GPU Computing on Business
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- れいが りゅうとう
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1 GPU Computing on Business 2010 Numerical Technologies Incorporated 1
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10 GPU Computing $$$ Revenue Total Cost low BEP Quantity 10
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16 GPU Computing $$$ Revenue Total Cost high BEP Quantity 16
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18 CUDA C/C++ Perl PHP Python Java C# 18
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20 GPU 20
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25 (NtParallel DLL) NtParallel DLL NVIDIA Tesla driver 25
26 CUDA (NtParallel DLL) 26
27 CUDA (NtParallel DLL) NtParallel DLL NVIDIA Tesla driver 27
28 GPU nt_parallel_for bool nt_parallel_for( for (string), for (int), for 1(void*), for 2(void*), )... 28
29 // Black Scholes Option Formula Batch Processing Demo. void batch_black_scholes_pricer( int array_size, double* o_data, double* r_data, double* sigma_data, double* s_data, double* k_data, double* t_data ) { // for-loop program. for (int i = 0; i < array_size; ++i) { double R = r_data[i]; double Sigma = sigma_data[i]; double S = s_data[i]; double K = k_data[i]; double T = t_data[i]; double rt = R * T; double sigmasqrtt = Sigma * sqrt(t); double d = (log(s / K) + rt) / sigmasqrtt + sigmasqrtt * 0.5; o_data[i] = S * NormDist(d) - K * NormDist(d - sigmasqrtt) * exp(- rt); } // now you have output in o_data. } 29
30 for // Black Scholes Option Formula Batch Processing Demo. void batch_black_scholes_pricer( int array_size, double* o_data, double* r_data, double* sigma_data, double* s_data, double* k_data, double* t_data ) { // for-loop program. for (int i = 0; i < array_size; ++i) { double R = r_data[i]; double Sigma = sigma_data[i]; double S = s_data[i]; double K = k_data[i]; double T = t_data[i]; double rt = R * T; double sigmasqrtt = Sigma * sqrt(t); double d = (log(s / K) + rt) / sigmasqrtt + sigmasqrtt * 0.5; o_data[i] = S * NormDist(d) - K * NormDist(d - sigmasqrtt) * exp(- rt); } // now you have output in o_data. } 30
31 for ( )... for (int i = 0; i < array_size; ++i) { double R = r_data[i]; double Sigma = sigma_data[i]; double S = s_data[i]; double K = k_data[i]; double T = t_data[i]; double rt = R * T; double sigmasqrtt = Sigma * sqrt(t); double d = (log(s / K) + rt) / sigmasqrtt + sigmasqrtt * 0.5; o_data[i] = S * NormDist(d) - K * NormDist(d - sigmasqrtt) * exp(- rt); } string code = [](int i, double R, double Sigma, double S, double K, double T) => double {! double rt = R * T;! double sigmasqrtt = Sigma * sqrt(t);! double d = (log(s / K) + rt) / sigmasqrtt + sigmasqrtt * 0.5;! return S * NormDist(d) - K * NormDist(d - sigmasqrtt) * exp(- rt); } ;... 31
32 // Black Scholes Option Formula Batch Processing Demo. void batch_black_scholes_pricer( int array_size, double* o_data, double* r_data, double* sigma_data, double* s_data, double* k_data, double* t_data ) { // for-loop program. string code = [](int i, double R, double Sigma, double S, double K, double T) => double {! double rt = R * T;! double sigmasqrtt = Sigma * sqrt(t);! double d = (log(s / K) + rt) / sigmasqrtt + sigmasqrtt * 0.5;! return S * NormDist(d) - K * NormDist(d - sigmasqrtt) * exp(- rt); } ; // call the GPU. nt_parallel_for(code, array_size, o_data, r_data, sigma_data, s_data, k_data, t_data); // now you have output in o_data. } 32
33 Excel GPU code is here! 33
