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1 C , C C Hello world for for (2) : while if ( ) prog10.c prog11.c prog11-c99.c prog11-c++.c ( ) prog12.c prog12a.c prog12b.c

2 A 30 A A ( ) 2 C C (, machine language) C (C compiler) ( ) Mac Apple Xcode Clang+LLVM cc, gcc Mac GLSC C cglsc cc Clang+LLVM cc, gcc UNIX cc C 1. 1 ( ) ( ) cc -S C cc C prog.c prog.s prog.s a.out 1 2

3 % ls prog.c % cat prog.c int a,b,c,d; a = 1; b = 2; c = 3; d = a * b + c; printf("%d*%d+%d=%d\n", a, b, c, d); % cc -S prog.c % ls prog.c prog.s % cat prog.s ( ) % cc prog.s % ls a.out* prog.c prog.s %./a.out 1*2+3=5 % (macos cc ) prog.s printf() 3

4 prog.s.section TEXT, text,regular,pure_instructions.macosx_version_min 10, 13.globl _main ## -- Begin function main.p2align 4, 0x90 _main: ## BB#0: pushq %rbp Lcfi0:.cfi_def_cfa_offset 16 Lcfi1:.cfi_offset %rbp, -16 movq %rsp, %rbp Lcfi2:.cfi_def_cfa_register %rbp subq $32, %rsp leaq L_.str(%rip), %rdi movl $0, -4(%rbp) movl $1, -8(%rbp) movl $2, -12(%rbp) movl $3, -16(%rbp) movl -8(%rbp), %eax imull -12(%rbp), %eax addl -16(%rbp), %eax movl %eax, -20(%rbp) movl -8(%rbp), %esi movl -12(%rbp), %edx movl -16(%rbp), %ecx movl -20(%rbp), %r8d movb $0, %al callq _printf xorl %ecx, %ecx movl %eax, -24(%rbp) ## 4-byte Spill movl %ecx, %eax addq $32, %rsp popq %rbp retq.cfi_endproc ## -- End function.section TEXT, cstring,cstring_literals L_.str: "%d*%d+%d=%d\n".subsections_via_symbols C C main() ( ) C (/* */ ) 4

5 prog01.c /* prog01.c --- ( ) C */ % cc -o prog01 prog01.c ( cglsc prog01.c) %./prog01 % C ( ) main() 8 C // 1 1 // prog01.c --- ( ) C (main() return ) OS 0 echo $status 0 OS Hello world 2 Hello world prog02.c /* prog02.c --- Hello world */ printf("hello, world.\n"); % cc -o prog02 prog02.c ( cglsc prog02.c) %./prog02 Hello, world. % 2 & 5

6 printf() ( ) " " \n ( \ JIS Y ) printf() printf( ); printf(" \n"); printf() stdio.h #include (stdio=standard input and output, h header file ) /usr/include/stdio.h printf() ( ) prog03.c /* prog03.c (?) */ int a, b; printf(" : "); scanf("%d%d", &a, &b); printf(" %d, %d \n", a, b); printf(" =%d, =%d, =%d, ( )=%d, =%d\n", a + b, a - b, a * b, a / b, a % b); C 6

7 ( 3 ) int ( integer, integral) int ( ) int ; int a; int b, c, d; /* */ ( ) scanf() (scanf() ) ( ) ( ) printf() scanf(), printf() (format) %d (d decimal (10 ) 8 16 ) print() 10 ) printf(" %d\n", ); printf("a=%d, b=%d\n", a, b); printf("a 3 =%d\n", 3 * a); scanf() 10 scanf("%d", & ); scanf("%d", &a); scanf("%d%d", &b, &c); & ( ) scanf() scanf() +, -, *, /, % 3.4 C (floating point numbers) 3 Mac cc ( Clang+LLVM ) 2 31 n n = = long long int ( LL ll LL ll printf() scanf() %lld ) int128 7

8 prog04.c /* prog04.c --- */ double a, b; printf(" : "); scanf("%lf%lf", &a, &b); printf(" %f, %f \n", a, b); printf(" =%f, =%f, =%f, =%f\n", a + b, a - b, a * b, a / b); float, double, long double IEEE float 7, double 16 float , double double ( ) printf() double %f printf("a=%f\n", a); printf("b=%f, c=%f\n", b, c); scanf() double %lf ( ) (l L ) scanf("%lf", &a); scanf("%lf%lf", &b, &c); %lf, %f %e, ( ) %g (n), (m) %n.mf printf("%20.15f\n", a); ( ) 8

9 int double int double double (1) double (2) ( ) int (3) ( ) int int double double long long int a a long long int ( ) 64 double (IEEE754 ) 53 long long int , n n, C (1) (2) (argument) math.h /usr/include/math.h -lm 4 4 libname.a -lname libm.a ( ) -lm 9

