path: root/src/System.Private.CoreLib/src/System/Number.CoreRT.cs

// Licensed to the .NET Foundation under one or more agreements.
// The .NET Foundation licenses this file to you under the MIT license.
// See the LICENSE file in the project root for more information.

using System.Globalization;

namespace System
{
    // The Number class implements methods for formatting and parsing
    // numeric values. To format and parse numeric values, applications should
    // use the Format and Parse methods provided by the numeric
    // classes (Byte, Int16, Int32, Int64,
    // Single, Double, Currency, and Decimal). Those
    // Format and Parse methods share a common implementation
    // provided by this class, and are thus documented in detail here.
    //
    // Formatting
    //
    // The Format methods provided by the numeric classes are all of the
    // form
    //
    //  public static String Format(XXX value, String format);
    //  public static String Format(XXX value, String format, NumberFormatInfo info);
    //
    // where XXX is the name of the particular numeric class. The methods convert
    // the numeric value to a string using the format string given by the
    // format parameter. If the format parameter is null or
    // an empty string, the number is formatted as if the string "G" (general
    // format) was specified. The info parameter specifies the
    // NumberFormatInfo instance to use when formatting the number. If the
    // info parameter is null or omitted, the numeric formatting information
    // is obtained from the current culture. The NumberFormatInfo supplies
    // such information as the characters to use for decimal and thousand
    // separators, and the spelling and placement of currency symbols in monetary
    // values.
    //
    // Format strings fall into two categories: Standard format strings and
    // user-defined format strings. A format string consisting of a single
    // alphabetic character (A-Z or a-z), optionally followed by a sequence of
    // digits (0-9), is a standard format string. All other format strings are
    // used-defined format strings.
    //
    // A standard format string takes the form Axx, where A is an
    // alphabetic character called the format specifier and xx is a
    // sequence of digits called the precision specifier. The format
    // specifier controls the type of formatting applied to the number and the
    // precision specifier controls the number of significant digits or decimal
    // places of the formatting operation. The following table describes the
    // supported standard formats.
    //
    // C c - Currency format. The number is
    // converted to a string that represents a currency amount. The conversion is
    // controlled by the currency format information of the NumberFormatInfo
    // used to format the number. The precision specifier indicates the desired
    // number of decimal places. If the precision specifier is omitted, the default
    // currency precision given by the NumberFormatInfo is used.
    //
    // D d - Decimal format. This format is
    // supported for integral types only. The number is converted to a string of
    // decimal digits, prefixed by a minus sign if the number is negative. The
    // precision specifier indicates the minimum number of digits desired in the
    // resulting string. If required, the number will be left-padded with zeros to
    // produce the number of digits given by the precision specifier.
    //
    // E e Engineering (scientific) format.
    // The number is converted to a string of the form
    // "-d.ddd...E+ddd" or "-d.ddd...e+ddd", where each
    // 'd' indicates a digit (0-9). The string starts with a minus sign if the
    // number is negative, and one digit always precedes the decimal point. The
    // precision specifier indicates the desired number of digits after the decimal
    // point. If the precision specifier is omitted, a default of 6 digits after
    // the decimal point is used. The format specifier indicates whether to prefix
    // the exponent with an 'E' or an 'e'. The exponent is always consists of a
    // plus or minus sign and three digits.
    //
    // F f Fixed point format. The number is
    // converted to a string of the form "-ddd.ddd....", where each
    // 'd' indicates a digit (0-9). The string starts with a minus sign if the
    // number is negative. The precision specifier indicates the desired number of
    // decimal places. If the precision specifier is omitted, the default numeric
    // precision given by the NumberFormatInfo is used.
    //
    // G g - General format. The number is
    // converted to the shortest possible decimal representation using fixed point
    // or scientific format. The precision specifier determines the number of
    // significant digits in the resulting string. If the precision specifier is
    // omitted, the number of significant digits is determined by the type of the
    // number being converted (10 for int, 19 for long, 7 for
    // float, 15 for double, 19 for Currency, and 29 for
    // Decimal). Trailing zeros after the decimal point are removed, and the
    // resulting string contains a decimal point only if required. The resulting
