa.Precision);
            BigFloat one = new BigFloat(1, mantissa.Precision);

            int precision = 32;
            int normalPrecision = mantissa.Precision.NumBits;

            int iterations = 0;

            while (true)
            {
                term.Assign(xn);
                term.mantissa.Sign = true;
                term.Exp(precision);
                term.Mul(this);
                term.Sub(one);

                iterations++;
                if (term.exponent < -((precision >> 1) - 4))
                {
                    if (precision == normalPrecision)
                    {
                        if (term.exponent < -(precision - 4)) break;
                    }
                    else
                    {
                        precision = precision << 1;
                        if (precision > normalPrecision) precision = normalPrecision;
                    }
                }

                xn.Add(term);
            }

            //log(2^n*s) = log(2^n) + log(s) = nlog(2) + log(s)
            term.Assign(ln2cache);
            term.Mul(oldExponent);

            this.Assign(xn);
            this.Add(term);
        }
Esempio n. 17
0
        /// <summary>
        /// Uses the Gauss-Legendre formula for pi
        /// Taken from http://en.wikipedia.org/wiki/Gauss%E2%80%93Legendre_algorithm
        /// </summary>
        /// <param name="numBits"></param>
        private static void CalculatePi(int numBits)
        {
            int bits = numBits + 32;
            //Precision extend taken out.
            PrecisionSpec normalPres = new PrecisionSpec(numBits, PrecisionSpec.BaseType.BIN);
            PrecisionSpec extendedPres = new PrecisionSpec(bits, PrecisionSpec.BaseType.BIN);

            if (scratch.Precision.NumBits != bits)
            {
                scratch = new BigInt(extendedPres);
            }

            //a0 = 1
            BigFloat an = new BigFloat(1, extendedPres);

            //b0 = 1/sqrt(2)
            BigFloat bn = new BigFloat(2, extendedPres);
            bn.Sqrt();
            bn.exponent--;

            //to = 1/4
            BigFloat tn = new BigFloat(1, extendedPres);
            tn.exponent -= 2;

            int pn = 0;

            BigFloat anTemp = new BigFloat(extendedPres);

            int iteration = 0;
            int cutoffBits = numBits >> 5;

            for (iteration = 0; ; iteration++)
            {
                //Save a(n)
                anTemp.Assign(an);

                //Calculate new an
                an.Add(bn);
                an.exponent--;

                //Calculate new bn
                bn.Mul(anTemp);
                bn.Sqrt();

                //Calculate new tn
                anTemp.Sub(an);
                anTemp.mantissa.SquareHiFast(scratch);
                anTemp.exponent += anTemp.exponent + pn + 1 - anTemp.mantissa.Normalise();
                tn.Sub(anTemp);

                anTemp.Assign(an);
                anTemp.Sub(bn);

                if (anTemp.exponent < -(bits - cutoffBits)) break;

                //New pn
                pn++;
            }

            an.Add(bn);
            an.mantissa.SquareHiFast(scratch);
            an.exponent += an.exponent + 1 - an.mantissa.Normalise();
            tn.exponent += 2;
            an.Div(tn);

            pi = new BigFloat(an, normalPres);
            piBy2 = new BigFloat(pi);
            piBy2.exponent--;
            twoPi = new BigFloat(pi, normalPres);
            twoPi.exponent++;
            piRecip = new BigFloat(an.Reciprocal(), normalPres);
            twoPiRecip = new BigFloat(piRecip);
            twoPiRecip.exponent--;
            //1/3 is going to be useful for sin.
            threeRecip = new BigFloat((new BigFloat(3, extendedPres)).Reciprocal(), normalPres);
        }
Esempio n. 18
0
        /// <summary>
        /// Log(x) implemented as an Arithmetic-Geometric Mean. Fast for high precisions.
        /// </summary>
        private void LogAGM1()
        {
            if (mantissa.IsZero() || mantissa.Sign)
            {
                return;
            }

            //Compute ln2.
            if (ln2cache == null || mantissa.Precision.NumBits > ln2cache.mantissa.Precision.NumBits)
            {
                CalculateLog2(mantissa.Precision.NumBits);
            }

            //Compute ln(x) using AGM formula

            //1. Re-write the input as 2^n * (0.5 <= x < 1)
            int power2 = exponent + 1;
            exponent = -1;

