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SHARC Processor Characteristics Number Representations When = BUT 2 *2 != 4
M. R. Smith, Electrical and Computer Engineering University of Calgary, Alberta, Canada
ucalgary.ca

2. To tackled Number Representations are varied
Make sure you understand them
Can solve many coding errors by recognizing improper use of number representations
SHARC default number representation for integers is not what is expected.
Understanding Number Representations allows for extra speed in that 1 in 1000 situation
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Number Representations -- SHARC ADSP21061 Copyright M. Smith --

3. Number Representations
Number representations are important.
This is a talk about the number representations on the Analog Devices ADSP SHARC
Processor has “C-like” syntax for assembly code
Both single cycle integer and float operations
32-bit registers (integer and float)
For more information see the article Smith, M. R., "Quirks and SHARCs -- Issues in programming the Analog Devices SHARC processor. When = 2 but != 4", Circuit Cellar, March 2001.
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Number Representations -- SHARC ADSP21061 Copyright M. Smith --

4. Recap -- Bit patterns in memory
Bit values stored in memory
Can represent what you like
hash table, ascii characters, signed and unsigned integer numbers (various precisions), floating point numbers etc.
Certain number representations more easily supported by the processor for various operations than others.
On SHARC bit integers and FP, also 40-bit FP (extended FP).
5/1/2019
Number Representations -- SHARC ADSP21061 Copyright M. Smith --

5. Example -- Eight Bit Values
Unsigned 8-bit integers
Range , resolution 1
e.g. 0x00 = 0, 0x10 = 16, 0x7F = 127
0x80 = 128, 0x81 = 129, 0x90 = ????, 0xC0 = ????
0xF0 = ????, 0xFE = 254, 0xFF = 255
Signed 8-bit integers -- 2’s complement
Range -128 to + 127, resolution 1
e.g. 0x00 = 0, 0x10 = +16, 0x7F = +127
0x80 = -128, 0x81 = = -127, 0x90 = ???
0xF0 = ????, 0xFE = -2, 0xFF = -1
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Number Representations -- SHARC ADSP21061 Copyright M. Smith --

6. Floating Point in Binary Representation
20 (decimal) = 0x14 hex = % (binary)
= %
Normalize binary -- express as %1.frac * 2N
% = % * 24
6 = % = % * 22
Sign = 0 Fraction part = Biased Exponent = 129 = %
Stored as FP Number
etc
0x40C =
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Number Representations -- SHARC ADSP21061 Copyright M. Smith --

7. Display Program Code -- Float
32-bit registers
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Number Representations -- SHARC ADSP21061 Copyright M. Smith --

8. Code displayed in Mixed Mode
No such instruction as F4 = Only R4 = WARNING --- F4 = 2 is the same as R4 = 2 and is DIFFERENT F4 = 2.0
Note how FP looks like VERY LARGE integer
32 bit registers 40 bit display Ultra High precision FP
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Number Representations -- SHARC ADSP21061 Copyright M. Smith --

9. Need to learn to recognize
What do “integers” look like when they are displayed as “floats”
What do “floats” look like when displayed as “integers”
Happens when you pass a pointer to the start of an array and then treat the array incorrectly
I consider the following a BUG IN ASSEMBLER
F4 = 6 is actually the same as F4 = 3 * 10-45
FN = value does not exist -- only RN = value
Make sure that you add the decimal point!!!!
var array_of_FLOATS[] = { 2.8, 3, 3.2, 3.4};
NOT INTENDED AS A
VERY SMALL VALUE
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Number Representations -- SHARC ADSP21061 Copyright M. Smith --

10. Display Program Code -- Integer
32 BIT registers
Top 32 bits means something
Note how integers look like VERY SMALL floats -- note also wrong values
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Number Representations -- SHARC ADSP21061 Copyright M. Smith --

11. Unexpected default integer representation
68k processor
Default operations
Signed and unsigned integer representation
21k processor / Blackfin / TigerSHARC
Signed and unsigned integer representation of “fractional” values
Signed and unsigned integer “need to be switched on”
See difference in multiplication
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Number Representations -- SHARC ADSP21061 Copyright M. Smith --

12. Code displayed in Mixed Mode Q9 – What happens with Blackfin
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Number Representations -- SHARC ADSP21061 Copyright M. Smith --

13. Proper Integer Coding sequence
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Number Representations -- SHARC ADSP21061 Copyright M. Smith --

14. Bit meaning in 8-bit signed fractional number
^ ACTS AS IF “BINARY POINT” HERE Binary Pattern % =
-1 * * * * * * * * 2-7
Decimal Calculation = ( 0x93 / 128) = ( 0x80 + 0x13 ) / = ( ) / 128
= / 128
5/1/2019
Number Representations -- SHARC ADSP21061 Copyright M. Smith --

