Approximate Program Synthesis

Transcription

1 Approximate Program Synthesis James Bornholt Emina Torlak Luis Ceze Dan Grossman University of Washington

2 Writing approximate programs is hard Precise Implementation

3 Writing approximate programs is hard Precise Implementation

4 Writing approximate programs is hard Precise Implementation Desired Quality

5 Writing approximate programs is hard Precise Implementation Desired Quality Approximate Compiler ACCEPT, Chisel, iact, ExpAX,

6 Writing approximate programs is hard Precise Implementation Desired Quality Approximate Compiler ACCEPT, Chisel, iact, ExpAX, Approximate Program

7 Writing approximate programs is hard program annotations specific approximation opportunities Precise Implementation Desired Quality Approximate Compiler ACCEPT, Chisel, iact, ExpAX, Approximate Program target language quality metric global optimization

8 Synthesis: write programs automatically Programs Semantics

9 Synthesis: write programs automatically Target Behavior f(x) =4x +1 Programs Semantics

10 Synthesis: write programs automatically Target Behavior f(x) =4x +1 Programs Semantics

11 Synthesis: write programs automatically 4*x + 1 Target Behavior f(x) =4x +1 Programs Semantics

12 Synthesis: write programs automatically 4*x + 1 Target Behavior f(x) =4x +1 Programs Semantics

13 Synthesis: write programs automatically 4*x + 1 (x<<2) + 1 Target Behavior f(x) =4x +1 x + x + x + x + 1 Programs Semantics

14 Synthesizing approximate programs 4*x + 1 (x<<2) + 1 Target Behavior f(x) =4x +1 x + x + x + x + 1 Programs Semantics

15 Synthesizing approximate programs 4*x + 1 (x<<2) + 1 Approximate Behavior Target Behavior f(x) =4x +1 x + x + x + x + 1 Programs Semantics

16 Synthesizing approximate programs 4*x + 1 (x<<2) + 1 x<<2 Approximate Behavior Target Behavior f(x) =4x +1 x + x + x + x + 1 Programs Semantics

17 Synthesizing approximate programs 4*x + 1 (x<<2) + 1 x<<2 apple =4 apple = 10 apple =6 apple =8 Approximate Behavior Target Behavior f(x) =4x +1 x + x + x + x + 1 Programs Semantics

18 Synthesizing approximate programs 4*x + 1 (x<<2) + 1 x<<2 apple =4 apple = 10 apple =6 apple =8 Approximate Behavior Target Behavior f(x) =4x +1 x + x + x + x + 1 Programs Semantics

19 Synthesis automates approximation program annotations specific approximation opportunities Precise Implementation Desired Quality Approximate Compiler ACCEPT, Chisel, iact, ExpAX, Approximate Program target language quality metric global optimization

20 Synthesis automates approximation program annotations specific approximation opportunities Precise Implementation Desired Quality quality metric Approximate Program Synthesis global optimization Approximate Program target language

21 Synthesis automates approximation Precise Implementation Desired Quality Approximate Program Synthesis program annotations specific approximation opportunities global optimization Approximate Program target language quality metric

22 Existing synthesizers don t scale enough Approximate benchmarks fft kmeans inversek2j sobel 8p, c. dist(p, c) f(p, c) < 50% Alur et al. Syntax-Guided Synthesis. FMCAD 2013.

23 Existing synthesizers don t scale enough Approximate benchmarks fft kmeans inversek2j sobel Off-the-shelf synthesizers Symbolic Stochastic Brute-force 8p, c. dist(p, c) f(p, c) < 50% Alur et al. Syntax-Guided Synthesis. FMCAD 2013.

24 Existing synthesizers don t scale enough Approximate benchmarks fft kmeans inversek2j sobel Off-the-shelf synthesizers Symbolic Stochastic Brute-force float dist(float p[3], float c[3]) { float r = 0; r += (p[0] - c[0])*(p[0] - c[0]); r += (p[1] - c[1])*(p[1] - c[1]); r += (p[2] - c[2])*(p[2] - c[2]); float ret = sqrt(r); return ret; } float f(float p[3], float c[3]) {?? } assert 8p, c. dist(p, c) f(p, c) < 50% Alur et al. Syntax-Guided Synthesis. FMCAD 2013.

25 Existing synthesizers don t scale enough Approximate benchmarks fft kmeans inversek2j sobel Off-the-shelf synthesizers Symbolic Stochastic Brute-force float dist(float p[3], float c[3]) { float r = 0; r += (p[0] - c[0])*(p[0] - c[0]); r += (p[1] - c[1])*(p[1] - c[1]); r += (p[2] - c[2])*(p[2] - c[2]); float ret = sqrt(r); return ret; } float f(float p[3], float c[3]) {?? } + - * / & ^ << >> assert 8p, c. dist(p, c) f(p, c) < 50% Alur et al. Syntax-Guided Synthesis. FMCAD 2013.

26 Existing synthesizers don t scale enough Approximate benchmarks fft kmeans inversek2j sobel Off-the-shelf synthesizers Symbolic Stochastic Brute-force float dist(float p[3], float c[3]) { float r = 0; r += (p[0] - c[0])*(p[0] - c[0]); r += (p[1] - c[1])*(p[1] - c[1]); r += (p[2] - c[2])*(p[2] - c[2]); float ret = sqrt(r); return ret; } float f(float p[3], float c[3]) {?? } + - * / & ^ << >> assert 8p, c. dist(p, c) f(p, c) < 50% Reference program Program being synthesized Alur et al. Syntax-Guided Synthesis. FMCAD 2013.

