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Use Stirling's approximation for n!

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This commit is contained in:
John Scipione
2016-03-03 10:07:25 -08:00
parent d20632f53c
commit fb4dcb4965
1 changed files with 10 additions and 1 deletions
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src/kits/shared/ExpressionParser.cpp
+10 -1
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@@ -709,7 +709,16 @@ ExpressionParser::_ParseFactorial(MAPM value)
if (fTokenizer->NextToken().type == TOKEN_FACTORIAL) { if (fTokenizer->NextToken().type == TOKEN_FACTORIAL) {
fTokenizer->RewindToken(); fTokenizer->RewindToken();
_EatToken(TOKEN_FACTORIAL); _EatToken(TOKEN_FACTORIAL);
return value.factorial(); if (value < 1000)
return value.factorial();
else {
// Use Stirling's approximation (with extra term)
// http://hyperphysics.phy-astr.gsu.edu/hbase/math/stirling.html
// n! ≈ (n/e)^n * sqrt(2πn) * (1 + (1/12n))
return value.pow(value) / value.exp()
* (MAPM(2) * MAPM(MM_PI) * value).sqrt()
* (MAPM(1) + (MAPM(1) / (MAPM(12) * value)));
}
} }
fTokenizer->RewindToken(); fTokenizer->RewindToken();