How to calculate the number of significant decimal

问题:

When dealing with floating point values in Java, calling the toString() method gives a printed value that has the correct number of floating point significant figures. However, in C++, printing a float via stringstream will round the value after 5 or less digits. Is there a way to "pretty print" a float in C++ to the (assumed) correct number of significant figures?

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EDIT: I think I am being misunderstood. I want the output to be of dynamic length, not a fixed precision. I am familiar with setprecision. If you look at the java source for Double, it calculates the number of significant digits somehow, and I would really like to understand how it works and/or how feasible it is to replicate this easily in C++.

/*
 * FIRST IMPORTANT CONSTRUCTOR: DOUBLE
 */
public FloatingDecimal( double d )
{
    long    dBits = Double.doubleToLongBits( d );
    long    fractBits;
    int     binExp;
    int     nSignificantBits;

    // discover and delete sign
    if ( (dBits&signMask) != 0 ){
        isNegative = true;
        dBits ^= signMask;
    } else {
        isNegative = false;
    }
    // Begin to unpack
    // Discover obvious special cases of NaN and Infinity.
    binExp = (int)( (dBits&expMask) >> expShift );
    fractBits = dBits&fractMask;
    if ( binExp == (int)(expMask>>expShift) ) {
        isExceptional = true;
        if ( fractBits == 0L ){
            digits =  infinity;
        } else {
            digits = notANumber;
            isNegative = false; // NaN has no sign!
        }
        nDigits = digits.length;
        return;
    }
    isExceptional = false;
    // Finish unpacking
    // Normalize denormalized numbers.
    // Insert assumed high-order bit for normalized numbers.
    // Subtract exponent bias.
    if ( binExp == 0 ){
        if ( fractBits == 0L ){
            // not a denorm, just a 0!
            decExponent = 0;
            digits = zero;
            nDigits = 1;
            return;
        }
        while ( (fractBits&fractHOB) == 0L ){
            fractBits <<= 1;
            binExp -= 1;
        }
        nSignificantBits = expShift + binExp +1; // recall binExp is  - shift count.
        binExp += 1;
    } else {
        fractBits |= fractHOB;
        nSignificantBits = expShift+1;
    }
    binExp -= expBias;
    // call the routine that actually does all the hard work.
    dtoa( binExp, fractBits, nSignificantBits );
}

After this function, it calls dtoa( binExp, fractBits, nSignificantBits ); which handles a bunch of cases - this is from OpenJDK6

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For more clarity, an example: Java:

double test1 = 1.2593;
double test2 = 0.004963;
double test3 = 1.55558742563;

System.out.println(test1);
System.out.println(test2);
System.out.println(test3);

Output:

1.2593
0.004963
1.55558742563

C++:

std::cout << test1 << "\n";
std::cout << test2 << "\n";
std::cout << test3 << "\n";

Output:

1.2593
0.004963
1.55559

回答1:

I think you are talking about how to print the minimum number of floating point digits that allow you to read the exact same floating point number back. This paper is a good introduction to this tricky problem.

http://grouper.ieee.org/groups/754/email/pdfq3pavhBfih.pdf

The dtoa function looks like David Gay's work, you can find the source here http://www.netlib.org/fp/dtoa.c (although this is C not Java).

Gay also wrote a paper about his method. I don't have a link but it's referenced in the above paper so you can probably google it.

回答2:

You can use the ios_base::precision technique where you can specify the number of digits you want

For example

#include <iostream>
using namespace std;

int main () {
double f = 3.14159;
cout.unsetf(ios::floatfield);            // floatfield not set
cout.precision(5);
cout << f << endl;
cout.precision(10);
cout << f << endl;
cout.setf(ios::fixed,ios::floatfield);   // floatfield set to fixed
cout << f << endl;
return 0;

The above code with output
3.1416
3.14159
3.1415900000

回答3:

There is a utility called numeric_limits:

#include <limits>

    ...
    int num10 = std::numeric_limits<double>::digits10;
    int max_num10 = std::numeric_limits<double>::max_digits10;

Note that IEEE numbers are not represented exactly bydecimal digits. These are binary quantities. A more accurate number is the number of binary bits:

    int bits = std::numeric_limits<double>::digits;

To pretty print all the significant digits use setprecision with this:

out.setprecision(std::numeric_limits<double>::digits10);