10 prog05.c /* prog05.c --- ( ) */ #include <math.h> /* */ double x; printf(" : "); scanf("%lf", &x); /* ( ) */ printf("sqrt(%g) =%g\n", x, sqrt(x)); /* sin */ printf("sin(%g) =%g\n", x, sin(x)); /* e */ printf("exp(%g) =%g\n", x, exp(x)); /* */ printf("log(%g) =%g\n", x, log(x)); /* (10 ) */ printf("log10(%g) =%g\n", x, log10(x)); /* hyperbolic sin) */ printf("sinh(%g) =%g\n", x, sinh(x)); /* (power) */ printf("pow(%g,%g)=%g\n", x, 1.0/3.0, pow(x, 1.0/3.0)); /* Arctan */ printf("atan(%g) =%g\n", x, atan(x)); /* */ printf("fabs(%g) =%g\n", x, fabs(x)); /* (- = Gauss ) */ printf("floor(%g) =%g\n", x, floor(x)); /* */ printf("ceil(%g) =%g\n", x, ceil(x)); % cc -o prog05 prog05.c -lm (-lm l L ) %./prog05 ( ) / 1 1.0/3.0 1/3 0 3 (double)1/(double)3 1.0/ /3 ( )

11 π, e π = (Napier ) e = #include <math.h> double pi, e;... int main()... /* main() pi, e */ pi = 4.0 * atan(1.0); e = exp(1.0); int main() ( ) C C++ 2 ax 2 + bx + c = 0 (a, b, c R, a 0) 3.6 for for() for ( ; ; ) ; for ( ; ; ) 1; 2;... n; n n for (i = 0; i < n; i++) ; ; n = 1, 2,... 2 n, 2 n 11

12 x n := 2 n, y n := 2 n x n, y n x 0 = 1, x n = 2x n 1 (n = 1, 2,... ), y 0 = 1, y n = y n 1 /2 (n = 1, 2,... ) prog06.c /* prog06.c --- for (1) */ int i, n; double x, y; printf(" : "); scanf("%d", &n); x = 1.0; y = 1.0; for (i = 1; i <= n; i++) /* x 2 y 1/2 */ x = 2 * x; y = y / 2; /* %g %f %e */ printf("2 %d =%g, 1/2 %d =%g\n", i, x, i, y); prog06 %./prog06 : =2, 1/2 1 = =4, 1/2 2 = =8, 1/2 3 = =16, 1/2 4 = =32, 1/2 5 = =64, 1/2 6 = =128, 1/2 7 = =256, 1/2 8 = =512, 1/2 9 = =1024, 1/2 10 = =2048, 1/2 11 = =4096, 1/2 12 = =8192, 1/2 13 = =16384, 1/2 14 = e =32768, 1/2 15 = e =65536, 1/2 16 = e =131072, 1/2 17 = e =262144, 1/2 18 =3.8147e =524288, 1/2 19 = e = e+06, 1/2 20 = e-07 % while ()... do... while () 12

13 3.7 for (2) : S n = a 1 + a a n S 0 = 0 S i = S i 1 + a i (i = 1, 2,..., n) S n = n i=1 a i (1) S i s (2) s = 0; (3) s = s + a i ; i = 1, 2,..., n n n 2 prog07.c /* * prog07.c --- for (2) */ int i, n; double s; printf(" : "); scanf("%d", &n); s = 0.0; for (i = 1; i <= n; i++) /* s i s = s + i * i; */ s += i * i; printf(" 1 %d =%g\n", n, s); n 1 S n = k! k=0 : a k = 1/k! while if ( ) while

14 while ( ) ; == ( )!= ( ) < ( ) <= ( ) > ( ) >= ( ) if (1) if ( ) ; (2) if ( ) 1; else 2; prog08a.c /* * prog08a.c */ #include <math.h> double a, b, c, D, sqrtd, re, im, x1, x2; printf("2 a x^2+b x+c=0 \n"); printf("a, b, c: "); scanf("%lf%lf%lf", &a, &b, &c); D = b * b - 4 * a * c; if (D > 0) sqrtd = sqrt(d); x1 = (- b + sqrtd) / (2 * a); x2 = (- b - sqrtd) / (2 * a); printf(" 2 : %20.15g, %20.15g\n", x1, x2); else if (D == 0.0) printf(" ( ): %20.15g\n", - b / (2 * a)); else re = - b / (2 * a); im = sqrt(- D) / (2 * a); printf(" 2 : %20.15g %20.15g \n", re, im); 14

15 prog08.c /* prog08.c --- while if ( ) */ /* * * 1 * ( ) * */ int n; printf(" : "); scanf("%d", &n); while (n!= 1) printf("%d\n", n); if (n % 2 == 0) n = n / 2; else n = 3 * n + 1; printf("%d\n", n); 3.9 ( ) ( ); double square(double); double square(double x); ( )

