--- /dev/null
+// http://www.fractal-landscapes.co.uk/bigint.html\r
+\r
+using System;\r
+\r
+namespace BigNum\r
+{\r
+ /// <summary>\r
+ /// An arbitrary-precision floating-point class\r
+ /// \r
+ /// Format:\r
+ /// Each number is stored as an exponent (32-bit signed integer), and a mantissa\r
+ /// (n-bit) BigInteger. The sign of the number is stored in the BigInteger\r
+ /// \r
+ /// Applicability and Performance:\r
+ /// This class is designed to be used for small extended precisions. It may not be\r
+ /// safe (and certainly won't be fast) to use it with mixed-precision arguments.\r
+ /// It does support, but will not be efficient for, numbers over around 2048 bits.\r
+ /// \r
+ /// Notes:\r
+ /// All conversions to and from strings are slow.\r
+ /// \r
+ /// Conversions from simple integer types Int32, Int64, UInt32, UInt64 are performed\r
+ /// using the appropriate constructor, and are relatively fast.\r
+ /// \r
+ /// The class is written entirely in managed C# code, with not native or managed\r
+ /// assembler. The use of native assembler would speed up the multiplication operations\r
+ /// many times over, and therefore all higher-order operations too.\r
+ /// </summary>\r
+ public class BigFloat\r
+ {\r
+ /// <summary>\r
+ /// Floats can have 4 special value types:\r
+ /// \r
+ /// NaN: Not a number (cannot be changed using any operations)\r
+ /// Infinity: Positive infinity. Some operations e.g. Arctan() allow this input.\r
+ /// -Infinity: Negative infinity. Some operations allow this input.\r
+ /// Zero\r
+ /// </summary>\r
+ public enum SpecialValueType\r
+ {\r
+ /// <summary>\r
+ /// Not a special value\r
+ /// </summary>\r
+ NONE = 0,\r
+ /// <summary>\r
+ /// Zero\r
+ /// </summary>\r
+ ZERO,\r
+ /// <summary>\r
+ /// Positive infinity\r
+ /// </summary>\r
+ INF_PLUS,\r
+ /// <summary>\r
+ /// Negative infinity\r
+ /// </summary>\r
+ INF_MINUS,\r
+ /// <summary>\r
+ /// Not a number\r
+ /// </summary>\r
+ NAN\r
+ }\r
+\r
+ /// <summary>\r
+ /// This affects the ToString() method. \r
+ /// \r
+ /// With Trim rounding, all insignificant zero digits are drip\r
+ /// </summary>\r
+ public enum RoundingModeType\r
+ {\r
+ /// <summary>\r
+ /// Trim non-significant zeros from ToString output after rounding\r
+ /// </summary>\r
+ TRIM,\r
+ /// <summary>\r
+ /// Keep all non-significant zeroes in ToString output after rounding\r
+ /// </summary>\r
+ EXACT\r
+ }\r
+\r
+ /// <summary>\r
+ /// A wrapper for the signed exponent, avoiding overflow.\r
+ /// </summary>\r
+ protected struct ExponentAdaptor\r
+ {\r
+ /// <summary>\r
+ /// The 32-bit exponent\r
+ /// </summary>\r
+ public Int32 exponent\r
+ {\r
+ get { return expValue; }\r
+ set { expValue = value; }\r
+ }\r
+\r
+ /// <summary>\r
+ /// Implicit cast to Int32\r
+ /// </summary>\r
+ public static implicit operator Int32(ExponentAdaptor adaptor)\r
+ {\r
+ return adaptor.expValue;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Implicit cast from Int32 to ExponentAdaptor\r
+ /// </summary>\r
+ /// <param name="value"></param>\r
+ /// <returns></returns>\r
+ public static implicit operator ExponentAdaptor(Int32 value)\r
+ {\r
+ ExponentAdaptor adaptor = new ExponentAdaptor();\r
+ adaptor.expValue = value;\r
+ return adaptor;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Overloaded increment operator\r
+ /// </summary>\r
+ public static ExponentAdaptor operator ++(ExponentAdaptor adaptor)\r
+ {\r
+ adaptor = adaptor + 1;\r
+ return adaptor;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Overloaded decrement operator\r
+ /// </summary>\r
+ public static ExponentAdaptor operator --(ExponentAdaptor adaptor)\r
+ {\r
+ adaptor = adaptor - 1;\r
+ return adaptor;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Overloaded addition operator\r
+ /// </summary>\r
+ public static ExponentAdaptor operator +(ExponentAdaptor a1, ExponentAdaptor a2)\r
+ {\r
+ if (a1.expValue == Int32.MaxValue) return a1;\r
+\r
+ Int64 temp = (Int64)a1.expValue;\r
+ temp += (Int64)(a2.expValue);\r
+\r
+ if (temp > (Int64)Int32.MaxValue)\r
+ {\r
+ a1.expValue = Int32.MaxValue;\r
+ }\r
+ else if (temp < (Int64)Int32.MinValue)\r
+ {\r
+ a1.expValue = Int32.MinValue;\r
+ }\r
+ else\r
+ {\r
+ a1.expValue = (Int32)temp;\r
+ }\r
+\r
+ return a1;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Overloaded subtraction operator\r
+ /// </summary>\r
+ public static ExponentAdaptor operator -(ExponentAdaptor a1, ExponentAdaptor a2)\r
+ {\r
+ if (a1.expValue == Int32.MaxValue) return a1;\r
+\r
+ Int64 temp = (Int64)a1.expValue;\r
+ temp -= (Int64)(a2.expValue);\r
+\r
+ if (temp > (Int64)Int32.MaxValue)\r
+ {\r
+ a1.expValue = Int32.MaxValue;\r
+ }\r
+ else if (temp < (Int64)Int32.MinValue)\r
+ {\r
+ a1.expValue = Int32.MinValue;\r
+ }\r
+ else\r
+ {\r
+ a1.expValue = (Int32)temp;\r
+ }\r
+\r
+ return a1;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Overloaded multiplication operator\r
+ /// </summary>\r
+ public static ExponentAdaptor operator *(ExponentAdaptor a1, ExponentAdaptor a2)\r
+ {\r
+ if (a1.expValue == Int32.MaxValue) return a1;\r
+\r
+ Int64 temp = (Int64)a1.expValue;\r
+ temp *= (Int64)a2.expValue;\r
+\r
+ if (temp > (Int64)Int32.MaxValue)\r
+ {\r
+ a1.expValue = Int32.MaxValue;\r
+ }\r
+ else if (temp < (Int64)Int32.MinValue)\r
+ {\r
+ a1.expValue = Int32.MinValue;\r
+ }\r
+ else\r
+ {\r
+ a1.expValue = (Int32)temp;\r
+ }\r
+\r
+ return a1;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Overloaded division operator\r
+ /// </summary>\r
+ public static ExponentAdaptor operator /(ExponentAdaptor a1, ExponentAdaptor a2)\r
+ {\r
+ if (a1.expValue == Int32.MaxValue) return a1;\r
+\r
+ ExponentAdaptor res = new ExponentAdaptor();\r
+ res.expValue = a1.expValue / a2.expValue;\r
+ return res;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Overloaded right-shift operator\r
+ /// </summary>\r
+ public static ExponentAdaptor operator >>(ExponentAdaptor a1, int shift)\r
+ {\r
+ if (a1.expValue == Int32.MaxValue) return a1;\r
+\r
+ ExponentAdaptor res = new ExponentAdaptor();\r
+ res.expValue = a1.expValue >> shift;\r
+ return res;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Overloaded left-shift operator\r
+ /// </summary>\r
+ /// <param name="a1"></param>\r
+ /// <param name="shift"></param>\r
+ /// <returns></returns>\r
+ public static ExponentAdaptor operator <<(ExponentAdaptor a1, int shift)\r
+ {\r
+ if (a1.expValue == 0) return a1;\r
+\r
+ ExponentAdaptor res = new ExponentAdaptor();\r
+ res.expValue = a1.expValue;\r
+\r
+ if (shift > 31)\r
+ {\r
+ res.expValue = Int32.MaxValue;\r
+ }\r
+ else\r
+ {\r
+ Int64 temp = a1.expValue;\r
+ temp = temp << shift;\r
+\r
+ if (temp > (Int64)Int32.MaxValue)\r
+ {\r
+ res.expValue = Int32.MaxValue;\r
+ }\r
+ else if (temp < (Int64)Int32.MinValue)\r
+ {\r
+ res.expValue = Int32.MinValue;\r
+ }\r
+ else\r
+ {\r
+ res.expValue = (Int32)temp;\r
+ }\r
+ }\r
+\r
+ return res;\r
+ }\r
+\r
+ private Int32 expValue;\r
+ }\r
+\r
+ //************************ Constructors **************************\r
+\r
+ /// <summary>\r
+ /// Constructs a 128-bit BigFloat\r
+ /// \r
+ /// Sets the value to zero\r
+ /// </summary>\r
+ static BigFloat()\r
+ {\r
+ RoundingDigits = 3;\r
+ RoundingMode = RoundingModeType.TRIM;\r
+ scratch = new BigInt(new PrecisionSpec(128, PrecisionSpec.BaseType.BIN));\r
+ }\r
+\r
+ /// <summary>\r
+ /// Constructs a BigFloat of the required precision\r
+ /// \r
+ /// Sets the value to zero\r
+ /// </summary>\r
+ /// <param name="mantissaPrec"></param>\r
+ public BigFloat(PrecisionSpec mantissaPrec)\r
+ {\r
+ Init(mantissaPrec);\r
+ }\r
+\r
+ /// <summary>\r
+ /// Constructs a big float from a UInt32 to the required precision\r
+ /// </summary>\r
+ /// <param name="value"></param>\r
+ /// <param name="mantissaPrec"></param>\r
+ public BigFloat(UInt32 value, PrecisionSpec mantissaPrec)\r
+ {\r
+ int mbWords = ((mantissaPrec.NumBits) >> 5);\r
+ if ((mantissaPrec.NumBits & 31) != 0) mbWords++;\r
+ int newManBits = mbWords << 5;\r
+\r
+ //For efficiency, we just use a 32-bit exponent\r
+ exponent = 0;\r
+\r
+ mantissa = new BigInt(value, new PrecisionSpec(newManBits, PrecisionSpec.BaseType.BIN));\r
+ //scratch = new BigInt(mantissa.Precision);\r
+\r
+ int bit = BigInt.GetMSB(value);\r
+ if (bit == -1) return;\r
+\r
+ int shift = mantissa.Precision.NumBits - (bit + 1);\r
+ mantissa.LSH(shift);\r
+ exponent = bit;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Constructs a BigFloat from an Int32 to the required precision\r
+ /// </summary>\r
+ /// <param name="value"></param>\r
+ /// <param name="mantissaPrec"></param>\r
+ public BigFloat(Int32 value, PrecisionSpec mantissaPrec)\r
+ {\r
+ int mbWords = ((mantissaPrec.NumBits) >> 5);\r
+ if ((mantissaPrec.NumBits & 31) != 0) mbWords++;\r
+ int newManBits = mbWords << 5;\r
+\r
+ //For efficiency, we just use a 32-bit exponent\r
+ exponent = 0;\r
+ UInt32 uValue;\r
+ \r
+ if (value < 0)\r
+ {\r
+ if (value == Int32.MinValue)\r
+ {\r
+ uValue = 0x80000000;\r
+ }\r
+ else\r
+ {\r
+ uValue = (UInt32)(-value);\r
+ }\r
+ }\r
+ else\r
+ {\r
+ uValue = (UInt32)value;\r
+ }\r
+\r
+ mantissa = new BigInt(value, new PrecisionSpec(newManBits, PrecisionSpec.BaseType.BIN));\r
+ //scratch = new BigInt(new PrecisionSpec(newManBits, PrecisionSpec.BaseType.BIN));\r
+\r
+ int bit = BigInt.GetMSB(uValue);\r
+ if (bit == -1) return;\r
+\r
+ int shift = mantissa.Precision.NumBits - (bit + 1);\r
+ mantissa.LSH(shift);\r
+ exponent = bit;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Constructs a BigFloat from a 64-bit integer\r
+ /// </summary>\r
+ /// <param name="value"></param>\r
+ /// <param name="mantissaPrec"></param>\r
+ public BigFloat(Int64 value, PrecisionSpec mantissaPrec)\r
+ {\r
+ int mbWords = ((mantissaPrec.NumBits) >> 5);\r
+ if ((mantissaPrec.NumBits & 31) != 0) mbWords++;\r
+ int newManBits = mbWords << 5;\r
+\r
+ //For efficiency, we just use a 32-bit exponent\r
+ exponent = 0;\r
+ UInt64 uValue;\r
+\r
+ if (value < 0)\r
+ {\r
+ if (value == Int64.MinValue)\r
+ {\r
+ uValue = 0x80000000;\r
+ }\r
+ else\r
+ {\r
+ uValue = (UInt64)(-value);\r
+ }\r
+ }\r
+ else\r
+ {\r
+ uValue = (UInt64)value;\r
+ }\r
+\r
+ mantissa = new BigInt(value, new PrecisionSpec(newManBits, PrecisionSpec.BaseType.BIN));\r
+ //scratch = new BigInt(new PrecisionSpec(newManBits, PrecisionSpec.BaseType.BIN));\r
+\r
+ int bit = BigInt.GetMSB(uValue);\r
+ if (bit == -1) return;\r
+\r
+ int shift = mantissa.Precision.NumBits - (bit + 1);\r
+ if (shift > 0)\r
+ {\r
+ mantissa.LSH(shift);\r
+ }\r
+ else\r
+ {\r
+ mantissa.SetHighDigit((uint)(uValue >> (-shift)));\r
+ }\r
+ exponent = bit;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Constructs a BigFloat from a 64-bit unsigned integer\r
+ /// </summary>\r
+ /// <param name="value"></param>\r
+ /// <param name="mantissaPrec"></param>\r
+ public BigFloat(UInt64 value, PrecisionSpec mantissaPrec)\r
+ {\r
+ int mbWords = ((mantissaPrec.NumBits) >> 5);\r
+ if ((mantissaPrec.NumBits & 31) != 0) mbWords++;\r
+ int newManBits = mbWords << 5;\r
+\r
+ //For efficiency, we just use a 32-bit exponent\r
+ exponent = 0;\r
+\r
+ int bit = BigInt.GetMSB(value);\r
+\r
+ mantissa = new BigInt(value, new PrecisionSpec(newManBits, PrecisionSpec.BaseType.BIN));\r
+ //scratch = new BigInt(mantissa.Precision);\r
+\r
+ int shift = mantissa.Precision.NumBits - (bit + 1);\r
+ if (shift > 0)\r
+ {\r
+ mantissa.LSH(shift);\r
+ }\r
+ else\r
+ {\r
+ mantissa.SetHighDigit((uint)(value >> (-shift)));\r
+ }\r
+ exponent = bit;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Constructs a BigFloat from a BigInt, using the specified precision\r
+ /// </summary>\r
+ /// <param name="value"></param>\r
+ /// <param name="mantissaPrec"></param>\r
+ public BigFloat(BigInt value, PrecisionSpec mantissaPrec)\r
+ {\r
+ if (value.IsZero())\r
+ {\r
+ Init(mantissaPrec);\r
+ SetZero();\r
+ return;\r
+ }\r
+\r
+ mantissa = new BigInt(value, mantissaPrec);\r
+ exponent = BigInt.GetMSB(value);\r
+ mantissa.Normalise();\r
+ }\r
+\r
+ /// <summary>\r
+ /// Construct a BigFloat from a double-precision floating point number\r
+ /// </summary>\r
+ /// <param name="value"></param>\r
+ /// <param name="mantissaPrec"></param>\r
+ public BigFloat(double value, PrecisionSpec mantissaPrec)\r
+ {\r
+ if (value == 0.0)\r
