nextafter, nextafterf, nextafterl, nexttoward, nexttowardf, nexttowardl

参数

返回值

如果未发生错误，则返回 from 沿 to 方向的下一个可表示值。若 from 等于 to ，则返回转换为函数类型的 to 值。

如果发生因溢出导致的范围错误，将返回 ± HUGE_VAL 、 ±HUGE_VALF 或 ±HUGE_VALL （其符号与 from 相同）。

如果由于下溢导致范围错误，将返回正确结果。

错误处理

错误报告方式遵循 math_errhandling 中的规范。

如果实现支持 IEEE 浮点算术 (IEC 60559)，

• 如果 from 为有限值，但预期结果为无穷大，则引发 FE_INEXACT 和 FE_OVERFLOW 。
• 如果 from 不等于 to 且结果为次正规数或零，则引发 FE_INEXACT 和 FE_UNDERFLOW 。
• 任何情况下，返回值均与当前舍入模式无关
• 如果 from 或 to 为 NaN，则返回 NaN。

注释

POSIX 规范 规定溢出和下溢条件属于范围错误（ errno 可能被设置）。

IEC 60559建议当 from 等于 to 时应返回 from 。但这些函数会返回 to ，这使得零值附近的行为保持一致： nextafter(-0.0, +0.0) 返回 + 0.0 ，而 nextafter(+0.0, -0.0) 返回 - 0.0 。

nextafter 通常通过操作 IEEE 浮点表示来实现（ glibc musl ）。

示例

#include <fenv.h>
#include <float.h>
#include <math.h>
#include <stdio.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);
}

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)

参考文献

参阅