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

Algorithm 6

Pseudo code for the type 4 digit recurrence.

(1) select

 𝑧³_𝑗+1=𝑗𝑗𝑗1if0.9≤10𝑤0if−1.5≤10𝑤<0.9−1if10𝑤<−1.5

 and compute

 𝑣¹_𝑠𝑗+𝑣¹_𝑐𝑗=10𝑤_𝑠𝑗+𝑤_𝑐𝑗−𝑧³_𝑗+1⋅5𝑑

(2) select

 𝑧³_𝑗+1=1if0.1≤𝑣¹𝑗0if−0.7≤𝑣¹𝑗𝑣<0.1−1if¹𝑗<−0.7

and compute

 𝑣²_𝑠𝑗+𝑣²_𝑐𝑗=𝑣¹_𝑠𝑗+𝑣¹_𝑐𝑗−𝑧²_𝑗+1⋅2𝑑

(3) select

 𝑧¹_𝑗+1=1if0.1≤𝑣²𝑗0if−0.3≤𝑣²𝑗𝑣<0.1−1if²𝑗<−0.3

 and compute 𝑤_𝑠𝑗+1+𝑤_𝑐𝑗+1=

      𝑣²_𝑠𝑗+𝑣²_𝑐𝑗−𝑧¹_𝑗+1𝑑