+ {\r
+ Init(mantissaPrec);\r
+ return;\r
+ }\r
+\r
+ bool sign = (value < 0) ? true : false;\r
+\r
+ long bits = BitConverter.DoubleToInt64Bits(value);\r
+ // Note that the shift is sign-extended, hence the test against -1 not 1\r
+ int valueExponent = (int)((bits >> 52) & 0x7ffL);\r
+ long valueMantissa = bits & 0xfffffffffffffL;\r
+\r
+ //The mantissa is stored with the top bit implied.\r
+ valueMantissa = valueMantissa | 0x10000000000000L;\r
+\r
+ //The exponent is biased by 1023.\r
+ exponent = valueExponent - 1023;\r
+\r
+ //Round the number of bits to the nearest word.\r
+ int mbWords = ((mantissaPrec.NumBits) >> 5);\r
+ if ((mantissaPrec.NumBits & 31) != 0) mbWords++;\r
+ int newManBits = mbWords << 5;\r
+\r
+ mantissa = new BigInt(new PrecisionSpec(newManBits, PrecisionSpec.BaseType.BIN));\r
+ //scratch = new BigInt(new PrecisionSpec(newManBits, PrecisionSpec.BaseType.BIN));\r
+\r
+ if (newManBits >= 64)\r
+ {\r
+ //The mantissa is 53 bits now, so add 11 to put it in the right place.\r
+ mantissa.SetHighDigits(valueMantissa << 11);\r
+ }\r
+ else\r
+ {\r
+ //To get the top word of the mantissa, shift up by 11 and down by 32 = down by 21\r
+ mantissa.SetHighDigit((uint)(valueMantissa >> 21));\r
+ }\r
+\r
+ mantissa.Sign = sign;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Copy constructor\r
+ /// </summary>\r
+ /// <param name="value"></param>\r
+ public BigFloat(BigFloat value)\r
+ {\r
+ Init(value.mantissa.Precision);\r
+ exponent = value.exponent;\r
+ mantissa.Assign(value.mantissa);\r
+ }\r
+\r
+ /// <summary>\r
+ /// Copy Constructor - constructs a new BigFloat with the specified precision, copying the old one.\r
+ /// \r
+ /// The value is rounded towards zero in the case where precision is decreased. The Round() function\r
+ /// should be used beforehand if a correctly rounded result is required.\r
+ /// </summary>\r
+ /// <param name="value"></param>\r
+ /// <param name="mantissaPrec"></param>\r
+ public BigFloat(BigFloat value, PrecisionSpec mantissaPrec)\r
+ {\r
+ Init(mantissaPrec);\r
+ exponent = value.exponent;\r
+ if (mantissa.AssignHigh(value.mantissa)) exponent++;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Constructs a BigFloat from a string\r
+ /// </summary>\r
+ /// <param name="value"></param>\r
+ /// <param name="mantissaPrec"></param>\r
+ public BigFloat(string value, PrecisionSpec mantissaPrec)\r
+ {\r
+ Init(mantissaPrec);\r
+\r
+ PrecisionSpec extendedPres = new PrecisionSpec(mantissa.Precision.NumBits + 1, PrecisionSpec.BaseType.BIN);\r
+ BigFloat ten = new BigFloat(10, extendedPres);\r
+ BigFloat iPart = new BigFloat(extendedPres);\r
+ BigFloat fPart = new BigFloat(extendedPres);\r
+ BigFloat tenRCP = ten.Reciprocal();\r
+\r
+ if (value.Contains(System.Globalization.CultureInfo.CurrentCulture.NumberFormat.NaNSymbol))\r
+ {\r
+ SetNaN();\r
+ return;\r
+ }\r
+ else if (value.Contains(System.Globalization.CultureInfo.CurrentCulture.NumberFormat.PositiveInfinitySymbol))\r
+ {\r
+ SetInfPlus();\r
+ return;\r
+ }\r
+ else if (value.Contains(System.Globalization.CultureInfo.CurrentCulture.NumberFormat.NegativeInfinitySymbol))\r
+ {\r
+ SetInfMinus();\r
+ return;\r
+ }\r
+\r
+ string decimalpoint = System.Globalization.CultureInfo.CurrentCulture.NumberFormat.NumberDecimalSeparator;\r
+\r
+ char[] digitChars = { '0', '1', '2', '3', '4', '5', '6', '7', '8', '9', ',', '.' };\r
+\r
+ //Read in the integer part up the the decimal point.\r
+ bool sign = false;\r
+ value = value.Trim();\r
+\r
+ int i = 0;\r
+\r
+ if (value.Length > i && value[i] == '-')\r
+ {\r
+ sign = true;\r
+ i++;\r
+ }\r
+\r
+ if (value.Length > i && value[i] == '+')\r
+ {\r
+ i++;\r
+ }\r
+\r
+ for ( ; i < value.Length; i++)\r
+ {\r
+ //break on decimal point\r
+ if (value[i] == decimalpoint[0]) break;\r
+\r
+ int digit = Array.IndexOf(digitChars, value[i]);\r
+ if (digit < 0) break;\r
+\r
+ //Ignore place separators (assumed either , or .)\r
+ if (digit > 9) continue;\r
+\r
+ if (i > 0) iPart.Mul(ten);\r
+ iPart.Add(new BigFloat(digit, extendedPres));\r
+ }\r
+\r
+ //If we've run out of characters, assign everything and return\r
+ if (i == value.Length)\r
+ {\r
+ iPart.mantissa.Sign = sign;\r
+ exponent = iPart.exponent;\r
+ if (mantissa.AssignHigh(iPart.mantissa)) exponent++;\r
+ return;\r
+ }\r
+\r
+ //Assign the characters after the decimal point to fPart\r
+ if (value[i] == '.' && i < value.Length - 1)\r
+ {\r
+ BigFloat RecipToUse = new BigFloat(tenRCP);\r
+\r
+ for (i++; i < value.Length; i++)\r
+ {\r
+ int digit = Array.IndexOf(digitChars, value[i]);\r
+ if (digit < 0) break;\r
+ BigFloat temp = new BigFloat(digit, extendedPres);\r
+ temp.Mul(RecipToUse);\r
+ RecipToUse.Mul(tenRCP);\r
+ fPart.Add(temp);\r
+ }\r
+ }\r
+\r
+ //If we're run out of characters, add fPart and iPart and return\r
+ if (i == value.Length)\r
+ {\r
+ iPart.Add(fPart);\r
+ iPart.mantissa.Sign = sign;\r
+ exponent = iPart.exponent;\r
+ if (mantissa.AssignHigh(iPart.mantissa)) exponent++;\r
+ return;\r
+ }\r
+\r
+ if (value[i] == '+' || value[i] == '-') i++;\r
+\r
+ if (i == value.Length)\r
+ {\r
+ iPart.Add(fPart);\r
+ iPart.mantissa.Sign = sign;\r
+ exponent = iPart.exponent;\r
+ if (mantissa.AssignHigh(iPart.mantissa)) exponent++;\r
+ return;\r
+ }\r
+\r
+ //Look for exponential notation.\r
+ if ((value[i] == 'e' || value[i] == 'E') && i < value.Length - 1)\r
+ {\r
+ //Convert the exponent to an int.\r
+ int exp;\r
+\r
+ try\r
+ {\r
+ exp = System.Convert.ToInt32(new string(value.ToCharArray()));// i + 1, value.Length - (i + 1))));\r
+ }\r
+ catch (Exception)\r
+ {\r
+ iPart.Add(fPart);\r
+ iPart.mantissa.Sign = sign;\r
+ exponent = iPart.exponent;\r
+ if (mantissa.AssignHigh(iPart.mantissa)) exponent++;\r
+ return;\r
+ }\r
+\r
+ //Raise or lower 10 to the power of the exponent\r
+ BigFloat acc = new BigFloat(1, extendedPres);\r
+ BigFloat temp = new BigFloat(1, extendedPres);\r
+\r
+ int powerTemp = exp;\r
+\r
+ BigFloat multiplierToUse;\r
+\r
+ if (exp < 0)\r
+ {\r
+ multiplierToUse = new BigFloat(tenRCP);\r
+ powerTemp = -exp;\r
+ }\r
+ else\r
+ {\r
+ multiplierToUse = new BigFloat(ten);\r
+ }\r
+\r
+ //Fast power function\r
+ while (powerTemp != 0)\r
+ {\r
+ temp.Mul(multiplierToUse);\r
+ multiplierToUse.Assign(temp);\r
+\r
+ if ((powerTemp & 1) != 0)\r
+ {\r
+ acc.Mul(temp);\r
+ }\r
+\r
+ powerTemp >>= 1;\r
+ }\r
+\r
+ iPart.Add(fPart);\r
+ iPart.Mul(acc);\r
+ iPart.mantissa.Sign = sign;\r
+ exponent = iPart.exponent;\r
+ if (mantissa.AssignHigh(iPart.mantissa)) exponent++;\r
+\r
+ return;\r
+ }\r
+\r
+ iPart.Add(fPart);\r
+ iPart.mantissa.Sign = sign;\r
+ exponent = iPart.exponent;\r
+ if (mantissa.AssignHigh(iPart.mantissa)) exponent++;\r
+\r
+ }\r
+\r
+ private void Init(PrecisionSpec mantissaPrec)\r
+ {\r
+ int mbWords = ((mantissaPrec.NumBits) >> 5);\r
+ if ((mantissaPrec.NumBits & 31) != 0) mbWords++;\r
+ int newManBits = mbWords << 5;\r
+\r
+ //For efficiency, we just use a 32-bit exponent\r
+ exponent = 0;\r
+ mantissa = new BigInt(new PrecisionSpec(newManBits, PrecisionSpec.BaseType.BIN));\r
+ //scratch = new BigInt(new PrecisionSpec(newManBits, PrecisionSpec.BaseType.BIN));\r
+ }\r
+\r
+ //************************** Properties *************************\r
+\r
+ /// <summary>\r
+ /// Read-only property. Returns the precision specification of the mantissa.\r
+ /// \r
+ /// Floating point numbers are represented as 2^exponent * mantissa, where the\r
+ /// mantissa and exponent are integers. Note that the exponent in this class is\r
+ /// always a 32-bit integer. The precision therefore specifies how many bits\r
+ /// the mantissa will have.\r
+ /// </summary>\r
+ public PrecisionSpec Precision\r
+ {\r
+ get { return mantissa.Precision; }\r
+ }\r
+\r
+ /// <summary>\r
+ /// Writable property:\r
+ /// true iff the number is negative or in some cases zero (<0)\r
+ /// false iff the number if positive or in some cases zero (>0)\r
+ /// </summary>\r
+ public bool Sign \r
+ { \r
+ get { return mantissa.Sign; }\r
+ set { mantissa.Sign = value; }\r
+ }\r
+\r
+ /// <summary>\r
+ /// Read-only property. \r
+ /// True if the number is NAN, INF_PLUS, INF_MINUS or ZERO\r
+ /// False if the number has any other value.\r
+ /// </summary>\r
+ public bool IsSpecialValue\r
+ {\r
+ get\r
+ {\r
+ return (exponent == Int32.MaxValue || mantissa.IsZero());\r
+ }\r
+ }\r
+\r
+ /// <summary>\r
+ /// Read-only property, returns the type of number this is. Special values include:\r
+ /// \r
+ /// NONE - a regular number\r
+ /// ZERO - zero\r
+ /// NAN - Not a Number (some operations will return this if their inputs are out of range)\r
+ /// INF_PLUS - Positive infinity, not really a number, but a valid input to and output of some functions.\r
+ /// INF_MINUS - Negative infinity, not really a number, but a valid input to and output of some functions.\r
+ /// </summary>\r
+ public SpecialValueType SpecialValue\r
+ {\r
+ get\r
+ {\r
+ if (exponent == Int32.MaxValue)\r
+ {\r
+ if (mantissa.IsZero())\r
+ {\r
+ if (mantissa.Sign) return SpecialValueType.INF_MINUS;\r
+ return SpecialValueType.INF_PLUS;\r
+ }\r
+\r
+ return SpecialValueType.NAN;\r
+ }\r
+ else\r
+ {\r
+ if (mantissa.IsZero()) return SpecialValueType.ZERO;\r
+ return SpecialValueType.NONE;\r
+ }\r
+ }\r
+ }\r
+\r
+ //******************** Mathematical Constants *******************\r
+\r
+ /// <summary>\r
+ /// Gets pi to the indicated precision\r
+ /// </summary>\r
+ /// <param name="precision">The precision to perform the calculation to</param>\r
+ /// <returns>pi (the ratio of the area of a circle to its diameter)</returns>\r
+ public static BigFloat GetPi(PrecisionSpec precision)\r
+ {\r
+ if (pi == null || precision.NumBits <= pi.mantissa.Precision.NumBits)\r
+ {\r
+ CalculatePi(precision.NumBits);\r
+ }\r
+\r
+ BigFloat ret = new BigFloat (precision);\r
+ ret.Assign(pi);\r
+\r
+ return ret;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Get e to the indicated precision\r
+ /// </summary>\r
+ /// <param name="precision">The preicision to perform the calculation to</param>\r
+ /// <returns>e (the number for which the d/dx(e^x) = e^x)</returns>\r
+ public static BigFloat GetE(PrecisionSpec precision)\r
+ {\r
+ if (eCache == null || eCache.mantissa.Precision.NumBits < precision.NumBits)\r
+ {\r
+ CalculateEOnly(precision.NumBits);\r
+ //CalculateFactorials(precision.NumBits);\r
+ }\r
+\r
+ BigFloat ret = new BigFloat(precision);\r
+ ret.Assign(eCache);\r
+\r
+ return ret;\r
+ }\r
+\r
+\r
+ //******************** Arithmetic Functions ********************\r
+\r
+ /// <summary>\r
+ /// Addition (this = this + n2)\r
+ /// </summary>\r
+ /// <param name="n2">The number to add</param>\r
+ public void Add(BigFloat n2)\r
+ {\r
+ if (SpecialValueAddTest(n2)) return;\r
+\r
+ if (scratch.Precision.NumBits != n2.mantissa.Precision.NumBits)\r
+ {\r
+ scratch = new BigInt(n2.mantissa.Precision);\r
+ }\r
+\r
+ if (exponent <= n2.exponent)\r
+ {\r
+ int diff = n2.exponent - exponent;\r
+ exponent = n2.exponent;\r
+\r
+ if (diff != 0)\r
+ {\r
+ mantissa.RSH(diff);\r
+ }\r
+\r
+ uint carry = mantissa.Add(n2.mantissa);\r
+\r
+ if (carry != 0)\r
+ {\r
+ mantissa.RSH(1);\r
+ mantissa.SetBit(mantissa.Precision.NumBits - 1);\r
+ exponent++;\r
+ }\r
+\r
+ exponent -= mantissa.Normalise();\r
+ }\r
+ else\r
+ {\r
+ int diff = exponent - n2.exponent;\r
+\r
+ scratch.Assign(n2.mantissa);\r
+ scratch.RSH(diff);\r
+\r
+ uint carry = scratch.Add(mantissa);\r
+\r
+ if (carry != 0)\r
+ {\r
+ scratch.RSH(1);\r
+ scratch.SetBit(mantissa.Precision.NumBits - 1);\r
+ exponent++;\r
+ }\r
+\r
+ mantissa.Assign(scratch);\r
+\r
+ exponent -= mantissa.Normalise();\r
+ }\r
+ }\r
+\r
+ /// <summary>\r
+ /// Subtraction (this = this - n2)\r
+ /// </summary>\r
+ /// <param name="n2">The number to subtract from this</param>\r
+ public void Sub(BigFloat n2)\r
+ {\r
+ n2.mantissa.Sign = !n2.mantissa.Sign;\r
+ Add(n2);\r
+ n2.mantissa.Sign = !n2.mantissa.Sign;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Multiplication (this = this * n2)\r
+ /// </summary>\r
+ /// <param name="n2">The number to multiply this by</param>\r
+ public void Mul(BigFloat n2)\r
+ {\r
+ if (SpecialValueMulTest(n2)) return;\r
+\r
+ //Anything times 0 = 0\r
+ if (n2.mantissa.IsZero())\r
+ {\r
+ mantissa.Assign(n2.mantissa);\r
+ exponent = 0;\r
+ return;\r
+ }\r
+\r
+ mantissa.MulHi(n2.mantissa);\r
