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# `std.math.pow` - multiple declarations

## Function pow

Compute the value of x n, where n is an integer

``` Unqual!F pow(F, G) (   F x,   G n ) pure nothrow @nogc @trusted if (isFloatingPoint!F && isIntegral!G); ```

### Example

``````writeln(pow(2.0, 5)); // 32.0
assert(pow(1.5, 9).feqrel(38.4433) > 16);
assert(pow(real.nan, 2) is real.nan);
writeln(pow(real.infinity, 2)); // real.infinity
``````

## Function pow

Compute the power of two integral numbers.

``` typeof(Unqual!F.init*Unqual!G.init) pow(F, G) (   F x,   G n ) pure nothrow @nogc @trusted if (isIntegral!F && isIntegral!G); ```

NameDescription
x base
n exponent

### Returns

x raised to the power of n. If n is negative the result is 1 / pow(x, -n), which is calculated as integer division with remainder. This may result in a division by zero error.

If both x and n are 0, the result is 1.

### Throws

If x is 0 and n is negative, the result is the same as the result of a division by zero.

### Example

``````writeln(pow(2, 3)); // 8
writeln(pow(3, 2)); // 9

writeln(pow(2, 10)); // 1_024
writeln(pow(2, 20)); // 1_048_576
writeln(pow(2, 30)); // 1_073_741_824

writeln(pow(0, 0)); // 1

writeln(pow(1, -5)); // 1
writeln(pow(1, -6)); // 1
writeln(pow(-1, -5)); // -1
writeln(pow(-1, -6)); // 1

writeln(pow(-2, 5)); // -32
writeln(pow(-2, -5)); // 0
writeln(pow(cast(double)-2, -5)); // -0.03125
``````

## Function pow

Computes integer to floating point powers.

``` real pow(I, F) (   I x,   F y ) pure nothrow @nogc @trusted if (isIntegral!I && isFloatingPoint!F); ```

### Example

``````writeln(pow(2, 5.0)); // 32.0
writeln(pow(7, 3.0)); // 343.0
assert(pow(2, real.nan) is real.nan);
writeln(pow(2, real.infinity)); // real.infinity
``````

## Function pow

Calculates xy.

``` Unqual!(Largest!(F,G)) pow(F, G) (   F x,   G y ) pure nothrow @nogc @trusted if (isFloatingPoint!F && isFloatingPoint!G); ```

Special Values
x y pow(x, y) div 0 invalid?
anything ±0.0 1.0 no no
|x| > 1 +∞ +∞ no no
|x| < 1 +∞ +0.0 no no
|x| > 1 -∞ +0.0 no no
|x| < 1 -∞ +∞ no no
+∞ > 0.0 +∞ no no
+∞ < 0.0 +0.0 no no
-∞ odd integer > 0.0 -∞ no no
-∞ > 0.0, not odd integer +∞ no no
-∞ odd integer < 0.0 -0.0 no no
-∞ < 0.0, not odd integer +0.0 no no
±1.0 ±∞ -NAN no yes
< 0.0 finite, nonintegral NAN no yes
±0.0 odd integer < 0.0 ±∞ yes no
±0.0 < 0.0, not odd integer +∞ yes no
±0.0 odd integer > 0.0 ±0.0 no no
±0.0 > 0.0, not odd integer +0.0 no no

### Example

``````writeln(pow(1.0, 2.0)); // 1.0
writeln(pow(0.0, 0.0)); // 1.0
assert(pow(1.5, 10.0).feqrel(57.665) > 16);

// special values
writeln(pow(1.5, real.infinity)); // real.infinity
writeln(pow(0.5, real.infinity)); // 0.0
writeln(pow(1.5, -real.infinity)); // 0.0
writeln(pow(0.5, -real.infinity)); // real.infinity
writeln(pow(real.infinity, 1.0)); // real.infinity
writeln(pow(real.infinity, -1.0)); // 0.0
writeln(pow(-real.infinity, 1.0)); // -real.infinity
writeln(pow(-real.infinity, 2.0)); // real.infinity
writeln(pow(-real.infinity, -1.0)); // -0.0
writeln(pow(-real.infinity, -2.0)); // 0.0
assert(pow(1.0, real.infinity) is -real.nan);
writeln(pow(0.0, -1.0)); // real.infinity
writeln(pow(real.nan, 0.0)); // 1.0
``````

## Authors

Walter Bright, Don Clugston, Conversion of CEPHES math library to D by Iain Buclaw and David Nadlinger