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--- functions:math [2016/09/12 16:19] – [Math functions] korshun
+++ functions:math [2017/06/12 15:36] (current) – removed korshun
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-====== Math functions ======
-===== Constants =====
-  * ''fixed MATH_E'' -- the number E.
-  * ''fixed PI'' -- the number π (pi).
-  * ''fixed SQRT_2'' -- square root of 2
-  * ''fixed LOG2_E'' -- value of log2(e).
-  * ''fixed LOG2_10'' -- value of log2(10);
-===== Generic math functions =====
-==== abs ====
-''num abs(num x)''
-Returns the absolute value of x.
-**Example**
-<code>
-abs(2.0) == 2.0;
-abs(-123) == 123;
-</code>
-==== clamp ====
-''num clamp(num x, num a, num b)''
-Limits x to the range [a; b]. If x falls in the range, returns x. If x is less than a, returns a. If x is greater than b, returns b.
-**Example**
-<code>
-clamp(7, 6, 8) == 7;
-clamp(0.1, 0.2, 0.3) == 0.2;
-</code>
-==== cmp ====
-''int cmp(num a, num b)''
-Compares two numbers and returns the result:
-  * ''1'' -- a is greater than b
-  * ''-1'' -- a is less than b
-  * ''0'' -- a and b are equal
-==== cond ====
-''any cond(bool condition, any a, any b)''
-Returns a if the condition is true, b otherwise.
-It's a simulation of the ternary operator ?: in ACS.
-<note important>Both a and b are evaluated. Do not do this:
-<code>
-int y = cond(x, DoSomething(), DoSomethingElse)
-</code>
-as both ''DoSomething()'' and ''DoSomethingElse()'' will be called.
-</note>
-==== max ====
-''num max(num a, num b)''
-Returns the greater of two numbers.
-**Example**
-<code>
-max(3, 5) == 5;
-max(8.0, 7.5) == 8.0;
-</code>
-==== min ====
-''num min(num a, num b)''
-Returns the lesser of two numbers.
-**Example**
-<code>
-min(3, 5) == 3;
-min(8.0, 7.5) == 7.5;
-</code>
-==== sgn ====
-''int sgn(num x)''
-Returns the sign of x.
-  * ''1'' -- x is positive
-  * ''-1'' -- x is negative
-  * ''0'' -- x is zero
-**Example**
-<code>
-sgn(12.3) == 1;
-sgn(0) == 0;
-sgn(-7) == -1;
-</code>
-==== swap ====
-''any, any swap(any a, any b)''
-Swaps two variables. Is a function to improve readability.
-<code>
-swap(x, y);
-x = r1;
-y = r2;
-</code>
-===== Rounding =====
-There are four rounding modes:
-  * trunc -- zeroes the fractional part of the number
-  * floor -- rounds the number down
-  * ceil -- round the number up
-  * round -- rounds the number to the closest integer
-Rounding table:
-<code>
-   x  round(x) floor(x)  ceil(x) trunc(x)
------ -------- -------- -------- --------
-.3         2        2        3        2
-.8         4        3        4        3
-.5         6        5        6        5
--2.3        -2       -3       -2       -2
--3.8        -4       -4       -3       -3
--5.5        -5       -6       -5       -5
-</code>
-Every rounding mode is available as two functions. The ones with the "i" in the name return an integer, while the ones without the "i" return a fixed.
-==== ceil ====
-''fixed ceil(fixed x)''
-''int iceil(fixed x)''
-Returns x rounded up.
-==== floor ====
-''fixed floor(fixed x)''
-''int ifloor(fixed x)''
-Returns x rounded down.
-==== round ====
-''fixed round(fixed x)''
-''int iround(fixed x)''
-Returns x rounded to the closest integer.
-==== trunc ====
-''fixed trunc(fixed x)''
-''int itrunc(fixed x)''
-Returns x with fractional part removed.
-===== Numerical algorithms =====
-==== IntDiv ====
-''fixed IntDiv(int a, int b)''
-Divides two integers and returns a fixed-point result. Allows division of any 2 integers whose ratio is not higher than 32767.
-==== lerp ====
-''fixed lerp(fixed a, fixed b, fixed alpha)''
-Performs [[wp>Linear interpolation|linear interpolation]] (or extrapolation) between two numbers and returns the result.
-**Examples**
-<code>
-lerp(a, b, 0.0) == a;
-lerp(a, b, 1.0) == b;
-lerp(a, b, 0.5) == (a + b) / 2; // Average of a and b.
-</code>
-<code>
-// Simple animation.
-for (int time = 0; time < 1.0; time += 0.05)
-{
-    int x = lerp(x1, x2, time);
-    int y = lerp(y1, y2, time);
-    DrawSomething(x, y);
-    Delay(1);
-}
-</code>
-==== gcf ====
-''num gcf(num a, num b)''
-Returns the greatest common factor of two numbers. The returned factor will be negative if one or both numbers are negative.
-**Example**
-<code>
-gcf(18,   24)   == 6;
-gcf(18.0, 24.0) == 6.0;
-gcf(-18,  -24)  == -6;
-</code>
-==== mod ====
-''num mod(num a, num b)''
-Returns ''a % b'', but the result is always positive. Only positive b values are supported.
