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

I use the following implementation of round in asm for x86 architecture and MS VS specific C++:

__forceinline int Round(const double v)
{
    int r;
    __asm
    {
        FLD     v
        FISTP   r
        FWAIT
    };
    return r;
}

UPD: to return double value

__forceinline double dround(const double v)
{
    double r;
    __asm
    {
        FLD     v
        FRNDINT
        FSTP    r
        FWAIT
    };
    return r;
}

Output:

dround(0.1): 0.000000000000000
dround(-0.1): -0.000000000000000
dround(0.9): 1.000000000000000
dround(-0.9): -1.000000000000000
dround(1.1): 1.000000000000000
dround(-1.1): -1.000000000000000
dround(0.49999999999999994): 0.000000000000000
dround(-0.49999999999999994): -0.000000000000000
dround(0.5): 0.000000000000000
dround(-0.5): -0.000000000000000

Answer 2

There's no round() in the C++98 standard library. You can write one yourself though. The following is an implementation of round-half-up:

double round(double d)
{
  return floor(d + 0.5);
}

The probable reason there is no round function in the C++98 standard library is that it can in fact be implemented in different ways. The above is one common way but there are others such as round-to-even, which is less biased and generally better if you're going to do a lot of rounding; it's a bit more complex to implement though.

Answer 3

It's available since C++11 in cmath (according to http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2012/n3337.pdf)

#include <cmath>
#include <iostream>

int main(int argc, char** argv) {
  std::cout << "round(0.5):\t" << round(0.5) << std::endl;
  std::cout << "round(-0.5):\t" << round(-0.5) << std::endl;
  std::cout << "round(1.4):\t" << round(1.4) << std::endl;
  std::cout << "round(-1.4):\t" << round(-1.4) << std::endl;
  std::cout << "round(1.6):\t" << round(1.6) << std::endl;
  std::cout << "round(-1.6):\t" << round(-1.6) << std::endl;
  return 0;
}

Output:

round(0.5):  1
round(-0.5): -1
round(1.4):  1
round(-1.4): -1
round(1.6):  2
round(-1.6): -2

Answer 4

These days it shouldn't be a problem to use a C++11 compiler which includes a C99/C++11 math library. But then the question becomes: which rounding function do you pick?

C99/C++11 round() is often not actually the rounding function you want. It uses a funky rounding mode that rounds away from 0 as a tie-break on half-way cases (+-xxx.5000). If you do specifically want that rounding mode, or you're targeting a C++ implementation where round() is faster than rint(), then use it (or emulate its behaviour with one of the other answers on this question which took it at face value and carefully reproduced that specific rounding behaviour.)

round()'s rounding is different from the IEEE754 default round to nearest mode with even as a tie-break. Nearest-even avoids statistical bias in the average magnitude of numbers, but does bias towards even numbers.

There are two math library rounding functions that use the current default rounding mode: std::nearbyint() and std::rint(), both added in C99/C++11, so they're available any time std::round() is. The only difference is that nearbyint never raises FE_INEXACT.

Prefer rint() for performance reasons: gcc and clang both inline it more easily, but gcc never inlines nearbyint() (even with -ffast-math)

---

gcc/clang for x86-64 and AArch64

I put some test functions on Matt Godbolt's Compiler Explorer, where you can see source + asm output (for multiple compilers). For more about reading compiler output, see this Q&A, and Matt's CppCon2017 talk: “What Has My Compiler Done for Me Lately? Unbolting the Compiler's Lid”,

In FP code, it's usually a big win to inline small functions. Especially on non-Windows, where the standard calling convention has no call-preserved registers, so the compiler can't keep any FP values in XMM registers across a call. So even if you don't really know asm, you can still easily see whether it's just a tail-call to the library function or whether it inlined to one or two math instructions. Anything that inlines to one or two instructions is better than a function call (for this particular task on x86 or ARM).

On x86, anything that inlines to SSE4.1 roundsd can auto-vectorize with SSE4.1 roundpd (or AVX vroundpd). (FP->integer conversions are also available in packed SIMD form, except for FP->64-bit integer which requires AVX512.)

• std::nearbyint():

  • x86 clang: inlines to a single insn with -msse4.1.
  • x86 gcc: inlines to a single insn only with -msse4.1 -ffast-math, and only on gcc 5.4 and earlier. Later gcc never inlines it (maybe they didn't realize that one of the immediate bits can suppress the inexact exception? That's what clang uses, but older gcc uses the same immediate as for rint when it does inline it)
  • AArch64 gcc6.3: inlines to a single insn by default.

• std::rint:

  • x86 clang: inlines to a single insn with -msse4.1
  • x86 gcc7: inlines to a single insn with -msse4.1. (Without SSE4.1, inlines to several instructions)
  • x86 gcc6.x and earlier: inlines to a single insn with -ffast-math -msse4.1.
  • AArch64 gcc: inlines to a single insn by default

• std::round:

  • x86 clang: doesn't inline
  • x86 gcc: inlines to multiple instructions with -ffast-math -msse4.1, requiring two vector constants.
  • AArch64 gcc: inlines to a single instruction (HW support for this rounding mode as well as IEEE default and most others.)