    // string uses fixed point format if the exponent of the number is less than
    // the number of significant digits and greater than or equal to -4. Otherwise,
    // the resulting string uses scientific format, and the case of the format
    // specifier controls whether the exponent is prefixed with an 'E' or an
    // 'e'.
    //
    // N n Number format. The number is
    // converted to a string of the form "-d,ddd,ddd.ddd....", where
    // each 'd' indicates a digit (0-9). The string starts with a minus sign if the
    // number is negative. Thousand separators are inserted between each group of
    // three digits to the left of the decimal point. The precision specifier
    // indicates the desired number of decimal places. If the precision specifier
    // is omitted, the default numeric precision given by the
    // NumberFormatInfo is used.
    //
    // X x - Hexadecimal format. This format is
    // supported for integral types only. The number is converted to a string of
    // hexadecimal digits. The format specifier indicates whether to use upper or
    // lower case characters for the hexadecimal digits above 9 ('X' for 'ABCDEF',
    // and 'x' for 'abcdef'). The precision specifier indicates the minimum number
    // of digits desired in the resulting string. If required, the number will be
    // left-padded with zeros to produce the number of digits given by the
    // precision specifier.
    //
    // Some examples of standard format strings and their results are shown in the
    // table below. (The examples all assume a default NumberFormatInfo.)
    //
    // Value        Format  Result
    // 12345.6789   C       $12,345.68
    // -12345.6789  C       ($12,345.68)
    // 12345        D       12345
    // 12345        D8      00012345
    // 12345.6789   E       1.234568E+004
    // 12345.6789   E10     1.2345678900E+004
    // 12345.6789   e4      1.2346e+004
    // 12345.6789   F       12345.68
    // 12345.6789   F0      12346
    // 12345.6789   F6      12345.678900
    // 12345.6789   G       12345.6789
    // 12345.6789   G7      12345.68
    // 123456789    G7      1.234568E8
    // 12345.6789   N       12,345.68
    // 123456789    N4      123,456,789.0000
    // 0x2c45e      x       2c45e
    // 0x2c45e      X       2C45E
    // 0x2c45e      X8      0002C45E
    //
    // Format strings that do not start with an alphabetic character, or that start
    // with an alphabetic character followed by a non-digit, are called
    // user-defined format strings. The following table describes the formatting
    // characters that are supported in user defined format strings.
    //
    // 
    // 0 - Digit placeholder. If the value being
    // formatted has a digit in the position where the '0' appears in the format
    // string, then that digit is copied to the output string. Otherwise, a '0' is
    // stored in that position in the output string. The position of the leftmost
    // '0' before the decimal point and the rightmost '0' after the decimal point
    // determines the range of digits that are always present in the output
    // string.
    //
    // # - Digit placeholder. If the value being
    // formatted has a digit in the position where the '#' appears in the format
    // string, then that digit is copied to the output string. Otherwise, nothing
    // is stored in that position in the output string.
    //
    // . - Decimal point. The first '.' character
    // in the format string determines the location of the decimal separator in the
    // formatted value; any additional '.' characters are ignored. The actual
    // character used as a the decimal separator in the output string is given by
    // the NumberFormatInfo used to format the number.
    //
    // , - Thousand separator and number scaling.
    // The ',' character serves two purposes. First, if the format string contains
    // a ',' character between two digit placeholders (0 or #) and to the left of
    // the decimal point if one is present, then the output will have thousand
    // separators inserted between each group of three digits to the left of the
    // decimal separator. The actual character used as a the decimal separator in
    // the output string is given by the NumberFormatInfo used to format the
    // number. Second, if the format string contains one or more ',' characters
    // immediately to the left of the decimal point, or after the last digit
    // placeholder if there is no decimal point, then the number will be divided by
    // 1000 times the number of ',' characters before it is formatted. For example,
    // the format string '0,,' will represent 100 million as just 100. Use of the
    // ',' character to indicate scaling does not also cause the formatted number
    // to have thousand separators. Thus, to scale a number by 1 million and insert
    // thousand separators you would use the format string '#,##0,,'.
    //
    // % - Percentage placeholder. The presence of
    // a '%' character in the format string causes the number to be multiplied by
    // 100 before it is formatted. The '%' character itself is inserted in the
    // output string where it appears in the format string.
