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std.math.exponential.pow
- multiple declarations
Function pow
Compute the value of x n, where n is an integer
Example
import std .math .operations : feqrel;
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);
Parameters
Name | Description |
---|---|
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);
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
import std .math .operations : isClose;
assert(isClose(pow(2.0, 3.0), 8.0));
assert(isClose(pow(1.5, 10.0), 57.6650390625));
// square root of 9
assert(isClose(pow(9.0, 0.5), 3.0));
// 10th root of 1024
assert(isClose(pow(1024.0, 0.1), 2.0));
assert(isClose(pow(-4.0, 3.0), -64.0));
// reciprocal of 4 ^^ 2
assert(isClose(pow(4.0, -2.0), 0.0625));
// reciprocal of (-2) ^^ 3
assert(isClose(pow(-2.0, -3.0), -0.125));
assert(isClose(pow(-2.5, 3.0), -15.625));
// reciprocal of 2.5 ^^ 3
assert(isClose(pow(2.5, -3.0), 0.064));
// reciprocal of (-2.5) ^^ 3
assert(isClose(pow(-2.5, -3.0), -0.064));
// reciprocal of square root of 4
assert(isClose(pow(4.0, -0.5), 0.5));
// per definition
assert(isClose(pow(0.0, 0.0), 1.0));
Example
import std .math .operations : isClose;
// the result is a complex number
// which cannot be represented as floating point number
import std .math .traits : isNaN;
assert(isNaN(pow(-2.5, -1.5)));
// use the ^^-operator of std.complex instead
import std .complex : complex;
auto c1 = complex(-2.5, 0.0);
auto c2 = complex(-1.5, 0.0);
auto result = c1 ^^ c2;
// exact result apparently depends on `real` precision => increased tolerance
assert(isClose(result .re, -4.64705438e-17, 2e-4));
assert(isClose(result .im, 2.52982e-1, 2e-4));
Authors
Walter Bright, Don Clugston, Conversion of CEPHES math library to D by Iain Buclaw and David Nadlinger
License
Copyright © 1999-2022 by the D Language Foundation | Page generated by ddox.