What are the characteristics of DSP algorithms? M. Smith and S. Daeninck

DSP Introduction, M. Smith, ECE, University of Calgary, Canada 2 Tackled today  What are the basic characteristics of a DSP algorithm?  Information on the TigerSHARC arithmetic, multiplier and shifter units  Practice examples of C++ to assembly code conversion

DSP Introduction, M. Smith, ECE, University of Calgary, Canada 3 IEEE Micro Magazine Article  How RISCy is DSP? Smith, M.R.; IEEE Micro, Volume: 12, Issue: 6, Dec. 1992, Pages:  Available on line via the library “Electronic web links”  Copy placed on ENCM515 Web site. Make sure you read it before midterm 1

DSP Introduction, M. Smith, ECE, University of Calgary, Canada 4 Characteristics of an FIR algorithm  Involves one of the three basic types of DSP algorithms FIR (Type 1), IIR (Type 2) and FFT (Type 3)  Representative of DSP equations found in filtering, convolution and modeling Multiplication / addition intensive Simple format within a (long) loop Many memory fetches of fixed and changing data Handle “infinite amount of input data” – need FIFO buffer when handling ON-LINE data All calculations “MUST” be completed in the time interval between samples

DSP Introduction, M. Smith, ECE, University of Calgary, Canada 5 FIR  Input Value must be stored in circular buffer  Filter operation must be performed on circular buffer  For operational efficiency X array = {X m-1, X m-2, X m-3, … X 1, X 0 } H array = {H m-1, H m-2, H m-3, … H 1, H 0 }

DSP Introduction, M. Smith, ECE, University of Calgary, Canada 6 FIR  X[n – 1] = NewInputValue Into last place of Input Buffer  Sum = 0;  For (count = 0 to N – 1) -- N of size 100+ Xvalue = X[count]; Hvalue = H[count]; Product = Xvalue * Hvalue; Sum = Sum + Product; Multiply and Accumulate -- MAC  NewOutputValue = Sum;  Update Buffer – The T-operation in the picture For (count = 1 to N – 1) -- Discard oldest X[0];  X[count – 1] = X[count];

DSP Introduction, M. Smith, ECE, University of Calgary, Canada 7 Comparing IIR and FIR filters Infinite Impulse Response filters – few operations to produce output from input for each IIR stage 3 – 7 stages Finite Impulse Response filters – many operations to produce output from input. Long FIFO buffer which may require as many operations As FIR calculation itself. Easy to optimize

DSP Introduction, M. Smith, ECE, University of Calgary, Canada 8 IIR -- Biquad  For (Stages = 0 to 3) Do S0 = X in * H5 + S2 * H3 + S1 * H4 Y out = S0 * H0 + S1 * H1 + S2 * H2 S2 = S1 S1 = S0  This second solution gives different result. The difference depends on how frequently samples are taken relative to how rapidly the signal changes CALCULATION SPEED IS DIFFEREBR Y out = S0 * H0 + S1 * H1 + S2 * H2 S2 = S1 S1 = S0 S0 = X in * H5 + S2 * H3 + S1 * H4 S0 S1 S2

DSP Introduction, M. Smith, ECE, University of Calgary, Canada 9 We need to know how the processor architecture affects speed of calculation  Register File and Compute Block  Volatile registers Data Summation Multiply and Accumulate (MAC)

DSP Introduction, M. Smith, ECE, University of Calgary, Canada 10 Register File and COMPUTE Units  Key Points DAB – Data Alignment Buffer (special for quad fetches NOT writes ) Each block can load/store 4x32bit registers in a cycle. 4 inputs to Compute block, but only 3 Outputs to Register Block. Highly parallel operations UNDER THE RIGHT CONDITIONS

DSP Introduction, M. Smith, ECE, University of Calgary, Canada 11 NOTE – DATA PATH ISSUES OF THE X-REGISTER FILE  1 output path (128 bit) TO memory  2 input paths FROM memory  4 output (64-bit) paths TO ALU, multiplier, shifter  3 input paths (64- bit) FROM ALU, multiplier, shifter  NUMBER OF PATHS HAS IMPLICATIONS ON WHAT THINGS CAN HAPPEN IN PARALLEL

DSP Introduction, M. Smith, ECE, University of Calgary, Canada 12 Register File - Syntax  Key Points Each Block has 32x32 bit Data registers Each register can store 4x8 bit, 2x16 bit or 1x32 bit words. Registers can be combined into dual or quad groups. These groups can store 8, 16, 32, 40 or 64 bit words. Register Syntax XSR3:2 -> 4x16 bit words XFR1:0 -> 1x40 bit float XR7 -> 1x32 bit word XBR3:0 -> 16x8 bit words Multiple of 4 Multiple of 2 XLR7:6 -> 1x64 bit word