            //BigFloat res = new BigFloat(firstAGMcache);
            BigFloat a0 = new BigFloat(1, mantissa.Precision);
            BigFloat b0 = new BigFloat(pow10cache);
            b0.Mul(this);

            BigFloat r = R(a0, b0);

            this.Assign(firstAGMcache);
            this.Sub(r);

            a0.Assign(ln2cache);
            a0.Mul(new BigFloat(power2, mantissa.Precision));
            this.Add(a0);
        }
Esempio n. 19
0
 /// <summary>
 /// Copy constructor
 /// </summary>
 /// <param name="value"></param>
 public BigFloat(BigFloat value)
 {
     Init(value.mantissa.Precision);
     exponent = value.exponent;
     mantissa.Assign(value.mantissa);
 }
Esempio n. 20
0
        private void Exp(int numBits)
        {
            if (IsSpecialValue)
            {
                if (SpecialValue == SpecialValueType.ZERO)
                {
                    //e^0 = 1
                    exponent = 0;
                    mantissa.SetHighDigit(0x80000000);
                }
                else if (SpecialValue == SpecialValueType.INF_MINUS)
                {
                    //e^-inf = 0
                    SetZero();
                }

                return;
            }

            PrecisionSpec prec = new PrecisionSpec(numBits, PrecisionSpec.BaseType.BIN);
            numBits = prec.NumBits;

            if (scratch.Precision.NumBits != prec.NumBits)
            {
                scratch = new BigInt(prec);
            }

            if (inverseFactorialCache == null || invFactorialCutoff < numBits)
            {
                CalculateFactorials(numBits);
            }

            //let x = 1 * 'this'.mantissa (i.e. 1 <= x < 2)
            //exp(2^n * x) = e^(2^n * x) = (e^x)^2n = exp(x)^2n

            int oldExponent = 0;

            if (exponent > -4)
            {
                oldExponent = exponent + 4;
                exponent = -4;
            }

            BigFloat thisSave = new BigFloat(this, prec);
            BigFloat temp = new BigFloat(1, prec);
            BigFloat temp2 = new BigFloat(this, prec);
            BigFloat res = new BigFloat(1, prec);
            int length = inverseFactorialCache.Length;

            int iterations;
            for (int i = 1; i < length; i++)
            {
                //temp = x^i
                temp.Mul(thisSave);
                temp2.Assign(inverseFactorialCache[i]);
                temp2.Mul(temp);

                if (temp2.exponent < -(numBits + 4)) { iterations = i; break; }

                res.Add(temp2);
            }

            //res = exp(x)
            //Now... x^(2^n) = (x^2)^(2^(n - 1))
            for (int i = 0; i < oldExponent; i++)
            {
                res.mantissa.SquareHiFast(scratch);
                int shift = res.mantissa.Normalise();
                res.exponent = res.exponent << 1;
                res.exponent += 1 - shift;
            }

            //Deal with +/- inf
            if (res.exponent == Int32.MaxValue)
            {
                res.mantissa.Zero();
            }

            Assign(res);
        }
Esempio n. 21
0
        /// <summary>
        /// Constructs a BigFloat from a string
        /// </summary>
        /// <param name="value"></param>
        /// <param name="mantissaPrec"></param>
        public BigFloat(string value, PrecisionSpec mantissaPrec)
        {
            Init(mantissaPrec);

            PrecisionSpec extendedPres = new PrecisionSpec(mantissa.Precision.NumBits + 1, PrecisionSpec.BaseType.BIN);
            BigFloat ten = new BigFloat(10, extendedPres);
            BigFloat iPart = new BigFloat(extendedPres);
            BigFloat fPart = new BigFloat(extendedPres);
            BigFloat tenRCP = ten.Reciprocal();

            if (value.Contains(System.Globalization.CultureInfo.CurrentCulture.NumberFormat.NaNSymbol))
            {
                SetNaN();
                return;
            }
            else if (value.Contains(System.Globalization.CultureInfo.CurrentCulture.NumberFormat.PositiveInfinitySymbol))
            {
                SetInfPlus();
                return;
            }
            else if (value.Contains(System.Globalization.CultureInfo.CurrentCulture.NumberFormat.NegativeInfinitySymbol))
            {
                SetInfMinus();
                return;
            }

            string decimalpoint = System.Globalization.CultureInfo.CurrentCulture.NumberFormat.NumberDecimalSeparator;

            char[] digitChars = { '0', '1', '2', '3', '4', '5', '6', '7', '8', '9', ',', '.' };

