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在头文件<math.h>中定义



float       log1pf( float arg );

(1)

(since C99)

double      log1p( double arg );

(2)

(since C99)

long double log1pl( long double arg );

(3)

(since C99)

Defined in header <tgmath.h>



#define log1p( arg )

(4)

(since C99)

1-3）计算的自然（基数e）对数1+arg。log(1+arg)如果arg接近于零，该函数比表达式更精确。

4）类型 - 通用宏：如果arg有类型long double，log1pl被调用。否则，如果arg有整数类型或类型double，log1p则调用。否则，log1pf被调用。

参数

arg

-

浮点值

返回值

如果没有错误发生，则返回ln（1 + arg）。

如果发生域错误，则返回实现定义的值（NaN，如果支持）。

如果发生极错误-HUGE_VAL，-HUGE_VALF或-HUGE_VALL返回。

如果由于下溢而发生范围错误，则返回正确的结果（舍入后）。

错误处理

按照math_errhandling中的指定报告错误。

如果arg小于-1，则会发生域错误。

如果arg是-1，可能会出现极点错误。

如果实现支持IEEE浮点运算（IEC 60559），

  • 如果参数为±0，则不加修改地返回

  • 如果参数为-1，则返回-∞并FE_DIVBYZERO引发。

  • 如果参数小于-1，则返回并FE_INVALID引发NaN 。

  • 如果参数是+∞，则返回+∞

  • 如果参数是NaN，则返回NaN

笔记

功能expm1和log1p是财务计算有用的，例如，计算每天小息时：（1 + X）N

-1可以表示为expm1(n * log1p(x))。这些功能还简化了写入准确的反双曲函数。

例

#include <stdio.h>#include <math.h>#include <float.h>#include <errno.h>#include <fenv.h>#pragma STDC FENV_ACCESS ON
int main(void){    printf("log1p(0) = %f\n", log1p(0));    printf("Interest earned in 2 days on $100, compounded daily at 1%%\n"           " on a 30/360 calendar = %f\n",           100*expm1(2*log1p(0.01/360)));    printf("log(1+1e-16) = %g, but log1p(1e-16) = %g\n",           log(1+1e-16), log1p(1e-16));    // special values    printf("log1p(-0) = %f\n", log1p(-0.0));    printf("log1p(+Inf) = %f\n", log1p(INFINITY));    //error handling
    errno = 0; feclearexcept(FE_ALL_EXCEPT);    printf("log1p(-1) = %f\n", log1p(-1));    if(errno == ERANGE) perror("    errno == ERANGE");    if(fetestexcept(FE_DIVBYZERO)) puts("    FE_DIVBYZERO raised");}

可能的输出：

log1p(0) = 0.000000Interest earned in 2 days on $100, compounded daily at 1%
 on a 30/360 calendar = 0.005556log(1+1e-16) = 0, but log1p(1e-16) = 1e-16log1p(-0) = -0.000000log1p(+Inf) = Inflog1p(-1) = -Inf
    errno == ERANGE: Result too large
    FE_DIVBYZERO raised

参考

  • C11标准（ISO / IEC 9899：2011）：

    • 7.12.6.9 log1p函数（p：245）

    • 7.25类型通用数学<tgmath.h>（p：373-375）

    • F.10.3.9 log1p函数（p：522）

  • C99标准（ISO / IEC 9899：1999）：

    • 7.12.6.9 log1p函数（p：226）

    • 7.22类型通用数学<tgmath.h>（p：335-337）

    • F.9.3.9 log1p函数（p：459）

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