Math device

This specification describes the math device of the Bedrock computer system.

Ports

x coordinate

Reading from this port group will return the x coordinate of the polar point after conversion to the cartesian coordinate system. If the coordinate exceeds the range of a signed 16-bit integer, the value returned will be zero.

Writing to this port group will set the x coordinate of the cartesian point to the value written.

y coordinate

Reading from this port group will return the y coordinate of the polar point after conversion to the cartesian coordinate system. If the coordinate exceeds the range of a signed 16-bit integer, the value returned will be zero.

Writing to this port group will set the y coordinate of the cartesian point to the value written.

r coordinate

Reading from this port group will return the r coordinate of the cartesian point after conversion to the polar coordinate system.

Writing to this port group will set the r coordinate of the polar point to the value written.

t coordinate

Reading from this port group will return the t coordinate of the cartesian point after conversion to the polar coordinate system.

Writing to this port group will set the t coordinate of the polar point to the value written.

Product

Reading from this port group will return the product of the multiplication of the x operand by the y operand.

Quotient

Reading from this port group will return the quotient of the division of the x operand by the y operand. If the y operand is zero, the value zero will be returned.

Remainder

Reading from this port group will return the remainder of the division of the x operand by the y operand. If the y operand is zero, the value zero will be returned.

Data structures

Cartesian point

The cartesian point is a pair of signed 16-bit coordinates representing a two-dimensional point in the cartesian coordinate system. The x coordinate represents the signed distance from the origin along the horizontal axis, and the y coordinate represents the signed distance from the origin along the vertical axis. The initial value of each coordinate is zero.

Polar point

The polar point is a pair of unsigned 16-bit coordinates representing a two-dimensional point in the polar coordinate system. The r coordinate represents the unsigned distance from the origin, and the t coordinate represents the angle counterclockwise around the origin from the positive horizontal axis. The angle unit is 1/65536 of a full turn. The initial value of each coordinate is zero.

x operand

The x operand is the x coordinate of the cartesian point interpreted as an unsigned 16-bit value.

y operand

The y operand is the y coordinate of the cartesian point interpreted as an unsigned 16-bit value.

Implementation

Coordinate conversion

The x coordinate of the polar point is calculated by taking the signed floor of cos(\frac{2 \pi t}{65536}) \times r, where the cosine function takes an angle in radians.

The y coordinate of the polar point is calculated by taking the signed floor of sin(\frac{2 \pi t}{65536}) \times r, where the sine function takes an angle in radians.

The r coordinate of the cartesian point is calculated by taking the unsigned floor of \sqrt{x^2 + y^2}.

The t coordinate of the cartesian point is calculated by taking the unsigned floor of atan2(y,x) \times \frac{65536}{2\pi}.

Wake

This device will never send a wake request to the system device.