            //Read in the integer part up the the decimal point.
            bool sign = false;
            value = value.Trim();

            int i = 0;

            if (value.Length > i && value[i] == '-')
            {
                sign = true;
                i++;
            }

            if (value.Length > i && value[i] == '+')
            {
                i++;
            }

            for ( ; i < value.Length; i++)
            {
                //break on decimal point
                if (value[i] == decimalpoint[0]) break;

                int digit = Array.IndexOf(digitChars, value[i]);
                if (digit < 0) break;

                //Ignore place separators (assumed either , or .)
                if (digit > 9) continue;

                if (i > 0) iPart.Mul(ten);
                iPart.Add(new BigFloat(digit, extendedPres));
            }

            //If we've run out of characters, assign everything and return
            if (i == value.Length)
            {
                iPart.mantissa.Sign = sign;
                exponent = iPart.exponent;
                if (mantissa.AssignHigh(iPart.mantissa)) exponent++;
                return;
            }

            //Assign the characters after the decimal point to fPart
            if (value[i] == '.' && i < value.Length - 1)
            {
                BigFloat RecipToUse = new BigFloat(tenRCP);

                for (i++; i < value.Length; i++)
                {
                    int digit = Array.IndexOf(digitChars, value[i]);
                    if (digit < 0) break;
                    BigFloat temp = new BigFloat(digit, extendedPres);
                    temp.Mul(RecipToUse);
                    RecipToUse.Mul(tenRCP);
                    fPart.Add(temp);
                }
            }

            //If we're run out of characters, add fPart and iPart and return
            if (i == value.Length)
            {
                iPart.Add(fPart);
                iPart.mantissa.Sign = sign;
                exponent = iPart.exponent;
                if (mantissa.AssignHigh(iPart.mantissa)) exponent++;
                return;
            }

            if (value[i] == '+' || value[i] == '-') i++;

            if (i == value.Length)
            {
                iPart.Add(fPart);
                iPart.mantissa.Sign = sign;
                exponent = iPart.exponent;
                if (mantissa.AssignHigh(iPart.mantissa)) exponent++;
                return;
            }

            //Look for exponential notation.
            if ((value[i] == 'e' || value[i] == 'E') && i < value.Length - 1)
            {
                //Convert the exponent to an int.
                int exp;

                try
                {
                    exp = System.Convert.ToInt32(new string(value.ToCharArray(i + 1, value.Length - (i + 1))));
                }
                catch (Exception)
                {
                    iPart.Add(fPart);
                    iPart.mantissa.Sign = sign;
                    exponent = iPart.exponent;
                    if (mantissa.AssignHigh(iPart.mantissa)) exponent++;
                    return;
                }

                //Raise or lower 10 to the power of the exponent
                BigFloat acc = new BigFloat(1, extendedPres);
                BigFloat temp = new BigFloat(1, extendedPres);

                int powerTemp = exp;

                BigFloat multiplierToUse;

                if (exp < 0)
                {
                    multiplierToUse = new BigFloat(tenRCP);
                    powerTemp = -exp;
                }
                else
                {
                    multiplierToUse = new BigFloat(ten);
                }

                //Fast power function
                while (powerTemp != 0)
                {
                    temp.Mul(multiplierToUse);
                    multiplierToUse.Assign(temp);

                    if ((powerTemp & 1) != 0)
                    {
                        acc.Mul(temp);
                    }

                    powerTemp >>= 1;
                }

                iPart.Add(fPart);
                iPart.Mul(acc);
                iPart.mantissa.Sign = sign;
                exponent = iPart.exponent;
                if (mantissa.AssignHigh(iPart.mantissa)) exponent++;

                return;
            }

            iPart.Add(fPart);
            iPart.mantissa.Sign = sign;
            exponent = iPart.exponent;
            if (mantissa.AssignHigh(iPart.mantissa)) exponent++;