    //
    // E+ E- e+ e-   - Scientific notation.
    // If any of the strings 'E+', 'E-', 'e+', or 'e-' are present in the format
    // string and are immediately followed by at least one '0' character, then the
    // number is formatted using scientific notation with an 'E' or 'e' inserted
    // between the number and the exponent. The number of '0' characters following
    // the scientific notation indicator determines the minimum number of digits to
    // output for the exponent. The 'E+' and 'e+' formats indicate that a sign
    // character (plus or minus) should always precede the exponent. The 'E-' and
    // 'e-' formats indicate that a sign character should only precede negative
    // exponents.
    //
    // \ - Literal character. A backslash character
    // causes the next character in the format string to be copied to the output
    // string as-is. The backslash itself isn't copied, so to place a backslash
    // character in the output string, use two backslashes (\\) in the format
    // string.
    //
    // 'ABC' "ABC" - Literal string. Characters
    // enclosed in single or double quotation marks are copied to the output string
    // as-is and do not affect formatting.
    //
    // ; - Section separator. The ';' character is
    // used to separate sections for positive, negative, and zero numbers in the
    // format string.
    //
    // Other - All other characters are copied to
    // the output string in the position they appear.
    //
    // For fixed point formats (formats not containing an 'E+', 'E-', 'e+', or
    // 'e-'), the number is rounded to as many decimal places as there are digit
    // placeholders to the right of the decimal point. If the format string does
    // not contain a decimal point, the number is rounded to the nearest
    // integer. If the number has more digits than there are digit placeholders to
    // the left of the decimal point, the extra digits are copied to the output
    // string immediately before the first digit placeholder.
    //
    // For scientific formats, the number is rounded to as many significant digits
    // as there are digit placeholders in the format string.
    //
    // To allow for different formatting of positive, negative, and zero values, a
    // user-defined format string may contain up to three sections separated by
    // semicolons. The results of having one, two, or three sections in the format
    // string are described in the table below.
    //
    // Sections:
    //
    // One - The format string applies to all values.
    //
    // Two - The first section applies to positive values
    // and zeros, and the second section applies to negative values. If the number
    // to be formatted is negative, but becomes zero after rounding according to
    // the format in the second section, then the resulting zero is formatted
    // according to the first section.
    //
    // Three - The first section applies to positive
    // values, the second section applies to negative values, and the third section
    // applies to zeros. The second section may be left empty (by having no
    // characters between the semicolons), in which case the first section applies
    // to all non-zero values. If the number to be formatted is non-zero, but
    // becomes zero after rounding according to the format in the first or second
    // section, then the resulting zero is formatted according to the third
    // section.
    //
    // For both standard and user-defined formatting operations on values of type
    // float and double, if the value being formatted is a NaN (Not
    // a Number) or a positive or negative infinity, then regardless of the format
    // string, the resulting string is given by the NaNSymbol,
    // PositiveInfinitySymbol, or NegativeInfinitySymbol property of
    // the NumberFormatInfo used to format the number.
    //
    // Parsing
    //
    // The Parse methods provided by the numeric classes are all of the form
    //
    //  public static XXX Parse(String s);
    //  public static XXX Parse(String s, int style);
    //  public static XXX Parse(String s, int style, NumberFormatInfo info);
    //
    // where XXX is the name of the particular numeric class. The methods convert a
    // string to a numeric value. The optional style parameter specifies the
    // permitted style of the numeric string. It must be a combination of bit flags
    // from the NumberStyles enumeration. The optional info parameter
    // specifies the NumberFormatInfo instance to use when parsing the
    // string. If the info parameter is null or omitted, the numeric
    // formatting information is obtained from the current culture.
    //
    // Numeric strings produced by the Format methods using the Currency,
    // Decimal, Engineering, Fixed point, General, or Number standard formats
    // (the C, D, E, F, G, and N format specifiers) are guaranteed to be parseable
    // by the Parse methods if the NumberStyles.Any style is
    // specified. Note, however, that the Parse methods do not accept
    // NaNs or Infinities.
    //
    // This class contains only static members and does not need to be serializable 


