SRL::Math::Trigonometry Class Reference

Detailed Description

High-performance trigonometric function library optimized for Saturn hardware.

The Trigonometry class provides a comprehensive set of trigonometric and hyperbolic functions essential for 3D graphics, physics simulations, and signal processing. All functions are implemented using fixed-point arithmetic with lookup tables and intelligent interpolation to maximize performance on Saturn hardware while maintaining high precision.

Key features:

• Complete set of trigonometric functions (sin, cos, tan, etc.)
• Full hyperbolic function support (sinh, cosh, tanh, etc.)
• Inverse trigonometric functions (asin, acos, atan, atan2)
• No floating-point operations for consistent cross-platform behavior
• Constant-time execution for most operations regardless of input value
• Memory-efficient table design to minimize cache misses
• Automatic range handling and normalization for any input angle
• Multiple precision levels for performance-critical operations

Performance characteristics:

• Sine/cosine: O(1) complexity using table lookup with interpolation
• Tangent: O(1) complexity with dynamic table sizing near asymptotes
• Inverse functions: O(1) complexity with slightly higher cost than direct functions
• Hyperbolic functions: O(1) complexity using specialized tables

Common applications:

• 3D rotations and transformations
• Physics simulations (projectile motion, oscillations)
• Procedural animation and movement
• Signal processing and waveform generation
• Geometric calculations (angles, distances, projections)

Implementation details:

• Uses LookupCache for efficient interpolation between table entries
• Pre-calculated multiplicands to avoid expensive division operations
• Dynamic table sizing for functions with asymptotic behavior (like tan)
• Shared tables where mathematical relationships allow (sin/cos)
• Specialized implementations for critical angle values (0, 90, 180, 270 degrees)

Precision considerations:

• Standard functions maintain accuracy within 0.01% across the entire range
• Near asymptotes (tan at 90°), precision naturally decreases
• For highest precision, consider using Precision::Accurate template parameter

See also

Angle For angle representation and conversion

Fxp For details on the fixed-point implementation

Precision For available precision levels in calculations

#include <trigonometry.hpp>

Static Public Member Functions
Basic Trigonometric Functions
Core trigonometric operations using fixed-point arithmetic.
static constexpr Fxp	Sin (const Angle &angle)
	Calculates sine of an angle.
static constexpr Fxp	Cos (const Angle &angle)
	Calculates cosine of an angle.
static constexpr Fxp	Tan (const Angle &angle)
	Calculates tangent of an angle.
template<typename T = void>
static constexpr Angle	Asin (const Fxp &value)
	Calculates arcsine (inverse sine) of a value.
template<typename T = void>
static constexpr Angle	Acos (const Fxp &value)
	Calculates arccosine (inverse cosine) of a value.
static constexpr Angle	Atan2 (const Fxp &y, const Fxp &x)
	Calculates arctangent of y/x, handling all quadrants correctly.
template<typename T = void>
static constexpr Fxp	Sinh (const Fxp &value)
	Calculates hyperbolic sine of a value.
template<typename T = void>
static constexpr Fxp	Cosh (const Fxp &value)
	Calculates hyperbolic cosine of a value.
template<typename T = void>
static constexpr Fxp	Tanh (const Fxp &value)
	Calculates hyperbolic tangent of a value.
static constexpr Angle	SLerp (const Angle &start, const Angle &end, const Fxp &t)
	Spherical linear interpolation between two angles.