round() for float in C++

Question

I need a simple floating point rounding function, thus:

double round(double);

round(0.1) = 0
round(-0.1) = 0
round(-0.9) = -1

I can find ceil() and floor() in the math.h - but not round().

Is it present in the standard C++ library under another name, or is it missing??

Answer 1

If you ultimately want to convert the double output of your round() function to an int, then the accepted solutions of this question will look something like:

int roundint(double r) {
  return (int)((r > 0.0) ? floor(r + 0.5) : ceil(r - 0.5));
}

This clocks in at around 8.88 ns on my machine when passed in uniformly random values.

The below is functionally equivalent, as far as I can tell, but clocks in at 2.48 ns on my machine, for a significant performance advantage:

int roundint (double r) {
  int tmp = static_cast<int> (r);
  tmp += (r-tmp>=.5) - (r-tmp<=-.5);
  return tmp;
}

Among the reasons for the better performance is the skipped branching.

Answer 2

If you need to be able to compile code in environments that support the C++11 standard, but also need to be able to compile that same code in environments that don't support it, you could use a function macro to choose between std::round() and a custom function for each system. Just pass -DCPP11 or /DCPP11 to the C++11-compliant compiler (or use its built-in version macros), and make a header like this:

// File: rounding.h
#include <cmath>

#ifdef CPP11
    #define ROUND(x) std::round(x)
#else    /* CPP11 */
    inline double myRound(double x) {
        return (x >= 0.0 ? std::floor(x + 0.5) : std::ceil(x - 0.5));
    }

    #define ROUND(x) myRound(x)
#endif   /* CPP11 */

For a quick example, see http://ideone.com/zal709 .

This approximates std::round() in environments that aren't C++11-compliant, including preservation of the sign bit for -0.0. It may cause a slight performance hit, however, and will likely have issues with rounding certain known "problem" floating-point values such as 0.49999999999999994 or similar values.

Alternatively, if you have access to a C++11-compliant compiler, you could just grab std::round() from its <cmath> header, and use it to make your own header that defines the function if it's not already defined. Note that this may not be an optimal solution, however, especially if you need to compile for multiple platforms.

Answer 3

// Convert the float to a string
// We might use stringstream, but it looks like it truncates the float to only
//5 decimal points (maybe that's what you want anyway =P)

float MyFloat = 5.11133333311111333;
float NewConvertedFloat = 0.0;
string FirstString = " ";
string SecondString = " ";
stringstream ss (stringstream::in | stringstream::out);
ss << MyFloat;
FirstString = ss.str();

// Take out how ever many decimal places you want
// (this is a string it includes the point)
SecondString = FirstString.substr(0,5);
//whatever precision decimal place you want

// Convert it back to a float
stringstream(SecondString) >> NewConvertedFloat;
cout << NewConvertedFloat;
system("pause");

It might be an inefficient dirty way of conversion but heck, it works lol. And it's good, because it applies to the actual float. Not just affecting the output visually.

Answer 4

There are 2 problems we are looking at:

1. rounding conversions
2. type conversion.

Rounding conversions mean rounding ± float/double to nearest floor/ceil float/double. May be your problem ends here. But if you are expected to return Int/Long, you need to perform type conversion, and thus "Overflow" problem might hit your solution. SO, do a check for error in your function

long round(double x) {
   assert(x >= LONG_MIN-0.5);
   assert(x <= LONG_MAX+0.5);
   if (x >= 0)
      return (long) (x+0.5);
   return (long) (x-0.5);
}

#define round(x) ((x) < LONG_MIN-0.5 || (x) > LONG_MAX+0.5 ?\
      error() : ((x)>=0?(long)((x)+0.5):(long)((x)-0.5))

from : http://www.cs.tut.fi/~jkorpela/round.html

Answer 5

I did this:

#include <cmath.h>

using namespace std;

double roundh(double number, int place){

    /* place = decimal point. Putting in 0 will make it round to whole
                              number. putting in 1 will round to the
                              tenths digit.
    */

    number *= 10^place;
    int istack = (int)floor(number);
    int out = number-istack;
    if (out < 0.5){
        floor(number);
        number /= 10^place;
        return number;
    }
    if (out > 0.4) {
        ceil(number);
        number /= 10^place;
        return number;
    }
}

Answer 6

As pointed out in comments and other answers, the ISO C++ standard library did not add round() until ISO C++11, when this function was pulled in by reference to the ISO C99 standard math library.

