# separatore - Formattazione di numeri con cifre significative in C#

## vb net format percent (6)

È possibile ottenere un elegante arrotondamento bit perfetto utilizzando il metodo GetBits su Decimal e sfruttando BigInteger per eseguire il mascheramento.

Alcuni programmi di utilità

``````    public static int CountDigits
(BigInteger number) => ((int)BigInteger.Log10(number))+1;

= Enumerable.Range(0, 100)
.Select(v => BigInteger.Pow(10, v))
.ToArray();
``````

La funzione principale

``````    public static decimal RoundToSignificantDigits
(this decimal num,
short n)
{
var bits = decimal.GetBits(num);
var u0 = unchecked((uint)bits[0]);
var u1 = unchecked((uint)bits[1]);
var u2 = unchecked((uint)bits[2]);

var i = new BigInteger(u0)
+ (new BigInteger(u1) << 32)
+ (new BigInteger(u2) << 64);

var d = CountDigits(i);

var delta = d - n;
if (delta < 0)
return num;

var scale = BigPowers10[delta];
var div = i/scale;
var rem = i%scale;
var up = rem > scale/2;
if (up)
div += 1;
var shifted = div*scale;

return new decimal(bits);
}
``````

test case 0

``````    public void RoundToSignificantDigits()
{
WMath.RoundToSignificantDigits(0.0012345m, 2).Should().Be(0.0012m);
WMath.RoundToSignificantDigits(0.0012645m, 2).Should().Be(0.0013m);
WMath.RoundToSignificantDigits(0.040000000000000008, 6).Should().Be(0.04);
WMath.RoundToSignificantDigits(0.040000010000000008, 6).Should().Be(0.04);
WMath.RoundToSignificantDigits(0.040000100000000008, 6).Should().Be(0.0400001);
WMath.RoundToSignificantDigits(0.040000110000000008, 6).Should().Be(0.0400001);
WMath.RoundToSignificantDigits(0.20000000000000004, 6).Should().Be(0.2);
WMath.RoundToSignificantDigits(0.10000000000000002, 6).Should().Be(0.1);
WMath.RoundToSignificantDigits(0.0, 6).Should().Be(0.0);

}
``````

test case 1

``````     public void RoundToSigFigShouldWork()
{
1.2m.RoundToSignificantDigits(1).Should().Be(1m);
0.01235668m.RoundToSignificantDigits(3).Should().Be(0.0124m);
0.01m.RoundToSignificantDigits(3).Should().Be(0.01m);

1.23456789123456789123456789m.RoundToSignificantDigits(4)
.Should().Be(1.235m);

1.23456789123456789123456789m.RoundToSignificantDigits(16)
.Should().Be(1.234567891234568m);

1.23456789123456789123456789m.RoundToSignificantDigits(24)
.Should().Be(1.23456789123456789123457m);

1.23456789123456789123456789m.RoundToSignificantDigits(27)
.Should().Be(1.23456789123456789123456789m);
}
``````

Ho alcuni dati decimali che sto spingendo in un elenco di SharePoint in cui deve essere visualizzato. Mi piacerebbe limitare il numero di cifre significative visualizzate nei dati dei risultati in base alla mia conoscenza del calcolo specifico. A volte sarà 3, quindi 12345 diventerà 12300 e 0,012345 diventerà 0,0123. Occasionalmente sarà 4 o 5. C'è un modo conveniente per gestire questo?