    internal static partial class Number
    {
        private const int _CVTBUFSIZE = 349;

        /*===========================================================
            Portable NumberToDouble implementation
            --------------------------------------

            - does the conversion with the best possible precision.
            - does not use any float arithmetic so it is not sensitive
            to differences in precision of floating point calculations
            across platforms.

            The internal integer representation of the float number is
            UINT64 mantissa + INT exponent. The mantissa is kept normalized
            ie with the most significant one being 63-th bit of UINT64.
        ===========================================================*/

        //
        // get 32-bit integer from at most 9 digits
        //
        private static unsafe uint DigitsToInt(char* p, int count)
        {
            char* end = p + count;
            uint res = (uint)*p - '0';
            for (p = p + 1; p < end; p++)
                res = 10 * res + (uint)*p - '0';
            return res;
        }

        //
        // helper to multiply two 32-bit uints
        //
        private static ulong Mul32x32To64(uint a, uint b)
        {
            return (ulong)a * (ulong)b;
        }

        //
        // multiply two numbers in the internal integer representation
        //
        private static ulong Mul64Lossy(ulong a, ulong b, ref int pexp)
        {
            // it's ok to lose some precision here - Mul64 will be called
            // at most twice during the conversion, so the error won't propagate
            // to any of the 53 significant bits of the result
            ulong val = Mul32x32To64((uint)(a >> 32), (uint)(b >> 32)) +
                (Mul32x32To64((uint)(a >> 32), (uint)(b)) >> 32) +
                (Mul32x32To64((uint)(a), (uint)(b >> 32)) >> 32);

            // normalize
            if ((val & 0x8000000000000000) == 0)
            {
                val <<= 1;
                pexp -= 1;
            }

            return val;
        }

        //
        // precomputed tables with powers of 10. These allows us to do at most
        // two Mul64 during the conversion. This is important not only
        // for speed, but also for precision because of Mul64 computes with 1 bit error.
        //

        private static readonly ulong[] s_rgval64Power10 =
        {
            // powers of 10
            /*1*/ 0xa000000000000000,
            /*2*/ 0xc800000000000000,
            /*3*/ 0xfa00000000000000,
            /*4*/ 0x9c40000000000000,
            /*5*/ 0xc350000000000000,
            /*6*/ 0xf424000000000000,
            /*7*/ 0x9896800000000000,
            /*8*/ 0xbebc200000000000,
            /*9*/ 0xee6b280000000000,
            /*10*/ 0x9502f90000000000,
            /*11*/ 0xba43b74000000000,
            /*12*/ 0xe8d4a51000000000,
            /*13*/ 0x9184e72a00000000,
            /*14*/ 0xb5e620f480000000,
            /*15*/ 0xe35fa931a0000000,

            // powers of 0.1
            /*1*/ 0xcccccccccccccccd,
            /*2*/ 0xa3d70a3d70a3d70b,
            /*3*/ 0x83126e978d4fdf3c,
            /*4*/ 0xd1b71758e219652e,
            /*5*/ 0xa7c5ac471b478425,
            /*6*/ 0x8637bd05af6c69b7,
            /*7*/ 0xd6bf94d5e57a42be,
            /*8*/ 0xabcc77118461ceff,
            /*9*/ 0x89705f4136b4a599,
            /*10*/ 0xdbe6fecebdedd5c2,
            /*11*/ 0xafebff0bcb24ab02,
            /*12*/ 0x8cbccc096f5088cf,
            /*13*/ 0xe12e13424bb40e18,
            /*14*/ 0xb424dc35095cd813,
            /*15*/ 0x901d7cf73ab0acdc,
        };