+ int shift = mantissa.Normalise();\r
+ exponent = exponent + n2.exponent + 1 - shift;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Division (this = this / n2)\r
+ /// </summary>\r
+ /// <param name="n2">The number to divide this by</param>\r
+ public void Div(BigFloat n2)\r
+ {\r
+ if (SpecialValueDivTest(n2)) return;\r
+\r
+ if (mantissa.Precision.NumBits >= 8192)\r
+ {\r
+ BigFloat rcp = n2.Reciprocal();\r
+ Mul(rcp);\r
+ }\r
+ else\r
+ {\r
+ int shift = mantissa.DivAndShift(n2.mantissa);\r
+ exponent = exponent - (n2.exponent + shift);\r
+ }\r
+ }\r
+\r
+ /// <summary>\r
+ /// Multiply by a power of 2 (-ve implies division)\r
+ /// </summary>\r
+ /// <param name="pow2"></param>\r
+ public void MulPow2(int pow2)\r
+ {\r
+ exponent += pow2;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Division-based reciprocal, fastest for small precisions up to 15,000 bits.\r
+ /// </summary>\r
+ /// <returns>The reciprocal 1/this</returns>\r
+ public BigFloat Reciprocal()\r
+ {\r
+ if (mantissa.Precision.NumBits >= 8192) return ReciprocalNewton();\r
+\r
+ BigFloat reciprocal = new BigFloat(1u, mantissa.Precision);\r
+ reciprocal.Div(this);\r
+ return reciprocal;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Newton's method reciprocal, fastest for larger precisions over 15,000 bits.\r
+ /// </summary>\r
+ /// <returns>The reciprocal 1/this</returns>\r
+ public BigFloat ReciprocalNewton()\r
+ {\r
+ if (mantissa.IsZero())\r
+ {\r
+ exponent = Int32.MaxValue;\r
+ return null;\r
+ }\r
+\r
+ bool oldSign = mantissa.Sign;\r
+ int oldExponent = exponent;\r
+\r
+ //Kill exponent for now (will re-institute later)\r
+ exponent = 0;\r
+\r
+ bool topBit = mantissa.IsTopBitOnlyBit();\r
+\r
+ PrecisionSpec curPrec = new PrecisionSpec(32, PrecisionSpec.BaseType.BIN);\r
+\r
+ BigFloat reciprocal = new BigFloat(curPrec);\r
+ BigFloat constant2 = new BigFloat(curPrec);\r
+ BigFloat temp = new BigFloat(curPrec);\r
+ BigFloat thisPrec = new BigFloat(this, curPrec);\r
+\r
+ reciprocal.exponent = 1;\r
+ reciprocal.mantissa.SetHighDigit(3129112985u);\r
+\r
+ constant2.exponent = 1;\r
+ constant2.mantissa.SetHighDigit(0x80000000u);\r
+\r
+ //D is deliberately left negative for all the following operations.\r
+ thisPrec.mantissa.Sign = true;\r
+\r
+ //Initial estimate.\r
+ reciprocal.Add(thisPrec);\r
+\r
+ //mantissa.Sign = false;\r
+\r
+ //Shift down into 0.5 < this < 1 range\r
+ thisPrec.mantissa.RSH(1);\r
+\r
+ //Iteration.\r
+ int accuracyBits = 2;\r
+ int mantissaBits = mantissa.Precision.NumBits;\r
+\r
+ //Each iteration is a pass of newton's method for RCP.\r
+ //The is a substantial optimisation to be done here...\r
+ //You can double the number of bits for the calculations\r
+ //at each iteration, meaning that the whole process only\r
+ //takes some constant multiplier of the time for the\r
+ //full-scale multiplication.\r
+ while (accuracyBits < mantissaBits)\r
+ {\r
+ //Increase the precision as needed\r
+ if (accuracyBits >= curPrec.NumBits / 2)\r
+ {\r
+ int newBits = curPrec.NumBits * 2;\r
+ if (newBits > mantissaBits) newBits = mantissaBits;\r
+ curPrec = new PrecisionSpec(newBits, PrecisionSpec.BaseType.BIN);\r
+\r
+ reciprocal = new BigFloat(reciprocal, curPrec);\r
+\r
+ constant2 = new BigFloat(curPrec);\r
+ constant2.exponent = 1;\r
+ constant2.mantissa.SetHighDigit(0x80000000u);\r
+\r
+ temp = new BigFloat(temp, curPrec);\r
+\r
+ thisPrec = new BigFloat(this, curPrec);\r
+ thisPrec.mantissa.Sign = true;\r
+ thisPrec.mantissa.RSH(1);\r
+ }\r
+\r
+ //temp = Xn\r
+ temp.exponent = reciprocal.exponent;\r
+ temp.mantissa.Assign(reciprocal.mantissa);\r
+ //temp = -Xn * D\r
+ temp.Mul(thisPrec);\r
+ //temp = -Xn * D + 2 (= 2 - Xn * D)\r
+ temp.Add(constant2);\r
+ //reciprocal = X(n+1) = Xn * (2 - Xn * D)\r
+ reciprocal.Mul(temp);\r
+\r
+ accuracyBits *= 2;\r
+ }\r
+\r
+ //'reciprocal' is now the reciprocal of the shifted down, zero-exponent mantissa of 'this'\r
+ //Restore the mantissa.\r
+ //mantissa.LSH(1);\r
+ exponent = oldExponent;\r
+ //mantissa.Sign = oldSign;\r
+\r
+ if (topBit)\r
+ {\r
+ reciprocal.exponent = -(oldExponent);\r
+ }\r
+ else\r
+ {\r
+ reciprocal.exponent = -(oldExponent + 1);\r
+ }\r
+ reciprocal.mantissa.Sign = oldSign;\r
+\r
+ return reciprocal;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Newton's method reciprocal, fastest for larger precisions over 15,000 bits.\r
+ /// </summary>\r
+ /// <returns>The reciprocal 1/this</returns>\r
+ private BigFloat ReciprocalNewton2()\r
+ {\r
+ if (mantissa.IsZero())\r
+ {\r
+ exponent = Int32.MaxValue;\r
+ return null;\r
+ }\r
+\r
+ bool oldSign = mantissa.Sign;\r
+ int oldExponent = exponent;\r
+\r
+ //Kill exponent for now (will re-institute later)\r
+ exponent = 0;\r
+\r
+ BigFloat reciprocal = new BigFloat(mantissa.Precision);\r
+ BigFloat constant2 = new BigFloat(mantissa.Precision);\r
+ BigFloat temp = new BigFloat(mantissa.Precision);\r
+\r
+ reciprocal.exponent = 1;\r
+ reciprocal.mantissa.SetHighDigit(3129112985u);\r
+\r
+ constant2.exponent = 1;\r
+ constant2.mantissa.SetHighDigit(0x80000000u);\r
+\r
+ //D is deliberately left negative for all the following operations.\r
+ mantissa.Sign = true;\r
+\r
+ //Initial estimate.\r
+ reciprocal.Add(this);\r
+\r
+ //mantissa.Sign = false;\r
+\r
+ //Shift down into 0.5 < this < 1 range\r
+ mantissa.RSH(1);\r
+ \r
+ //Iteration.\r
+ int accuracyBits = 2;\r
+ int mantissaBits = mantissa.Precision.NumBits;\r
+\r
+ //Each iteration is a pass of newton's method for RCP.\r
+ //The is a substantial optimisation to be done here...\r
+ //You can double the number of bits for the calculations\r
+ //at each iteration, meaning that the whole process only\r
+ //takes some constant multiplier of the time for the\r
+ //full-scale multiplication.\r
+ while (accuracyBits < mantissaBits)\r
+ {\r
+ //temp = Xn\r
+ temp.exponent = reciprocal.exponent;\r
+ temp.mantissa.Assign(reciprocal.mantissa);\r
+ //temp = -Xn * D\r
+ temp.Mul(this);\r
+ //temp = -Xn * D + 2 (= 2 - Xn * D)\r
+ temp.Add(constant2);\r
+ //reciprocal = X(n+1) = Xn * (2 - Xn * D)\r
+ reciprocal.Mul(temp);\r
+\r
+ accuracyBits *= 2;\r
+ }\r
+\r
+ //'reciprocal' is now the reciprocal of the shifted down, zero-exponent mantissa of 'this'\r
+ //Restore the mantissa.\r
+ mantissa.LSH(1);\r
+ exponent = oldExponent;\r
+ mantissa.Sign = oldSign;\r
+\r
+ reciprocal.exponent = -(oldExponent + 1);\r
+ reciprocal.mantissa.Sign = oldSign;\r
+\r
+ return reciprocal;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Sets this equal to the input\r
+ /// </summary>\r
+ /// <param name="n2"></param>\r
+ public void Assign(BigFloat n2)\r
+ {\r
+ exponent = n2.exponent;\r
+ if (mantissa.AssignHigh(n2.mantissa)) exponent++;\r
+ }\r
+\r
+\r
+ //********************* Comparison Functions *******************\r
+\r
+ /// <summary>\r
+ /// Greater than comparison\r
+ /// </summary>\r
+ /// <param name="n2">the number to compare this to</param>\r
+ /// <returns>true iff this is greater than n2 (this > n2)</returns>\r
+ public bool GreaterThan(BigFloat n2)\r
+ {\r
+ if (IsSpecialValue || n2.IsSpecialValue)\r
+ {\r
+ SpecialValueType s1 = SpecialValue;\r
+ SpecialValueType s2 = SpecialValue;\r
+\r
+ if (s1 == SpecialValueType.NAN || s2 == SpecialValueType.NAN) return false;\r
+ if (s1 == SpecialValueType.INF_MINUS) return false;\r
+ if (s2 == SpecialValueType.INF_PLUS) return false;\r
+ if (s1 == SpecialValueType.INF_PLUS) return true;\r
+ if (s2 == SpecialValueType.INF_MINUS) return true;\r
+\r
+ if (s1 == SpecialValueType.ZERO)\r
+ {\r
+ if (s2 != SpecialValueType.ZERO && n2.Sign)\r
+ {\r
+ return true;\r
+ }\r
+ else\r
+ {\r
+ return false;\r
+ }\r
+ }\r
+\r
+ if (s2 == SpecialValueType.ZERO)\r
+ {\r
+ return !Sign;\r
+ }\r
+ }\r
+\r
+ if (!mantissa.Sign && n2.mantissa.Sign) return true;\r
+ if (mantissa.Sign && !n2.mantissa.Sign) return false;\r
+ if (!mantissa.Sign)\r
+ {\r
+ if (exponent > n2.exponent) return true;\r
+ if (exponent < n2.exponent) return false;\r
+ }\r
+ if (mantissa.Sign)\r
+ {\r
+ if (exponent > n2.exponent) return false;\r
+ if (exponent < n2.exponent) return true;\r
+ }\r
+\r
+ return mantissa.GreaterThan(n2.mantissa);\r
+ }\r
+\r
+ /// <summary>\r
+ /// Less than comparison\r
+ /// </summary>\r
+ /// <param name="n2">the number to compare this to</param>\r
+ /// <returns>true iff this is less than n2 (this < n2)</returns>\r
+ public bool LessThan(BigFloat n2)\r
+ {\r
+ if (IsSpecialValue || n2.IsSpecialValue)\r
+ {\r
+ SpecialValueType s1 = SpecialValue;\r
+ SpecialValueType s2 = SpecialValue;\r
+\r
+ if (s1 == SpecialValueType.NAN || s2 == SpecialValueType.NAN) return false;\r
+ if (s1 == SpecialValueType.INF_PLUS) return false;\r
+ if (s2 == SpecialValueType.INF_PLUS) return true;\r
+ if (s2 == SpecialValueType.INF_MINUS) return false;\r
+ if (s1 == SpecialValueType.INF_MINUS) return true;\r
+\r
+ if (s1 == SpecialValueType.ZERO)\r
+ {\r
+ if (s2 != SpecialValueType.ZERO && !n2.Sign)\r
+ {\r
+ return true;\r
+ }\r
+ else\r
+ {\r
+ return false;\r
+ }\r
+ }\r
+\r
+ if (s2 == SpecialValueType.ZERO)\r
+ {\r
+ return Sign;\r
+ }\r
+ }\r
+\r
+ if (!mantissa.Sign && n2.mantissa.Sign) return false;\r
+ if (mantissa.Sign && !n2.mantissa.Sign) return true;\r
+ if (!mantissa.Sign)\r
+ {\r
+ if (exponent > n2.exponent) return false;\r
+ if (exponent < n2.exponent) return true;\r
+ }\r
+ if (mantissa.Sign)\r
+ {\r
+ if (exponent > n2.exponent) return true;\r
+ if (exponent < n2.exponent) return false;\r
+ }\r
+\r
+ return mantissa.LessThan(n2.mantissa);\r
+ }\r
+\r
+ /// <summary>\r
+ /// Greater than comparison\r
+ /// </summary>\r
+ /// <param name="i">the number to compare this to</param>\r
+ /// <returns>true iff this is greater than n2 (this > n2)</returns>\r
+ public bool GreaterThan(int i)\r
+ {\r
+ BigFloat integer = new BigFloat(i, mantissa.Precision);\r
+ return GreaterThan(integer);\r
+ }\r
+\r
+ /// <summary>\r
+ /// Less than comparison\r
+ /// </summary>\r
+ /// <param name="i">the number to compare this to</param>\r
+ /// <returns>true iff this is less than n2 (this < n2)</returns>\r
+ public bool LessThan(int i)\r
+ {\r
+ BigFloat integer = new BigFloat(i, mantissa.Precision);\r
+ return LessThan(integer);\r
+ }\r
+\r
+ /// <summary>\r
+ /// Compare to zero\r
+ /// </summary>\r
+ /// <returns>true if this is zero (this == 0)</returns>\r
+ public bool IsZero()\r
+ {\r
+ return (mantissa.IsZero());\r
+ }\r
+\r
+\r
+ //******************** Mathematical Functions ******************\r
+\r
+ /// <summary>\r
+ /// Sets the number to the biggest integer numerically closer to zero, if possible.\r
+ /// </summary>\r
+ public void Floor()\r
+ {\r
+ //Already an integer.\r
+ if (exponent >= mantissa.Precision.NumBits) return;\r
+\r
+ if (exponent < 0)\r
+ {\r
+ mantissa.ZeroBits(mantissa.Precision.NumBits);\r
+ exponent = 0;\r
+ return;\r
+ }\r
+\r
+ mantissa.ZeroBits(mantissa.Precision.NumBits - (exponent + 1));\r
+ }\r
+\r
+ /// <summary>\r
+ /// Sets the number to its fractional component (equivalent to 'this' - (int)'this')\r
+ /// </summary>\r
+ public void FPart()\r
+ {\r
+ //Already fractional\r
+ if (exponent < 0)\r
+ {\r
+ return;\r
+ }\r
+\r
+ //Has no fractional part\r
+ if (exponent >= mantissa.Precision.NumBits)\r
+ {\r
+ mantissa.Zero();\r
+ exponent = 0;\r
+ return;\r
+ }\r
+\r
+ mantissa.ZeroBitsHigh(exponent + 1);\r
+ exponent -= mantissa.Normalise();\r
+ }\r
+\r
+ /// <summary>\r
+ /// Calculates tan(x)\r
+ /// </summary>\r
+ public void Tan()\r
+ {\r
+ if (IsSpecialValue)\r
+ {\r
+ //Tan(x) has no limit as x->inf\r
+ if (SpecialValue == SpecialValueType.INF_MINUS || SpecialValue == SpecialValueType.INF_PLUS)\r
+ {\r
+ SetNaN();\r
+ }\r
+ else if (SpecialValue == SpecialValueType.ZERO)\r
+ {\r
+ SetZero();\r
+ }\r
+\r
+ return;\r
+ }\r
+\r
+ if (pi == null || pi.mantissa.Precision.NumBits != mantissa.Precision.NumBits)\r
+ {\r
+ CalculatePi(mantissa.Precision.NumBits);\r
+ }\r
+\r
+ //Work out the sign change (involves replicating some rescaling).\r
+ bool sign = mantissa.Sign;\r
+ mantissa.Sign = false;\r
+\r
+ if (mantissa.IsZero())\r
+ {\r
+ return;\r
+ }\r
+\r
+ //Rescale into 0 <= x < pi\r
+ if (GreaterThan(pi))\r
+ {\r
+ //There will be an inherent loss of precision doing this.\r
+ BigFloat newAngle = new BigFloat(this);\r
+ newAngle.Mul(piRecip);\r