        }
Esempio n. 22
0
        /// <summary>
        /// Calculates ln(2) and returns -10^(n/2 + a bit) for reuse, using the AGM method as described in
        /// http://lacim.uqam.ca/~plouffe/articles/log2.pdf
        /// </summary>
        /// <param name="numBits"></param>
        /// <returns></returns>
        private static void CalculateLog2(int numBits)
        {
            //Use the AGM method formula to get log2 to N digits.
            //R(a0, b0) = 1 / (1 - Sum(2^-n*(an^2 - bn^2)))
            //log(1/2) = R(1, 10^-n) - R(1, 10^-n/2)
            PrecisionSpec normalPres = new PrecisionSpec(numBits, PrecisionSpec.BaseType.BIN);
            PrecisionSpec extendedPres = new PrecisionSpec(numBits + 1, PrecisionSpec.BaseType.BIN);
            BigFloat a0 = new BigFloat(1, extendedPres);
            BigFloat b0 = TenPow(-(int)((double)((numBits >> 1) + 2) * 0.302), extendedPres);
            BigFloat pow10saved = new BigFloat(b0);
            BigFloat firstAGMcacheSaved = new BigFloat(extendedPres);

            //save power of 10 (in normal precision)
            pow10cache = new BigFloat(b0, normalPres);

            ln2cache = R(a0, b0);

            //save the first half of the log calculation
            firstAGMcache = new BigFloat(ln2cache, normalPres);
            firstAGMcacheSaved.Assign(ln2cache);

            b0.MulPow2(-1);
            ln2cache.Sub(R(a0, b0));

            //Convert to log(2)
            ln2cache.mantissa.Sign = false;

            //Save magic constant for newton log
            //First guess in range 1 <= x < 2 is x0 = ln2 * (x - 1) + C
            logNewtonConstant = new BigFloat(ln2cache);
            logNewtonConstant.Mul(new BigFloat(3, extendedPres));
            logNewtonConstant.exponent--;
            logNewtonConstant.Sub(new BigFloat(1, extendedPres));
            logNewtonConstant = new BigFloat(logNewtonConstant, normalPres);

            //Save the inverse.
            log2ecache = new BigFloat(ln2cache);
            log2ecache = new BigFloat(log2ecache.Reciprocal(), normalPres);

            //Now cache log10
            //Because the log functions call this function to the precision to which they
            //are called, we cannot call them without causing an infinite loop, so we need
            //to inline the code.
            log10recip = new BigFloat(10, extendedPres);

            {
                int power2 = log10recip.exponent + 1;
                log10recip.exponent = -1;

                //BigFloat res = new BigFloat(firstAGMcache);
                BigFloat ax = new BigFloat(1, extendedPres);
                BigFloat bx = new BigFloat(pow10saved);
                bx.Mul(log10recip);

                BigFloat r = R(ax, bx);

                log10recip.Assign(firstAGMcacheSaved);
                log10recip.Sub(r);

                ax.Assign(ln2cache);
                ax.Mul(new BigFloat(power2, log10recip.mantissa.Precision));
                log10recip.Add(ax);
            }

            log10recip = log10recip.Reciprocal();
            log10recip = new BigFloat(log10recip, normalPres);


            //Trim to n bits
            ln2cache = new BigFloat(ln2cache, normalPres);
        }
Esempio n. 23
0
        /// <summary>
        /// Get e to the indicated precision
        /// </summary>
        /// <param name="precision">The preicision to perform the calculation to</param>
        /// <returns>e (the number for which the d/dx(e^x) = e^x)</returns>
        public static BigFloat GetE(PrecisionSpec precision)
        {
            if (eCache == null || eCache.mantissa.Precision.NumBits < precision.NumBits)
            {
                CalculateEOnly(precision.NumBits);
                //CalculateFactorials(precision.NumBits);
            }

            BigFloat ret = new BigFloat(precision);
            ret.Assign(eCache);

            return ret;
        }
Esempio n. 24
0
        private static BigFloat TenPow(int power, PrecisionSpec precision)
        {
            BigFloat acc = new BigFloat(1, precision);
            BigFloat temp = new BigFloat(1, precision);

            int powerTemp = power;

            BigFloat multiplierToUse = new BigFloat(10, precision);

            if (power < 0)
            {
                multiplierToUse = multiplierToUse.Reciprocal();
                powerTemp = -power;
            }