        private static readonly sbyte[] s_rgexp64Power10 =
        {
            // exponents for both powers of 10 and 0.1
            /*1*/ 4,
            /*2*/ 7,
            /*3*/ 10,
            /*4*/ 14,
            /*5*/ 17,
            /*6*/ 20,
            /*7*/ 24,
            /*8*/ 27,
            /*9*/ 30,
            /*10*/ 34,
            /*11*/ 37,
            /*12*/ 40,
            /*13*/ 44,
            /*14*/ 47,
            /*15*/ 50,
        };

        private static readonly ulong[] s_rgval64Power10By16 =
        {
            // powers of 10^16
            /*1*/ 0x8e1bc9bf04000000,
            /*2*/ 0x9dc5ada82b70b59e,
            /*3*/ 0xaf298d050e4395d6,
            /*4*/ 0xc2781f49ffcfa6d4,
            /*5*/ 0xd7e77a8f87daf7fa,
            /*6*/ 0xefb3ab16c59b14a0,
            /*7*/ 0x850fadc09923329c,
            /*8*/ 0x93ba47c980e98cde,
            /*9*/ 0xa402b9c5a8d3a6e6,
            /*10*/ 0xb616a12b7fe617a8,
            /*11*/ 0xca28a291859bbf90,
            /*12*/ 0xe070f78d39275566,
            /*13*/ 0xf92e0c3537826140,
            /*14*/ 0x8a5296ffe33cc92c,
            /*15*/ 0x9991a6f3d6bf1762,
            /*16*/ 0xaa7eebfb9df9de8a,
            /*17*/ 0xbd49d14aa79dbc7e,
            /*18*/ 0xd226fc195c6a2f88,
            /*19*/ 0xe950df20247c83f8,
            /*20*/ 0x81842f29f2cce373,
            /*21*/ 0x8fcac257558ee4e2,

            // powers of 0.1^16
            /*1*/ 0xe69594bec44de160,
            /*2*/ 0xcfb11ead453994c3,
            /*3*/ 0xbb127c53b17ec165,
            /*4*/ 0xa87fea27a539e9b3,
            /*5*/ 0x97c560ba6b0919b5,
            /*6*/ 0x88b402f7fd7553ab,
            /*7*/ 0xf64335bcf065d3a0,
            /*8*/ 0xddd0467c64bce4c4,
            /*9*/ 0xc7caba6e7c5382ed,
            /*10*/ 0xb3f4e093db73a0b7,
            /*11*/ 0xa21727db38cb0053,
            /*12*/ 0x91ff83775423cc29,
            /*13*/ 0x8380dea93da4bc82,
            /*14*/ 0xece53cec4a314f00,
            /*15*/ 0xd5605fcdcf32e217,
            /*16*/ 0xc0314325637a1978,
            /*17*/ 0xad1c8eab5ee43ba2,
            /*18*/ 0x9becce62836ac5b0,
            /*19*/ 0x8c71dcd9ba0b495c,
            /*20*/ 0xfd00b89747823938,
            /*21*/ 0xe3e27a444d8d991a,
        };

        private static readonly short[] s_rgexp64Power10By16 =
        {
            // exponents for both powers of 10^16 and 0.1^16
            /*1*/ 54,
            /*2*/ 107,
            /*3*/ 160,
            /*4*/ 213,
            /*5*/ 266,
            /*6*/ 319,
            /*7*/ 373,
            /*8*/ 426,
            /*9*/ 479,
            /*10*/ 532,
            /*11*/ 585,
            /*12*/ 638,
            /*13*/ 691,
            /*14*/ 745,
            /*15*/ 798,
            /*16*/ 851,
            /*17*/ 904,
            /*18*/ 957,
            /*19*/ 1010,
            /*20*/ 1064,
            /*21*/ 1117,
        };

        private static int abs(int value)
        {
            if (value < 0)
                return -value;
            return value;
        }

        private static unsafe double NumberToDouble(ref NumberBuffer number)
        {
            ulong val;
            int exp;
            char* src = number.digits;
            int remaining;
            int total;
            int count;
            int scale;
            int absscale;
            int index;

            total = string.wcslen(src);
            remaining = total;

