math.h File Reference

SNES Fixed-Point Math. More...

#include <snes/types.h>

Go to the source code of this file.

Macros
#define	FIX(x)   ((fixed)((x) << 8))
	Convert integer to fixed-point.
#define	FIX_FRAC(x)   ((u8)((x) & 0xFF))
	Get fractional part of fixed-point.
#define	FIX_MAKE(i, f)   ((fixed)(((i) << 8) | (f)))
	Create fixed-point from integer and fraction.
#define	UNFIX(x)   ((s16)((x) >> 8))
	Convert fixed-point to integer (truncate)
#define	UNFIX_ROUND(x)   ((s16)(((x) + 128) >> 8))
	Convert fixed-point to integer (rounded)

Typedefs
typedef s16	fixed
	8.8 signed fixed-point type

Functions
u16	div16 (u16 dividend, u16 divisor)
	Safe 16-bit division.
fixed	fixAbs (fixed x)
	Absolute value of fixed-point.
fixed	fixClamp (fixed x, fixed min, fixed max)
	Clamp value to range.
fixed	fixCos (u8 angle)
	Get cosine value for angle.
fixed	fixDiv (fixed a, fixed b)
	Divide two fixed-point values.
fixed	fixLerp (fixed a, fixed b, u8 t)
	Linear interpolation.
fixed	fixMul (fixed a, fixed b)
	Multiply two fixed-point values.
fixed	fixSin (u8 angle)
	Get sine value for angle.
u16	mod16 (u16 dividend, u16 divisor)
	Get remainder of division.
u16	mul16 (u16 a, u16 b)
	Safe 16-bit multiplication.

Detailed Description

SNES Fixed-Point Math.

Fixed-point arithmetic for smooth movement and physics.

Overview

This module provides:

• 8.8 fixed-point type and macros
• Sine/cosine lookup tables (256 angles = full circle)
• Fixed-point multiplication
• Integer multiplication (safe alternative to compiler's *)

Fixed-Point Format

The fixed type is 16-bit signed (s16) in 8.8 format:

• High byte: integer part (-128 to 127)
• Low byte: fractional part (0-255, representing 0.0 to 0.996)

fixed pos_x = FIX(100);        // 100.0
fixed velocity = FIX(1) / 4;   // 0.25 (64 in fixed)
pos_x = pos_x + velocity;      // 100.25
s16 screen_x = UNFIX(pos_x);   // 100 (truncated)

Angles

Angles are 8-bit values (0-255) representing 0-360 degrees:

• 0 = 0°, 64 = 90°, 128 = 180°, 192 = 270°

u8 angle = 64;                       // 90 degrees
fixed dx = fixSin(angle);            // 1.0 (256)
fixed dy = fixCos(angle);            // 0.0 (0)
player_x = player_x + fixMul(speed, dx);

Author

OpenSNES Team

Copyright

MIT License

Macro Definition Documentation

FIX

#define FIX

(

x

)

((fixed)((x) << 8))

Convert integer to fixed-point.

Parameters

x	Integer value (-128 to 127)

Returns

Fixed-point representation

fixed pos = FIX(50);   // 50.0 in fixed-point
fixed half = FIX(1) / 2;  // 0.5

FIX_FRAC

#define FIX_FRAC

(

x

)

((u8)((x) & 0xFF))

Get fractional part of fixed-point.

Parameters

x	Fixed-point value

Returns

Fractional part (0-255)

FIX_MAKE

#define FIX_MAKE	(		i,
			f
	)		((fixed)(((i) << 8) | (f)))

Create fixed-point from integer and fraction.

