CascadiaPHP 2024


(PHP 4 >= 4.1.0, PHP 5, PHP 7, PHP 8)

log1p Retorna log(1 + número), calculado de forma que seja preciso mesmo quando o valor do número seja próximo de zero.


log1p(float $num): float

log1p() retorna log(1 + num) computado de forma que seja preciso mesmo quando o valor de num esteja próximo de zero. log() poderia retornar apenas log(1) neste caso devido à falta de precisão.



O argumento a ser processado

Valor Retornado

log(1 + num)

Veja Também

  • expm1() - Retorna exp($num) - 1, computado de forma precisa mesmo quando o valor do número está próximo de zero.
  • log() - Logaritmo natural
  • log10() - Logaritmo na base 10

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User Contributed Notes 1 note

21 years ago
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.
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