            //Fast power function
            while (powerTemp != 0)
            {
                temp.Mul(multiplierToUse);
                multiplierToUse.Assign(temp);

                if ((powerTemp & 1) != 0)
                {
                    acc.Mul(temp);
                }

                powerTemp >>= 1;
            }

            return acc;
        }
Esempio n. 25
0
 /// <summary>
 /// Subtraction (this = this - n2)
 /// </summary>
 /// <param name="n2">The number to subtract from this</param>
 public void Sub(BigFloat n2)
 {
     n2.mantissa.Sign = !n2.mantissa.Sign;
     Add(n2);
     n2.mantissa.Sign = !n2.mantissa.Sign;
 }
Esempio n. 26
0
        private static BigFloat R(BigFloat a0, BigFloat b0)
        {
            //Precision extend taken out.
            int bits = a0.mantissa.Precision.NumBits;
            PrecisionSpec extendedPres = new PrecisionSpec(bits, PrecisionSpec.BaseType.BIN);
            BigFloat an = new BigFloat(a0, extendedPres);
            BigFloat bn = new BigFloat(b0, extendedPres);
            BigFloat sum = new BigFloat(extendedPres);
            BigFloat term = new BigFloat(extendedPres);
            BigFloat temp1 = new BigFloat(extendedPres);
            BigFloat one = new BigFloat(1, extendedPres);

            int iteration = 0;

            for (iteration = 0; ; iteration++)
            {
                //Get the sum term for this iteration.
                term.Assign(an);
                term.Mul(an);
                temp1.Assign(bn);
                temp1.Mul(bn);
                //term = an^2 - bn^2
                term.Sub(temp1);
                //term = 2^(n-1) * (an^2 - bn^2)
                term.exponent += iteration - 1;
                sum.Add(term);

                if (term.exponent < -(bits - 8)) break;

                //Calculate the new AGM estimates.
                temp1.Assign(an);
                an.Add(bn);
                //a(n+1) = (an + bn) / 2
                an.MulPow2(-1);

                //b(n+1) = sqrt(an*bn)
                bn.Mul(temp1);
                bn.Sqrt();
            }

            one.Sub(sum);
            one = one.Reciprocal();
            return new BigFloat(one, a0.mantissa.Precision);
        }
Esempio n. 27
0
        /// <summary>
        /// Division (this = this / n2)
        /// </summary>
        /// <param name="n2">The number to divide this by</param>
        public void Div(BigFloat n2)
        {
            if (SpecialValueDivTest(n2)) return;

            if (mantissa.Precision.NumBits >= 8192)
            {
                BigFloat rcp = n2.Reciprocal();
                Mul(rcp);
            }
            else
            {
                int shift = mantissa.DivAndShift(n2.mantissa);
                exponent = exponent - (n2.exponent + shift);
            }
        }
Esempio n. 28
0
        private static void CalculateFactorials(int numBits)
        {
            System.Collections.Generic.List<BigFloat> list = new System.Collections.Generic.List<BigFloat>(64);
            System.Collections.Generic.List<BigFloat> list2 = new System.Collections.Generic.List<BigFloat>(64);

            PrecisionSpec extendedPrecision = new PrecisionSpec(numBits + 1, PrecisionSpec.BaseType.BIN);
            PrecisionSpec normalPrecision = new PrecisionSpec(numBits, PrecisionSpec.BaseType.BIN);

            BigFloat factorial = new BigFloat(1, extendedPrecision);
            BigFloat reciprocal;

            //Calculate e while we're at it
            BigFloat e = new BigFloat(1, extendedPrecision);

            list.Add(new BigFloat(factorial, normalPrecision));

            for (int i = 1; i < Int32.MaxValue; i++)
            {
                BigFloat number = new BigFloat(i, extendedPrecision);
                factorial.Mul(number);

                if (factorial.exponent > numBits) break;

                list2.Add(new BigFloat(factorial, normalPrecision));
                reciprocal = factorial.Reciprocal();

                e.Add(reciprocal);
                list.Add(new BigFloat(reciprocal, normalPrecision));
            }

