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

Algorithm 9

Exponent calculation.

offset2 = 783 − 398 = 385

if (QP ≤ QNI) or (QNI + TZ < QP)

      or (QP > 𝑞_max) then

 (a) QNI > 𝑞_max ⇒ overflow!

 (b) 𝑞_min ≤ QNI ≤ 𝑞_max ⇒

       𝑞_𝑍 = QNI − offset2

       Z_𝑒=Z

      ZP1′_e = ZP1

 (c) QNI < 𝑞_min ⇒ underflow!

else

 (a) 𝑞_min ≤ QP ≤ 𝑞_max ⇒

     𝑞_𝑍 = QP − offset2

     Z_𝑒 = Z ≫ (QP − QNI)

     ZP1_𝑒 = ZP1 ≫ (QP − QNI)

 (b) QNI < 𝑞_min⇒ underflow!