+ newAngle.FPart();\r
+ newAngle.Mul(pi);\r
+ Assign(newAngle);\r
+ }\r
+\r
+ //Rescale to -pi/2 <= x < pi/2\r
+ if (!LessThan(piBy2))\r
+ {\r
+ Sub(pi);\r
+ }\r
+\r
+ //Now the sign of the sin determines the sign of the tan.\r
+ //tan(x) = sin(x) / sqrt(1 - sin^2(x))\r
+ Sin();\r
+ BigFloat denom = new BigFloat(this);\r
+ denom.Mul(this);\r
+ denom.Sub(new BigFloat(1, mantissa.Precision));\r
+ denom.mantissa.Sign = !denom.mantissa.Sign;\r
+\r
+ if (denom.mantissa.Sign)\r
+ {\r
+ denom.SetZero();\r
+ }\r
+\r
+ denom.Sqrt();\r
+ Div(denom);\r
+ if (sign) mantissa.Sign = !mantissa.Sign;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Calculates Cos(x)\r
+ /// </summary>\r
+ public void Cos()\r
+ {\r
+ if (IsSpecialValue)\r
+ {\r
+ //Cos(x) has no limit as x->inf\r
+ if (SpecialValue == SpecialValueType.INF_MINUS || SpecialValue == SpecialValueType.INF_PLUS)\r
+ {\r
+ SetNaN();\r
+ }\r
+ else if (SpecialValue == SpecialValueType.ZERO)\r
+ {\r
+ Assign(new BigFloat(1, mantissa.Precision));\r
+ }\r
+\r
+ return;\r
+ }\r
+\r
+ if (pi == null || pi.mantissa.Precision.NumBits != mantissa.Precision.NumBits)\r
+ {\r
+ CalculatePi(mantissa.Precision.NumBits);\r
+ }\r
+\r
+ Add(piBy2);\r
+ Sin();\r
+ }\r
+\r
+ /// <summary>\r
+ /// Calculates Sin(x):\r
+ /// This takes a little longer and is less accurate if the input is out of the range (-pi, pi].\r
+ /// </summary>\r
+ public void Sin()\r
+ {\r
+ if (IsSpecialValue)\r
+ {\r
+ //Sin(x) has no limit as x->inf\r
+ if (SpecialValue == SpecialValueType.INF_MINUS || SpecialValue == SpecialValueType.INF_PLUS)\r
+ {\r
+ SetNaN();\r
+ }\r
+\r
+ return;\r
+ }\r
+\r
+ //Convert to positive range (0 <= x < inf)\r
+ bool sign = mantissa.Sign;\r
+ mantissa.Sign = false;\r
+\r
+ if (pi == null || pi.mantissa.Precision.NumBits != mantissa.Precision.NumBits)\r
+ {\r
+ CalculatePi(mantissa.Precision.NumBits);\r
+ }\r
+\r
+ if (inverseFactorialCache == null || invFactorialCutoff != mantissa.Precision.NumBits)\r
+ {\r
+ CalculateFactorials(mantissa.Precision.NumBits);\r
+ }\r
+\r
+ //Rescale into 0 <= x < 2*pi\r
+ if (GreaterThan(twoPi))\r
+ {\r
+ //There will be an inherent loss of precision doing this.\r
+ BigFloat newAngle = new BigFloat(this);\r
+ newAngle.Mul(twoPiRecip);\r
+ newAngle.FPart();\r
+ newAngle.Mul(twoPi);\r
+ Assign(newAngle);\r
+ }\r
+\r
+ //Rescale into range 0 <= x < pi\r
+ if (GreaterThan(pi))\r
+ {\r
+ //sin(pi + a) = sin(pi)cos(a) + sin(a)cos(pi) = 0 - sin(a) = -sin(a)\r
+ Sub(pi);\r
+ sign = !sign;\r
+ }\r
+\r
+ BigFloat temp = new BigFloat(mantissa.Precision);\r
+\r
+ //Rescale into range 0 <= x < pi/2\r
+ if (GreaterThan(piBy2))\r
+ {\r
+ temp.Assign(this);\r
+ Assign(pi);\r
+ Sub(temp);\r
+ }\r
+\r
+ //Rescale into range 0 <= x < pi/6 to accelerate convergence.\r
+ //This is done using sin(3x) = 3sin(x) - 4sin^3(x)\r
+ Mul(threeRecip);\r
+\r
+ if (mantissa.IsZero())\r
+ {\r
+ exponent = 0;\r
+ return;\r
+ }\r
+\r
+ BigFloat term = new BigFloat(this);\r
+\r
+ BigFloat square = new BigFloat(this);\r
+ square.Mul(term);\r
+\r
+ BigFloat sum = new BigFloat(this);\r
+\r
+ bool termSign = true;\r
+ int length = inverseFactorialCache.Length;\r
+ int numBits = mantissa.Precision.NumBits;\r
+\r
+ for (int i = 3; i < length; i += 2)\r
+ {\r
+ term.Mul(square);\r
+ temp.Assign(inverseFactorialCache[i]);\r
+ temp.Mul(term);\r
+ temp.mantissa.Sign = termSign;\r
+ termSign = !termSign;\r
+\r
+ if (temp.exponent < -numBits) break;\r
+\r
+ sum.Add(temp);\r
+ }\r
+\r
+ //Restore the triple-angle: sin(3x) = 3sin(x) - 4sin^3(x)\r
+ Assign(sum);\r
+ sum.Mul(this);\r
+ sum.Mul(this);\r
+ Mul(new BigFloat(3, mantissa.Precision));\r
+ sum.exponent += 2;\r
+ Sub(sum);\r
+\r
+ //Restore the sign\r
+ mantissa.Sign = sign;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Hyperbolic Sin (sinh) function\r
+ /// </summary>\r
+ public void Sinh()\r
+ {\r
+ if (IsSpecialValue)\r
+ {\r
+ return;\r
+ }\r
+\r
+ Exp();\r
+ Sub(Reciprocal());\r
+ exponent--;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Hyperbolic cosine (cosh) function\r
+ /// </summary>\r
+ public void Cosh()\r
+ {\r
+ if (IsSpecialValue)\r
+ {\r
+ if (SpecialValue == SpecialValueType.ZERO)\r
+ {\r
+ Assign(new BigFloat(1, mantissa.Precision));\r
+ }\r
+ else if (SpecialValue == SpecialValueType.INF_MINUS)\r
+ {\r
+ SetInfPlus();\r
+ }\r
+\r
+ return;\r
+ }\r
+\r
+ Exp();\r
+ Add(Reciprocal());\r
+ exponent--;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Hyperbolic tangent function (tanh)\r
+ /// </summary>\r
+ public void Tanh()\r
+ {\r
+ if (IsSpecialValue)\r
+ {\r
+ if (SpecialValue == SpecialValueType.INF_MINUS)\r
+ {\r
+ Assign(new BigFloat(-1, mantissa.Precision));\r
+ }\r
+ else if (SpecialValue == SpecialValueType.INF_PLUS)\r
+ {\r
+ Assign(new BigFloat(1, mantissa.Precision));\r
+ }\r
+\r
+ return;\r
+ }\r
+\r
+ exponent++;\r
+ Exp();\r
+ BigFloat temp = new BigFloat(this);\r
+ BigFloat one = new BigFloat(1, mantissa.Precision);\r
+ temp.Add(one);\r
+ Sub(one);\r
+ Div(temp);\r
+ }\r
+\r
+ /// <summary>\r
+ /// arcsin(): the inverse function of sin(), range of (-pi/2..pi/2)\r
+ /// </summary>\r
+ public void Arcsin()\r
+ {\r
+ if (IsSpecialValue)\r
+ {\r
+ if (SpecialValue == SpecialValueType.INF_MINUS || SpecialValue == SpecialValueType.INF_PLUS || SpecialValue == SpecialValueType.NAN)\r
+ {\r
+ SetNaN();\r
+ return;\r
+ }\r
+\r
+ return;\r
+ }\r
+\r
+ BigFloat one = new BigFloat(1, mantissa.Precision);\r
+ BigFloat plusABit = new BigFloat(1, mantissa.Precision);\r
+ plusABit.exponent -= (mantissa.Precision.NumBits - (mantissa.Precision.NumBits >> 6));\r
+ BigFloat onePlusABit = new BigFloat(1, mantissa.Precision);\r
+ onePlusABit.Add(plusABit);\r
+\r
+ bool sign = mantissa.Sign;\r
+ mantissa.Sign = false;\r
+\r
+ if (GreaterThan(onePlusABit))\r
+ {\r
+ SetNaN();\r
+ }\r
+ else if (LessThan(one))\r
+ {\r
+ BigFloat temp = new BigFloat(this);\r
+ temp.Mul(this);\r
+ temp.Sub(one);\r
+ temp.mantissa.Sign = !temp.mantissa.Sign;\r
+ temp.Sqrt();\r
+ temp.Add(one);\r
+ Div(temp);\r
+ Arctan();\r
+ exponent++;\r
+ mantissa.Sign = sign;\r
+ }\r
+ else\r
+ {\r
+ if (pi == null || pi.mantissa.Precision.NumBits != mantissa.Precision.NumBits)\r
+ {\r
+ CalculatePi(mantissa.Precision.NumBits);\r
+ }\r
+\r
+ Assign(piBy2);\r
+ if (sign) mantissa.Sign = true;\r
+ }\r
+ }\r
+\r
+ /// <summary>\r
+ /// arccos(): the inverse function of cos(), range (0..pi)\r
+ /// </summary>\r
+ public void Arccos()\r
+ {\r
+ if (IsSpecialValue)\r
+ {\r
+ if (SpecialValue == SpecialValueType.INF_MINUS || SpecialValue == SpecialValueType.INF_PLUS || SpecialValue == SpecialValueType.NAN)\r
+ {\r
+ SetNaN();\r
+ }\r
+ else if (SpecialValue == SpecialValueType.ZERO)\r
+ {\r
+ Assign(new BigFloat(1, mantissa.Precision));\r
+ exponent = 0;\r
+ Sign = false;\r
+ }\r
+\r
+ return;\r
+ }\r
+\r
+ BigFloat one = new BigFloat(1, mantissa.Precision);\r
+ BigFloat plusABit = new BigFloat(1, mantissa.Precision);\r
+ plusABit.exponent -= (mantissa.Precision.NumBits - (mantissa.Precision.NumBits >> 6));\r
+ BigFloat onePlusABit = new BigFloat(1, mantissa.Precision);\r
+ onePlusABit.Add(plusABit);\r
+\r
+ bool sign = mantissa.Sign;\r
+ mantissa.Sign = false;\r
+\r
+ if (GreaterThan(onePlusABit))\r
+ {\r
+ SetNaN();\r
+ }\r
+ else if (LessThan(one))\r
+ {\r
+ if (pi == null || pi.mantissa.Precision.NumBits != mantissa.Precision.NumBits)\r
+ {\r
+ CalculatePi(mantissa.Precision.NumBits);\r
+ }\r
+\r
+ mantissa.Sign = sign;\r
+ BigFloat temp = new BigFloat(this);\r
+ Mul(temp);\r
+ Sub(one);\r
+ mantissa.Sign = !mantissa.Sign;\r
+ Sqrt();\r
+ temp.Add(one);\r
+ Div(temp);\r
+ Arctan();\r
+ exponent++;\r
+ }\r
+ else\r
+ {\r
+ if (sign)\r
+ {\r
+ if (pi == null || pi.mantissa.Precision.NumBits != mantissa.Precision.NumBits)\r
+ {\r
+ CalculatePi(mantissa.Precision.NumBits);\r
+ }\r
+\r
+ Assign(pi);\r
+ }\r
+ else\r
+ {\r
+ mantissa.Zero();\r
+ exponent = 0;\r
+ }\r
+ }\r
+ }\r
+\r
+ /// <summary>\r
+ /// arctan(): the inverse function of sin(), range of (-pi/2..pi/2)\r
+ /// </summary>\r
+ public void Arctan()\r
+ {\r
+ //With 2 argument reductions, we increase precision by a minimum of 4 bits per term.\r
+ int numBits = mantissa.Precision.NumBits;\r
+ int maxTerms = numBits >> 2;\r
+\r
+ if (pi == null || pi.mantissa.Precision.NumBits != numBits)\r
+ {\r
+ CalculatePi(mantissa.Precision.NumBits);\r
+ }\r
+\r
+ //Make domain positive\r
+ bool sign = mantissa.Sign;\r
+ mantissa.Sign = false;\r
+\r
+ if (IsSpecialValue)\r
+ {\r
+ if (SpecialValue == SpecialValueType.INF_MINUS || SpecialValue == SpecialValueType.INF_PLUS)\r
+ {\r
+ Assign(piBy2);\r
+ mantissa.Sign = sign;\r
+ return;\r
+ }\r
+\r
+ return;\r
+ }\r
+\r
+ if (reciprocals == null || reciprocals[0].mantissa.Precision.NumBits != numBits || reciprocals.Length < maxTerms)\r
+ {\r
+ CalculateReciprocals(numBits, maxTerms);\r
+ }\r
+\r
+ bool invert = false;\r
+ BigFloat one = new BigFloat(1, mantissa.Precision);\r
+\r
+ //Invert if outside of convergence\r
+ if (GreaterThan(one))\r
+ {\r
+ invert = true;\r
+ Assign(Reciprocal());\r
+ }\r
+\r
+ //Reduce using half-angle formula:\r
+ //arctan(2x) = 2 arctan (x / (1 + sqrt(1 + x)))\r
+\r
+ //First reduction (guarantees 2 bits per iteration)\r
+ BigFloat temp = new BigFloat(this);\r
+ temp.Mul(this);\r
+ temp.Add(one);\r
+ temp.Sqrt();\r
+ temp.Add(one);\r
+ this.Div(temp);\r
+\r
+ //Second reduction (guarantees 4 bits per iteration)\r
+ temp.Assign(this);\r
+ temp.Mul(this);\r
+ temp.Add(one);\r
+ temp.Sqrt();\r
+ temp.Add(one);\r
+ this.Div(temp);\r
+\r
+ //Actual series calculation\r
+ int length = reciprocals.Length;\r
+ BigFloat term = new BigFloat(this);\r
+\r
+ //pow = x^2\r
+ BigFloat pow = new BigFloat(this);\r
+ pow.Mul(this);\r
+\r
+ BigFloat sum = new BigFloat(this);\r
+\r
+ for (int i = 1; i < length; i++)\r
+ {\r
+ //u(n) = u(n-1) * x^2\r
+ //t(n) = u(n) / (2n+1)\r
+ term.Mul(pow);\r
+ term.Sign = !term.Sign;\r
+ temp.Assign(term);\r
+ temp.Mul(reciprocals[i]);\r
+\r
+ if (temp.exponent < -numBits) break;\r
+\r
+ sum.Add(temp);\r
+ }\r
+\r
+ //Undo the reductions.\r
+ Assign(sum);\r
+ exponent += 2;\r
+\r
+ if (invert)\r
+ {\r
+ //Assign(Reciprocal());\r
+ mantissa.Sign = true;\r
+ Add(piBy2);\r
+ }\r
+\r
+ if (sign)\r
+ {\r
+ mantissa.Sign = sign;\r
+ }\r
+ }\r
+\r
+ /// <summary>\r
+ /// Arcsinh(): the inverse sinh function\r
+ /// </summary>\r
+ public void Arcsinh()\r
+ {\r
+ //Just let all special values fall through\r
+ if (IsSpecialValue)\r
+ {\r
+ return;\r
+ }\r
+\r
+ BigFloat temp = new BigFloat(this);\r
+ temp.Mul(this);\r
+ temp.Add(new BigFloat(1, mantissa.Precision));\r
+ temp.Sqrt();\r
+ Add(temp);\r
+ Log();\r
+ }\r
+\r
+ /// <summary>\r
+ /// Arccosh(): the inverse cosh() function\r
+ /// </summary>\r
+ public void Arccosh()\r
+ {\r
+ //acosh isn't defined for x < 1\r
+ if (IsSpecialValue)\r
+ {\r
+ if (SpecialValue == SpecialValueType.INF_MINUS || SpecialValue == SpecialValueType.ZERO)\r
+ {\r
+ SetNaN();\r
+ return;\r
+ }\r
+\r
+ return;\r
+ }\r
+\r
+ BigFloat one = new BigFloat(1, mantissa.Precision);\r
+ if (LessThan(one))\r
+ {\r
+ SetNaN();\r
+ return;\r
+ }\r
+\r
+ BigFloat temp = new BigFloat(this);\r
+ temp.Mul(this);\r
+ temp.Sub(one);\r
+ temp.Sqrt();\r
+ Add(temp);\r
+ Log();\r
+ }\r
+\r
+ /// <summary>\r
+ /// Arctanh(): the inverse tanh function\r
+ /// </summary>\r
+ public void Arctanh()\r
+ {\r
+ //|x| <= 1 for a non-NaN output\r
+ if (IsSpecialValue)\r
+ {\r
+ if (SpecialValue == SpecialValueType.INF_MINUS || SpecialValue == SpecialValueType.INF_PLUS)\r
+ {\r
+ SetNaN();\r
+ return;\r
+ }\r
+\r
+ return;\r
+ }\r
+\r
+ BigFloat one = new BigFloat(1, mantissa.Precision);\r
+ BigFloat plusABit = new BigFloat(1, mantissa.Precision);\r
+ plusABit.exponent -= (mantissa.Precision.NumBits - (mantissa.Precision.NumBits >> 6));\r
+ BigFloat onePlusABit = new BigFloat(1, mantissa.Precision);\r
+ onePlusABit.Add(plusABit);\r
+\r
+ bool sign = mantissa.Sign;\r
+ mantissa.Sign = false;\r
+\r
+ if (GreaterThan(onePlusABit))\r
+ {\r
+ SetNaN();\r
+ }\r
+ else if (LessThan(one))\r
+ {\r
+ BigFloat temp = new BigFloat(this);\r
+ Add(one);\r
+ one.Sub(temp);\r
+ Div(one);\r
+ Log();\r
+ exponent--;\r
+ mantissa.Sign = sign;\r
+ }\r
+ else\r
+ {\r
+ if (sign)\r
+ {\r
+ SetInfMinus();\r
+ }\r
+ else\r
+ {\r
+ SetInfPlus();\r
+ }\r
+ }\r
+ }\r
+\r
+ /// <summary>\r
