From 4e96e8724d9368e6bd8c868774a8224d15f70577 Mon Sep 17 00:00:00 2001 From: Eugene Lin Date: Thu, 10 Mar 2022 22:31:37 +0800 Subject: [PATCH 1/7] Finish 5_moving_average.c In this assignment, I wrote two versions of moving average one in O(NM) and the other is in O(N). I use result of O(NM) to test the result of O(N) because I think the method to write O(NM) is easier and unlikely to have bug in there. --- 5_moving_average.c | 73 ++++++++++++++++++++++++++++++++++++++++++---- 1 file changed, 67 insertions(+), 6 deletions(-) diff --git a/5_moving_average.c b/5_moving_average.c index 6bb9dc4..84b2eee 100644 --- a/5_moving_average.c +++ b/5_moving_average.c @@ -2,34 +2,95 @@ #include // for memory allocation #include // for time calculation #include // for sine and cosine functions -int main() { +#include + +#define TEST + +#ifdef TEST +#include +#endif + +int main(int argc, const char *argv[]) { // Declare all the variables int k, n, M, N; double *x, *y; time_t t; - // Input the number N - + // Input the number N, M + printf("N = "); + scanf("%d", &N); + printf("M = "); + scanf("%d", &M); + double size = 2*M + 1; // Locate the memory for x, y; + x = (double*)malloc(sizeof(double)*N); + y = (double*)malloc(sizeof(double)*N); + +#ifdef TEST + double *y_test = (double*)malloc(sizeof(double)*N); + memset(y, 0, sizeof(double)*N); +#endif // Initial setting for x[k] = sin(2*Pi*k/N), k = 0..N-1 - + for(int i = 0; i < N; ++i){ + x[i] = sin(2*M_PI*i/(double)N); + } + memset(y, 0, sizeof(double)*N); + +#ifdef TEST + // use O(NM) moving average to perform test + for(int n = 0; n < N; ++n){ + for(int k = n-M, upper_bound = n+M; k <= upper_bound; ++k){ + if(k >= 0 && k < N){ + y_test[n] += x[k]; + } + } + y_test[n] /= size; + } +#endif t = clock(); // y[n] = sum(x[k], k=n-M..n+M)/(2M+1), n=0..N-1 // zero padding for x[k] if k<0 or k>=N + //initialize y[0] + for(int i = 0; i <= M; ++i) y[0] += x[i]; + + for(int i = 1; i < N; ++i){ + // middle is i + if(i - 1 - M >= 0){ + y[i] = y[i - 1] - x[i - 1 - M]; + }else{ + y[i] = y[i - 1]; + } + + if(i + M < N){ + y[i] += x[i + M]; + } + } + + for(int i = 0; i < N; ++i) y[i] /= size; // Output the results t = clock() - t; + for(int i = 0; i < N; ++i){ +#ifdef TEST + assert(y[i] - y_test[i] < 0.00001); // 0.00001 for floating number bias +#endif + printf("%.3f\n", y[i]); + } printf("\n"); // free the memory located by x, y - - + free(x); + free(y); + +#ifdef TEST + free(y_test); +#endif return 100; } From c4eef725ce964b126022d62d48cf760a1703f1c0 Mon Sep 17 00:00:00 2001 From: Eugene Lin Date: Thu, 10 Mar 2022 22:42:34 +0800 Subject: [PATCH 2/7] Use branchless method in for-loop to optimize --- 5_moving_average.c | 21 +++++++-------------- 1 file changed, 7 insertions(+), 14 deletions(-) diff --git a/5_moving_average.c b/5_moving_average.c index 84b2eee..4e24130 100644 --- a/5_moving_average.c +++ b/5_moving_average.c @@ -4,7 +4,7 @@ #include // for sine and cosine functions #include -#define TEST +// #define TEST #ifdef TEST #include @@ -51,24 +51,17 @@ int main(int argc, const char *argv[]) { } #endif - t = clock(); // y[n] = sum(x[k], k=n-M..n+M)/(2M+1), n=0..N-1 // zero padding for x[k] if k<0 or k>=N //initialize y[0] for(int i = 0; i <= M; ++i) y[0] += x[i]; + - for(int i = 1; i < N; ++i){ - // middle is i - if(i - 1 - M >= 0){ - y[i] = y[i - 1] - x[i - 1 - M]; - }else{ - y[i] = y[i - 1]; - } - - if(i + M < N){ - y[i] += x[i + M]; - } + // Use branchless method to reduce if-else + for(int i = 1, lower = - M, upper = 1 + M; i < N; ++i, ++lower, ++upper){ + y[i] = (y[i - 1] - x[lower]) * (lower >= 0) + y[i-1]*(lower < 0); + y[i] += x[i + M] * (upper < N); } for(int i = 0; i < N; ++i) y[i] /= size; @@ -78,7 +71,7 @@ int main(int argc, const char *argv[]) { t = clock() - t; for(int i = 0; i < N; ++i){ #ifdef TEST - assert(y[i] - y_test[i] < 0.00001); // 0.00001 for floating number bias + assert(y[i] - y_test[i] < 0.001); // 0.001 for floating number bias #endif printf("%.3f\n", y[i]); } From 136a3c1f5f88e1947bb094b3650396fa5b231ad2 Mon Sep 17 00:00:00 2001 From: Eugene Lin Date: Thu, 10 Mar 2022 22:44:49 +0800 Subject: [PATCH 3/7] Remove unused and declared variables k and n --- 5_moving_average.c | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/5_moving_average.c b/5_moving_average.c index 4e24130..aa8f23b 100644 --- a/5_moving_average.c +++ b/5_moving_average.c @@ -12,7 +12,7 @@ int main(int argc, const char *argv[]) { // Declare all the variables - int k, n, M, N; + int M, N; double *x, *y; time_t t; From 1f518457e68ac226ccdd24b3d8f958afceebeed6 Mon Sep 17 00:00:00 2001 From: Eugene Lin Date: Thu, 10 Mar 2022 23:00:03 +0800 Subject: [PATCH 4/7] Finish 5_practice.c --- 5_practice.c | 42 ++++++++++++++++++++++++++++-------------- 1 file changed, 28 insertions(+), 14 deletions(-) diff --git a/5_practice.c b/5_practice.c index 70d6651..8686c77 100644 --- a/5_practice.c +++ b/5_practice.c @@ -2,37 +2,51 @@ #include // for memory allocation #include // for time calculation #include // for sine and cosine functions +#include // for memset + + int main() { // Declare all the variables - int k, n, N; + int N; double *x, *yr, *yi; - time_t t; + clock_t t; // Input the number N - + printf("Please input N = "); + scanf("%d", &N); // Locate the memory for x, yr, yi; + x = (double*)malloc(sizeof(double)*N); + yr = (double*)malloc(sizeof(double)*N); + yi = (double*)malloc(sizeof(double)*N); // Initial setting for x, for example, x[k] = k - - - - + for(int i = 0; i < N; ++i) x[i] = i; + + memset(yr, 0, sizeof(double)*N); + memset(yi, 0, sizeof(double)*N); + + double pi_2_n_div_N, theta; t = clock(); // yr[n]+i*yi[n] = sum(exp(-i 2 Pi k n / N)*x[k], k=0..N-1), n=0..N-1 - - - - - + for(int n = 0; n < N; ++n){ + pi_2_n_div_N = 2*M_PI*n / (double)N; + for(int k = 0; k < N; ++k){ + theta = pi_2_n_div_N * k; + yr[n] += cos(theta) * x[k]; + yi[n] -= sin(theta) * x[k]; + } + } // output the results t = clock() - t; - printf("%d ms for discrete Fourier Transform of %d elements\n", t, N); + printf("%.0f ms for discrete Fourier Transform of %d elements\n", 1000*(double)t/CLOCKS_PER_SEC, N); // free the memory located by x, yr, yi - + free(x); + free(yr); + free(yi); return 100; From 63a413698e317c18aa42717d68caa471b9e49634 Mon Sep 17 00:00:00 2001 From: Eugene Lin Date: Sat, 19 Mar 2022 22:21:24 +0800 Subject: [PATCH 5/7] Add hw4 --- hw4 | 1 + 1 file changed, 1 insertion(+) create mode 160000 hw4 diff --git a/hw4 b/hw4 new file mode 160000 index 0000000..caaed10 --- /dev/null +++ b/hw4 @@ -0,0 +1 @@ +Subproject commit caaed102aa8dc22c7fbac05fa27d3597bd514fc0 From 6bbbeec25bf221c4ba4347c3e22def1292fd48fc Mon Sep 17 00:00:00 2001 From: Yu-Chun Lin <40990767+yuchun1214@users.noreply.github.com> Date: Tue, 29 Mar 2022 11:23:17 +0800 Subject: [PATCH 6/7] Add files via upload --- hw5 .pdf | Bin 0 -> 2841705 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 hw5 .pdf diff --git a/hw5 .pdf b/hw5 .pdf new file mode 100644 index 0000000000000000000000000000000000000000..f9354fa92d7796972577d552d1606eb230b42c60 GIT binary patch literal 2841705 zcmeEO_g_=lwjUiG1u2RYr6Wyh=n$%cN(oI`giu79)L`f(K}La5RFK{y0zxPWJ@lYa z=>+LLAdpa`h7N&;bKkwM%zWmEwgya-&sMMbi}Iqb7U)(p6J6Egv7Pi1%g@-Vv(jsZaag&-VWw*ZY|> 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