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functions:lllog [2014-05-21 15:06 SLT] sei Add a definition of natural logarithm |
functions:lllog [2015-02-04 08:18 SLT] (current) sei pinf minf nan econst |
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| ===== Function: llLog ===== | ===== Function: llLog ===== | ||
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| </code> | </code> | ||
| - | Returns the natural logarithm of the argument. The natural logarithm is a logarithm in base **e** (the Euler constant, which is approximately 2.7182818). | + | Returns the natural logarithm of the argument. The natural logarithm is a logarithm in base $econst (the Euler constant, which is approximately 2.7182818). |
| ===== Parameters ===== | ===== Parameters ===== | ||
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| ===== Return value ===== | ===== Return value ===== | ||
| - | Returns a [[types/float]] which is the natural logarithm of the argument. | + | Returns a $lty[float] which is the natural logarithm of the argument. |
| ===== Notes ===== | ===== Notes ===== | ||
| * In order to make sense, the argument must be greater than 0.0; a value of 0.0 or less yields 0.0. | * In order to make sense, the argument must be greater than 0.0; a value of 0.0 or less yields 0.0. | ||
| - | * The function returns **Infinity** if the input is **Infinity**, and 0.0 if the input is **-Infinity** or **NaN**. | + | * The function returns $pinf if the input is $pinf, and 0.0 if the input is $minf or $nan. |
| - | * To calculate the logarithm in base 10, [[llLog10]] can be used. | + | * To calculate the logarithm in base 10, $lfn[llLog10] can be used. |
| * To calculate the logarithm in any other base, divide the result of this function by the logarithm of that base. | * To calculate the logarithm in any other base, divide the result of this function by the logarithm of that base. | ||
| * For example, to calculate the logarithm in base 2 of a number, use ''llLog(number)/llLog(2)''. Since the latter is constant, to save calculations and memory you can instead pre-calculate the reciprocal and multiply by it, like this: ''llLog(number)*1.44269504'' will give you the logarithm in base 2, because ''1/llLog(2)'' equals approx. 1.44269504. | * For example, to calculate the logarithm in base 2 of a number, use ''llLog(number)/llLog(2)''. Since the latter is constant, to save calculations and memory you can instead pre-calculate the reciprocal and multiply by it, like this: ''llLog(number)*1.44269504'' will give you the logarithm in base 2, because ''1/llLog(2)'' equals approx. 1.44269504. | ||
| - | * There is no built-in inverse of this function. To raise the Euler constant to a power, use [[llPow]]. But there is also no built-in Euler constant either, so you will need to use its value, which is approx. 2.7182818. | + | * There is no built-in inverse of this function. To raise the Euler constant to a power, use $lfn[llPow]. But there is also no built-in definition for the Euler constant either, so you will need to use its value, which is approx. 2.7182818. |
| ===== Short examples ===== | ===== Short examples ===== | ||
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| ===== See also ===== | ===== See also ===== | ||
| - | * [[llLog10]] to calculate the logarithm in base 10. | + | * $lfn[llLog10] to calculate the logarithm in base 10. |
| - | * [[llPow]] to raise a number to a power (also called antilogarithm). | + | * $lfn[llPow] to raise a number to a power (also called antilogarithm). |
| - | * [[types/float]] type and associated caveats and limitations. | + | * $lty[float] type and associated caveats and limitations. |