            //Set the cached static values.
            inverseFactorialCache = list.ToArray();
            factorialCache = list2.ToArray();
            invFactorialCutoff = numBits;
            eCache = new BigFloat(e, normalPrecision);
            eRCPCache = new BigFloat(e.Reciprocal(), normalPrecision);
        }
Esempio n. 29
0
        /// <summary>
        /// Newton's method reciprocal, fastest for larger precisions over 15,000 bits.
        /// </summary>
        /// <returns>The reciprocal 1/this</returns>
        public BigFloat ReciprocalNewton()
        {
            if (mantissa.IsZero())
            {
                exponent = Int32.MaxValue;
                return null;
            }

            bool oldSign = mantissa.Sign;
            int oldExponent = exponent;

            //Kill exponent for now (will re-institute later)
            exponent = 0;

            bool topBit = mantissa.IsTopBitOnlyBit();

            PrecisionSpec curPrec = new PrecisionSpec(32, PrecisionSpec.BaseType.BIN);

            BigFloat reciprocal = new BigFloat(curPrec);
            BigFloat constant2 = new BigFloat(curPrec);
            BigFloat temp = new BigFloat(curPrec);
            BigFloat thisPrec = new BigFloat(this, curPrec);

            reciprocal.exponent = 1;
            reciprocal.mantissa.SetHighDigit(3129112985u);

            constant2.exponent = 1;
            constant2.mantissa.SetHighDigit(0x80000000u);

            //D is deliberately left negative for all the following operations.
            thisPrec.mantissa.Sign = true;

            //Initial estimate.
            reciprocal.Add(thisPrec);

            //mantissa.Sign = false;

            //Shift down into 0.5 < this < 1 range
            thisPrec.mantissa.RSH(1);

            //Iteration.
            int accuracyBits = 2;
            int mantissaBits = mantissa.Precision.NumBits;

            //Each iteration is a pass of newton's method for RCP.
            //The is a substantial optimisation to be done here...
            //You can double the number of bits for the calculations
            //at each iteration, meaning that the whole process only
            //takes some constant multiplier of the time for the
            //full-scale multiplication.
            while (accuracyBits < mantissaBits)
            {
                //Increase the precision as needed
                if (accuracyBits >= curPrec.NumBits / 2)
                {
                    int newBits = curPrec.NumBits * 2;
                    if (newBits > mantissaBits) newBits = mantissaBits;
                    curPrec = new PrecisionSpec(newBits, PrecisionSpec.BaseType.BIN);

                    reciprocal = new BigFloat(reciprocal, curPrec);

                    constant2 = new BigFloat(curPrec);
                    constant2.exponent = 1;
                    constant2.mantissa.SetHighDigit(0x80000000u);

                    temp = new BigFloat(temp, curPrec);

                    thisPrec = new BigFloat(this, curPrec);
                    thisPrec.mantissa.Sign = true;
                    thisPrec.mantissa.RSH(1);
                }

                //temp = Xn
                temp.exponent = reciprocal.exponent;
                temp.mantissa.Assign(reciprocal.mantissa);
                //temp = -Xn * D
                temp.Mul(thisPrec);
                //temp = -Xn * D + 2 (= 2 - Xn * D)
                temp.Add(constant2);
                //reciprocal = X(n+1) = Xn * (2 - Xn * D)
                reciprocal.Mul(temp);

                accuracyBits *= 2;
            }

            //'reciprocal' is now the reciprocal of the shifted down, zero-exponent mantissa of 'this'
            //Restore the mantissa.
            //mantissa.LSH(1);
            exponent = oldExponent;
            //mantissa.Sign = oldSign;

            if (topBit)
            {
                reciprocal.exponent = -(oldExponent);
            }
            else
            {
                reciprocal.exponent = -(oldExponent + 1);
            }
            reciprocal.mantissa.Sign = oldSign;

            return reciprocal;
        }
Esempio n. 30
0
 /// <summary>
 /// Subtracts two numbers and assigns the result to res.
 /// </summary>
 /// <param name="res">a pre-existing BigFloat to take the result</param>
 /// <param name="n1">the first number</param>
 /// <param name="n2">the second number</param>
 /// <returns>a handle to res</returns>
 public static BigFloat Sub(BigFloat res, BigFloat n1, BigFloat n2)
 {
     res.Assign(n1);
     res.Sub(n2);
     return res;
 }