+ /// Two-variable iterative square root, taken from\r
+ /// http://en.wikipedia.org/wiki/Methods_of_computing_square_roots#A_two-variable_iterative_method\r
+ /// </summary>\r
+ public void Sqrt()\r
+ {\r
+ if (mantissa.Sign || IsSpecialValue)\r
+ {\r
+ if (SpecialValue == SpecialValueType.ZERO)\r
+ {\r
+ return;\r
+ }\r
+\r
+ if (SpecialValue == SpecialValueType.INF_MINUS || mantissa.Sign)\r
+ {\r
+ SetNaN();\r
+ }\r
+\r
+ return;\r
+ }\r
+\r
+ BigFloat temp2;\r
+ BigFloat temp3 = new BigFloat(mantissa.Precision);\r
+ BigFloat three = new BigFloat(3, mantissa.Precision);\r
+\r
+ int exponentScale = 0;\r
+\r
+ //Rescale to 0.5 <= x < 2\r
+ if (exponent < -1)\r
+ {\r
+ int diff = -exponent;\r
+ if ((diff & 1) != 0)\r
+ {\r
+ diff--;\r
+ }\r
+\r
+ exponentScale = -diff;\r
+ exponent += diff;\r
+ }\r
+ else if (exponent > 0)\r
+ {\r
+ if ((exponent & 1) != 0)\r
+ {\r
+ exponentScale = exponent + 1;\r
+ exponent = -1;\r
+ }\r
+ else\r
+ {\r
+ exponentScale = exponent;\r
+ exponent = 0;\r
+ }\r
+ }\r
+\r
+ temp2 = new BigFloat(this);\r
+ temp2.Sub(new BigFloat(1, mantissa.Precision));\r
+\r
+ //if (temp2.mantissa.IsZero())\r
+ //{\r
+ // exponent += exponentScale;\r
+ // return;\r
+ //}\r
+\r
+ int numBits = mantissa.Precision.NumBits;\r
+\r
+ while ((exponent - temp2.exponent) < numBits && temp2.SpecialValue != SpecialValueType.ZERO)\r
+ {\r
+ //a(n+1) = an - an*cn / 2\r
+ temp3.Assign(this);\r
+ temp3.Mul(temp2);\r
+ temp3.MulPow2(-1);\r
+ this.Sub(temp3);\r
+\r
+ //c(n+1) = cn^2 * (cn - 3) / 4\r
+ temp3.Assign(temp2);\r
+ temp2.Sub(three);\r
+ temp2.Mul(temp3);\r
+ temp2.Mul(temp3);\r
+ temp2.MulPow2(-2);\r
+ }\r
+\r
+ exponent += (exponentScale >> 1);\r
+ }\r
+\r
+ /// <summary>\r
+ /// The natural logarithm, ln(x)\r
+ /// </summary>\r
+ public void Log()\r
+ {\r
+ if (IsSpecialValue || mantissa.Sign)\r
+ {\r
+ if (SpecialValue == SpecialValueType.INF_MINUS || mantissa.Sign)\r
+ {\r
+ SetNaN();\r
+ }\r
+ else if (SpecialValue == SpecialValueType.ZERO)\r
+ {\r
+ SetInfMinus();\r
+ }\r
+\r
+ return;\r
+ }\r
+\r
+ if (mantissa.Precision.NumBits >= 512)\r
+ {\r
+ LogAGM1();\r
+ return;\r
+ }\r
+\r
+ //Compute ln2.\r
+ if (ln2cache == null || mantissa.Precision.NumBits > ln2cache.mantissa.Precision.NumBits)\r
+ {\r
+ CalculateLog2(mantissa.Precision.NumBits);\r
+ }\r
+\r
+ Log2();\r
+ Mul(ln2cache);\r
+ }\r
+\r
+ /// <summary>\r
+ /// Log to the base 10\r
+ /// </summary>\r
+ public void Log10()\r
+ {\r
+ if (IsSpecialValue || mantissa.Sign)\r
+ {\r
+ if (SpecialValue == SpecialValueType.INF_MINUS || mantissa.Sign)\r
+ {\r
+ SetNaN();\r
+ }\r
+ else if (SpecialValue == SpecialValueType.ZERO)\r
+ {\r
+ SetInfMinus();\r
+ }\r
+\r
+ return;\r
+ }\r
+\r
+ //Compute ln2.\r
+ if (ln2cache == null || mantissa.Precision.NumBits > ln2cache.mantissa.Precision.NumBits)\r
+ {\r
+ CalculateLog2(mantissa.Precision.NumBits);\r
+ }\r
+\r
+ Log();\r
+ Mul(log10recip);\r
+ }\r
+\r
+ /// <summary>\r
+ /// The exponential function. Less accurate for high exponents, scales poorly with the number\r
+ /// of bits.\r
+ /// </summary>\r
+ public void Exp()\r
+ {\r
+ Exp(mantissa.Precision.NumBits);\r
+ }\r
+\r
+ /// <summary>\r
+ /// Raises a number to an integer power (positive or negative). This is a very accurate and fast function,\r
+ /// comparable to or faster than division (although it is slightly slower for\r
+ /// negative powers, obviously)\r
+ /// \r
+ /// </summary>\r
+ /// <param name="power"></param>\r
+ public void Pow(int power)\r
+ {\r
+ BigFloat acc = new BigFloat(1, mantissa.Precision);\r
+ BigFloat temp = new BigFloat(1, mantissa.Precision);\r
+\r
+ int powerTemp = power;\r
+\r
+ if (power < 0)\r
+ {\r
+ Assign(Reciprocal());\r
+ powerTemp = -power;\r
+ }\r
+\r
+ //Fast power function\r
+ while (powerTemp != 0)\r
+ {\r
+ temp.Mul(this);\r
+ Assign(temp);\r
+\r
+ if ((powerTemp & 1) != 0)\r
+ {\r
+ acc.Mul(temp);\r
+ }\r
+\r
+ powerTemp >>= 1;\r
+ }\r
+\r
+ Assign(acc);\r
+ }\r
+\r
+ /// <summary>\r
+ /// Raises to an aribitrary power. This is both slow (uses Log) and inaccurate. If you need to\r
+ /// raise e^x use exp(). If you need an integer power, use the integer power function Pow(int)\r
+ /// Accuracy Note:\r
+ /// The function is only ever accurate to a maximum of 4 decimal digits\r
+ /// For every 10x larger (or smaller) the power gets, you lose an additional decimal digit\r
+ /// If you really need a precise result, do the calculation with an extra 32-bits and round\r
+ /// Domain Note:\r
+ /// This only works for powers of positive real numbers. Negative numbers will fail.\r
+ /// </summary>\r
+ /// <param name="power"></param>\r
+ public void Pow(BigFloat power)\r
+ {\r
+ Log();\r
+ Mul(power);\r
+ Exp();\r
+ }\r
+\r
+\r
+ //******************** Static Math Functions *******************\r
+\r
+ /// <summary>\r
+ /// Returns the integer component of the input\r
+ /// </summary>\r
+ /// <param name="n1">The input number</param>\r
+ /// <remarks>The integer component returned will always be numerically closer to zero\r
+ /// than the input: an input of -3.49 for instance would produce a value of 3.</remarks>\r
+ public static BigFloat Floor(BigFloat n1)\r
+ {\r
+ BigFloat res = new BigFloat(n1);\r
+ n1.Floor();\r
+ return n1;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Returns the fractional (non-integer component of the input)\r
+ /// </summary>\r
+ /// <param name="n1">The input number</param>\r
+ public static BigFloat FPart(BigFloat n1)\r
+ {\r
+ BigFloat res = new BigFloat(n1);\r
+ n1.FPart();\r
+ return n1;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Calculates tan(x)\r
+ /// </summary>\r
+ /// <param name="n1">The angle (in radians) to find the tangent of</param>\r
+ public static BigFloat Tan(BigFloat n1)\r
+ {\r
+ BigFloat res = new BigFloat(n1);\r
+ n1.Tan();\r
+ return n1;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Calculates Cos(x)\r
+ /// </summary>\r
+ /// <param name="n1">The angle (in radians) to find the cosine of</param>\r
+ /// <remarks>This is a reasonably fast function for smaller precisions, but\r
+ /// doesn't scale well for higher precision arguments</remarks>\r
+ public static BigFloat Cos(BigFloat n1)\r
+ {\r
+ BigFloat res = new BigFloat(n1);\r
+ n1.Cos();\r
+ return n1;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Calculates Sin(x):\r
+ /// This takes a little longer and is less accurate if the input is out of the range (-pi, pi].\r
+ /// </summary>\r
+ /// <param name="n1">The angle to find the sine of (in radians)</param>\r
+ /// <remarks>This is a resonably fast function, for smaller precision arguments, but doesn't\r
+ /// scale very well with the number of bits in the input.</remarks>\r
+ public static BigFloat Sin(BigFloat n1)\r
+ {\r
+ BigFloat res = new BigFloat(n1);\r
+ n1.Sin();\r
+ return n1;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Hyperbolic Sin (sinh) function\r
+ /// </summary>\r
+ /// <param name="n1">The number to find the hyperbolic sine of</param>\r
+ public static BigFloat Sinh(BigFloat n1)\r
+ {\r
+ BigFloat res = new BigFloat(n1);\r
+ n1.Sinh();\r
+ return n1;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Hyperbolic cosine (cosh) function\r
+ /// </summary>\r
+ /// <param name="n1">The number to find the hyperbolic cosine of</param>\r
+ public static BigFloat Cosh(BigFloat n1)\r
+ {\r
+ BigFloat res = new BigFloat(n1);\r
+ n1.Cosh();\r
+ return n1;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Hyperbolic tangent function (tanh)\r
+ /// </summary>\r
+ /// <param name="n1">The number to find the hyperbolic tangent of</param>\r
+ public static BigFloat Tanh(BigFloat n1)\r
+ {\r
+ BigFloat res = new BigFloat(n1);\r
+ n1.Tanh();\r
+ return n1;\r
+ }\r
+\r
+ /// <summary>\r
+ /// arcsin(): the inverse function of sin(), range of (-pi/2..pi/2)\r
+ /// </summary>\r
+ /// <param name="n1">The number to find the arcsine of (-pi/2..pi/2)</param>\r
+ /// <remarks>Note that inverse trig functions are only defined within a specific range.\r
+ /// Values outside this range will return NaN, although some margin for error is assumed.\r
+ /// </remarks>\r
+ public static BigFloat Arcsin(BigFloat n1)\r
+ {\r
+ BigFloat res = new BigFloat(n1);\r
+ n1.Arcsin();\r
+ return n1;\r
+ }\r
+\r
+ /// <summary>\r
+ /// arccos(): the inverse function of cos(), input range (0..pi)\r
+ /// </summary>\r
+ /// <param name="n1">The number to find the arccosine of (0..pi)</param>\r
+ /// <remarks>Note that inverse trig functions are only defined within a specific range.\r
+ /// Values outside this range will return NaN, although some margin for error is assumed.\r
+ /// </remarks>\r
+ public static BigFloat Arccos(BigFloat n1)\r
+ {\r
+ BigFloat res = new BigFloat(n1);\r
+ n1.Arccos();\r
+ return n1;\r
+ }\r
+\r
+ /// <summary>\r
+ /// arctan(): the inverse function of sin(), input range of (-pi/2..pi/2)\r
+ /// </summary>\r
+ /// <param name="n1">The number to find the arctangent of (-pi/2..pi/2)</param>\r
+ /// <remarks>Note that inverse trig functions are only defined within a specific range.\r
+ /// Values outside this range will return NaN, although some margin for error is assumed.\r
+ /// </remarks>\r
+ public static BigFloat Arctan(BigFloat n1)\r
+ {\r
+ BigFloat res = new BigFloat(n1);\r
+ n1.Arctan();\r
+ return n1;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Arcsinh(): the inverse sinh function\r
+ /// </summary>\r
+ /// <param name="n1">The number to find the inverse hyperbolic sine of</param>\r
+ public static BigFloat Arcsinh(BigFloat n1)\r
+ {\r
+ BigFloat res = new BigFloat(n1);\r
+ n1.Arcsinh();\r
+ return n1;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Arccosh(): the inverse cosh() function\r
+ /// </summary>\r
+ /// <param name="n1">The number to find the inverse hyperbolic cosine of</param>\r
+ public static BigFloat Arccosh(BigFloat n1)\r
+ {\r
+ BigFloat res = new BigFloat(n1);\r
+ n1.Arccosh();\r
+ return n1;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Arctanh(): the inverse tanh function\r
+ /// </summary>\r
+ /// <param name="n1">The number to fine the inverse hyperbolic tan of</param>\r
+ public static BigFloat Arctanh(BigFloat n1)\r
+ {\r
+ BigFloat res = new BigFloat(n1);\r
+ n1.Arctanh();\r
+ return n1;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Two-variable iterative square root, taken from\r
+ /// http://en.wikipedia.org/wiki/Methods_of_computing_square_roots#A_two-variable_iterative_method\r
+ /// </summary>\r
+ /// <remarks>This is quite a fast function, as elementary functions go. You can expect it to take\r
+ /// about twice as long as a floating-point division.\r
+ /// </remarks>\r
+ public static BigFloat Sqrt(BigFloat n1)\r
+ {\r
+ BigFloat res = new BigFloat(n1);\r
+ n1.Sqrt();\r
+ return n1;\r
+ }\r
+\r
+ /// <summary>\r
+ /// The natural logarithm, ln(x) (log base e)\r
+ /// </summary>\r
+ /// <remarks>This is a very slow function, despite repeated attempts at optimisation.\r
+ /// To make it any faster, different strategies would be needed for integer operations.\r
+ /// It does, however, scale well with the number of bits.\r
+ /// </remarks>\r
+ /// <param name="n1">The number to find the natural logarithm of</param>\r
+ public static BigFloat Log(BigFloat n1)\r
+ {\r
+ BigFloat res = new BigFloat(n1);\r
+ n1.Log();\r
+ return n1;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Base 10 logarithm of a number\r
+ /// </summary>\r
+ /// <remarks>This is a very slow function, despite repeated attempts at optimisation.\r
+ /// To make it any faster, different strategies would be needed for integer operations.\r
+ /// It does, however, scale well with the number of bits.\r
+ /// </remarks>\r
+ /// <param name="n1">The number to find the base 10 logarithm of</param>\r
+ public static BigFloat Log10(BigFloat n1)\r
+ {\r
+ BigFloat res = new BigFloat(n1);\r
+ n1.Log10();\r
+ return n1;\r
+ }\r
+\r
+ /// <summary>\r
+ /// The exponential function. Less accurate for high exponents, scales poorly with the number\r
+ /// of bits. This is quite fast for low-precision arguments.\r
+ /// </summary>\r
+ public static BigFloat Exp(BigFloat n1)\r
+ {\r
+ BigFloat res = new BigFloat(n1);\r
+ n1.Exp();\r
+ return n1;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Raises a number to an integer power (positive or negative). This is a very accurate and fast function,\r