Ho finito per impadronirci del codice da http://ostermiller.org/utils/SignificantFigures.java.html . Era in java, quindi ho fatto una rapida ricerca / sostituzione e qualche riformattazione del programma di reinstallazione per realizzare la build di C #. Sembra funzionare bene per le mie esigenze di figure significative. FWIW, ho rimosso i suoi commenti javadoc per renderlo più conciso qui, ma il codice originale è documentato abbastanza bene.

``````/*
* Copyright (C) 2002-2007 Stephen Ostermiller
* http://ostermiller.org/contact.pl?regarding=Java+Utilities
*
* This program is free software; you can redistribute it and/or modify
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
* GNU General Public License for more details.
*
* See COPYING.TXT for details.
*/
public class SignificantFigures
{
private String original;
private StringBuilder _digits;
private int mantissa = -1;
private bool sign = true;
private bool isZero = false;
private bool useScientificNotation = true;

public SignificantFigures(String number)
{
original = number;
Parse(original);
}

public SignificantFigures(double number)
{
original = Convert.ToString(number);
try
{
Parse(original);
}
catch (Exception nfe)
{
_digits = null;
}
}

public bool UseScientificNotation
{
get { return useScientificNotation; }
set { useScientificNotation = value; }
}

public int GetNumberSignificantFigures()
{
if (_digits == null) return 0;
return _digits.Length;
}

public SignificantFigures SetLSD(int place)
{
SetLMSD(place, Int32.MinValue);
return this;
}

public SignificantFigures SetLMSD(int leastPlace, int mostPlace)
{
if (_digits != null && leastPlace != Int32.MinValue)
{
int significantFigures = _digits.Length;
int current = mantissa - significantFigures + 1;
int newLength = significantFigures - leastPlace + current;
if (newLength <= 0)
{
if (mostPlace == Int32.MinValue)
{
original = "NaN";
_digits = null;
}
else
{
newLength = mostPlace - leastPlace + 1;
_digits.Length = newLength;
mantissa = leastPlace;
for (int i = 0; i < newLength; i++)
{
_digits[i] = '0';
}
isZero = true;
sign = true;
}
}
else
{
_digits.Length = newLength;
for (int i = significantFigures; i < newLength; i++)
{
_digits[i] = '0';
}
}
}
return this;
}

public int GetLSD()
{
if (_digits == null) return Int32.MinValue;
return mantissa - _digits.Length + 1;
}

public int GetMSD()
{
if (_digits == null) return Int32.MinValue;
return mantissa + 1;
}

public override String ToString()
{
if (_digits == null) return original;
StringBuilder digits = new StringBuilder(this._digits.ToString());
int length = digits.Length;
if ((mantissa <= -4 || mantissa >= 7 ||
(mantissa >= length &&
digits[digits.Length - 1] == '0') ||
(isZero && mantissa != 0)) && useScientificNotation)
{
// use scientific notation.
if (length > 1)
{
digits.Insert(1, '.');
}
if (mantissa != 0)
{
digits.Append("E" + mantissa);
}
}
else if (mantissa <= -1)
{
digits.Insert(0, "0.");
for (int i = mantissa; i < -1; i++)
{
digits.Insert(2, '0');
}
}
else if (mantissa + 1 == length)
{
if (length > 1 && digits[digits.Length - 1] == '0')
{
digits.Append('.');
}
}
else if (mantissa < length)
{
digits.Insert(mantissa + 1, '.');
}
else
{
for (int i = length; i <= mantissa; i++)
{
digits.Append('0');
}
}
if (!sign)
{
digits.Insert(0, '-');
}
return digits.ToString();
}

public String ToScientificNotation()
{
if (_digits == null) return original;
StringBuilder digits = new StringBuilder(this._digits.ToString());
int length = digits.Length;
if (length > 1)
{
digits.Insert(1, '.');
}
if (mantissa != 0)
{
digits.Append("E" + mantissa);
}
if (!sign)
{
digits.Insert(0, '-');
}
return digits.ToString();
}

private const int INITIAL = 0;
private const int LEADZEROS = 1;
private const int MIDZEROS = 2;
private const int DIGITS = 3;
private const int LEADZEROSDOT = 4;
private const int DIGITSDOT = 5;
private const int MANTISSA = 6;
private const int MANTISSADIGIT = 7;

private void Parse(String number)
{
int length = number.Length;
_digits = new StringBuilder(length);
int state = INITIAL;
int mantissaStart = -1;
// sometimes we don't know if a zero will be
// significant or not when it is encountered.
// keep track of the number of them so that
// the all can be made significant if we find
// out that they are.
int zeroCount = 0;

for (int i = 0; i < length; i++)
{
char c = number[i];
switch (c)
{
case '.':
{
switch (state)
{
case INITIAL:
{
}
break;
case MIDZEROS:
{
// we now know that these zeros
// are more than just trailing place holders.
for (int j = 0; j < zeroCount; j++)
{
_digits.Append('0');
}
zeroCount = 0;
state = DIGITSDOT;
}
break;
case DIGITS:
{
state = DIGITSDOT;
}
break;