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35 GPU CPU GPU 35
36 NVIDIA NVIDIA Tesla driver NtParallel DLL Other company s driver SSE, AVX 36
37 Scientific Wall St. 1. Mandelbrot 2. Kirkwood Gaps 3. Wavelet Analysis 4. Binomial Tree Option Model 5. Black Scholes Option Model 6. Housing Loan Calculation Boring Accounting Stuff 37
38 : Mandelbrot 38
39 98 : Kirkwood Gaps 39
40 29 : Wavelet Analysis 40
41 7 : Binomial Tree Option Model 41
42 5 : Black Scholes Option Model 42
43 40 : 35 43
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46 GPU Computing 46
47 GPU API nvcc 47
48 nt_parallel_for shared nothing CUDA 48
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52 Relative Performance vs. for-loop Iterations Acceleration Ratio Iterations 52
53 Relative Performance vs. for-loop Iterations Acceleration Ratio Iterations
54 Relative Performance vs. for-loop Iterations Acceleration Ratio Iterations 54
55 Relative Performance vs. for-loop Iterations Acceleration Ratio Iterations C/C++ C#,Java,Perl,Python GPU 55
56 56
57 for-loop Iterations Tesla GPU
58 Complexity Ops/Bytes 58
59 2 Complexity for-loop Iterations 59
60 Complexity Iterations GPU Complexity x5 x10 x50 faster for-loop Iterations 60
61 2 8 Complexity 10 GPU x5 x10 x50 faster GPU has advantage CPU has advantage for-loop Iterations 61
62 Complexity x5 x10 x50 faster Housing Loan for-loop Iterations 62
63 x10 Complexity x5 x10 x50 faster GPU has advantage Break Even Point Housing Loan CPU has advantage for-loop Iterations 63
64 Complexity x5 x10 x50 faster Binomial Tree for-loop Iterations 64
65 GPU Complexity x5 x10 x50 faster GPU resource exhausted Binomial Tree for-loop Iterations 65
66 Complexity x5 x10 x50 faster Mandelbrot Kirkwood Housing Loan Wavelet Binomial Tree Black Scholes for-loop Iterations 66
67 GPU x5: Black Scholes x40: Housing Loan 67
68 Complexity... string code = [] (int i, double annualizedrate, int term, double monthlypayment) => double {! const int t = term;! const double m = monthlypayment;! const double monthlydf = 1.0 / (1.0 + annualizedrate / 12.0);! int elapsedmonth;! double val = 0.0;! double df = 1.0;! for (elapsedmonth = 0; elapsedmonth < t; elapsedmonth = elapsedmonth + 1) {!! df = df * monthlydf;!! val = val + m * df;! }! return val; } ;... x40: Housing Loan... string code = [](int i, double R, double Sigma, double S, double K, double T) => double {! double rt = R * T;! double sigmasqrtt = Sigma * sqrt(t);! double d = (log(s / K) + rt) / sigmasqrtt + sigmasqrtt * 0.5;! return S * NormDist(d) - K * NormDist(d - sigmasqrtt) * exp(- rt); } ;... x5: Black Scholes 68
69 Q. GPU Complexity Iterations 69
70 A. IFRS ECF Complexity Housing Loan 70
71 Complexity x5 x10 x50 faster Mandelbrot Kirkwood Housing Loan Wavelet Binomial Tree Black Scholes Annuities, IFRS ECF depletion models (estimated) for-loop Iterations 71
72 Iterations x10 GPU Complexity x5 x10 x50 faster GPU has advantage Break Even Point Mandelbrot Kirkwood Housing Loan Wavelet Binomial Tree Black Scholes Annuities, IFRS ECF depletion models CPU has advantage (estimated) for-loop Iterations 72
73 Rule of Thumb... 73
74 nt_parallel_for 74
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OpenMP (1) 1, 12 1 UNIX (FUJITSU GP7000F model 900), 13 1 (COMPAQ GS320) FUJITSU VPP5000/64 1 (a) (b) 1: ( 1(a))
OpenMP (1) 1, 12 1 UNIX (FUJITSU GP7000F model 900), 13 1 (COMPAQ GS320) FUJITSU VPP5000/64 1 (a) (b) 1: ( 1(a)) E-mail: {nanri,amano}@cc.kyushu-u.ac.jp 1 ( ) 1. VPP Fortran[6] HPF[3] VPP Fortran 2. MPI[5]