我需要一个简单的浮点舍入函数,这样:

double round(double);

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

我可以在math.h中找到ceil()和floor() -但没有round()。

它是否以另一个名字出现在标准c++库中,或者它是否丢失了??


当前回答

它在cmath中从c++ 11开始提供(根据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;
}

输出:

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

其他回答

Boost中还实现了某种类型的舍入:

#include <iostream>

#include <boost/numeric/conversion/converter.hpp>

template<typename T, typename S> T round2(const S& x) {
  typedef boost::numeric::conversion_traits<T, S> Traits;
  typedef boost::numeric::def_overflow_handler OverflowHandler;
  typedef boost::numeric::RoundEven<typename Traits::source_type> Rounder;
  typedef boost::numeric::converter<T, S, Traits, OverflowHandler, Rounder> Converter;
  return Converter::convert(x);
}

int main() {
  std::cout << round2<int, double>(0.1) << ' ' << round2<int, double>(-0.1) << ' ' << round2<int, double>(-0.9) << std::endl;
}

注意,这仅在执行到整数的转换时有效。

从c++ 11开始简单地:

#include <cmath>
std::round(1.1)

或者得到int

static_cast<int>(std::round(1.1))

值得注意的是,如果想要从舍入中得到整数结果,则不需要通过上下限或上下限。也就是说,

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

正如在评论和其他回答中指出的那样,ISO c++标准库直到ISO c++ 11才添加round(),当时该函数是通过引用ISO C99标准数学库而引入的。

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).

这导致了下面的压缩代码。它在各种平台上编译成合理数量的机器指令。我观察到gpu上最紧凑的代码,其中my_roundf()需要大约12条指令。根据处理器架构和工具链的不同,这种基于浮点的方法可能比在不同答案中引用的newlib基于整数的实现更快或更慢。

我使用Intel编译器版本13对my_roundf()与newlib roundf()实现进行了详尽的测试,同时使用/fp:strict和/fp:fast。我还检查了newlib版本是否与Intel编译器mathimf库中的roundf()匹配。对于双精度round()不可能进行详尽的测试,但是代码在结构上与单精度实现相同。

#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;
}

如果你最终想要将round()函数的双输出转换为int型,那么这个问题的可接受的解决方案将如下所示:

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

当传入均匀随机值时,在我的机器上大约为8.88 ns。

据我所知,下面的功能是等效的,但在我的机器上是2.48 ns,具有显著的性能优势:

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

性能更好的原因之一是跳过了分支。