default:
{
throw new Exception(
"Unexpected character '" + c + "' at position " + i
);
}
}
}
break;
case '+':
{
switch (state)
{
case INITIAL:
{
sign = true;
}
break;
case MANTISSA:
{
}
break;
default:
{
throw new Exception(
"Unexpected character '" + c + "' at position " + i
);
}
}
}
break;
case '-':
{
switch (state)
{
case INITIAL:
{
sign = false;
}
break;
case MANTISSA:
{
}
break;
default:
{
throw new Exception(
"Unexpected character '" + c + "' at position " + i
);
}
}
}
break;
case '0':
{
switch (state)
{
case INITIAL:
{
// only significant if number
// is all zeros.
zeroCount++;
}
break;
case MIDZEROS:
case DIGITS:
{
// only significant if followed
// by a decimal point or nonzero digit.
mantissa++;
zeroCount++;
state = MIDZEROS;
}
break;
{
// only significant if number
// is all zeros.
mantissa--;
zeroCount++;
}
break;
case DIGITSDOT:
{
// a decimal point are always
// significant.
_digits.Append(c);
}
break;
case MANTISSA:
{
}
break;
default:
{
throw new Exception(
"Unexpected character '" + c + "' at position " + i
);
}
}
}
break;
case '1':
case '2':
case '3':
case '4':
case '5':
case '6':
case '7':
case '8':
case '9':
{
switch (state)
{
case INITIAL:
case DIGITS:
{
zeroCount = 0;
_digits.Append(c);
mantissa++;
state = DIGITS;
}
break;
case MIDZEROS:
{
// we now know that these zeros
// are more than just trailing place holders.
for (int j = 0; j < zeroCount; j++)
{
_digits.Append('0');
}
zeroCount = 0;
_digits.Append(c);
mantissa++;
state = DIGITS;
}
break;
case DIGITSDOT:
{
zeroCount = 0;
_digits.Append(c);
state = DIGITSDOT;
}
break;
case MANTISSA:
{
}
break;
default:
{
throw new Exception(
"Unexpected character '" + c + "' at position " + i
);
}
}
}
break;
case 'E':
case 'e':
{
switch (state)
{
case INITIAL:
case DIGITS:
case DIGITSDOT:
{
// record the starting point of the mantissa
// so we can do a substring to get it back later
mantissaStart = i + 1;
state = MANTISSA;
}
break;
default:
{
throw new Exception(
"Unexpected character '" + c + "' at position " + i
);
}
}
}
break;
default:
{
throw new Exception(
"Unexpected character '" + c + "' at position " + i
);
}
}
}
if (mantissaStart != -1)
{
// if we had found an 'E'
{
// we didn't actually find a mantissa to go with.
throw new Exception(
"No digits in mantissa."
);
}
// parse the mantissa.
mantissa += Convert.ToInt32(number.Substring(mantissaStart));
}
if (_digits.Length == 0)
{
if (zeroCount > 0)
{
// if nothing but zeros all zeros are significant.
for (int j = 0; j < zeroCount; j++)
{
_digits.Append('0');
}
isZero = true;
sign = true;
}
else
{
// a hack to catch some cases that we could catch
// by adding a ton of extra states.  Things like:
// "e2" "+e2" "+." "." "+" etc.
throw new Exception(
"No digits in number."
);
}
}
}

public SignificantFigures SetNumberSignificantFigures(int significantFigures)
{
if (significantFigures <= 0)
throw new ArgumentException("Desired number of significant figures must be positive.");
if (_digits != null)
{
int length = _digits.Length;
if (length < significantFigures)
{
// number is not long enough, pad it with zeros.
for (int i = length; i < significantFigures; i++)
{
_digits.Append('0');
}
}
else if (length > significantFigures)
{
// number is too long chop some of it off with rounding.
bool addOne; // we need to round up if true.
char firstInSig = _digits[significantFigures];
if (firstInSig < '5')
{
// first non-significant digit less than five, round down.
}
else if (firstInSig == '5')
{
// first non-significant digit equal to five
for (int i = significantFigures + 1; !addOne && i < length; i++)
{
// if its followed by any non-zero digits, round up.
if (_digits[i] != '0')
{
}
}
{
// if it was not followed by non-zero digits
// if the last significant digit is odd round up
// if the last significant digit is even round down
addOne = (_digits[significantFigures - 1] & 1) == 1;
}
}
else
{
// first non-significant digit greater than five, round up.
}
// loop to add one (and carry a one if added to a nine)
// to the last significant digit
for (int i = significantFigures - 1; addOne && i >= 0; i--)
{
char digit = _digits[i];
if (digit < '9')
{
_digits[i] = (char) (digit + 1);
}
else
{
_digits[i] = '0';
}
}
{
// if the number was all nines
_digits.Insert(0, '1');
mantissa++;
}
// chop it to the correct number of figures.
_digits.Length = significantFigures;
}
}
return this;
}

public double ToDouble()
{
return Convert.ToDouble(original);
}

public static String Format(double number, int significantFigures)
{
SignificantFigures sf = new SignificantFigures(number);
sf.SetNumberSignificantFigures(significantFigures);
return sf.ToString();
}
}
``````