27 Existing synthesizers don t scale enough Approximate benchmarks fft kmeans inversek2j sobel Off-the-shelf synthesizers Symbolic Stochastic Brute-force float dist(float p[3], float c[3]) { float r = 0; r += (p[0] - c[0])*(p[0] - c[0]); r += (p[1] - c[1])*(p[1] - c[1]); r += (p[2] - c[2])*(p[2] - c[2]); float ret = sqrt(r); return ret; } float f(float p[3], float c[3]) {?? } + - * / & ^ << >> assert 8p, c. dist(p, c) f(p, c) < 50% Reference program Program being synthesized Alur et al. Syntax-Guided Synthesis. FMCAD 2013.

28 Existing synthesizers don t scale enough float dist(float p[3], float c[3]) { float r = 0; r += (p[0] - c[0])*(p[0] - c[0]); r += (p[1] - c[1])*(p[1] - c[1]); r += (p[2] - c[2])*(p[2] - c[2]); float ret = sqrt(r); return ret; } float f(float p[3], float c[3]) {?? } + - * / & ^ << >> Programs assert 8p, c. dist(p, c) f(p, c) < 50% Reference program Program being synthesized

29 Existing synthesizers don t scale enough float dist(float p[3], float c[3]) { float r = 0; r += (p[0] - c[0])*(p[0] - c[0]); r += (p[1] - c[1])*(p[1] - c[1]); r += (p[2] - c[2])*(p[2] - c[2]); float ret = sqrt(r); return ret; } float f(float p[3], float c[3]) {?? } + - * / & ^ << >> Programs assert 8p, c. dist(p, c) f(p, c) < 50% Reference program Program being synthesized

30 Existing synthesizers don t scale enough programs Programs float dist(float p[3], float c[3]) { float r = 0; r += (p[0] - c[0])*(p[0] - c[0]); r += (p[1] - c[1])*(p[1] - c[1]); r += (p[2] - c[2])*(p[2] - c[2]); float ret = sqrt(r); return ret; } float f(float p[3], float c[3]) {?? } + - * / & ^ << >> assert 8p, c. dist(p, c) f(p, c) < 50% Reference program Program being synthesized

31 Use reference programs to guide synthesis programs Programs float dist(float p[3], float c[3]) { float r = 0; r += (p[0] - c[0])*(p[0] - c[0]); r += (p[1] - c[1])*(p[1] - c[1]); r += (p[2] - c[2])*(p[2] - c[2]); float ret = sqrt(r); return ret; } float f(float p[3], float c[3]) {?? } + - * / & ^ << >> assert 8p, c. dist(p, c) f(p, c) < 50% Reference program Program being synthesized

32 Use reference programs to guide synthesis programs Programs float dist(float p[3], float c[3]) { float r = 0; r += (p[0] - c[0])*(p[0] - c[0]); r += (p[1] - c[1])*(p[1] - c[1]); r += (p[2] - c[2])*(p[2] - c[2]); float ret = sqrt(r); return ret; } float f(float p[3], float c[3]) {?? } + - * / & ^ << >> assert 8p, c. dist(p, c) f(p, c) < 50% Reference program Program being synthesized

33 Use reference programs to guide synthesis programs Programs float dist(float p[3], float c[3]) { float r = 0; r += (p[0] - c[0])*(p[0] - c[0]); r += (p[1] - c[1])*(p[1] - c[1]); r += (p[2] - c[2])*(p[2] - c[2]); float ret = sqrt(r); return ret; } float f(float p[3], float c[3]) {?? } + - * / & ^ << >> assert 8p, c. dist(p, c) f(p, c) < 50% Reference program Program being synthesized

34 Use reference programs to guide synthesis programs Programs float dist(float p[3], float c[3]) { float r = 0; r += (p[0] - c[0])*(p[0] - c[0]); r += (p[1] - c[1])*(p[1] - c[1]); r += (p[2] - c[2])*(p[2] - c[2]); float ret = sqrt(r); return ret; } float f(float p[3], float c[3]) {?? } + - * / & ^ << >> assert 8p, c. dist(p, c) f(p, c) < 50% Reference program Program being synthesized

35 Synthesis produces good approximations Spec: < 50% average error Benchmark Speedup Error fft s % fft c % dist % sobel x % sobel y % inversek2j % inversek2j %

36 Synthesis produces good approximations Spec: < 50% average error Benchmark Speedup Error fft s % fft c % dist % sobel x % sobel y % inversek2j % inversek2j % Missed compiler optimisation optimization

37 Synthesis produces clever approximations float dist_approx(int a[3], int b[3]) { int c1 = abs(b[0] - a[0]); int c2 = abs(b[1] - a[1]); int c3 = abs(a[2] - b[2]); int c4 = c1 c2; int c5 = abs(c3 > c4? c3 : c4); return (float)c5; } 3D Euclidean distance 1.6 faster, 14.9% error

38 Thanks! Precise Implementation Desired Quality Approximate Program Synthesis Approximate Program