DSP Introduction, M. Smith, ECE, University of Calgary, Canada 13 Register File – BIT STORAGE Both 32 bit and 64 bit registers

DSP Introduction, M. Smith, ECE, University of Calgary, Canada 14 Volatile Data Registers Non-preserved during a function call  Volatile registers – no need to save  24 Volatile DATA registers in each block XR0 – XR23 YR0 – YR23  2 ALU SUMMATION registers in each block XPR0, XPR1, YPR0, YPR1  5 MAC ACCUMULATE registers in each block XMR0 – XMR3, YMR0 – YMR3 XMR4, YMR4 – Overflow registers

DSP Introduction, M. Smith, ECE, University of Calgary, Canada 15 Arithmetic Logic Unit (ALU)  2x64 bit input paths  2x64 bit output paths  8, 16, 32, or 64 bit addition/subtraction - Fixed-point  32 or 64 bit logical operations - fixed-point  32 or 40 bit floating-point operations  Can do the same on Y ALU AT THE SAME TIME

DSP Introduction, M. Smith, ECE, University of Calgary, Canada 16 Sample ALU Instruction Example of 16 bit addition XYSR1:0 = R31:30 + R25:24 Performs “short” addition in X and Y Compute Blocks XR1.HH = XR31.HH + XR25.HH XR1.HL = XR31.HL + XR25.HL XR0.LH = XR30.LH + XR24.LH XR0.LL = XR30.LL + XR24.LL YR1.HH = YR31.HH + YR25.HH 8 additions at the same time YR1.HL = YR31.HL + YR25.HL YR0.LH = YR30.LH + YR24.LH.LH,.HH is my notation YR0.LL = YR30.LL + YR24.LL

DSP Introduction, M. Smith, ECE, University of Calgary, Canada 17 Sample ALU Instructions Fixed-Point long word, word, short word, byte (char) Floating-Point Single, double precision

DSP Introduction, M. Smith, ECE, University of Calgary, Canada 18 Pass is an interesting instruction  XR4 = R5 Assignment statement -- makes XR4  XR5  XR4 = PASS R5 Still makes XR4  XR5 BUT USES A DIFFERENT PATH THROUGH THE PROCESSOR Sets the ALU flags (so that they can be used for conditional tests) PASS instructions can be put in parallel with different instructions than assignments

DSP Introduction, M. Smith, ECE, University of Calgary, Canada 19 Example int x_two = 64, y_two = 16; int x_three = 128, y_three = 8; int x_four = 128, y_four = 8; int x_five = 64, y_five = 16; int x_odd = 0, y_odd = 0; int x_even = 0, y_even = 0; x_odd = x_five + x_three; x_even = x_four + x_two; y_odd = y_five + y_three; y_even = y_four + y_two; XR2 = 64;; XR3 = 128;; XR4 = 128;; XR5 = 64;; YR2 = 16;; YR3 = 8;; YR4 = 8;; YR5 = 16;; XYR1:0 = R5:4 + R3:2;; //XR1 = x_odd, XR0 = x_even //YR1 = y_odd, YR1 = y_even

DSP Introduction, M. Smith, ECE, University of Calgary, Canada 20 Multiplier  Operates on fixed, floating and complex numbers.  Fixed-Point numbers 32x32 bit with 32 or 64 bit results 4 (16x16 bit) with 4x16 or 4x32 bit results Data compaction inputs – 16, 32, 64 bits, outputs 16, 32 bit results  Floating-Point numbers 32x32 bit with 32 bit result 40x40 bit with 40 bit result  COMPLEX Numbers 32x32 bit with results stored in MR register FIXED-POINT ONLY

DSP Introduction, M. Smith, ECE, University of Calgary, Canada 21 Multiplier XR0 = R1*R2;; XR1:0 = R3*R5;; XMR1:0 = R3*R5;; //uses XMR4 overflow XR2 = MR3:2, XMR3:2 = R3*R5;; XR3:2 = MR1:0, XMR1:0 = R3*R5;; XFR0 = R1*R2;; // 32 bit mult – 24 bit mantissa XFR1:0 = R3:2*R5:4;; //40 bit MULTIPLY //32 bit mantissa // high precision float