For positive operands in [½, ub] round(x) == floor (x + 0.5), where ub is 2²³ for float when mapped to IEEE-754 (2008) binary32, and 2⁵² for double when it is mapped to IEEE-754 (2008) binary64. The numbers 23 and 52 correspond to the number of stored mantissa bits in these two floating-point formats. For positive operands in [+0, ½) round(x) == 0, and for positive operands in (ub, +∞] round(x) == x. As the function is symmetric about the x-axis, negative arguments x can be handled according to round(-x) == -round(x).

This leads to the compact code below. It compiles into a reasonable number of machine instructions across various platforms. I observed the most compact code on GPUs, where my_roundf() requires about a dozen instructions. Depending on processor architecture and toolchain, this floating-point based approach could be either faster or slower than the integer-based implementation from newlib referenced in a different answer.

I tested my_roundf() exhaustively against the newlib roundf() implementation using Intel compiler version 13, with both /fp:strict and /fp:fast. I also checked that the newlib version matches the roundf() in the mathimf library of the Intel compiler. Exhaustive testing is not possible for double-precision round(), however the code is structurally identical to the single-precision implementation.

#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include <string.h>
#include <math.h>

float my_roundf (float x)
{
    const float half = 0.5f;
    const float one = 2 * half;
    const float lbound = half;
    const float ubound = 1L << 23;
    float a, f, r, s, t;
    s = (x < 0) ? (-one) : one;
    a = x * s;
    t = (a < lbound) ? x : s;
    f = (a < lbound) ? 0 : floorf (a + half);
    r = (a > ubound) ? x : (t * f);
    return r;
}

double my_round (double x)
{
    const double half = 0.5;
    const double one = 2 * half;
    const double lbound = half;
    const double ubound = 1ULL << 52;
    double a, f, r, s, t;
    s = (x < 0) ? (-one) : one;
    a = x * s;
    t = (a < lbound) ? x : s;
    f = (a < lbound) ? 0 : floor (a + half);
    r = (a > ubound) ? x : (t * f);
    return r;
}

uint32_t float_as_uint (float a)
{
    uint32_t r;
    memcpy (&r, &a, sizeof(r));
    return r;
}

float uint_as_float (uint32_t a)
{
    float r;
    memcpy (&r, &a, sizeof(r));
    return r;
}

float newlib_roundf (float x)
{
    uint32_t w;
    int exponent_less_127;

    w = float_as_uint(x);
    /* Extract exponent field. */
    exponent_less_127 = (int)((w & 0x7f800000) >> 23) - 127;
    if (exponent_less_127 < 23) {
        if (exponent_less_127 < 0) {
            /* Extract sign bit. */
            w &= 0x80000000;
            if (exponent_less_127 == -1) {
                /* Result is +1.0 or -1.0. */
                w |= ((uint32_t)127 << 23);
            }
        } else {
            uint32_t exponent_mask = 0x007fffff >> exponent_less_127;
            if ((w & exponent_mask) == 0) {
                /* x has an integral value. */
                return x;
            }
            w += 0x00400000 >> exponent_less_127;
            w &= ~exponent_mask;
        }
    } else {
        if (exponent_less_127 == 128) {
            /* x is NaN or infinite so raise FE_INVALID by adding */
            return x + x;
        } else {
            return x;
        }
    }
    x = uint_as_float (w);
    return x;
}

int main (void)
{
    uint32_t argi, resi, refi;
    float arg, res, ref;

    argi = 0;
    do {
        arg = uint_as_float (argi);
        ref = newlib_roundf (arg);
        res = my_roundf (arg);
        resi = float_as_uint (res);
        refi = float_as_uint (ref);
        if (resi != refi) { // check for identical bit pattern
            printf ("!!!! arg=%08x  res=%08x  ref=%08x\n", argi, resi, refi);
            return EXIT_FAILURE;
        }
        argi++;
    } while (argi);
    return EXIT_SUCCESS;
}