let8-Division II

Computer Arithmetic: Algorithms and Hardware Designs

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CSE 246: Computer Arithmetic Algorithms and Hardware Design Instructor: Prof. Chung-Kuan Cheng Fall 2006 Lecture 8: Division
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CSE 246 2 Topics: Radix-4 SRT Division Division by a Constant Division by a Repeated Multiplication
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CSE 246 3 Project Update Come in to speak briefly about the final project Status Update 2:30 – 3:00 p.m. Tuesday or Thursday
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CSE 246 4 Radix-4 SRT Division 4s j-1 = q j d + s j where q j is in [-2,2] and s j-1 is in [-hd,+hd] h is less than or equal to 2/3 Therefore, s j-1 is in [-2d/3, 2d/3] And, 4s j-1 is in [-8d/3, 8d/3] s shifts to the left by 2 bits
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CSE 246 5 Radix-4 SRT Division 0.0 0.1 1.0 1.1 10.0 10.1 11.0 .101 .110 .111 1.00 .1 2d/3 -2d/3 q j =1 q j =0 q j =2 The overlap regions of q j denote a choice still allowing for recursion. The gap defines the precision for carry save addition. Anything above 8d/3 goes against our assumption and is therefore the infeasible region 4s j-1 d d/3 8d/3 5d/3 4d/3
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CSE 246 6 Radix-4 SRT Division The value of q j determines the range it governs For example, q j = 1 1 + 2/3 = 5/3 1 – 2/3 = 1/3 The range is 1/3 to 5/3
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CSE 246 7 Division by a Constant Multiplication is O(log n) but division is linear…much slower Try to convert division to multiplication Property: Given an odd number d m such that d*m = 2 n – 1 Ex. d = 3, m = 5 3*5 = 2 4 – 1 d = 7, m =9 7*9 = 2 6 – 1 d = 11, m = 93 11 * 93 = 2 10 - 1 E
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CSE 246 8 Division by a Constant 1/d = m/(2 n – 1) 1/(1-r) = 1+r+r
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let8-Division II - CSE 246: Computer Arithmetic Algorithms...

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