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Efficient search space exploration and feature description based on the floating point arithmetic of FPGA. 李海娥. 1 Introduction. IP reuse; parameterized IP( number,pipeline,resource ) meet the needs of many different designs and reduce design time and risk); Power

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slide1
Efficient search space exploration and feature description based on the floating point arithmetic of FPGA

李海娥

1 introduction
1 Introduction
  • IP reuse;
  • parameterized IP(number,pipeline,resource)

meet the needs of many different designs and reduce design time and risk);

  • Power
  • Floating point arithmetic

Tianjin University

2 the purpose
2 the purpose

How to set the parameters of the floating point to meet requirements:

  • Meet the function
  • Save resources
  • Running time
  • Reduce the power dissipation

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3 the method
3 the method
  • Fully pipelined single precision floating point multiply and adder;
  • Different parameters(LUTS or DSP, latency, ports);
  • Latency:describes the number of clock cycles between an operand input and the result output.

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the design architecture
the design architecture

Figure 1. Data-path designs for MAC c=c+ai*bi, i=1..N.

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a signal operation
A Signal operation

One AM

One ADD

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b combinations
B combinations

1 resources(slice luts、registers)

2 power

3 the maximum frequency of the combinations is less then the related AM and ADD

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the two optimization models
the two optimization models
  • design space of the system includes:

power consumption

resource usage

the speed

The latency

  • P=fp* ( PAM + PADD) /(100MHZ)
  • L=m* LAM +n* LADD
  • R=m* RAM +n* RADD
  • F< =min (FAM, FADD)
  • Running time constraints

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running time constraints
Running time constraints

C=N/zm-1 + Lm + La *(log2za+1) + La*(log2La+1)

za=zm=2z

C – fp*T<=0

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3 1 1 linear models
3.1.1 linear models

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3 1 2 modeling based on regression analysis
3.1.2 Modeling based on regression analysis

Modeling based on regression analysis

  • x=intvar(1);
  • y=intvar(1);
  • z=intvar(1);
  • fp=sdpvar(1);
  • f=0.01*fp*1.75*(2^z)*(x+11)+0.01*fp*1.04545*(2^z)*(y+15.08696);
  • F=[0<=fp<=min(36.28571*(x+2.12598),30.78182*(y+2.30597)),x+(z+1)*y+2^(10-z)+y*(log(y)/log(2)+1)<3*fp,(2^z)*639.14286+(2^z)*2.69752*(y+146.01506)<=6000,(2^z)*92*(x+0.06677)+(2^z)*47.67273*(y+0.18993)<=6000,2<=y<=12,2<=x<=8,0<=z<=4];
  • % options = sdpsettings('verbose',1,'solver','bmibnb');
  • solvesdp(F,f);
  • disp(double(f));
  • disp(double(x));
  • disp(double(y));
  • disp(double(2^z));
  • disp(double(fp));
  • disp(double(1000/fp));

The number of the floating

point multiply and adder

2z

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3 2 the polynomial models
3.2 the polynomial models

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3 2 1 modeling based on simulated annealing
3.2.1 Modeling based on Simulated annealing
  • Parameters x[2,8,0],y[2,12,0],z[0,4,0],rf[0,500];
  • MinFunction 0.01*rf*(2^z)*(93.73807-89.77205*x+40.53269*x^2-8.26548*x^3+0.7934*x^4-0.02916*x^5)+0.01*rf*(2^z)*(-10.71794+24.35363*y-7.40564*y^2+1.08772*y^3-0.07455*y^4+ 0.00192*y^5);
  • (2^z)*(-3384.85647+5039.78552*x-2312.30642*x^2+494.61355*x^3-50.02651*x^4+ 1.93333*x^5)+(2^z)*(122.23825+239.21494*y-68.6165*y^2+8.59996*y^3-0.47702*y^4+ 0.00944*y^5)<=6000;
  • (2^z)*(2223.14264-2720.01336*x+1270.69305*x^2-262.053*x^3+25.30682*x^4-0.93333*x^5) +(2^z)*(-219.77249+252.99128*y-73.2325*y^2+12.26375*y^3-0.9434*y^4+0.02675*y^5)<=6000;
  • x+(z+1)*y+2^(10-z)+y*(log(y)/log(2)+1)<=1.0*rf;
  • rf<=min(-54.8162+151.86111*x-42.53182*x^2+9.09894*x^3-1.06665*x^4+0.04994*x^5,88.24364-24.82321*y+28.04692*y^2-5.27886*y^3+0.43151*y^4-0.01299*y^5);

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4 the verification
4 the verification
  • The verification is based on the dot product:
  • 1024*1024

1 Slice luts<=9000;

Slice registers<=9000;

running time constraints:

0.9ms,1.0ms,1.1ms……

2 Slice luts<=6000;

Slice registers<=6000;

running time constraints:

0.9ms,1.0ms,1.1ms……

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result 1
Result 1

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result 2
Result 2

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