-**Example**
-<code>
-mod(2, 5) == 3;
-mod(-3, 5) == 3;
-</code>
-==== npo2 ====
-''num npo2(num x)''
-Rounds the number up to the Next Power Of 2. The input must be positive.
-**Example**
-<code>
-npo2(17) == 32;
-npo2(6.5) == 8.0;
-</code>
-==== sqrt ====
-''int zan_Sqrt(int number)''
-''fixed zan_FixedSqrt(fixed number)''
-Zandronum implementations of corresponding [[zdoom>Sqrt|ZDoom 2.7.0-only functions]].
-===== Logarithms =====
-All logarithm functions come in two versions: fixed-point and integer.
-All logarithm functions return fixed-point values.
-<note tip>The integer versions are all prefixed with ''i''.</note>
-==== ln ====
-''fixed ln(fixed x)''
-''fixed iln(int x)''
-Returns the natual logaritm (base e) of the given number.
-<note>This function is called ''ln'' instead of ''log'' like in C because ZDoom already has a function called ''[[zdoom>Log]]'' that is used for logging.</note>
-==== log2 ====
-''fixed log2(fixed x)''
-''fixed ilog2(int x)''
-Returns the logarithm in base 2 of the given number.
-==== log10 ====
-''fixed log10(fixed x)''
-''fixed ilog10(int x)''
-Returns the logarithm in base 10 of the given number.
-==== logb ====
-''fixed logb(fixed x, fixed base)''
-''fixed ilogb(int x, fixed base)''
-Returns the logarithm in an arbitrary fixed-point base. Base must be a fixed number greater than 1.0.
-===== Trigonometry =====
-Sin and cos are already in ZDoom.
-==== tan ====
-''fixed tan(angle x)''
-Returns the tangent of x.
-==== cot ====
-''fixed cot(angle x)''
-Returns the cotangent of x.
-==== sec ====
-''fixed sec(angle x)''
-Returns the secant of x.
-==== cosec ====
-''fixed cosec(angle x)''
-Returns the cosecant of x.
-==== asin ====
-''angle asin(fixed x)''
-Returns the arcsine of x.
-==== acos ====
-''angle acos(fixed x)''
-Returns the arccosine of x.
-==== atan ====
-''angle atan(fixed x)''
-Returns the arctangent of x.
-==== acot ====
-''angle acot(fixed x)''
-Returns the arccotangent of x.
-==== asec ====
-''angle asec(fixed x)''
-Returns the arcsecant of x.
-==== acosec ====
-''angle acosec(fixed x)''
-Returns the arccosecant of x.
-===== Vectors =====
-==== dot2 ====
-''fixed dot2(fixed x1, fixed y1, fixed x2, fixed y2)''
-Returns the dot product of two 2D vectors.
-==== dot3 ====
-''fixed dot3(fixed x1, fixed y1, fixed z1, fixed x2, fixed y2, fixed z2)''
-Returns the dot product of two 3D vectors.
-==== length2d ====
-''fixed length2d(fixed x, fixed y)''
-Returns the length of the given 2D vector. This is a Zandronum replacement for
-[[zdoom>VectorLength]].
-==== length2d2 ====
-''fixed length2d2(int x, int y)''
-Returns the **squared** length of the given 2D vector.
-==== length3d ====
-''fixed length3d(fixed x, fixed y, fixed z)''
-Returns the length of the given 3D vector.
-==== length3d2 ====
-''fixed length3d2(int x, int y, int z)''
-Returns the **squared** length of the given 3D vector.
-==== normalize2d ====
-''fixed, fixed normalize2d(fixed x, fixed y)''
-Normalizes the given 2D vector and returns the result.
-[[..mulretval|This function returns multiple values.]]
-==== normalize3d ====
-''fixed, fixed, fixed normalize3d(fixed x, fixed y, fixed z)''
-Normalizes the given 3D vector and returns the result.
-[[..mulretval|This function returns multiple values.]]
-==== RotatePoint ====
-''fixed, fixed RotatePoint(fixed x, fixed y, fixed originX, fixed originY, angle angle)''
-Rotates the given point (x; y) around the given origin by the given angle and returns the resulting coordinates of the point.
-[[..mulretval|This function returns multiple values.]]
-==== RotateVector ====
-''fixed, fixed RotateVector(fixed x, fixed y, angle angle)''
-Rotates the vector by the given angle and returns its new coordinates.
-[[..mulretval|This function returns multiple values.]]
-**Example**
-<code>
-RotateVector(x, y, angle);
-int newX = r1;
-int newY = r2;
-</code>
-==== VectorToAngles ====
-''angle, angle VectorToAngles(fixed x, fixed y, fixed z)''
-Converts a vector to a pair of angles (yaw and pitch) that point to the same direction.
-[[..mulretval|This function returns multiple values.]]
-**Example**
-<code>
-// Make the player look along the vector
-VectorToAngles(1.0, 2.0, 3.0);
-int angle = r1;
-int pitch = r2;
-SetActorAngle(tid, angle);
-SetActorPitch(tid, -pitch); // Note that actor pitch is inverted in ZDoom.
-</code>
-<note tip>Use ''[[functions:zdoom#lookatpoint|LookAtPoint]]'' instead of the example code above.</note>

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