+ /// comparable to or faster than division (although it is slightly slower for\r
+ /// negative powers, obviously).\r
+ /// </summary>\r
+ /// <param name="n1">The number to raise to the power</param>\r
+ /// <param name="power">The power to raise it to</param>\r
+ public static BigFloat Pow(BigFloat n1, int power)\r
+ {\r
+ BigFloat res = new BigFloat(n1);\r
+ n1.Pow(power);\r
+ return n1;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Raises to an aribitrary power. This is both slow (uses Log) and inaccurate. If you need to\r
+ /// raise e^x use exp(). If you need an integer power, use the integer power function Pow(int)\r
+ /// </summary>\r
+ /// <remarks>\r
+ /// Accuracy Note:\r
+ /// The function is only ever accurate to a maximum of 4 decimal digits\r
+ /// For every 10x larger (or smaller) the power gets, you lose an additional decimal digit\r
+ /// If you really need a precise result, do the calculation with an extra 32-bits and round\r
+ /// \r
+ /// Domain Note:\r
+ /// This only works for powers of positive real numbers. Negative numbers will fail.\r
+ /// </remarks>\r
+ /// <param name="n1">The number to raise to a power</param>\r
+ /// <param name="power">The power to raise it to</param>\r
+ public static BigFloat Pow(BigFloat n1, BigFloat power)\r
+ {\r
+ BigFloat res = new BigFloat(n1);\r
+ n1.Pow(power);\r
+ return n1;\r
+ }\r
+\r
+ //********************** Static functions **********************\r
+\r
+ /// <summary>\r
+ /// Adds two numbers and returns the result\r
+ /// </summary>\r
+ public static BigFloat Add(BigFloat n1, BigFloat n2)\r
+ {\r
+ BigFloat ret = new BigFloat(n1);\r
+ ret.Add(n2);\r
+ return ret;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Subtracts two numbers and returns the result\r
+ /// </summary>\r
+ public static BigFloat Sub(BigFloat n1, BigFloat n2)\r
+ {\r
+ BigFloat ret = new BigFloat(n1);\r
+ ret.Sub(n2);\r
+ return ret;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Multiplies two numbers and returns the result\r
+ /// </summary>\r
+ public static BigFloat Mul(BigFloat n1, BigFloat n2)\r
+ {\r
+ BigFloat ret = new BigFloat(n1);\r
+ ret.Mul(n2);\r
+ return ret;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Divides two numbers and returns the result\r
+ /// </summary>\r
+ public static BigFloat Div(BigFloat n1, BigFloat n2)\r
+ {\r
+ BigFloat ret = new BigFloat(n1);\r
+ ret.Div(n2);\r
+ return ret;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Tests whether n1 is greater than n2\r
+ /// </summary>\r
+ public static bool GreaterThan(BigFloat n1, BigFloat n2)\r
+ {\r
+ return n1.GreaterThan(n2);\r
+ }\r
+\r
+ /// <summary>\r
+ /// Tests whether n1 is less than n2\r
+ /// </summary>\r
+ public static bool LessThan(BigFloat n1, BigFloat n2)\r
+ {\r
+ return n1.LessThan(n2);\r
+ }\r
+\r
+\r
+ //******************* Fast static functions ********************\r
+\r
+ /// <summary>\r
+ /// Adds two numbers and assigns the result to res.\r
+ /// </summary>\r
+ /// <param name="res">a pre-existing BigFloat to take the result</param>\r
+ /// <param name="n1">the first number</param>\r
+ /// <param name="n2">the second number</param>\r
+ /// <returns>a handle to res</returns>\r
+ public static BigFloat Add(BigFloat res, BigFloat n1, BigFloat n2)\r
+ {\r
+ res.Assign(n1);\r
+ res.Add(n2);\r
+ return res;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Subtracts two numbers and assigns the result to res.\r
+ /// </summary>\r
+ /// <param name="res">a pre-existing BigFloat to take the result</param>\r
+ /// <param name="n1">the first number</param>\r
+ /// <param name="n2">the second number</param>\r
+ /// <returns>a handle to res</returns>\r
+ public static BigFloat Sub(BigFloat res, BigFloat n1, BigFloat n2)\r
+ {\r
+ res.Assign(n1);\r
+ res.Sub(n2);\r
+ return res;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Multiplies two numbers and assigns the result to res.\r
+ /// </summary>\r
+ /// <param name="res">a pre-existing BigFloat to take the result</param>\r
+ /// <param name="n1">the first number</param>\r
+ /// <param name="n2">the second number</param>\r
+ /// <returns>a handle to res</returns>\r
+ public static BigFloat Mul(BigFloat res, BigFloat n1, BigFloat n2)\r
+ {\r
+ res.Assign(n1);\r
+ res.Mul(n2);\r
+ return res;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Divides two numbers and assigns the result to res.\r
+ /// </summary>\r
+ /// <param name="res">a pre-existing BigFloat to take the result</param>\r
+ /// <param name="n1">the first number</param>\r
+ /// <param name="n2">the second number</param>\r
+ /// <returns>a handle to res</returns>\r
+ public static BigFloat Div(BigFloat res, BigFloat n1, BigFloat n2)\r
+ {\r
+ res.Assign(n1);\r
+ res.Div(n2);\r
+ return res;\r
+ }\r
+\r
+\r
+ //************************* Operators **************************\r
+\r
+ /// <summary>\r
+ /// The addition operator\r
+ /// </summary>\r
+ public static BigFloat operator +(BigFloat n1, BigFloat n2)\r
+ {\r
+ return Add(n1, n2);\r
+ }\r
+\r
+ /// <summary>\r
+ /// The subtraction operator\r
+ /// </summary>\r
+ public static BigFloat operator -(BigFloat n1, BigFloat n2)\r
+ {\r
+ return Sub(n1, n2);\r
+ }\r
+\r
+ /// <summary>\r
+ /// The multiplication operator\r
+ /// </summary>\r
+ public static BigFloat operator *(BigFloat n1, BigFloat n2)\r
+ {\r
+ return Mul(n1, n2);\r
+ }\r
+\r
+ /// <summary>\r
+ /// The division operator\r
+ /// </summary>\r
+ public static BigFloat operator /(BigFloat n1, BigFloat n2)\r
+ {\r
+ return Div(n1, n2);\r
+ }\r
+\r
+ //************************** Conversions *************************\r
+\r
+ /// <summary>\r
+ /// Converts a BigFloat to an BigInt with the specified precision\r
+ /// </summary>\r
+ /// <param name="n1">The number to convert</param>\r
+ /// <param name="precision">The precision to convert it with</param>\r
+ /// <param name="round">Do we round the number if we are truncating the mantissa?</param>\r
+ /// <returns></returns>\r
+ public static BigInt ConvertToInt(BigFloat n1, PrecisionSpec precision, bool round)\r
+ {\r
+ BigInt ret = new BigInt(precision);\r
+\r
+ int numBits = n1.mantissa.Precision.NumBits;\r
+ int shift = numBits - (n1.exponent + 1);\r
+\r
+ BigFloat copy = new BigFloat(n1);\r
+ bool inc = false;\r
+\r
+ //Rounding\r
+ if (copy.mantissa.Precision.NumBits > ret.Precision.NumBits)\r
+ {\r
+ inc = true;\r
+\r
+ for (int i = copy.exponent + 1; i <= ret.Precision.NumBits; i++)\r
+ {\r
+ if (copy.mantissa.GetBitFromTop(i) == 0)\r
+ {\r
+ inc = false;\r
+ break;\r
+ }\r
+ }\r
+ }\r
+\r
+ if (shift > 0)\r
+ {\r
+ copy.mantissa.RSH(shift);\r
+ }\r
+ else if (shift < 0)\r
+ {\r
+ copy.mantissa.LSH(-shift);\r
+ }\r
+\r
+ ret.Assign(copy.mantissa);\r
+\r
+ if (inc) ret.Increment();\r
+\r
+ return ret;\r
+ }\r
+\r
+ /// <summary>\r
+ /// Returns a base-10 string representing the number.\r
+ /// \r
+ /// Note: This is inefficient and possibly inaccurate. Please use with enough\r
+ /// rounding digits (set using the RoundingDigits property) to ensure accuracy\r
+ /// </summary>\r
+ public override string ToString()\r
+ {\r
+ if (IsSpecialValue)\r
+ {\r
+ SpecialValueType s = SpecialValue;\r
+ if (s == SpecialValueType.ZERO)\r
+ {\r
+ return String.Format("0{0}0", System.Globalization.CultureInfo.CurrentCulture.NumberFormat.NumberDecimalSeparator);\r
+ }\r
+ else if (s == SpecialValueType.INF_PLUS)\r
+ {\r
+ return System.Globalization.CultureInfo.CurrentCulture.NumberFormat.PositiveInfinitySymbol;\r
+ }\r
+ else if (s == SpecialValueType.INF_MINUS)\r
+ {\r
+ return System.Globalization.CultureInfo.CurrentCulture.NumberFormat.NegativeInfinitySymbol;\r
+ }\r
+ else if (s == SpecialValueType.NAN)\r
+ {\r
+ return System.Globalization.CultureInfo.CurrentCulture.NumberFormat.NaNSymbol;\r
+ }\r
+ else\r
+ {\r
+ return "Unrecognised special type";\r
+ }\r
+ }\r
+\r
+ if (scratch.Precision.NumBits != mantissa.Precision.NumBits)\r
+ {\r
+ scratch = new BigInt(mantissa.Precision);\r
+ }\r
+\r
+ //The mantissa expresses 1.xxxxxxxxxxx\r
+ //The highest possible value for the mantissa without the implicit 1. is 0.9999999...\r
+ scratch.Assign(mantissa);\r
+ //scratch.Round(3);\r
+ scratch.Sign = false;\r
+ BigInt denom = new BigInt("0", mantissa.Precision);\r
+ denom.SetBit(mantissa.Precision.NumBits - 1);\r
+\r
+ bool useExponentialNotation = false;\r
+ int halfBits = mantissa.Precision.NumBits / 2;\r
+ if (halfBits > 60) halfBits = 60;\r
+ int precDec = 10;\r
+\r
+ if (exponent > 0)\r
+ {\r
+ if (exponent < halfBits)\r
+ {\r
+ denom.RSH(exponent);\r
+ }\r
+ else\r
+ {\r
+ useExponentialNotation = true;\r
+ }\r
+ }\r
+ else if (exponent < 0)\r
+ {\r
+ int shift = -(exponent);\r
+ if (shift < precDec)\r
+ {\r
+ scratch.RSH(shift);\r
+ }\r
+ else\r
+ {\r
+ useExponentialNotation = true;\r
+ }\r
+ }\r
+\r
+ string output;\r
+\r
+ if (useExponentialNotation)\r
+ {\r
+ int absExponent = exponent;\r
+ if (absExponent < 0) absExponent = -absExponent;\r
+ int powerOf10 = (int)((double)absExponent * Math.Log10(2.0));\r
+\r
+ //Use 1 extra digit of precision (this is actually 32 bits more, nb)\r
+ BigFloat thisFloat = new BigFloat(this, new PrecisionSpec(mantissa.Precision.NumBits + 1, PrecisionSpec.BaseType.BIN));\r
+ thisFloat.mantissa.Sign = false;\r
+\r
+ //Multiplicative correction factor to bring number into range.\r
+ BigFloat one = new BigFloat(1, new PrecisionSpec(mantissa.Precision.NumBits + 1, PrecisionSpec.BaseType.BIN));\r
+ BigFloat ten = new BigFloat(10, new PrecisionSpec(mantissa.Precision.NumBits + 1, PrecisionSpec.BaseType.BIN));\r
+ BigFloat tenRCP = ten.Reciprocal();\r
+\r
+ //Accumulator for the power of 10 calculation.\r
+ BigFloat acc = new BigFloat(1, new PrecisionSpec(mantissa.Precision.NumBits + 1, PrecisionSpec.BaseType.BIN));\r
+\r
+ BigFloat tenToUse;\r
+\r
+ if (exponent > 0)\r
+ {\r
+ tenToUse = new BigFloat(tenRCP, new PrecisionSpec(mantissa.Precision.NumBits + 1, PrecisionSpec.BaseType.BIN));\r
+ }\r
+ else\r
+ {\r
+ tenToUse = new BigFloat(ten, new PrecisionSpec(mantissa.Precision.NumBits + 1, PrecisionSpec.BaseType.BIN));\r
+ }\r
+\r
+ BigFloat tenToPower = new BigFloat(1, new PrecisionSpec(mantissa.Precision.NumBits + 1, PrecisionSpec.BaseType.BIN));\r
+\r
+ int powerTemp = powerOf10;\r
+\r
+ //Fast power function\r
+ while (powerTemp != 0)\r
+ {\r
+ tenToPower.Mul(tenToUse);\r
+ tenToUse.Assign(tenToPower);\r
+\r
+ if ((powerTemp & 1) != 0)\r
+ {\r
+ acc.Mul(tenToPower);\r
+ }\r
+\r
+ powerTemp >>= 1;\r
+ }\r
+\r
+ thisFloat.Mul(acc);\r
+\r
+ //If we are out of range, correct. \r
+ if (thisFloat.GreaterThan(ten))\r
+ {\r
+ thisFloat.Mul(tenRCP);\r
+ if (exponent > 0)\r
+ {\r
+ powerOf10++;\r
+ }\r
+ else\r
+ {\r
+ powerOf10--;\r
+ }\r
+ }\r
+ else if (thisFloat.LessThan(one))\r
+ {\r
+ thisFloat.Mul(ten);\r
+ if (exponent > 0)\r
+ {\r
+ powerOf10--;\r
+ }\r
+ else\r
+ {\r
+ powerOf10++;\r
+ }\r
+ }\r
+\r
+ //Restore the precision and the sign.\r
+ BigFloat printable = new BigFloat(thisFloat, mantissa.Precision);\r
+ printable.mantissa.Sign = mantissa.Sign;\r
+ output = printable.ToString();\r
+\r
+ if (exponent < 0) powerOf10 = -powerOf10;\r
+\r
+ output = String.Format("{0}E{1}", output, powerOf10);\r
+ }\r
+ else\r
+ {\r
+ BigInt bigDigit = BigInt.Div(scratch, denom);\r
+ bigDigit.Sign = false;\r
+ scratch.Sub(BigInt.Mul(denom, bigDigit));\r
+\r
+ if (mantissa.Sign)\r
+ {\r
+ output = String.Format("-{0}.", bigDigit);\r
+ }\r
+ else\r
+ {\r
+ output = String.Format("{0}.", bigDigit);\r
+ }\r
+\r
+ denom = BigInt.Div(denom, 10u);\r
+\r
+ while (!denom.IsZero())\r
+ {\r
+ uint digit = (uint)BigInt.Div(scratch, denom);\r
+ if (digit == 10) digit--;\r
+ scratch.Sub(BigInt.Mul(denom, digit));\r
+ output = String.Format("{0}{1}", output, digit);\r
+ denom = BigInt.Div(denom, 10u);\r
+ }\r
+\r
+ output = RoundString(output, RoundingDigits);\r
+ }\r
+\r
+ return output;\r
+ }\r
+\r
+ //**************** Special value handling for ops ***************\r
+\r
+ private void SetNaN()\r
+ {\r
+ exponent = Int32.MaxValue;\r
+ mantissa.SetBit(mantissa.Precision.NumBits - 1);\r
+ }\r
+\r
+ private void SetZero()\r
+ {\r
+ exponent = 0;\r
+ mantissa.Zero();\r
+ Sign = false;\r
+ }\r
+\r
+ private void SetInfPlus()\r
+ {\r
+ Sign = false;\r
+ exponent = Int32.MaxValue;\r