15. Signed fractional
Integer interpreted with a binary point just after the sign bit
Using 32-bit values
Smallest value -1.0
Largest almost = = ^-31
Steps (accuracy) 2^-31
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Number Representations -- SHARC ADSP21061 Copyright M. Smith --

16. 68k equivalence -- 8-bit example
Standard number format
Range -128 to + 127, resolution 1
0x0A+ 0x01 = 0x0B
% % = %
In any given DSP algorithm it could be useful to scale input values so that we have an alternative number format where binary point is effectively placed between bit #3 and #4
Range -8 to 7 7/8, resolution 1/8
0xA0 + 0x10 = 0xB0 (Means 0xA.0, 0x1.0, 0xB.0)
% % = %
Addition supported in both number formats
5/1/2019
Number Representations -- SHARC ADSP21061 Copyright M. Smith --

17. 68k equivalence -- 8-bit example
Standard number format
Range -128 to + 127, resolution 1
0x0A * 0x01 = 0x0A
% * % = %
Alternative number format where binary point is placed between bit #3 and #4
Range -8 to 7 7/8, resolution 1/8
0xA.0 * 0x1.0 = 0x??
% * % = %
Must now adjust by >> 8 to get correct answer. When SHARC in SSF format, the scaling occurs automatically
5/1/2019
Number Representations -- SHARC ADSP21061 Copyright M. Smith --

18. Equivalent decimal calculation
As done in grade 6 *
Perform 75 * 125 then adjust for 5 decimal places.
-9375 then adjust to give
68k multiplication was
0xA.0 * 0x1.0
Perform 0xA0 * 0x10 then adjust for hex places
0xA00 then adjust to give 0xA.00
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Number Representations -- SHARC ADSP21061 Copyright M. Smith --

19. Displayed as “signed fractional”
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Number Representations -- SHARC ADSP21061 Copyright M. Smith --

20. SHARC DIVISION APPEARS WEIRD TOO
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Number Representations -- SHARC ADSP21061 Copyright M. Smith --

21. Actual SHARC division operations Note the parallel instructions
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Number Representations -- SHARC ADSP21061 Copyright M. Smith --

22. Division is slow Integer division on 68K -- 70 cycles
60000 / 3 takes 70 cycles
60000 / 2 takes 70 cycles
Integer shift takes much less
60000 / 2 = >> 1
ASR #1, D0 (with D0 = 60000) takes 4 cycles
ASHIFT D0 BY -1 takes 1 cycle
Can we find an equivalent operation for floating point scaling (by 2, 4, 8, 16 etc.)?
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Number Representations -- SHARC ADSP21061 Copyright M. Smith --

23. Signed Fractional -- ASHIFT of integer
Works here but that’s cheating since SF format is an floating point interpretation of an integer format
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Number Representations -- SHARC ADSP21061 Copyright M. Smith --

24. Binary Pattern of TRUE floats
SIGN BIT
EXPONENT BITS
FRACTIONAL BITS
Floating point division is often SLOW
DIVIDE BY 2, 4, 8, 16 fast with integers
CAN ALSO MAKE FAST WITH FLOATS If you understand number representations
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Number Representations -- SHARC ADSP21061 Copyright M. Smith --

25. Fast scaling -- Floats as Integers
Differ
in value
by 4.0
Differ
in BEXP
by 2
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Number Representations -- SHARC ADSP21061 Copyright M. Smith --

26. Complete Fast Scaling
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Number Representations -- SHARC ADSP21061 Copyright M. Smith --

27. Nothing but a party trick!
F8 = ;
F0 = 4.0;
F1 = F0 * F8;
F2 = 2.0;
F3 = F3 * F8;
F4 = 0.0;
F5 = F4 * F8;
Since this processor has single cycle multiply operation
R8 = -4;
F0 = 4.0;
F1 = SCALEB F0 BY R8;
F2 = 2.0;
F3 = SCALEB F2 BY R8;
F4 = 0.0;
F5 = SCALEB F4 BY R8;
Works just like our code
Advantage – this is a COMPUTE operation and NOT a MAC operation
5/1/2019
Number Representations -- SHARC ADSP21061 Copyright M. Smith --

28. Learnt today Number Representations are varied
Make sure you understand them
Can solve many coding errors by recognizing improper use of number representations -- Limitation in SHARC assembler for F4 =
Signed Fractional is default SHARC integer representation
Understanding Number Representations allows for that 1 in 1000 situation when somebody at a party likes to play with DSP processors.
5/1/2019
Number Representations -- SHARC ADSP21061 Copyright M. Smith --