Standard Library - Trigonometry

Overview

Romasm's trigonometric functions use Taylor series expansions to calculate sine and cosine. These functions are located in stdlib/trig.romasm and stdlib/sine-taylor.romasm.

Note: All angles are in degrees and scaled by 100. Results are scaled by 1000.

Available Functions

sin

Calculates the sine of an angle using a 6-term Taylor series expansion.

Taylor Series:

sin(x) = x - x³/6 + x⁵/120 - x⁷/5040 + x⁹/362880 - x¹¹/39916800

Input	Output
R0 = angle in degrees (scaled by 100) Example: 3000 = 30.00°	R0 = sin(angle) × 1000 Example: ~500 for sin(30°) ≈ 0.5

Example:

LOAD R0, 3000    ; 30 degrees (scaled by 100)
CALL sin
PRINT R0         ; Outputs ~500 (0.5 × 1000)

Implementation: Uses argument reduction to handle angles > 90°, then applies Taylor series.

cos

Calculates the cosine of an angle. Uses the identity: cos(x) = sin(90° - x)

Input	Output
R0 = angle in degrees (scaled by 100)	R0 = cos(angle) × 1000

Example:

LOAD R0, 0       ; 0 degrees
CALL cos
PRINT R0         ; Outputs ~1000 (1.0 × 1000)

sin_cordic

Simplified CORDIC (Coordinate Rotation Digital Computer) algorithm for sine. More efficient for hardware implementation.

Note: This is a simplified version. For full accuracy, use the sin function with Taylor series.

Input	Output
R0 = angle in degrees (0-45°, scaled by 100)	R0 = sin(angle) × 1000

Scaling & Fixed-Point Arithmetic

Input Scaling

Angles are specified in degrees, scaled by 100:

3000 = 30.00°
4500 = 45.00°
9000 = 90.00°

Output Scaling

Results are scaled by 1000:

1000 = 1.0
500 = 0.5
866 ≈ 0.866 (sin(60°))

Argument Reduction

For angles greater than 90°, the functions use argument reduction to map them to the 0-90° range where the Taylor series converges quickly.

How It Works

Angles are reduced modulo 360°
Angles > 90° use trigonometric identities:
- sin(180° - x) = sin(x)
- sin(180° + x) = -sin(x)
- sin(360° - x) = -sin(x)

Complete Example

; Calculate sin(30°) and cos(60°)
; sin(30°) = 0.5
; cos(60°) = 0.5

; Calculate sin(30°)
LOAD R0, 3000    ; 30 degrees (scaled by 100)
CALL sin
LOAD R1, R0       ; Save result in R1
PRINT R1          ; Outputs ~500

; Calculate cos(60°)
LOAD R0, 6000    ; 60 degrees (scaled by 100)
CALL cos
PRINT R0          ; Outputs ~500 (same as sin(30°))