GPGPU Programming for Games and Science

CPU Computing 55

a 1-bit followed by the trailing significand bits and then followed by zero or

more 0-bits. Therefore, x is an integer and round

e

(x)=x.

Pseudocode for the rounding is presented next. The generic types

Integer

and UInteger represent signed and unsigned integers, respectively, with the

same number of bits as the binary encoding for the floating-point number.

Listing 2.17 is an implementation of the default rounding mode: rounding

with ties-to-even.

binaryN RoundToIntegralTiesToEven ( binaryN x )

{

UInteger sign , biased , t ra ili ng ;

GetEncoding(x , sign , biased , trail in g );

Integer exponent = biased − binaryN : :EXPONENT

BIAS ;

if (ex