Tomas, No magic, moderns FPGA have DSP blocks with dedicated hardware multipliers in silicon, on the other hand division need be implement into the logic farm; using one of the well know algorithms to keep logic resources within reasonable limits. Simulator waveforms show the process, 11 divided by 3, quotient = 3 remainder = 2; one clock period for bit. In practise, one clock for setting up values, results can be read one clock after calculus done; so, divide a 32 bit number use 34 clocks. Waveforms correspond to our own VHDL version of RISC-5. Walter, El miércoles-2017-05-24 a las 13:21, Tomas Kral escribió:
Hi,
This example of binary multiply needs >>>fixed size font<<< to display properly.
[a] Shift & addition
0101 =5(4+1) 0101 x =5(4+1) _________
0101 0000 shift 0101 shift _________ add above 011001 =25(16+8+1)
[b] Repeated addition, 5+5+5+5+5
0101 0101 0101 0101 0101 __________
011001 =25(16+8+1)
To multiply 32 bit integers upto 32 cycles are needed. There is some FPGA magic used, to complete each `MUL'tiply in two cycles only.
How many cycles does `DIV'require? Looking for the above analogy.
Tomas
On Tue, 23 May 2017 12:36:04 +0200 Tomas Kral<thomas.kral@email.cz> wrote:
Hi Joerg,
Multiplication ~ repeated addition Division ~ repeated subtraction
That is a simplification but is not the way implemented in RISC. Consider 65536 DIV 1, that would require 65536 iterations.
Instead shift (left | right) + (add | sub) is used for DIV and MUL. This requires much fewer iterations.
My argument is right about the example given in the 16.2.3.
14 DIV 4, is 3 with remainder 2
But the example gives 4 and the remainder 2
Tomas
On Tue, 23 May 2017 11:23:14 +0200 Jörg<joerg.straube@iaeth.ch> wrote:
Tomas
http://www.homeschoolmath.net/teaching/md/division-repeated-subtraction.php
Jörg
Am 23.05.2017 um 11:09 schrieb Tomas Kral<thomas.kral@email.cz>:
Hi,
I am reading chapters on RISC implementation. I managed to understand multiplication - `MUL' instruction, consisting of shifting x and adding y to the product.
I seem not understanding the division, chapter 16.2.3. In the example for x=14, y=4 gives quotient q=4, and the remainder r=2.
But... q = x DIV y = 3, r = x MOD y = 2 ???
-- Tomas Kral<thomas.kral@email.cz> -- Oberon@lists.inf.ethz.ch mailing list for ETH Oberon and related systemshttps://lists.inf.ethz.ch/mailman/listinfo/oberon
