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2nd December 2019, 14:51 #1
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fastest multiplication alghorithms
Hi,
What do you think is the fastest multiplication alghorithms in the world?

2nd December 2019, 14:56 #2

2nd December 2019, 16:48 #3
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2nd December 2019, 16:54 #4
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Re: fastest multiplication alghorithms
Hi,
I vote for a big lookup table.
KlausPlease donīt contact me via PM, because there is no time to respond to them. No friend requests. Thank you.

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2nd December 2019, 17:15 #5
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Re: fastest multiplication alghorithms
Hello,
i agree with @KlausST. If you are looking for theoretical information see links to these algorithms:
https://en.wikipedia.org/wiki/Karatsuba_algorithm
https://en.wikipedia.org/wiki/Toom%E...multiplication
https://en.wikipedia.org/wiki/Sch%C3...ssen_algorithm
https://en.wikipedia.org/wiki/F%C3%BCrer%27s_algorithm
If you wanna fast multiplication operation using FPGA just use "hardware multipliers" or "DSP blocks" from FPGA fabric.
RegardsLast edited by FlyingDutch; 2nd December 2019 at 17:20.
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2nd December 2019, 20:27 #6
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Re: fastest multiplication alghorithms
I am looking for fast ASIC implementation. Booth looks good.
But I want a 4 step pipelined multiplier.
   Updated   
Really I want a fast pipelined implementation of 24 bit multiplier for 32 bit floating point multiplication. I prefer four or six stage pipelined multiplier.

2nd December 2019, 21:53 #7
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Re: fastest multiplication alghorithms
Hi,
Do you recognize that you jump from one requirenent to the other.
unsigned 8 bit24 bit multiplier32 bit floating pointI want a 4 step pipelined multiplier.four or six stage pipelined multiplier.
KlausPlease donīt contact me via PM, because there is no time to respond to them. No friend requests. Thank you.

3rd December 2019, 07:54 #8
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Re: fastest multiplication alghorithms
I am so sorry. You are right.
But i was thinking about difference ways to multiply two 32bit floating point. And its the effect of different solutions.
Actually in 32bit floating point multiplication, we should multiply two mantissa and add two exponent. so the bottleneck of speed is multiplication of two mantissa. Initially i was looking for a fast multiplication algorithm. but later i thought about a pipelined multiplication algorithm to increase clock ratio in some sequential independent multiplication.
What is you idea?

3rd December 2019, 08:09 #9
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Re: fastest multiplication alghorithms
See my multiplication implementation in verilog
https://github.com/promach/multiply

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3rd December 2019, 13:58 #10
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Re: fastest multiplication alghorithms
Hi,
I think there is a big difference whether you do 8x8 bit integer multiplication or 32bit x 32bit floating point multiplication.
One is the lower end, the other is the higher end ( or at least good middle range)
the one has a dynamic of 1:256, the other about 1:144700000000000000000000000000000000000000000000 000000000000000000000000000
(dont know whether there is a zero too much or too less)
So itīs something totally different.
*********************************
If I understand you right, then you donīt need "fast" code, but code with high "throughput".
(pipelined code is not fast (input to output) but it has high throughput (maybe one calculation per clock cycle))
KlausPlease donīt contact me via PM, because there is no time to respond to them. No friend requests. Thank you.

4th December 2019, 09:20 #11
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4th December 2019, 13:02 #12
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Re: fastest multiplication alghorithms
I vote for a big lookup table...
For the slowest method (school book way) it is just 8 shifts and 8 additions.

4th December 2019, 17:18 #13
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Re: fastest multiplication alghorithms
...and every stage of that shift and add can be pipelined to run at very high clock frequencies. Depending on how much pipelining is done you will have increased latency for the first output but you will get all successive outputs on every clock cycle.
Also unlike the RAM this is scalable in an FPGA, i.e. a 32x32 multiply no problem just more pipeline latency. a look up table for 2^32x2^32 bits won't fit in any FPGA.
   Updated   
One of the methods to reduce the latency of a multiplier is to perform radix lookups for multiple bits of the calculation. This is primarily how most of the hard IP multipliers are designed in processors along with pipelining the multiplier.
That is how the original Pentium multiplication error was introduced due to a miscalculated Radix4 entry.
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6th December 2019, 03:59 #14
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Re: fastest multiplication alghorithms
That is how the original Pentium multiplication error was introduced...
Wikipedia has a nontechnical article: https://en.wikipedia.org/wiki/Pentium_FDIV_bug
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