Parameters

i	Integer part
f	Fractional part (0-255)

Returns

Fixed-point value

fixed half = FIX_MAKE(0, 128);  // 0.5
fixed quarter = FIX_MAKE(0, 64);  // 0.25

UNFIX

#define UNFIX

(

x

)

((s16)((x) >> 8))

Convert fixed-point to integer (truncate)

Parameters

x	Fixed-point value

Returns

Integer part (truncated toward zero)

fixed pos = FIX(50) + 128;  // 50.5
s16 screen_pos = UNFIX(pos);  // 50

UNFIX_ROUND

#define UNFIX_ROUND

(

x

)

((s16)(((x) + 128) >> 8))

Convert fixed-point to integer (rounded)

Parameters

x	Fixed-point value

Returns

Integer part (rounded to nearest)

fixed pos = FIX(50) + 128;  // 50.5
s16 screen_pos = UNFIX_ROUND(pos);  // 51

Typedef Documentation

fixed

typedef s16 fixed

8.8 signed fixed-point type

Range: -128.0 to 127.996 (approximately) Precision: 1/256 = 0.00390625

Function Documentation

div16()

u16 div16	(	u16	dividend,
		u16	divisor
	)

Safe 16-bit division.

Parameters

dividend	Number to divide
divisor	Number to divide by (must not be zero)

Returns

Quotient

Warning

Returns 0 if divisor is 0

fixAbs()

fixed fixAbs

(

fixed

x

)

Absolute value of fixed-point.

Parameters

x	Fixed-point value

Returns

Absolute value

fixClamp()

fixed fixClamp	(	fixed	x,
		fixed	min,
		fixed	max
	)

Clamp value to range.

Parameters

x	Value to clamp
min	Minimum value
max	Maximum value

Returns

Clamped value

fixCos()

fixed fixCos

(

u8

angle

)

Get cosine value for angle.

Parameters

angle

8-bit angle (0-255 = 0°-360°)

Returns

Cosine value in 8.8 fixed-point (-256 to 256)

u8 angle = 0;  // 0 degrees
fixed cos_val = fixCos(angle);  // 256 = 1.0

fixDiv()

fixed fixDiv	(	fixed	a,
		fixed	b
	)

Divide two fixed-point values.

Parameters

a	Dividend (fixed-point)
b	Divisor (fixed-point, must not be zero)

Returns

Quotient in fixed-point format

fixed distance = FIX(100);
fixed time = FIX(5);
fixed speed = fixDiv(distance, time);  // 20.0

Warning

Division by zero returns 0

fixLerp()

fixed fixLerp	(	fixed	a,
		fixed	b,
		u8	t
	)

Linear interpolation.

Parameters

a	Start value
b	End value
t	Interpolation factor (0-256 = 0.0-1.0)

Returns

Interpolated value

fixed start = FIX(0);
fixed end = FIX(100);
fixed mid = fixLerp(start, end, 128);  // 50.0

fixMul()

fixed fixMul	(	fixed	a,
		fixed	b
	)

Multiply two fixed-point values.

Parameters

a	First fixed-point operand
b	Second fixed-point operand

Returns

Product in fixed-point format

fixed speed = FIX(2);
fixed scale = FIX(1) / 2;  // 0.5
fixed result = fixMul(speed, scale);  // 1.0

Note

Uses 32-bit intermediate for accuracy

fixSin()

fixed fixSin

(

u8

angle

)

Get sine value for angle.

Parameters

angle

8-bit angle (0-255 = 0°-360°)

Returns

Sine value in 8.8 fixed-point (-256 to 256, i.e., -1.0 to 1.0)

u8 angle = 64;  // 90 degrees
fixed sin_val = fixSin(angle);  // 256 = 1.0

Note

Table-based lookup, very fast

mod16()

u16 mod16	(	u16	dividend,
		u16	divisor
	)

Get remainder of division.

Parameters

dividend	Number to divide
divisor	Number to divide by (must not be zero)

Returns

Remainder

mul16()

u16 mul16	(	u16	a,
		u16	b
	)

Safe 16-bit multiplication.

Multiplies two 16-bit values safely. Use this instead of the compiler's * operator for important calculations, as the compiler's runtime multiplication can have bugs.

Parameters

a	First operand
b	Second operand

Returns

Product (may overflow for large values)

u16 result = mul16(width, height);