FastTrig

Fast trigonometry from tables, for games and demos (raycasting, rotations, fake 3D) on computers without an FPU: angles are integers with 1024 steps per full circle, the results are fixed point numbers. No floating point is used, so it is fast on a 68000 as well.

int angle = FastTrig.FromDegrees(30);            // 85 (1024 steps = 360 degrees)
int x = (radius * FastTrig.Cos(angle)) >> 14;    // Sin and Cos: 1.14 fixed point, 16384 = 1.0
int y = (radius * FastTrig.Sin(angle)) >> 14;
int dir = FastTrig.Atan2(dy, dx);                // the angle of a vector, 0..1023

Every int is an angle: it is taken modulo 1024 (with a mask), so negative angles and sums past a full turn work. FastTrig.Tan, FastTrig.Cot, FastTrig.Sec (1/cos) and FastTrig.Csc (1/sin) are 16.16 fixed point (65536 = 1.0); at their poles (tan at 90 degrees, …) they return 2147483647 or -2147483647. Sec and Csc give the step lengths of a raycaster’s grid walk (DDA). The tables are generated by stdlib/tools/fasttrig.py.

Constants

Name	Description
Steps	The number of angle steps in a full circle (360 degrees).
Mask	angle & Mask is the angle in 0..1023.
Quarter	The angle of 90 degrees.
Half	The angle of 180 degrees.
SinOne	1.0 in the results of FastTrig.Sin and FastTrig.Cos (1.14 fixed point).
FixedOne	1.0 in the results of FastTrig.Tan, FastTrig.Cot, FastTrig.Sec and FastTrig.Csc (16.16 fixed point).

Steps

const int Steps = 1024

The number of angle steps in a full circle (360 degrees).

Since 0.15

Mask

const int Mask = 1023

angle & Mask is the angle in 0..1023.

Since 0.15

Quarter

const int Quarter = 256

The angle of 90 degrees.

Since 0.15

Half

const int Half = 512

The angle of 180 degrees.

Since 0.15

SinOne

const int SinOne = 16384

1.0 in the results of FastTrig.Sin and FastTrig.Cos (1.14 fixed point).

Since 0.15

FixedOne

const int FixedOne = 65536

1.0 in the results of FastTrig.Tan, FastTrig.Cot, FastTrig.Sec and FastTrig.Csc (16.16 fixed point).

Since 0.15

Functions

Name	Description
Sin	The sine of angle (1024 steps per circle) in 1.14 fixed point: -16384 to 16384.
Cos	The cosine of angle (1024 steps per circle) in 1.14 fixed point: -16384 to 16384.
Tan	The tangent of angle in 16.16 fixed point.
Cot	The cotangent (1/tan) of angle in 16.16 fixed point.
Sec	The secant (1/cos) of angle in 16.16 fixed point: the length of the step of a ray to the next vertical grid line.
Csc	The cosecant (1/sin) of angle in 16.16 fixed point: the length of the step of a ray to the next horizontal grid line.
Atan2	The angle of the vector (x, y) in steps, 0 to 1023, exact to about half a step.
FromDegrees	An angle in degrees converted to steps (rounded): FromDegrees(90) is 256.
ToDegrees	An angle in steps converted to degrees, 0 to 359 (rounded).

Sin

int16 Sin(int angle)

The sine of angle (1024 steps per circle) in 1.14 fixed point: -16384 to 16384.

Since 0.15

Cos

int16 Cos(int angle)

The cosine of angle (1024 steps per circle) in 1.14 fixed point: -16384 to 16384.

Since 0.15

Tan

int Tan(int angle)

The tangent of angle in 16.16 fixed point.

Returns 2147483647 or -2147483647 at 90 and 270 degrees.

Since 0.15

Cot

int Cot(int angle)

The cotangent (1/tan) of angle in 16.16 fixed point.

Returns 2147483647 or -2147483647 at 0 and 180 degrees.

Since 0.15

Sec

int Sec(int angle)

The secant (1/cos) of angle in 16.16 fixed point: the length of the step of a ray to the next vertical grid line.

Returns 2147483647 or -2147483647 at 90 and 270 degrees.

Since 0.15

Csc

int Csc(int angle)

The cosecant (1/sin) of angle in 16.16 fixed point: the length of the step of a ray to the next horizontal grid line.

Returns 2147483647 or -2147483647 at 0 and 180 degrees.

Since 0.15

Atan2

int Atan2(int y, int x)

The angle of the vector (x, y) in steps, 0 to 1023, exact to about half a step.

Returns 0 for the zero vector.

Since 0.15

FromDegrees

int FromDegrees(int degrees)

An angle in degrees converted to steps (rounded): FromDegrees(90) is 256.

Since 0.15

ToDegrees

int ToDegrees(int angle)

An angle in steps converted to degrees, 0 to 359 (rounded).

Since 0.15