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log1p

(PHP 4 >= 4.1.0, PHP 5)

log1p Calcule précisément log(1 + nombre)

Description

float log1p ( float $number )

log1p() retourne log(1 + number) calculé de telle sorte qu'il sera précis même si la valeur de number est proche de 0. log() ne peut retourner que log(1) dans ce cas par manque de précision.

Liste de paramètres

number

L'argument à traiter

Valeurs de retour

log(1 + number)

Historique

Version Description
5.3.0 Cette fonction est maintenant disponible sur toutes les plate-formes

Voir aussi

  • expm1() - Calcule précisément exponentiel moins un
  • log() - Logarithme naturel (népérien)
  • log10() - Logarithme en base 10

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User Contributed Notes 1 note

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Anonymous
12 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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