Ho una risposta in cortocircuito al calcolo di cifre significative di un numero. Ecco il codice e i risultati del test ...

``````using System;
using System.Collections.Generic;

namespace ConsoleApplicationRound
{
class Program
{
static void Main(string[] args)
{
//char cDecimal = '.';    // for English cultures
char cDecimal = ',';    // for German cultures
List<double> l_dValue = new List<double>();
ushort usSignificants = 5;

foreach (double d in l_dValue)
{
Console.WriteLine("d = Maths.Round('" +
cDecimal + "', " + d + ", " + usSignificants +
") = " + Maths.Round(
cDecimal, d, usSignificants));
}

}
}
}
``````

La classe Maths utilizzata è la seguente:

``````using System;
using System.Text;

namespace ConsoleApplicationRound
{
class Maths
{
/// <summary>
///     The word "Window"
/// </summary>
private static String m_strZeros = "000000000000000000000000000000000";
/// <summary>
///     The minus sign
/// </summary>
public const char m_cDASH = '-';

/// <summary>
///     Determines the number of digits before the decimal point
/// </summary>
/// <param name="cDecimal">
///     Language-specific decimal separator
/// </param>
/// <param name="strValue">
///     Value to be scrutinised
/// </param>
/// <returns>
///     Nr. of digits before the decimal point
/// </returns>
private static ushort NrOfDigitsBeforeDecimal(char cDecimal, String strValue)
{
short sDecimalPosition = (short)strValue.IndexOf(cDecimal);
ushort usSignificantDigits = 0;

if (sDecimalPosition >= 0)
{
strValue = strValue.Substring(0, sDecimalPosition + 1);
}

for (ushort us = 0; us < strValue.Length; us++)
{
if (strValue[us] != m_cDASH) usSignificantDigits++;

if (strValue[us] == cDecimal)
{
usSignificantDigits--;
break;
}
}

return usSignificantDigits;
}

/// <summary>
///     Rounds to a fixed number of significant digits
/// </summary>
/// <param name="d">
///     Number to be rounded
/// </param>
/// <param name="usSignificants">
///     Requested significant digits
/// </param>
/// <returns>
///     The rounded number
/// </returns>
public static String Round(char cDecimal,
double d,
ushort usSignificants)
{
StringBuilder value = new StringBuilder(Convert.ToString(d));

short sDecimalPosition = (short)value.ToString().IndexOf(cDecimal);
ushort usAfterDecimal = 0;
ushort usDigitsBeforeDecimalPoint =
NrOfDigitsBeforeDecimal(cDecimal, value.ToString());

if (usDigitsBeforeDecimalPoint == 1)
{
usAfterDecimal = (d == 0)
? usSignificants
: (ushort)(value.Length - sDecimalPosition - 2);
}
else
{
if (usSignificants >= usDigitsBeforeDecimalPoint)
{
usAfterDecimal =
(ushort)(usSignificants - usDigitsBeforeDecimalPoint);
}
else
{
double dPower = Math.Pow(10,
usDigitsBeforeDecimalPoint - usSignificants);

d = dPower*(long)(d/dPower);
}
}

double dRounded = Math.Round(d, usAfterDecimal);
StringBuilder result = new StringBuilder();

result.Append(dRounded);
ushort usDigits = (ushort)result.ToString().Replace(
Convert.ToString(cDecimal), "").Replace(
Convert.ToString(m_cDASH), "").Length;

// Add lagging zeros, if necessary:
if (usDigits < usSignificants)
{
if (usAfterDecimal != 0)
{
if (result.ToString().IndexOf(cDecimal) == -1)
{
result.Append(cDecimal);
}

int i = (d == 0) ? 0 : Math.Min(0, usDigits - usSignificants);

result.Append(m_strZeros.Substring(0, usAfterDecimal + i));
}
}

return result.ToString();
}
}
}
``````

