Analysis of Fast Radix-10 Digit Recurrence Algorithms for Fixed-Point and Floating-Point Dividers on FPGAs

Table 3

Round-up detection.

Rounding mode	Round-up detection
Round Ties To Even	(𝑅>5)+(𝑅≡5)⋅sb
	+(𝑅≡5)⋅sb⋅LSD(0)
Round Ties To Away	(𝑅≥5)
Round Toward Positive	sign⋅((𝑅>0)+sb)
Round Toward Negative	sign⋅((𝑅>0)+sb)
Round Toward Zero	0

Legend: “+”: logical OR, “⋅”: logical AND.