GPGPU Programming for Games and Science

CPU Computing 75

to a number in this interval, the corresponding narrow subnormal number is

0.s

13

s

12

s

11

s

10

+ ε,whereε is zero or one based on rounding. Define integers

i and f by i.f = s

13

···s

10

.s

9

···s

0

. Using round-to-nearest with ties-to-even,

the value ε is one when 0.f > 1/2orwhen0.f =1/2andi is odd. If i =15

(all s-bits are 1), then ε = 1 and the addition causes a carry out of s

13

.The

result is i = 16. When using bit-manipulation methods in the source code, the

addition is to the trailing significand. The carry-out is to the low-order bit

of the biased exponent. In the current case, the (left-shifted) biased exponent

is zero (the target is a narrow subnormal), so OR-ing the trailing significand

into the final encoding amounts to increasing the expo ...