DSP Introduction, M. Smith, ECE, University of Calgary, Canada 22 Multiplier --- with 32 or 16 bit results Note minor changes in syntax XR5:4 = R1:0*R3:2;;(16 bit results) XR7:4 = R3:2*R5:4;; (32 bit results) XMR1:0 += R3:2*R5:4;;(16 bit results) XMR3:0 += R3:2*R5:4;; (32 bit results) XR3:2 = MR3:2, XMR3:2 = R1:0*R5:4;; (16 bit results)  one instruction XR3:0 = MR3:0, XMR3:0 = R1:0*R5:4;; (32 bit results)

DSP Introduction, M. Smith, ECE, University of Calgary, Canada 23 Practice Examples Convert from “C” into assembly code – use volatile registers long int value = 6; long int number = 7; long int temp = 8; value = number * temp; BAD DESIGN OF FLOATING PT CODE WILL INTRODUCE MANY ERRORS RE-WRITE CODE TO FIX float value = 6; float number = 7; long int temp = 8; value = number * temp;

DSP Introduction, M. Smith, ECE, University of Calgary, Canada 24 Avoiding common design errors Convert from “C” into assembly code – use volatile registers float value = 6.0; (XFR12) float number = 7.0; (XFR13) long int temp = 8; (XR18) value = number * temp; // Treat as value = number * (float) temp; XR12 = 6.0;; //valueF12 // Sets XFR12  6.0 XR13 = 7.0;;//numberF13 XR18 = 8;; //tempR18 //(float) tempR18 XFR18 = FLOAT R18;; //valueF12 = numberF13 * tempF18 XFR12 = R13 * R18;;

DSP Introduction, M. Smith, ECE, University of Calgary, Canada 25 Shifter Instructions 2x64 bit input paths and 2x64 bit output paths 32, or 64 bit shifting operations 32 or 64 bit manipulation operations

DSP Introduction, M. Smith, ECE, University of Calgary, Canada 26 Examples --- shift only integers There is a FSCALE for floats (not shifter) long int value = 128; long int high, low; low = value >> 2; high = value << 2; POSITIVE VALUE – LEFT SHIFT NEGATIVE VALUE – RIGHT SHIFT XR0 = 2;; XR1 = -XR2;; XR2 = 128;; //low = value >> 2; XR23 = ASHIFT XR2 BY –2;; Or XR23 = ASHIFT XR2 BY XR1;; //high = value << 2; XR22 = ASHIFT XR2 BY 2;; Or XR22 = ASHIFT XR2 BY XR0;;

DSP Introduction, M. Smith, ECE, University of Calgary, Canada 27 ALU instructions  Under the RIGHT conditions can do multiple operations in a single instruction. Instruction line has 4x32 bit instruction slots. Can do 2 Compute and 2 memory operations. This is actually 4 Compute operations counting both compute blocks. One instruction per unit of a compute block, ie. ALU. Since there are only 3 result buses, only one unit (ALU or Multiplier) can use 2 result buses.  Not all instructions can be used in parallel.

DSP Introduction, M. Smith, ECE, University of Calgary, Canada 28 Dual Operation Examples  FRm = Rx + Ry, FRn = Rx – Ry;; Note that uses 4(8) different registers and not 6(12)  FR4 = R2 + R1, FR5 = R2 - R1;; The source registers used around the + and – must be the same. Very useful in FFT code Can be floating(single or extended precision) or fixed(32 or 64 bit) add/subtract.  Rm = MRa, MRa += Rx * Ry;; MRa must be the same register(s) (MR1:0 or MR 3:2) Can be used on fixed(32 or 64 bit results) COMPLEX numbers (on 16 bit values)  Rm = MRa, MRa += Rx ** Ry;;

DSP Introduction, M. Smith, ECE, University of Calgary, Canada 29 Practice Examples Convert to assembly code Convert from “C” into assembly code – use volatile registers long int value = 6; long int number = 7; long int temp = 8; value = number * temp; #define value_XR12 XR12 Assignment operation value_XR12 = 6;; Multiply operations value_XR12 = R5 * R6;

DSP Introduction, M. Smith, ECE, University of Calgary, Canada 30 Avoiding common design errors Convert to assembly code float value = 6.0; float number = 7.0; long int temp = 8; value = value + 1; number = number + 2; temp = value + number;

DSP Introduction, M. Smith, ECE, University of Calgary, Canada 31 Tackled today  What are the basic characteristics of a DSP algorithm?  Information on the TigerSHARC arithmetic, multiplier and shifter units  Practice examples of C++ to assembly code conversion