+ mantissa.Zero();\r
+ }\r
+\r
+ private void SetInfMinus()\r
+ {\r
+ Sign = true;\r
+ exponent = Int32.MaxValue;\r
+ mantissa.Zero();\r
+ }\r
+\r
+ private bool SpecialValueAddTest(BigFloat n2)\r
+ {\r
+ if (IsSpecialValue || n2.IsSpecialValue)\r
+ {\r
+ SpecialValueType s1 = SpecialValue;\r
+ SpecialValueType s2 = n2.SpecialValue;\r
+\r
+ if (s1 == SpecialValueType.NAN) return true;\r
+ if (s2 == SpecialValueType.NAN)\r
+ {\r
+ //Set NaN and return.\r
+ SetNaN();\r
+ return true;\r
+ }\r
+\r
+ if (s1 == SpecialValueType.INF_PLUS)\r
+ {\r
+ //INF+ + INF- = NAN\r
+ if (s2 == SpecialValueType.INF_MINUS)\r
+ {\r
+ SetNaN();\r
+ return true;\r
+ }\r
+\r
+ return true;\r
+ }\r
+\r
+ if (s1 == SpecialValueType.INF_MINUS)\r
+ {\r
+ //INF+ + INF- = NAN\r
+ if (s2 == SpecialValueType.INF_PLUS)\r
+ {\r
+ SetNaN();\r
+ return true;\r
+ }\r
+\r
+ return true;\r
+ }\r
+\r
+ if (s2 == SpecialValueType.ZERO)\r
+ {\r
+ return true;\r
+ }\r
+\r
+ if (s1 == SpecialValueType.ZERO)\r
+ {\r
+ Assign(n2);\r
+ return true;\r
+ }\r
+ }\r
+\r
+ return false;\r
+ }\r
+\r
+ private bool SpecialValueMulTest(BigFloat n2)\r
+ {\r
+ if (IsSpecialValue || n2.IsSpecialValue)\r
+ {\r
+ SpecialValueType s1 = SpecialValue;\r
+ SpecialValueType s2 = n2.SpecialValue;\r
+\r
+ if (s1 == SpecialValueType.NAN) return true;\r
+ if (s2 == SpecialValueType.NAN)\r
+ {\r
+ //Set NaN and return.\r
+ SetNaN();\r
+ return true;\r
+ }\r
+\r
+ if (s1 == SpecialValueType.INF_PLUS)\r
+ {\r
+ //Inf+ * Inf- = Inf-\r
+ if (s2 == SpecialValueType.INF_MINUS)\r
+ {\r
+ Assign(n2);\r
+ return true;\r
+ }\r
+\r
+ //Inf+ * 0 = NaN\r
+ if (s2 == SpecialValueType.ZERO)\r
+ {\r
+ //Set NaN and return.\r
+ SetNaN();\r
+ return true;\r
+ }\r
+\r
+ return true;\r
+ }\r
+\r
+ if (s1 == SpecialValueType.INF_MINUS)\r
+ {\r
+ //Inf- * Inf- = Inf+\r
+ if (s2 == SpecialValueType.INF_MINUS)\r
+ {\r
+ Sign = false;\r
+ return true;\r
+ }\r
+\r
+ //Inf- * 0 = NaN\r
+ if (s2 == SpecialValueType.ZERO)\r
+ {\r
+ //Set NaN and return.\r
+ SetNaN();\r
+ return true;\r
+ }\r
+\r
+ return true;\r
+ }\r
+\r
+ if (s2 == SpecialValueType.ZERO)\r
+ {\r
+ SetZero();\r
+ return true;\r
+ }\r
+\r
+ if (s1 == SpecialValueType.ZERO)\r
+ {\r
+ return true;\r
+ }\r
+ }\r
+\r
+ return false;\r
+ }\r
+\r
+ private bool SpecialValueDivTest(BigFloat n2)\r
+ {\r
+ if (IsSpecialValue || n2.IsSpecialValue)\r
+ {\r
+ SpecialValueType s1 = SpecialValue;\r
+ SpecialValueType s2 = n2.SpecialValue;\r
+\r
+ if (s1 == SpecialValueType.NAN) return true;\r
+ if (s2 == SpecialValueType.NAN)\r
+ {\r
+ //Set NaN and return.\r
+ SetNaN();\r
+ return true;\r
+ }\r
+\r
+ if ((s1 == SpecialValueType.INF_PLUS || s1 == SpecialValueType.INF_MINUS))\r
+ {\r
+ if (s2 == SpecialValueType.INF_PLUS || s2 == SpecialValueType.INF_MINUS)\r
+ {\r
+ //Set NaN and return.\r
+ SetNaN();\r
+ return true;\r
+ }\r
+\r
+ if (n2.Sign)\r
+ {\r
+ if (s1 == SpecialValueType.INF_PLUS)\r
+ {\r
+ SetInfMinus();\r
+ return true;\r
+ }\r
+\r
+ SetInfPlus();\r
+ return true;\r
+ }\r
+\r
+ //Keep inf\r
+ return true;\r
+ }\r
+\r
+ if (s2 == SpecialValueType.ZERO)\r
+ {\r
+ if (s1 == SpecialValueType.ZERO)\r
+ {\r
+ SetNaN();\r
+ return true;\r
+ }\r
+\r
+ if (Sign)\r
+ {\r
+ SetInfMinus();\r
+ return true;\r
+ }\r
+\r
+ SetInfPlus();\r
+ return true;\r
+ }\r
+ }\r
+\r
+ return false;\r
+ }\r
+\r
+ //****************** Internal helper functions *****************\r
+\r
+ /// <summary>\r
+ /// Used for fixed point speed-ups (where the extra precision is not required). Note that Denormalised\r
+ /// floats break the assumptions that underly Add() and Sub(), so they can only be used for multiplication\r
+ /// </summary>\r
+ /// <param name="targetExponent"></param>\r
+ private void Denormalise(int targetExponent)\r
+ {\r
+ int diff = targetExponent - exponent;\r
+ if (diff <= 0) return;\r
+\r
+ //This only works to reduce the precision, so if the difference implies an increase, we can't do anything.\r
+ mantissa.RSH(diff);\r
+ exponent += diff;\r
+ }\r
+\r
+ /// <summary>\r
+ /// The binary logarithm, log2(x) - for precisions above 1000 bits, use Log() and convert the base.\r
+ /// </summary>\r
+ private void Log2()\r
+ {\r
+ if (scratch.Precision.NumBits != mantissa.Precision.NumBits)\r
+ {\r
+ scratch = new BigInt(mantissa.Precision);\r
+ }\r
+\r
+ int bits = mantissa.Precision.NumBits;\r
+ BigFloat temp = new BigFloat(this);\r
+ BigFloat result = new BigFloat(exponent, mantissa.Precision);\r
+ BigFloat pow2 = new BigFloat(1, mantissa.Precision);\r
+ temp.exponent = 0;\r
+ int bitsCalculated = 0;\r
+\r
+ while (bitsCalculated < bits)\r
+ {\r
+ int i;\r
+ for (i = 0; (temp.exponent == 0); i++)\r
+ {\r
+ temp.mantissa.SquareHiFast(scratch);\r
+ int shift = temp.mantissa.Normalise();\r
+ temp.exponent += 1 - shift;\r
+ if (i + bitsCalculated >= bits) break;\r
+ }\r
+\r
+ pow2.MulPow2(-i);\r
+ result.Add(pow2);\r
+ temp.exponent = 0;\r
+ bitsCalculated += i;\r
+ }\r
+\r
+ this.Assign(result);\r
+ }\r
+\r
+ /// <summary>\r
+ /// Tried the newton method for logs, but the exponential function is too slow to do it.\r
+ /// </summary>\r
+ private void LogNewton()\r
+ {\r
+ if (mantissa.IsZero() || mantissa.Sign)\r
+ {\r
+ return;\r
+ }\r
+\r
+ //Compute ln2.\r
+ if (ln2cache == null || mantissa.Precision.NumBits > ln2cache.mantissa.Precision.NumBits)\r
+ {\r
+ CalculateLog2(mantissa.Precision.NumBits);\r
+ }\r
+\r
+ int numBits = mantissa.Precision.NumBits;\r
+\r
+ //Use inverse exp function with Newton's method.\r
+ BigFloat xn = new BigFloat(this);\r
+ BigFloat oldExponent = new BigFloat(xn.exponent, mantissa.Precision);\r
+ xn.exponent = 0;\r
+ this.exponent = 0;\r
+ //Hack to subtract 1\r
+ xn.mantissa.ClearBit(numBits - 1);\r
+ //x0 = (x - 1) * log2 - this is a straight line fit between log(1) = 0 and log(2) = ln2\r
+ xn.Mul(ln2cache);\r
+ //x0 = (x - 1) * log2 + C - this corrects for minimum error over the range.\r
+ xn.Add(logNewtonConstant);\r
+ BigFloat term = new BigFloat(mantissa.Precision);\r
+ BigFloat one = new BigFloat(1, mantissa.Precision);\r
+\r
+ int precision = 32;\r
+ int normalPrecision = mantissa.Precision.NumBits;\r
+\r
+ int iterations = 0;\r
+\r
+ while (true)\r
+ {\r
+ term.Assign(xn);\r
+ term.mantissa.Sign = true;\r
+ term.Exp(precision);\r
+ term.Mul(this);\r
+ term.Sub(one);\r
+\r
+ iterations++;\r
+ if (term.exponent < -((precision >> 1) - 4))\r
+ {\r
+ if (precision == normalPrecision)\r
+ {\r
+ if (term.exponent < -(precision - 4)) break;\r
+ }\r
+ else\r
+ {\r
+ precision = precision << 1;\r
+ if (precision > normalPrecision) precision = normalPrecision;\r
+ }\r
+ }\r
+\r
+ xn.Add(term);\r
+ }\r
+\r
+ //log(2^n*s) = log(2^n) + log(s) = nlog(2) + log(s)\r
+ term.Assign(ln2cache);\r
+ term.Mul(oldExponent);\r
+\r
+ this.Assign(xn);\r
+ this.Add(term);\r
+ }\r
+\r
+ /// <summary>\r
+ /// Log(x) implemented as an Arithmetic-Geometric Mean. Fast for high precisions.\r
+ /// </summary>\r
+ private void LogAGM1()\r
+ {\r
+ if (mantissa.IsZero() || mantissa.Sign)\r
+ {\r
+ return;\r
+ }\r
+\r
+ //Compute ln2.\r
+ if (ln2cache == null || mantissa.Precision.NumBits > ln2cache.mantissa.Precision.NumBits)\r
+ {\r
+ CalculateLog2(mantissa.Precision.NumBits);\r
+ }\r
+\r
+ //Compute ln(x) using AGM formula\r
+\r
+ //1. Re-write the input as 2^n * (0.5 <= x < 1)\r
+ int power2 = exponent + 1;\r
+ exponent = -1;\r
+\r
+ //BigFloat res = new BigFloat(firstAGMcache);\r
+ BigFloat a0 = new BigFloat(1, mantissa.Precision);\r
+ BigFloat b0 = new BigFloat(pow10cache);\r
+ b0.Mul(this);\r
+\r
+ BigFloat r = R(a0, b0);\r
+\r
+ this.Assign(firstAGMcache);\r
+ this.Sub(r);\r
+\r
+ a0.Assign(ln2cache);\r
+ a0.Mul(new BigFloat(power2, mantissa.Precision));\r
+ this.Add(a0);\r
+ }\r
+\r
+ private void Exp(int numBits)\r
+ {\r
+ if (IsSpecialValue)\r
+ {\r
+ if (SpecialValue == SpecialValueType.ZERO)\r
+ {\r
+ //e^0 = 1\r
+ exponent = 0;\r
+ mantissa.SetHighDigit(0x80000000);\r
+ }\r
+ else if (SpecialValue == SpecialValueType.INF_MINUS)\r
+ {\r
+ //e^-inf = 0\r
+ SetZero();\r
+ }\r
+\r
+ return;\r
+ }\r
+\r
+ PrecisionSpec prec = new PrecisionSpec(numBits, PrecisionSpec.BaseType.BIN);\r
+ numBits = prec.NumBits;\r
+\r
+ if (scratch.Precision.NumBits != prec.NumBits)\r
+ {\r
+ scratch = new BigInt(prec);\r
+ }\r
+\r
+ if (inverseFactorialCache == null || invFactorialCutoff < numBits)\r
+ {\r
+ CalculateFactorials(numBits);\r
+ }\r
+\r
+ //let x = 1 * 'this'.mantissa (i.e. 1 <= x < 2)\r
+ //exp(2^n * x) = e^(2^n * x) = (e^x)^2n = exp(x)^2n\r
+\r
+ int oldExponent = 0;\r
+\r
+ if (exponent > -4)\r
+ {\r
+ oldExponent = exponent + 4;\r
+ exponent = -4;\r
+ }\r
+\r
+ BigFloat thisSave = new BigFloat(this, prec);\r
+ BigFloat temp = new BigFloat(1, prec);\r
+ BigFloat temp2 = new BigFloat(this, prec);\r
+ BigFloat res = new BigFloat(1, prec);\r
+ int length = inverseFactorialCache.Length;\r
+\r
+ int iterations;\r
+ for (int i = 1; i < length; i++)\r
+ {\r
+ //temp = x^i\r
+ temp.Mul(thisSave);\r
+ temp2.Assign(inverseFactorialCache[i]);\r
+ temp2.Mul(temp);\r
+\r
+ if (temp2.exponent < -(numBits + 4)) { iterations = i; break; }\r
+\r
+ res.Add(temp2);\r
+ }\r
+\r
+ //res = exp(x)\r
+ //Now... x^(2^n) = (x^2)^(2^(n - 1))\r
+ for (int i = 0; i < oldExponent; i++)\r
+ {\r
+ res.mantissa.SquareHiFast(scratch);\r
+ int shift = res.mantissa.Normalise();\r
+ res.exponent = res.exponent << 1;\r
+ res.exponent += 1 - shift;\r
+ }\r
+\r
+ //Deal with +/- inf\r
+ if (res.exponent == Int32.MaxValue)\r
+ {\r
+ res.mantissa.Zero();\r
+ }\r
+\r
+ Assign(res);\r
+ }\r
+\r
+ /// <summary>\r
+ /// Calculates ln(2) and returns -10^(n/2 + a bit) for reuse, using the AGM method as described in\r
+ /// http://lacim.uqam.ca/~plouffe/articles/log2.pdf\r
+ /// </summary>\r
+ /// <param name="numBits"></param>\r
+ /// <returns></returns>\r
+ private static void CalculateLog2(int numBits)\r
+ {\r
+ //Use the AGM method formula to get log2 to N digits.\r
+ //R(a0, b0) = 1 / (1 - Sum(2^-n*(an^2 - bn^2)))\r
+ //log(1/2) = R(1, 10^-n) - R(1, 10^-n/2)\r
+ PrecisionSpec normalPres = new PrecisionSpec(numBits, PrecisionSpec.BaseType.BIN);\r
+ PrecisionSpec extendedPres = new PrecisionSpec(numBits + 1, PrecisionSpec.BaseType.BIN);\r
+ BigFloat a0 = new BigFloat(1, extendedPres);\r
+ BigFloat b0 = TenPow(-(int)((double)((numBits >> 1) + 2) * 0.302), extendedPres);\r
+ BigFloat pow10saved = new BigFloat(b0);\r
+ BigFloat firstAGMcacheSaved = new BigFloat(extendedPres);\r
+\r
+ //save power of 10 (in normal precision)\r
+ pow10cache = new BigFloat(b0, normalPres);\r
+\r
+ ln2cache = R(a0, b0);\r
+\r
+ //save the first half of the log calculation\r
+ firstAGMcache = new BigFloat(ln2cache, normalPres);\r
+ firstAGMcacheSaved.Assign(ln2cache);\r
+\r
+ b0.MulPow2(-1);\r
+ ln2cache.Sub(R(a0, b0));\r
+\r
+ //Convert to log(2)\r
+ ln2cache.mantissa.Sign = false;\r
+\r
+ //Save magic constant for newton log\r
+ //First guess in range 1 <= x < 2 is x0 = ln2 * (x - 1) + C\r
+ logNewtonConstant = new BigFloat(ln2cache);\r
+ logNewtonConstant.Mul(new BigFloat(3, extendedPres));\r
+ logNewtonConstant.exponent--;\r
+ logNewtonConstant.Sub(new BigFloat(1, extendedPres));\r
+ logNewtonConstant = new BigFloat(logNewtonConstant, normalPres);\r
+\r
+ //Save the inverse.\r
+ log2ecache = new BigFloat(ln2cache);\r
+ log2ecache = new BigFloat(log2ecache.Reciprocal(), normalPres);\r
+\r
+ //Now cache log10\r
+ //Because the log functions call this function to the precision to which they\r
+ //are called, we cannot call them without causing an infinite loop, so we need\r
+ //to inline the code.\r
+ log10recip = new BigFloat(10, extendedPres);\r
+\r
+ {\r
+ int power2 = log10recip.exponent + 1;\r
+ log10recip.exponent = -1;\r
+\r
+ //BigFloat res = new BigFloat(firstAGMcache);\r
+ BigFloat ax = new BigFloat(1, extendedPres);\r
+ BigFloat bx = new BigFloat(pow10saved);\r
+ bx.Mul(log10recip);\r
+\r
+ BigFloat r = R(ax, bx);\r
+\r
+ log10recip.Assign(firstAGMcacheSaved);\r
+ log10recip.Sub(r);\r
+\r
+ ax.Assign(ln2cache);\r
+ ax.Mul(new BigFloat(power2, log10recip.mantissa.Precision));\r
+ log10recip.Add(ax);\r
+ }\r
+\r
+ log10recip = log10recip.Reciprocal();\r
+ log10recip = new BigFloat(log10recip, normalPres);\r
+\r
+\r
+ //Trim to n bits\r
+ ln2cache = new BigFloat(ln2cache, normalPres);\r
+ }\r
+\r
+ private static BigFloat TenPow(int power, PrecisionSpec precision)\r