Qualche risposta con un codice più breve?

Il seguente codice non soddisfa abbastanza le specifiche, poiché non tenta di arrotondare nulla alla sinistra del punto decimale. Ma è più semplice di qualsiasi altra cosa presentata qui (finora). Sono rimasto piuttosto sorpreso dal fatto che C # non abbia un metodo integrato per gestirlo.

``````static public string SignificantDigits(double d, int digits=10)
{
int magnitude = (d == 0.0) ? 0 : (int)Math.Floor(Math.Log10(Math.Abs(d))) + 1;
digits -= magnitude;
if (digits < 0)
digits = 0;
string fmt = "f" + digits.ToString();
return d.ToString(fmt);
}
``````

Questo potrebbe fare il trucco:

``````
double Input1 = 1234567;
string Result1 = Convert.ToDouble(String.Format("{0:G3}",Input1)).ToString("R0");

double Input2 = 0.012345;
string Result2 = Convert.ToDouble(String.Format("{0:G3}", Input2)).ToString("R6");
``````

Cambiare il G3 in G4 produce comunque il risultato più strano. Sembra di arrotondare le cifre significative?

Ho combinato il suo metodo con un altro che mi è piaciuto.

Arrotondare a cifre significative è molto più semplice in TSQL dove il metodo di arrotondamento si basa sulla posizione di arrotondamento, non sul numero di cifre decimali, come nel caso di .Net math.round. È possibile arrotondare un numero in TSQL a posizioni negative, che verrebbero arrotondate a numeri interi, quindi il ridimensionamento non è necessario.

Vedi anche questo altro thread . Il metodo pirolistico è buono.

