Note that the benefit of this function for small argument values is lost if PHP is compiled against a C library that that not have builtin support for the log1p() function.
In this case, log1p() will be compiled by using log() instead, and the precision of the result will be identical to log(1), i.e. it will always be 0 for small numbers.
Sample log1p(1.0e-20):
- returns 0.0 if log1p() is approximated by using log()
- returns something very near from 1.0e-20, if log1p() is supported by the underlying C library.
One way to support log1p() correctly on any platform, so that the magnitude of the expected result is respected:
function log1p($x) {
return ($x>-1.0e-8 && $x<1.0e-8) ? ($x - $x*$x/2) : log(1+$x);
}
If you want better precision, you may use a better limited development, for small positive or negative values of x:
log(1+x) = x - x^2/2 + x^3/3 - ... + (-1)^(n-1)*x^n/n + ...
(This serial sum converges only for values of x in [0 ... 1] inclusive, and the ^ operator in the above formula means the exponentiation operator, not the PHP xor operation)
Note that log1p() is undefined for arguments lower than or equal to -1, and that the implied base of the log function is the Neperian "e" constant.
log1p
说明
float log1p ( float number )| 警告 |
本函数是实验性的。本函数的行为，包括函数名称以及其它任何关于本函数的文档可能会在没有通知的情况下随 PHP 以后的发布而改变。使用本函数风险自担。 |
log1p() 返回 log(1 + number)，甚至当 number 的值接近零也能计算出准确结果
注: 本函数未在 Windows 平台下实现。
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User Contributed Notes
11-Sep-2002 05:29