+ {\r
+ BigFloat acc = new BigFloat(1, precision);\r
+ BigFloat temp = new BigFloat(1, precision);\r
+\r
+ int powerTemp = power;\r
+\r
+ BigFloat multiplierToUse = new BigFloat(10, precision);\r
+\r
+ if (power < 0)\r
+ {\r
+ multiplierToUse = multiplierToUse.Reciprocal();\r
+ powerTemp = -power;\r
+ }\r
+\r
+ //Fast power function\r
+ while (powerTemp != 0)\r
+ {\r
+ temp.Mul(multiplierToUse);\r
+ multiplierToUse.Assign(temp);\r
+\r
+ if ((powerTemp & 1) != 0)\r
+ {\r
+ acc.Mul(temp);\r
+ }\r
+\r
+ powerTemp >>= 1;\r
+ }\r
+\r
+ return acc;\r
+ }\r
+\r
+ private static BigFloat R(BigFloat a0, BigFloat b0)\r
+ {\r
+ //Precision extend taken out.\r
+ int bits = a0.mantissa.Precision.NumBits;\r
+ PrecisionSpec extendedPres = new PrecisionSpec(bits, PrecisionSpec.BaseType.BIN);\r
+ BigFloat an = new BigFloat(a0, extendedPres);\r
+ BigFloat bn = new BigFloat(b0, extendedPres);\r
+ BigFloat sum = new BigFloat(extendedPres);\r
+ BigFloat term = new BigFloat(extendedPres);\r
+ BigFloat temp1 = new BigFloat(extendedPres);\r
+ BigFloat one = new BigFloat(1, extendedPres);\r
+\r
+ int iteration = 0;\r
+\r
+ for (iteration = 0; ; iteration++)\r
+ {\r
+ //Get the sum term for this iteration.\r
+ term.Assign(an);\r
+ term.Mul(an);\r
+ temp1.Assign(bn);\r
+ temp1.Mul(bn);\r
+ //term = an^2 - bn^2\r
+ term.Sub(temp1);\r
+ //term = 2^(n-1) * (an^2 - bn^2)\r
+ term.exponent += iteration - 1;\r
+ sum.Add(term);\r
+\r
+ if (term.exponent < -(bits - 8)) break;\r
+\r
+ //Calculate the new AGM estimates.\r
+ temp1.Assign(an);\r
+ an.Add(bn);\r
+ //a(n+1) = (an + bn) / 2\r
+ an.MulPow2(-1);\r
+\r
+ //b(n+1) = sqrt(an*bn)\r
+ bn.Mul(temp1);\r
+ bn.Sqrt();\r
+ }\r
+\r
+ one.Sub(sum);\r
+ one = one.Reciprocal();\r
+ return new BigFloat(one, a0.mantissa.Precision);\r
+ }\r
+\r
+ private static void CalculateFactorials(int numBits)\r
+ {\r
+ System.Collections.Generic.List<BigFloat> list = new System.Collections.Generic.List<BigFloat>(64);\r
+ System.Collections.Generic.List<BigFloat> list2 = new System.Collections.Generic.List<BigFloat>(64);\r
+\r
+ PrecisionSpec extendedPrecision = new PrecisionSpec(numBits + 1, PrecisionSpec.BaseType.BIN);\r
+ PrecisionSpec normalPrecision = new PrecisionSpec(numBits, PrecisionSpec.BaseType.BIN);\r
+\r
+ BigFloat factorial = new BigFloat(1, extendedPrecision);\r
+ BigFloat reciprocal;\r
+\r
+ //Calculate e while we're at it\r
+ BigFloat e = new BigFloat(1, extendedPrecision);\r
+\r
+ list.Add(new BigFloat(factorial, normalPrecision));\r
+\r
+ for (int i = 1; i < Int32.MaxValue; i++)\r
+ {\r
+ BigFloat number = new BigFloat(i, extendedPrecision);\r
+ factorial.Mul(number);\r
+\r
+ if (factorial.exponent > numBits) break;\r
+\r
+ list2.Add(new BigFloat(factorial, normalPrecision));\r
+ reciprocal = factorial.Reciprocal();\r
+\r
+ e.Add(reciprocal);\r
+ list.Add(new BigFloat(reciprocal, normalPrecision));\r
+ }\r
+\r
+ //Set the cached static values.\r
+ inverseFactorialCache = list.ToArray();\r
+ factorialCache = list2.ToArray();\r
+ invFactorialCutoff = numBits;\r
+ eCache = new BigFloat(e, normalPrecision);\r
+ eRCPCache = new BigFloat(e.Reciprocal(), normalPrecision);\r
+ }\r
+\r
+ private static void CalculateEOnly(int numBits)\r
+ {\r
+ PrecisionSpec extendedPrecision = new PrecisionSpec(numBits + 1, PrecisionSpec.BaseType.BIN);\r
+ PrecisionSpec normalPrecision = new PrecisionSpec(numBits, PrecisionSpec.BaseType.BIN);\r
+\r
+ int iExponent = (int)(Math.Sqrt(numBits));\r
+\r
+ BigFloat factorial = new BigFloat(1, extendedPrecision);\r
+ BigFloat constant = new BigFloat(1, extendedPrecision);\r
+ constant.exponent -= iExponent;\r
+ BigFloat numerator = new BigFloat(constant);\r
+ BigFloat reciprocal;\r
+\r
+ //Calculate the 2^iExponent th root of e\r
+ BigFloat e = new BigFloat(1, extendedPrecision);\r
+\r
+ int i;\r
+ for (i = 1; i < Int32.MaxValue; i++)\r
+ {\r
+ BigFloat number = new BigFloat(i, extendedPrecision);\r
+ factorial.Mul(number);\r
+ reciprocal = factorial.Reciprocal();\r
+ reciprocal.Mul(numerator);\r
+\r
+ if (-reciprocal.exponent > numBits) break;\r
+\r
+ e.Add(reciprocal);\r
+ numerator.Mul(constant);\r
+ System.GC.Collect();\r
+ }\r
+\r
+ for (i = 0; i < iExponent; i++)\r
+ {\r
+ numerator.Assign(e);\r
+ e.Mul(numerator);\r
+ }\r
+\r
+ //Set the cached static values.\r
+ eCache = new BigFloat(e, normalPrecision);\r
+ eRCPCache = new BigFloat(e.Reciprocal(), normalPrecision);\r
+ }\r
+\r
+ /// <summary>\r
+ /// Uses the Gauss-Legendre formula for pi\r
+ /// Taken from http://en.wikipedia.org/wiki/Gauss%E2%80%93Legendre_algorithm\r
+ /// </summary>\r
+ /// <param name="numBits"></param>\r
+ private static void CalculatePi(int numBits)\r
+ {\r
+ int bits = numBits + 32;\r
+ //Precision extend taken out.\r
+ PrecisionSpec normalPres = new PrecisionSpec(numBits, PrecisionSpec.BaseType.BIN);\r
+ PrecisionSpec extendedPres = new PrecisionSpec(bits, PrecisionSpec.BaseType.BIN);\r
+\r
+ if (scratch.Precision.NumBits != bits)\r
+ {\r
+ scratch = new BigInt(extendedPres);\r
+ }\r
+\r
+ //a0 = 1\r
+ BigFloat an = new BigFloat(1, extendedPres);\r
+\r
+ //b0 = 1/sqrt(2)\r
+ BigFloat bn = new BigFloat(2, extendedPres);\r
+ bn.Sqrt();\r
+ bn.exponent--;\r
+\r
+ //to = 1/4\r
+ BigFloat tn = new BigFloat(1, extendedPres);\r
+ tn.exponent -= 2;\r
+\r
+ int pn = 0;\r
+\r
+ BigFloat anTemp = new BigFloat(extendedPres);\r
+\r
+ int iteration = 0;\r
+ int cutoffBits = numBits >> 5;\r
+\r
+ for (iteration = 0; ; iteration++)\r
+ {\r
+ //Save a(n)\r
+ anTemp.Assign(an);\r
+\r
+ //Calculate new an\r
+ an.Add(bn);\r
+ an.exponent--;\r
+\r
+ //Calculate new bn\r
+ bn.Mul(anTemp);\r
+ bn.Sqrt();\r
+\r
+ //Calculate new tn\r
+ anTemp.Sub(an);\r
+ anTemp.mantissa.SquareHiFast(scratch);\r
+ anTemp.exponent += anTemp.exponent + pn + 1 - anTemp.mantissa.Normalise();\r
+ tn.Sub(anTemp);\r
+\r
+ anTemp.Assign(an);\r
+ anTemp.Sub(bn);\r
+\r
+ if (anTemp.exponent < -(bits - cutoffBits)) break;\r
+\r
+ //New pn\r
+ pn++;\r
+ }\r
+\r
+ an.Add(bn);\r
+ an.mantissa.SquareHiFast(scratch);\r
+ an.exponent += an.exponent + 1 - an.mantissa.Normalise();\r
+ tn.exponent += 2;\r
+ an.Div(tn);\r
+\r
+ pi = new BigFloat(an, normalPres);\r
+ piBy2 = new BigFloat(pi);\r
+ piBy2.exponent--;\r
+ twoPi = new BigFloat(pi, normalPres);\r
+ twoPi.exponent++;\r
+ piRecip = new BigFloat(an.Reciprocal(), normalPres);\r
+ twoPiRecip = new BigFloat(piRecip);\r
+ twoPiRecip.exponent--;\r
+ //1/3 is going to be useful for sin.\r
+ threeRecip = new BigFloat((new BigFloat(3, extendedPres)).Reciprocal(), normalPres);\r
+ }\r
+\r
+ /// <summary>\r
+ /// Calculates the odd reciprocals of the natural numbers (for atan series)\r
+ /// </summary>\r
+ /// <param name="numBits"></param>\r
+ /// <param name="terms"></param>\r
+ private static void CalculateReciprocals(int numBits, int terms)\r
+ {\r
+ int bits = numBits + 32;\r
+ PrecisionSpec extendedPres = new PrecisionSpec(bits, PrecisionSpec.BaseType.BIN);\r
+ PrecisionSpec normalPres = new PrecisionSpec(numBits, PrecisionSpec.BaseType.BIN);\r
+\r
+ System.Collections.Generic.List<BigFloat> list = new System.Collections.Generic.List<BigFloat>(terms);\r
+\r
+ for (int i = 0; i < terms; i++)\r
+ {\r
+ BigFloat term = new BigFloat(i*2 + 1, extendedPres);\r
+ list.Add(new BigFloat(term.Reciprocal(), normalPres));\r
+ }\r
+\r
+ reciprocals = list.ToArray();\r
+ }\r
+\r
+ /// <summary>\r
+ /// Does decimal rounding, for numbers without E notation.\r
+ /// </summary>\r
+ /// <param name="input"></param>\r
+ /// <param name="places"></param>\r
+ /// <returns></returns>\r
+ private static string RoundString(string input, int places)\r
+ {\r
+ if (places <= 0) return input;\r
+ string trim = input.Trim();\r
+ char[] digits = { '0', '1', '2', '3', '4', '5', '6', '7', '8', '9'};\r
+\r
+ /*\r
+ for (int i = 1; i <= places; i++)\r
+ {\r
+ //Skip decimal points.\r
+ if (trim[trim.Length - i] == '.')\r
+ {\r
+ places++;\r
+ continue;\r
+ }\r
+\r
+ int index = Array.IndexOf(digits, trim[trim.Length - i]);\r
+\r
+ if (index < 0) return input;\r
+\r
+ value += ten * index;\r
+ ten *= 10;\r
+ }\r
+ * */\r
+\r
+ //Look for a decimal point\r
+ string decimalPoint = System.Globalization.CultureInfo.CurrentCulture.NumberFormat.NumberDecimalSeparator;\r
+\r
+ int indexPoint = trim.LastIndexOf(decimalPoint);\r
+ if (indexPoint < 0)\r
+ {\r
+ //We can't modify a string which doesn't have a decimal point.\r
+ return trim;\r
+ }\r
+\r
+ int trimPoint = trim.Length - places;\r
+ if (trimPoint < indexPoint) trimPoint = indexPoint;\r
+\r
+ bool roundDown = false;\r
+\r
+ if (trim[trimPoint] == '.')\r
+ {\r
+ if (trimPoint + 1 >= trim.Length)\r
+ {\r
+ roundDown = true;\r
+ }\r
+ else\r
+ {\r
+ int digit = Array.IndexOf(digits, trim[trimPoint + 1]);\r
+ if (digit < 5) roundDown = true;\r
+ }\r
+ }\r
+ else\r
+ {\r
+ int digit = Array.IndexOf(digits, trim[trimPoint]);\r
+ if (digit < 5) roundDown = true;\r
+ }\r
+\r
+ string output;\r
+\r
+ //Round down - just return a new string without the extra digits.\r
+ if (roundDown)\r
+ {\r
+ if (RoundingMode == RoundingModeType.EXACT)\r
+ {\r
+ return trim.Substring(0, trimPoint);\r
+ }\r
+ else\r
+ {\r
+ char[] trimChars = { '0' };\r
+ output = trim.Substring(0, trimPoint).TrimEnd(trimChars);\r
+ trimChars[0] = System.Globalization.CultureInfo.CurrentCulture.NumberFormat.NumberDecimalSeparator[0];\r
+ return output.TrimEnd(trimChars);\r
+ }\r
+ }\r
+ \r
+ //Round up - bit more complicated.\r
+ char [] arrayOutput = trim.ToCharArray();//0, trimPoint);\r
+\r
+ //Now, we round going from the back to the front.\r
+ int j;\r
+ for (j = trimPoint - 1; j >= 0; j--)\r
+ {\r
+ int index = Array.IndexOf(digits, arrayOutput[j]);\r
+\r
+ //Skip decimal points etc...\r
+ if (index < 0) continue;\r
+\r
+ if (index < 9)\r
+ {\r
+ arrayOutput[j] = digits[index + 1];\r
+ break;\r
+ }\r
+ else\r
+ {\r
+ arrayOutput[j] = digits[0];\r
+ }\r
+ }\r
+\r
+ output = new string(arrayOutput);\r
+\r
+ if (j < 0)\r
+ {\r
+ //Need to add a new digit.\r
+ output = String.Format("{0}{1}", "1", output);\r
+ }\r
+\r
+ if (RoundingMode == RoundingModeType.EXACT)\r
+ {\r
+ return output;\r
+ }\r
+ else\r
+ {\r
+ char[] trimChars = { '0' };\r
+ output = output.TrimEnd(trimChars);\r
+ trimChars[0] = System.Globalization.CultureInfo.CurrentCulture.NumberFormat.NumberDecimalSeparator[0];\r
+ return output.TrimEnd(trimChars);\r
+ }\r
+ }\r
+\r
+ //***************************** Data *****************************\r
+\r
+\r
+ //Side node - this way of doing things is far from optimal, both in terms of memory use and performance.\r
+ private ExponentAdaptor exponent;\r
+ private BigInt mantissa;\r
+\r
+ /// <summary>\r
+ /// Storage area for calculations.\r
+ /// </summary>\r
+ private static BigInt scratch;\r
+\r
+ private static BigFloat ln2cache; //Value of ln(2)\r
+ private static BigFloat log2ecache; //Value of log2(e) = 1/ln(2)\r
+ private static BigFloat pow10cache; //Cached power of 10 for AGM log calculation\r
+ private static BigFloat log10recip; //1/ln(10)\r
+ private static BigFloat firstAGMcache; //Cached half of AGM operation.\r
+ private static BigFloat[] factorialCache; //The values of n!\r
+ private static BigFloat[] inverseFactorialCache; //Values of 1/n! up to 2^-m where m = invFactorialCutoff (below)\r
+ private static int invFactorialCutoff; //The number of significant bits for the cutoff of the inverse factorials.\r
+ private static BigFloat eCache; //Value of e cached to invFactorialCutoff bits\r
+ private static BigFloat eRCPCache; //Reciprocal of e\r
+ private static BigFloat logNewtonConstant; //1.5*ln(2) - 1\r
+ private static BigFloat pi; //pi\r
+ private static BigFloat piBy2; //pi/2\r
+ private static BigFloat twoPi; //2*pi\r
+ private static BigFloat piRecip; //1/pi\r
+ private static BigFloat twoPiRecip; //1/2*pi\r
+ private static BigFloat threeRecip; //1/3\r
+ private static BigFloat[] reciprocals; //1/x\r
+ \r
+ /// <summary>\r
+ /// The number of decimal digits to round the output of ToString() by\r
+ /// </summary>\r
+ public static int RoundingDigits { get; set; }\r
+\r
+ /// <summary>\r
+ /// The way in which ToString() should deal with insignificant trailing zeroes\r
+ /// </summary>\r
+ public static RoundingModeType RoundingMode { get; set; }\r
+ }\r
+}
\ No newline at end of file
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