11. Arithmetic functions

This chapter introduces the various calculation library functions supported by SGL.

11-1. General arithmetic functions

First, we will introduce general arithmetic functions.

[FIXED slDivFX ( FIXED a , FIXED b );]

Performs division between the specified parameters (b/a).

[FIXED slMulFX ( FIXED a , FIXED b ) ;]

Multiplies the specified parameters (a*b).

[FIXED slSquartFX ( FIXED sqrtfx );]

Returns the square root of an unsigned fixed-point number (FIXED type).

[Uint32 slSquart ( Uint32 sqrt );]

Returns the square root of an unsigned integer value.

11-2. Trigonometric functions

Introducing arithmetic functions related to trigonometric functions.

[FIXED slSin (ANGLE angs);]

Returns the sine value for the specified angle (ANGLE type).

[FIXED slCos (ANGLE angc);]

Returns the cosine value for the specified angle (ANGLE type).

[FIXED slTan (ANGLE angt);]

Returns the tangent value for the specified angle (ANGLE type).

Figure 11-1 Trigonometric function image

[ANGLE slAtan ( FIXED tx , FIXED ty ) ;]

Returns the angle in the specified direction.

Figure 11-2 “slAtan” image

11-3. Special calculation functions

This section introduces special arithmetic functions.

[FIXED slCalcPoint ( FIXED cx , FIXED cy , FIXED cz , FIXED *ret ) ;]

Multiplies the current matrix by the specified point and assigns the calculation result to the parameter "ret".

[FIXED slInnerProduct ( VECTOR a , VECTOR b ) ;]

Takes the inner product of vectors between the specified parameters.
The return value shown in Figure 11-3 is returned.

Figure 11-3 Vector inner product return value

┌─● Vector inner product return value ●───┐
│A(X1,Y1,Z1)*B(X2,Y2,Z2)=X1*X2+Y1*Y2+Z1*Z2│
│                       =Return Value     │
└─────────────────────────────────────────┘

[Uint32 slDec2Hex ( Uint32 val ) ;]

Converts a number expressed in BCD code to hexadecimal code.

[Uint32 slHex2Dec ( Uint32 val );]

Converts a number expressed in hexadecimal code to BCD code.

[Uint16 slAng2Hex (ANGLE ang);]

Converts the angle value represented by ANGLE code to hexadecimal code.
Converted values are returned in the range 0x000 to 0x167.

[Uint16 slAng2Dec (ANGLE ang);]

Converts the angle value represented by ANGLE code to BCD code.
Converted values are returned in the range 0x000 to 0x359.

[FIXED slAng2FX (ANGLE ang);]

Converts an angular value represented by an ANGLE code to a FIXED code.
Converted values are returned in the range 0.0 to 359.99.

Table 11-1 Examples of numerical notation using each numerical notation method

	decimal number	B.C.D.	hexadecimal number
Notation	92	0x92	0x5CH

Additional notes: SGL library functions that appeared in this chapter

In this chapter, we explained the functions in the table below.

Table 11-2 SGL library functions that appeared in this chapter

functional type	Function name	Parameter	function
FIXED	slDivFX	FIXED a,FIXED b	Division (a/b)
FIXED	slMulFX	FIXED a,FIXED b	Multiplication (a*b)
FIXED	slSquartFX	FIXED sqrtfx	Unsigned fixed-point square root
Uint32	slSquart	Uint32 sqrt	square root of unsigned integer
FIXED	slSin	ANGLE angs	Returns the sine value for the specified angle
FIXED	slCos	ANGLE angc	Returns the cosine value for the specified angle
FIXED	slTan	ANGLE angt	Returns the tangent value for the specified angle
ANGLE	slAtan	FIXED tx,FIXED ty	returns the angle in the specified direction
FIXED	slCalcPoint	FIXED zx,cy,cz,FIXED *ret	Multiplies the current matrix by the specified point and returns it.
FIXED	slInnerProduct	VECTOR a,VECTOR b	Take the inner product of vectors
Uint32	slDec2Hex	Uint32 val	Conversion from BCD code to hexadecimal code
Uint32	slHex2Dec	Uint32 val	Conversion from hex code to BCD code
Uint16	slAng2Hex	ANGLE ang	Converting ANGLE code to hex code
Uint16	slAng2Dec	ANGLE ang	Conversion from ANGLE code to BCD code
FIXED	slAng2FX	ANGLE ang	Conversion from ANGLE code to FIXED code