Useful math functions and range-based statistic computations.
If you need real statistics, consider using the Dstats library.
pure nothrow @nogc T degrees(T)(T x) if (!isIntegral!T);
Convert from radians to degrees.
pure nothrow @nogc T radians(T)(T x) if (!isIntegral!T);
Convert from degrees to radians.
pure nothrow @nogc S lerp(S, T)(S a, S b, T t) if (is(typeof(t * b + (1 - t) * a) : S));
Linear interpolation, akin to GLSL's mix.
pure nothrow @nogc T clamp(T)(T x, T min, T max);
Clamp x in [min, max], akin to GLSL's clamp.
nothrow @nogc long ltrunc(real x);
Integer truncation.
nothrow @nogc long lfloor(real x);
Integer flooring.
nothrow @nogc T fract(T)(real x);
- Returns
- Fractional part of x.
pure nothrow @nogc T safeAsin(T)(T x);
Safe asin: input clamped to [-1, 1]
pure nothrow @nogc T safeAcos(T)(T x);
Safe acos: input clamped to [-1, 1]
pure nothrow @nogc T step(T)(T edge, T x);
Same as GLSL step function.
0.0 is returned if x < edge, and 1.0 is returned otherwise.
pure nothrow @nogc T smoothStep(T)(T a, T b, T t);
- See:
- http:
- //en.wikipedia.org/wiki/Smoothstep
Same as GLSL smoothstep function.
pure nothrow @nogc bool isPowerOf2(T)(T i) if (isIntegral!T);
- Returns
- true of i is a power of 2.
nothrow @nogc int ilog2(T)(T i) if (isIntegral!T);
- TODO:
- use bt intrinsics
Integer log2
pure nothrow @nogc int nextPowerOf2(int i);
Computes next power of 2.
pure nothrow @nogc long nextPowerOf2(long i);
Computes next power of 2.
pure nothrow @nogc T sinOverX(T)(T x);
- See Also
- www.plunk.org/~hatch/rightway.php
Computes sin(x)/x accurately.
pure nothrow @nogc T moduloWrap(T)(T a, T b) if (isSigned!T);
Signed integer modulo a/b where the remainder is guaranteed to be in [0..b[,
even if a is negative. Only support positive dividers.
pure nothrow @nogc int solveLinear(T)(T a, T b, out T root) if (isFloatingPoint!T);
- Returns
- Number of roots.
Find the root of a linear polynomial a + b x = 0
pure nothrow @nogc int solveQuadratic(T)(T a, T b, T c, T[] outRoots) if (isFloatingPoint!T);
- Parameters
T[] outRoots array of root results, should have room for at least 2 elements. - Returns
- Number of roots in outRoots.
Finds the root roots of a quadratic polynomial a + b x + c x^2 = 0
pure nothrow @nogc int solveCubic(T)(T a, T b, T c, T d, T[] outRoots) if (isFloatingPoint!T);
- Parameters
T[] outRoots array of root results, should have room for at least 2 elements. - Returns
- Number of roots in outRoots.
- See Also
- www.codeguru.com/forum/archive/index.php/t-265551.html
Finds the roots of a cubic polynomial a + b x + c x^2 + d x^3 = 0
pure nothrow @nogc int solveQuartic(T)(T a, T b, T c, T d, T e, T[] roots) if (isFloatingPoint!T);
- Known Bugs
- doesn't pass unit-test!
- See Also
- mathworld.wolfram.com/QuarticEquation.html
Returns the roots of a quartic polynomial a + b x + c x^2 + d x^3 + e x^4 = 0
Returns number of roots. roots slice should have room for up to 4 elements.
double average(R)(R r) if (isInputRange!R);
Arithmetic mean.
double minElement(R)(R r) if (isInputRange!R);
Minimum of a range.
double maxElement(R)(R r) if (isInputRange!R);
Maximum of a range.
double variance(R)(R r) if (isForwardRange!R);
Variance of a range.
double standardDeviation(R)(R r) if (isForwardRange!R);
Standard deviation of a range.
pure nothrow @nogc T inverseSqrt(T)(T x) if (isFloatingPoint!T);
SSE approximation of reciprocal square root.