            // skip the leading zeros
            while (*src == '0')
            {
                remaining--;
                src++;
            }

            if (remaining == 0)
                return 0;

            count = Math.Min(remaining, 9);
            remaining -= count;
            val = DigitsToInt(src, count);

            if (remaining > 0)
            {
                count = Math.Min(remaining, 9);
                remaining -= count;

                // get the denormalized power of 10
                uint mult = (uint)(s_rgval64Power10[count - 1] >> (64 - s_rgexp64Power10[count - 1]));
                val = Mul32x32To64((uint)val, mult) + DigitsToInt(src + 9, count);
            }

            scale = number.scale - (total - remaining);
            absscale = abs(scale);
            if (absscale >= 22 * 16)
            {
                // overflow / underflow
                ulong result = (scale > 0) ? 0x7FF0000000000000 : 0ul;
                if (number.sign)
                    result |= 0x8000000000000000;
                return *(double*)&result;
            }

            exp = 64;

            // normalize the mantissa
            if ((val & 0xFFFFFFFF00000000) == 0)
            { val <<= 32; exp -= 32; }
            if ((val & 0xFFFF000000000000) == 0)
            { val <<= 16; exp -= 16; }
            if ((val & 0xFF00000000000000) == 0)
            { val <<= 8; exp -= 8; }
            if ((val & 0xF000000000000000) == 0)
            { val <<= 4; exp -= 4; }
            if ((val & 0xC000000000000000) == 0)
            { val <<= 2; exp -= 2; }
            if ((val & 0x8000000000000000) == 0)
            { val <<= 1; exp -= 1; }

            index = absscale & 15;
            if (index != 0)
            {
                int multexp = s_rgexp64Power10[index - 1];
                // the exponents are shared between the inverted and regular table
                exp += (scale < 0) ? (-multexp + 1) : multexp;

                ulong multval = s_rgval64Power10[index + ((scale < 0) ? 15 : 0) - 1];
                val = Mul64Lossy(val, multval, ref exp);
            }

            index = absscale >> 4;
            if (index != 0)
            {
                int multexp = s_rgexp64Power10By16[index - 1];
                // the exponents are shared between the inverted and regular table
                exp += (scale < 0) ? (-multexp + 1) : multexp;

                ulong multval = s_rgval64Power10By16[index + ((scale < 0) ? 21 : 0) - 1];
                val = Mul64Lossy(val, multval, ref exp);
            }


            // round & scale down
            if (((int)val & (1 << 10)) != 0)
            {
                // IEEE round to even
                ulong tmp = val + ((1 << 10) - 1) + (ulong)(((int)val >> 11) & 1);
                if (tmp < val)
                {
                    // overflow
                    tmp = (tmp >> 1) | 0x8000000000000000;
                    exp += 1;
                }
                val = tmp;
            }

            // return the exponent to a biased state
            exp += 0x3FE;

            // handle overflow, underflow, "Epsilon - 1/2 Epsilon", denormalized, and the normal case
            if (exp <= 0)
            {
                if (exp == -52 && (val >= 0x8000000000000058))
                {
                    // round X where {Epsilon > X >= 2.470328229206232730000000E-324} up to Epsilon (instead of down to zero)
                    val = 0x0000000000000001;
                }
                else if (exp <= -52)
                {
                    // underflow
                    val = 0;
                }
                else
                {
                    // denormalized
                    val >>= (-exp + 11 + 1);
                }
            }
            else if (exp >= 0x7FF)
            {
                // overflow
                val = 0x7FF0000000000000;
            }
            else
            {
                // normal postive exponent case
                val = ((ulong)exp << 52) + ((val >> 11) & 0x000FFFFFFFFFFFFF);
            }

            if (number.sign)
                val |= 0x8000000000000000;

            return *(double*)&val;
        }
    }
}