• std::floor / std::ceil / std::trunc

  • x86 clang: inlines to a single insn with -msse4.1
  • x86 gcc7.x: inlines to a single insn with -msse4.1
  • x86 gcc6.x and earlier: inlines to a single insn with -ffast-math -msse4.1
  • AArch64 gcc: inlines by default to a single instruction

---

Rounding to int / long / long long:

You have two options here: use lrint (like rint but returns long, or long long for llrint), or use an FP->FP rounding function and then convert to an integer type the normal way (with truncation). Some compilers optimize one way better than the other.

long l = lrint(x);

int  i = (int)rint(x);

Note that int i = lrint(x) converts float or double -> long first, and then truncates the integer to int. This makes a difference for out-of-range integers: Undefined Behaviour in C++, but well-defined for the x86 FP -> int instructions (which the compiler will emit unless it sees the UB at compile time while doing constant propagation, then it's allowed to make code that breaks if it's ever executed).

On x86, an FP->integer conversion that overflows the integer produces INT_MIN or LLONG_MIN (a bit-pattern of 0x8000000 or the 64-bit equivalent, with just the sign-bit set). Intel calls this the "integer indefinite" value. (See the cvttsd2si manual entry, the SSE2 instruction that converts (with truncation) scalar double to signed integer. It's available with 32-bit or 64-bit integer destination (in 64-bit mode only). There's also a cvtsd2si (convert with current rounding mode), which is what we'd like the compiler to emit, but unfortunately gcc and clang won't do that without -ffast-math.

Also beware that FP to/from unsigned int / long is less efficient on x86 (without AVX512). Conversion to 32-bit unsigned on a 64-bit machine is pretty cheap; just convert to 64-bit signed and truncate. But otherwise it's significantly slower.

• x86 clang with/without -ffast-math -msse4.1: (int/long)rint inlines to roundsd / cvttsd2si. (missed optimization to cvtsd2si). lrint doesn't inline at all.

• x86 gcc6.x and earlier without -ffast-math: neither way inlines

• x86 gcc7 without -ffast-math: (int/long)rint rounds and converts separately (with 2 total instructions of SSE4.1 is enabled, otherwise with a bunch of code inlined for rint without roundsd). lrint doesn't inline.

• x86 gcc with -ffast-math: all ways inline to cvtsd2si (optimal), no need for SSE4.1.

• AArch64 gcc6.3 without -ffast-math: (int/long)rint inlines to 2 instructions. lrint doesn't inline

• AArch64 gcc6.3 with -ffast-math: (int/long)rint compiles to a call to lrint. lrint doesn't inline. This may be a missed optimization unless the two instructions we get without -ffast-math are very slow.

Answer 5

Function double round(double) with the use of the modf function:

double round(double x)
{
    using namespace std;

    if ((numeric_limits<double>::max() - 0.5) <= x)
        return numeric_limits<double>::max();

    if ((-1*std::numeric_limits<double>::max() + 0.5) > x)
        return (-1*std::numeric_limits<double>::max());

    double intpart;
    double fractpart = modf(x, &intpart);

    if (fractpart >= 0.5)
        return (intpart + 1);
    else if (fractpart >= -0.5)
        return intpart;
    else
        return (intpart - 1);
    }

To be compile clean, includes "math.h" and "limits" are necessary. The function works according to a following rounding schema:

• round of 5.0 is 5.0
• round of 3.8 is 4.0
• round of 2.3 is 2.0
• round of 1.5 is 2.0
• round of 0.501 is 1.0
• round of 0.5 is 1.0
• round of 0.499 is 0.0
• round of 0.01 is 0.0
• round of 0.0 is 0.0
• round of -0.01 is -0.0
• round of -0.499 is -0.0
• round of -0.5 is -0.0
• round of -0.501 is -1.0
• round of -1.5 is -1.0
• round of -2.3 is -2.0
• round of -3.8 is -4.0
• round of -5.0 is -5.0

Answer 6

There is no need to implement anything, so I'm not sure why so many answers involve defines, functions, or methods.

In C99

We have the following and and header <tgmath.h> for type-generic macros.

#include <math.h>
double round (double x);
float roundf (float x);
long double roundl (long double x);

If you cannot compile this, you have probably left out the math library. A command similar to this works on every C compiler I have (several).

gcc -lm -std=c99 ...

In C++11

We have the following and additional overloads in #include <cmath> that rely on IEEE double precision floating point.

#include <math.h>
double round (double x);
float round (float x);
long double round (long double x);
double round (T x);

There are equivalents in the std namespace too.

If you cannot compile this, you may be using C compilation instead of C++. The following basic command produces neither errors nor warnings with g++ 6.3.1, x86_64-w64-mingw32-g++ 6.3.0, clang-x86_64++ 3.8.0, and Visual C++ 2015 Community.

g++ -std=c++11 -Wall

With Ordinal Division

When dividing two ordinal numbers, where T is short, int, long, or another ordinal, the rounding expression is this.

T roundedQuotient = (2 * integerNumerator + 1)
    / (2 * integerDenominator);

Accuracy

There is no doubt that odd looking inaccuracies appear in floating point operations, but this is only when the numbers appear, and has little to do with rounding.

The source is not just the number of significant digits in the mantissa of the IEEE representation of a floating point number, it is related to our decimal thinking as humans.

Ten is the product of five and two, and 5 and 2 are relatively prime. Therefore the IEEE floating point standards cannot possibly be represented perfectly as decimal numbers for all binary digital representations.

This is not an issue with the rounding algorithms. It is mathematical reality that should be considered during the selection of types and the design of computations, data entry, and display of numbers. If an application displays the digits that show these decimal-binary conversion issues, then the application is visually expressing accuracy that does not exist in digital reality and should be changed.