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数值 | Numerics

nexttowardf

在头文件<math.h>中定义

float nextafterf( float from, float to );

(1)

(since C99)

double nextafter( double from, double to );

(2)

(since C99)

long double nextafterl( long double from, long double to );

(3)

(since C99)

float nexttowardf( float from, long double to );

(4)

(since C99)

double nexttoward( double from, long double to );

(5)

(since C99)

long double nexttowardl( long double from, long double to );

(6)

(since C99)

Defined in header <tgmath.h>

#define nextafter(from, to)

(7)

(since C99)

#define nexttoward(from, to)

(8)

(since C99)

1-3)首先,将两个参数都转换为函数的类型,然后返回下一个可表示值from的方向to。如果from等于toto则返回。

4-6)首先,将第一个参数转换为函数的类型,然后返回下一个可表示值from的方向to。如果from等于toto则返回,转换long double为函数的返回类型,但不会丢失范围或精度。

7)类型 - 通用宏:如果任何参数具有类型long doublenextafterl则被调用。否则,如果任何参数具有整数类型或具有类型doublenextafter则被调用。否则,nextafterf被调用。

8)类型 - 通用宏:如果参数from具有类型long doublenexttowardl则被调用。否则,如果from有整数类型或类型doublenexttoward则调用。否则,nexttowardf被调用。

参数

from, to

-

浮点值

返回值

如果没有错误发生,下一个可表示值from的方向to。返回。如果from等于to,则to返回,转换为函数的类型。

如果范围误差由于发生溢出,±HUGE_VAL±HUGE_VALF,或±HUGE_VALL被返回(与相同的符号from)。

如果由于下溢而发生范围错误,则返回正确的结果。

错误处理

按照math_errhandling中的指定报告错误。

如果实现支持IEEE浮点运算(IEC 60559),

  • 如果from是有限的,但预期的结果是无穷大,提高FE_INEXACTFE_OVERFLOW
  • 如果from不相等to,结果是低于正常或零,则引发FE_INEXACTFE_UNDERFLOW
  • 在任何情况下,返回值都与当前舍入模式无关
  • 如果是from或者to是NaN,则返回NaN

笔记

POSIX指定溢出和下溢条件是范围错误(可能会设置错误)。

IEC 60559建议from每当返回from==to。这些函数会返回to,这会使零之间的行为保持一致:nextafter(-0.0, +0.0)返回+0.0nextafter(+0.0, -0.0)返回–0.0

#include <math.h>
#include <stdio.h>
#include <float.h>
#include <fenv.h>
 
int main(void)
{
    float from1 = 0, to1 = nextafterf(from1, 1);
    printf("The next representable float after %.2f is %.20g (%a)\n", from1, to1, to1);
 
    float from2 = 1, to2 = nextafterf(from2, 2);
    printf("The next representable float after %.2f is %.20f (%a)\n", from2, to2, to2);
 
    double from3 = nextafter(0.1, 0), to3 = 0.1;
    printf("The number 0.1 lies between two valid doubles:\n"
           "    %.56f (%a)\nand %.55f  (%a)\n", from3, from3, to3, to3);
 
    // difference between nextafter and nexttoward:
    long double dir = nextafterl(from1, 1); // first subnormal long double
    float x = nextafterf(from1, dir); // first converts dir to float, giving 0
    printf("Using nextafter, next float after %.2f (%a) is %.20g (%a)\n",
           from1, from1, x, x);
    x = nexttowardf(from1, dir);
    printf("Using nexttoward, next float after %.2f (%a) is %.20g (%a)\n",
           from1, from1, x, x);
 
    // special values
    {
        #pragma STDC FENV_ACCESS ON
        feclearexcept(FE_ALL_EXCEPT);
        double from4 = DBL_MAX, to4 = nextafter(from4, INFINITY);
        printf("The next representable double after %.2g (%a) is %.23f (%a)\n",
               from4, from4, to4, to4);
        if(fetestexcept(FE_OVERFLOW)) puts("   raised FE_OVERFLOW");
        if(fetestexcept(FE_INEXACT)) puts("   raised FE_INEXACT");
    } // end FENV_ACCESS block
 
    float from5 = 0.0, to5 = nextafter(from5, -0.0);
    printf("nextafter(+0.0, -0.0) gives %.2g (%a)\n", to5, to5);
}

输出:

The next representable float after 0.00 is 1.4012984643248170709e-45 (0x1p-149)
The next representable float after 1.00 is 1.00000011920928955078 (0x1.000002p+0)
The number 0.1 lies between two valid doubles:
    0.09999999999999999167332731531132594682276248931884765625 (0x1.9999999999999p-4)
and 0.1000000000000000055511151231257827021181583404541015625  (0x1.999999999999ap-4)
Using nextafter, next float after 0.00 (0x0p+0) is 0 (0x0p+0)
Using nexttoward, next float after 0.00 (0x0p+0) is 1.4012984643248170709e-45 (0x1p-149)
The next representable double after 1.8e+308 (0x1.fffffffffffffp+1023) is inf (inf)
   raised FE_OVERFLOW
   raised FE_INEXACT
nextafter(+0.0, -0.0) gives -0 (-0x0p+0)

参考

  • C11标准(ISO / IEC 9899:2011):
    • 7.12.11.3 nextafter函数(p:256)
    • 7.12.11.4 nexttoward函数(p:257)
    • 7.25类型通用数学<tgmath.h>(p:373-375)
    • F.10.8.3 nextafter函数(p:529)
    • F.10.8.4 nexttoward函数(p:529)
  • C99标准(ISO / IEC 9899:1999):
    • 7.12.11.3 nextafter函数(p:237)
    • 7.12.11.4 nexttoward函数(p:238)
    • 7.22类型通用数学<tgmath.h>(p:335-337)
    • F.9.8.3 nextafter函数(p:466)
    • F.9.8.4 nexttoward函数(p:466)
C

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