La parte degli zeri finali del problema mi sembra più un'operazione di stringa, quindi ho incluso un metodo di estensione ToString () che riempirà gli zeri se necessario.

``````using System;
using System.Globalization;

public static class Precision
{
// 2^-24
public const float FLOAT_EPSILON = 0.0000000596046448f;

// 2^-53
public const double DOUBLE_EPSILON = 0.00000000000000011102230246251565d;

public static bool AlmostEquals(this double a, double b, double epsilon = DOUBLE_EPSILON)
{
// ReSharper disable CompareOfFloatsByEqualityOperator
if (a == b)
{
return true;
}
// ReSharper restore CompareOfFloatsByEqualityOperator

return (System.Math.Abs(a - b) < epsilon);
}

public static bool AlmostEquals(this float a, float b, float epsilon = FLOAT_EPSILON)
{
// ReSharper disable CompareOfFloatsByEqualityOperator
if (a == b)
{
return true;
}
// ReSharper restore CompareOfFloatsByEqualityOperator

return (System.Math.Abs(a - b) < epsilon);
}
}

public static class SignificantDigits
{
public static double Round(this double value, int significantDigits)
{
int unneededRoundingPosition;
return RoundSignificantDigits(value, significantDigits, out unneededRoundingPosition);
}

public static string ToString(this double value, int significantDigits)
{
// this method will round and then append zeros if needed.
// i.e. if you round .002 to two significant figures, the resulting number should be .0020.

var currentInfo = CultureInfo.CurrentCulture.NumberFormat;

if (double.IsNaN(value))
{
return currentInfo.NaNSymbol;
}

if (double.IsPositiveInfinity(value))
{
return currentInfo.PositiveInfinitySymbol;
}

if (double.IsNegativeInfinity(value))
{
return currentInfo.NegativeInfinitySymbol;
}

int roundingPosition;
var roundedValue = RoundSignificantDigits(value, significantDigits, out roundingPosition);

// when rounding causes a cascading round affecting digits of greater significance,
// need to re-round to get a correct rounding position afterwards
// this fixes a bug where rounding 9.96 to 2 figures yeilds 10.0 instead of 10
RoundSignificantDigits(roundedValue, significantDigits, out roundingPosition);

if (Math.Abs(roundingPosition) > 9)
{
// use exponential notation format
// ReSharper disable FormatStringProblem
return string.Format(currentInfo, "{0:E" + (significantDigits - 1) + "}", roundedValue);
// ReSharper restore FormatStringProblem
}

// string.format is only needed with decimal numbers (whole numbers won't need to be padded with zeros to the right.)
// ReSharper disable FormatStringProblem
return roundingPosition > 0 ? string.Format(currentInfo, "{0:F" + roundingPosition + "}", roundedValue) : roundedValue.ToString(currentInfo);
// ReSharper restore FormatStringProblem
}

private static double RoundSignificantDigits(double value, int significantDigits, out int roundingPosition)
{
// this method will return a rounded double value at a number of signifigant figures.
// the sigFigures parameter must be between 0 and 15, exclusive.

roundingPosition = 0;

if (value.AlmostEquals(0d))
{
roundingPosition = significantDigits - 1;
return 0d;
}

if (double.IsNaN(value))
{
return double.NaN;
}

if (double.IsPositiveInfinity(value))
{
return double.PositiveInfinity;
}

if (double.IsNegativeInfinity(value))
{
return double.NegativeInfinity;
}

if (significantDigits < 1 || significantDigits > 15)
{
throw new ArgumentOutOfRangeException("significantDigits", value, "The significantDigits argument must be between 1 and 15.");
}

// The resulting rounding position will be negative for rounding at whole numbers, and positive for decimal places.
roundingPosition = significantDigits - 1 - (int)(Math.Floor(Math.Log10(Math.Abs(value))));

// try to use a rounding position directly, if no scale is needed.
// this is because the scale mutliplication after the rounding can introduce error, although
// this only happens when you're dealing with really tiny numbers, i.e 9.9e-14.
if (roundingPosition > 0 && roundingPosition < 16)
{
return Math.Round(value, roundingPosition, MidpointRounding.AwayFromZero);
}

// Shouldn't get here unless we need to scale it.
// Set the scaling value, for rounding whole numbers or decimals past 15 places
var scale = Math.Pow(10, Math.Ceiling(Math.Log10(Math.Abs(value))));

return Math.Round(value / scale, significantDigits, MidpointRounding.AwayFromZero) * scale;
}
}
``````