Breaking News
Comments
Oldest First | Newest First | Threaded View
Page 1 / 3   >   >>
sa_penguin
User Rank
Author
Goldschmidt?
sa_penguin   12/6/2013 7:40:07 PM
NO RATINGS
Sounds a bit like Goldschmidt division: converting the factor 1/10 into X/(2^n). Multiply by X, shift N bits, done. Taking the upper 16 bits of a 32-bit word is equal to a 16-bit shift.

I suspect 1/10 doesn't translate perfectly to binary so, just like 1/3 becomes 0.33... you get a hex factor of 0x1999... in your division.

Brian_D
User Rank
Author
math links
Brian_D   12/6/2013 7:56:58 PM
NO RATINGS
There's some nice material about constant division on the companion website for "Hacker's Delight":

http://www.hackersdelight.org/divcMore.pdf

Also, VHDL has a nifty fixed point math package:

http://www.eda.org/fphdl/

-Brian

krisi
User Rank
Author
Re: math links
krisi   12/7/2013 10:01:00 AM
NO RATINGS
Pretty cool math...I wonder whether they teach something like that in vlsi classes...Kris

KarlS01
User Rank
Author
How computers used to do binary multiply and divide
KarlS01   12/7/2013 11:11:18 AM
NO RATINGS
Hi, Tom:  As you said, multiply is a series of additions -- but not dependent on the magnitude of the multiplier, only the number of 1 bits after making both operands positive by complementing if negative.

It is a shift and add sequence starting with the low order bit of the multiplier if it is a 1 add the multiplicand to the double wide product high order and shift right 1 into low order. if multiplier bit is zero, just shift product right one.

Repeat until higher multiplier bits are zero or shifts equal to multipl;ier width. If the high bits are all 0s, then just shift for the remaining word width.

Division was trial subtraction by subtracting the divisore fron the dividend, if the result was positive shift 1 into the quotient high bit else shift 0.  Remainder is left in the reg that held the high order dividend and the quotient in the low order.

If the signs of the dividend and divisor were different, complement at the end.

This is best I remember, maybe a few details missing. The shifts amounted to *2 and /2 and the add/subtract would wind up in the appropriate power of two positions.

I think the constant used in the compiler is 1/10 so they are multiplying by the reciprical of 10 to effectively divide by 10.

AZskibum
User Rank
Author
Re: Goldschmidt?
AZskibum   12/7/2013 11:52:18 AM
NO RATINGS
These are clever tricks, but why are you stuck on dealing with base 10, when ultimately you're implementing all the operations with shifts, adds & subtracts in base 2?

dtejada201
User Rank
Author
Fractional arithmetic
dtejada201   12/7/2013 1:13:51 PM
The way I look at this is as a modified form of Q15 arithmetic.  For starters, I can represent a fractional number as a 16 bit fixed point signed integer by the following relationship:

-32768 <--> -.5
 32768 <-->  .5

Thus .5 is 0x 7FFF (almost).  To get .1, I divide by 5 and .1 is 0x199A.  This is where the 0x199A factor comes from.   When I multiply 2 Q15 numbers, I get a 32 bit result a 32-bit Q31 result.  This means .25*.1 is as follows:

.25 => 0x4000
.1   => 0x199A

0x4000 * 0x199A => 0x06668000
0x666800 >> 16 is 0x0666 => which corresponds to .025

Hope this helps 

betajet
User Rank
Author
Fortran is lying to you
betajet   12/7/2013 2:49:25 PM
NO RATINGS
Floating-point numbers are not real numbers.  Real numbers obey the associative law of addition.  Floating-point numbers do not.  Try adding 1 to an accumulator 10^9 times with six-digit floating point.  Once the accumulator has reached 10^6, adding more ones doesn't change the accumulator, so the sum of 10^9 ones is 10^6 instead of 10^9.  If you add the 1's in groups of 10, and then add those sums in groups of 10, and so on, you'll get the correct value.  However, since the result depends on the order of addition, the floating-point numbers violate the associative law.  Don't expect floating-point to behave like real numbers without considering these effects.

Non-negative integers, OTOH, do behave mathemically like modulo 2^n numbers so you do get the correct result modulo 2^n.

I agree with the above poster regarding using a decimal radix.  Why not use base 2 like IEEE floating point or base 16 like IBM/360?

AZskibum
User Rank
Author
Re: Fortran is lying to you
AZskibum   12/7/2013 4:25:49 PM
NO RATINGS
Not only do floating point numbers not obey associativity, they also lack precision. Sure, if 24 bits of precision doesn't meet your needs, you can go to double precision, but both formats are wasteful when your doing arithmetic in hardware.

Fractional fixed point (often referred to as "Q" format) is efficient -- you choose exactly the precision you need, no less and no more -- and the bookkeeping exercise of keeping track of the radix point is not a big deal.

tom-ii
User Rank
Author
Re: Goldschmidt?
tom-ii   12/7/2013 5:43:27 PM
NO RATINGS
These are clever tricks, but why are you stuck on dealing with base 10, when ultimately you're implementing all the operations with shifts, adds & subtracts in base 2?

 

I didn't intend to imply that I was stuck with base 10.  Base 10 is just natural for us humans, and there are plenty of applications that use it a lot, especially when the end result is decimal math.  In this specific application, I am sending the computation engine decimal numbers, and expecting them in return.  It was worth my while to run down the rabbit hole to see if there was an immediately easy way to get it done this way.

 

 

tom-ii
User Rank
Author
Re: Fractional arithmetic
tom-ii   12/7/2013 5:45:42 PM
NO RATINGS

@dtejada201


I figured as much, but just hadn't actually sat down and worked it out.  Without knowing for a fact, I didn't want to spout complete nonsense. 

 

...

 

I spout enough nonsense as it is...

Page 1 / 3   >   >>


Datasheets.com Parts Search

185 million searchable parts
(please enter a part number or hit search to begin)
Radio
LATEST ARCHIVED BROADCAST

What are the engineering and design challenges in creating successful IoT devices? These devices are usually small, resource-constrained electronics designed to sense, collect, send, and/or interpret data. Some of the devices need to be smart enough to act upon data in real time, 24/7. Specifically the guests will discuss sensors, security, and lessons from IoT deployments.

Brought to you by:

Like Us on Facebook
Special Video Section
The LTC2380-24 is a versatile 24-bit SAR ADC that combines ...
In this short video we show an LED light demo to ...
02:46
Wireless Power enables applications where it is difficult ...
07:41
LEDs are being used in current luxury model automotive ...
With design sizes expected to increase by 5X through 2020, ...
01:48
Linear Technology’s LT8330 and LT8331, two Low Quiescent ...
The quality and reliability of Mill-Max's two-piece ...
LED lighting is an important feature in today’s and future ...
05:27
The LT8602 has two high voltage buck regulators with an ...
05:18
Silego Technology’s highly versatile Mixed-signal GreenPAK ...
The quality and reliability of Mill-Max's two-piece ...
01:34
Why the multicopter? It has every thing in it. 58 of ...
Security is important in all parts of the IoT chain, ...
Infineon explains their philosophy and why the multicopter ...
The LTC4282 Hot SwapTM controller allows a board to be ...
This video highlights the Zynq® UltraScale+™ MPSoC, and sho...
Homeowners may soon be able to store the energy generated ...
The LTC®6363 is a low power, low noise, fully differential ...
See the Virtex® UltraScale+™ FPGA with 32.75G backplane ...
Vincent Ching, applications engineer at Avago Technologies, ...