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Inside Macintosh: QuickDraw GX Environment and Utilities /

Chapter 8 - QuickDraw GX Mathematics / Using QuickDraw GX Mathematics

Performing Fixed-Point Operations

You can use QuickDraw GX functions to provide operations on Fixed, long, fract and wide numbers. The equivalent QuickDraw GX fixed-point functions for functions in the Macintosh Mathematical Utilities is shown in Table 8-2.

Table 8-2 QuickDraw GX and Macintosh Toolbox fixed-point functions

QuickDraw GX	Macintosh Mathematical Utilities
FractDivide	FracDiv
FractMultiply	FracMul
FractSquareRoot	FracSqrt
FixedDivide	FixDiv
FixedMultiply	FixMul
WideMultiply	LongMul

The Macintosh Mathematical Utilities are described in Inside Macintosh: Operating System Utilities.

Some functions combine multiple functions into a single function to increase calculation speed over that obtained using sequential function calls. For example, the FractSineCosine function returns both the sine and cosine of an angle.

Some functions support the use of 64-bit numbers to increase the accuracy of calculations. For example, the WideAdd function returns the 64-bit sum of two 64-bit numbers, and the WideDivide function returns the quotient of a 64-bit number and a 32-bit number. The MultiplyDivide function uses a 64-bit intermediate result to increase accuracy of the calculation and to prevent premature overflow.

The MultiplyDivide, Magnitude, and VectorMultiplyDivide functions are derivatives of other functions. For example, MultiplyDivide (x, y, z) is the same as:

wide temp;
WideDivide (WideMultiply(x, y, &temp), z, 0)

The final argument of 0 specifies that the returned number will be rounded with no remainder.

You can use the Magnitude function to determine the magnitude (length) of a two-dimensional vector, or the distance between two points on a plane. Figure 8-18 shows the use of function parameters deltaX and deltaY.

Figure 8-18 Determining the length of a line with the Magnitude function

Functions that provide arithmetic operations on fixed-point numbers are described in the section "Fixed-Point Operations" beginning on page 8-42. Functions that provide operations on wide numbers are described in the section "Operations on wide Numbers" beginning on page 8-49. The Magnitude function is described on page 8-45.