nextafter, nextafterf, nextafterl, nexttoward, nexttowardf, nexttowardl

来自cppreference.com
< c‎ | numeric‎ | math
 
 
 
常用数学函数
函数
基本运算
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指数函数
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幂函数
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三角及双曲函数
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误差及伽马函数
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临近整数的浮点运算
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浮点数操作函数
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nextafternexttoward
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分类
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类型
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宏常量
 
定义于头文件 <math.h>
float       nextafterf( float from, float to );
(1) (C99 起)
double      nextafter( double from, double to );
(2) (C99 起)
long double nextafterl( long double from, long double to );
(3) (C99 起)
float       nexttowardf( float from, long double to );
(4) (C99 起)
double      nexttoward( double from, long double to );
(5) (C99 起)
long double nexttowardl( long double from, long double to );
(6) (C99 起)
定义于头文件 <tgmath.h>
#define nextafter(from, to)
(7) (C99 起)
#define nexttoward(from, to)
(8) (C99 起)
1-3) 首先,转换两个参数为函数的类型,然后返回 fromto 方向的下个可表示值。若 from 等于 to ,则返回 to
4-6) 首先,转换两个参数为函数的类型,然后返回 fromto 方向的下个可表示值。若 from 等于 to ,则返回从 long double 转换到函数返回类型的 to ,而不带范围或精度的损失。
7) 泛型宏:若任何参数拥有 long double 类型,则调用 nextafterl 。否则,若任何参数拥有整数类型或 double 类型,则调用 nextafter 。否则调用 nextafterf
8) 泛型宏:若任何参数拥有 long double 类型,则调用 nexttowardl 。否则,若任何参数拥有整数类型或 double 类型,则调用 nexttoward 。否则调用 nexttowardf

目录

[编辑] 参数

from, to - 浮点值

[编辑] 返回值

若不出现错误,则返回 fromto 的方向的下个可表示值。若 from 等于 to ,则返回 to ,转换到函数的类型。

若出现上溢所致的值域错误,则返回 ±HUGE_VAL±HUGE_VALF±HUGE_VALL (所带符号同 from )。

若出现下溢所致的值域错误,则返回正确结果。

[编辑] 错误处理

报告 math_errhandling 中指定的错误。

若实现支持 IEEE 浮点算术( IEC 60559 ),则

  • from 有限,但期待的结果无限,则引发 FE_INEXACTFE_OVERFLOW
  • from 不等于 to 且结果为非正规或零,则引发 FE_INEXACTFE_UNDERFLOW
  • 任何情况下,返回值独立于当前舍入模式。
  • fromto 为 NaN ,则返回 NaN

[编辑] 注意

POSIX 指定上溢和下溢条件是值域错误(可以设置 errno )。

IEC 60559 推荐凡在 from==to 时返回 from 。这些函数替而返回 to ,这使得围绕零的行为一致: nextafter(-0.0, +0.0) 返回 +0.0nextafter(+0.0, -0.0) 返回 –0.0

[编辑] 示例

#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);
 
    // nextafter 和 nexttoward 间的差异:
    long double dir = nextafterl(from1, 1); // 第一个非正规 long double
    float x = nextafterf(from1, dir); // 首先转换 dir 为 float ,给出 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);
 
    // 特殊值
    {
        #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");
    } // 结束 FENV_ACCESS 块
 
    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)

[编辑] 引用

  • C11 standard (ISO/IEC 9899:2011):
  • 7.12.11.3 The nextafter functions (p: 256)
  • 7.12.11.4 The nexttoward functions (p: 257)
  • 7.25 Type-generic math <tgmath.h> (p: 373-375)
  • F.10.8.3 The nextafter functions (p: 529)
  • F.10.8.4 The nexttoward functions (p: 529)
  • C99 standard (ISO/IEC 9899:1999):
  • 7.12.11.3 The nextafter functions (p: 237)
  • 7.12.11.4 The nexttoward functions (p: 238)
  • 7.22 Type-generic math <tgmath.h> (p: 335-337)
  • F.9.8.3 The nextafter functions (p: 466)
  • F.9.8.4 The nexttoward functions (p: 466)

[编辑] 参阅

nextafterC++ 文档