16 return ; double square(double x) return x * x; sin x (x 0) f(x) := x 1 (x = 0) prog09.c 6 /* prog09.c --- */ #include <math.h> /* f */ double f(double); int i, n; double a; printf(" : "); scanf("%d", &n); a = 1.0; for (i = 0; i < n; i++) a /= 2; printf("1-sin(%g)/%g=%g\n", a, a, 1.0-f(a)); /* f() */ double f(double x) if (x == 0.0) return 1.0; else return sin(x) / x;

17 3.10 input.data output.data 5 prog13.c /* * prog13.c --- fopen(), fclose(), fprintf(), fscanf() * gcc -o prog13 prog13.c */ int a, b, sum; FILE *in, *out; in = fopen("input.data", "r"); /* in NULL */ fscanf(in, "%d%d", &a, &b); fclose(in); sum = a + b; printf("%d %d %d\n", a, b, sum); out = fopen("output.data", "w"); fprintf(out, "%d\n", sum); fclose(out); fopen() 17

18 prog13check.c /* * prog13check.c --- fopen(),fclose(),fprintf(),fscanf() * gcc -o prog13 prog13.c */ int a, b, sum; FILE *in, *out; if ((in = fopen("input.data", "r")) == NULL) fprintf(stderr, "input.data \n"); exit(1); fscanf(in, "%d%d", &a, &b); fclose(in); sum = a + b; printf("%d %d %d\n", a, b, sum); if ((out = fopen("output.data", "w")) == NULL) fprintf(stderr, "output.data \n"); exit(1); fprintf(out, "%d\n", sum); fclose(out); ( ) 1 ( ) malloc() double a[1000]; // 1000 double b[1000]; // Seg fault double *c; // c = malloc(sizeof(double) * 1000); // 1000 if (c == NULL) //... 18

19 prog10.c N /* * prog10.c --- * gcc -o prog10 prog10.c */ #define N (3) /* n x, y */ double inner_product(double x[], double y[], int n) int i; double s; s = 0.0; for (i = 0; i < n; i++) s += x[i] * y[i]; return s; int i; double a[n], b[n]; printf(" %d \n", N); printf(" a \n"); for (i = 0; i < N; i++) printf(" %d =", i + 1); scanf("%lf", &a[i]); printf(" b \n"); for (i = 0; i < N; i++) printf(" %d =", i + 1); scanf("%lf", &b[i]); printf(" =%g\n", inner_product(a, b, N)); prog11.c prog10.c N (C99 C ) malloc() /* * prog11.c --- * gcc -o prog11 prog11.c */ #include <stdlib.h> /* malloc() */ /* n x, y */ 19

20 double inner_product(double *x, double *y, int n) int i; double s; s = 0.0; for (i = 0; i < n; i++) s += x[i] * y[i]; return s; int i, N; double *a, *b; printf(" \n"); printf(" : "); scanf("%d", &N); a = malloc(sizeof(double) * N); b = malloc(sizeof(double) * N); if (a == NULL b == NULL) fprintf(stderr, " \n"); exit(1); printf(" a \n"); for (i = 0; i < N; i++) printf(" %d =", i + 1); scanf("%lf", &a[i]); printf(" b \n"); for (i = 0; i < N; i++) printf(" %d =", i + 1); scanf("%lf", &b[i]); printf(" =%g\n", inner_product(a, b, N)); /* a, b * */ free(a); free(b); prog11-c99.c C C99 (variable length array) ( C11 C++14 ( Mac 8 MB ) ) /* * prog11-c99.c --- * gcc -o prog11-c99 prog11-c99.c */ /* n x, y */ 20

21 double inner_product(double *x, double *y, int n) int i; double s; s = 0.0; for (i = 0; i < n; i++) s += x[i] * y[i]; return s; int i, N; printf(" \n"); printf(" : "); scanf("%d", &N); double a[n], b[n]; printf(" a \n"); for (i = 0; i < N; i++) printf(" %d =", i + 1); scanf("%lf", &a[i]); printf(" b \n"); for (i = 0; i < N; i++) printf(" %d =", i + 1); scanf("%lf", &b[i]); printf(" =%g\n", inner_product(a, b, N)); prog11-c++.c C++ malloc() free() new delete /* * prog11-c++.cpp --- * g++ -o prog11-c++ prog11-c++.cpp */ #include <iostream> #include <cstdlib> using namespace std; /* n x, y */ double inner_product(double *x, double *y, int n) int i; double s; s = 0.0; for (i = 0; i < n; i++) s += x[i] * y[i]; return s; 21

22 int i, N; double *a, *b; cout << " " << endl; cout << " : "; cin >> N; a = new double [N]; b = new double [N]; if (a == NULL b == NULL) cerr << " " << endl; exit(1); cout << " a \n"; for (i = 0; i < N; i++) cout << i+1 << " = "; cin >> a[i]; cout << " b " << endl; for (i = 0; i < N; i++) cout << i+1 << " ="; cin >> b[i]; cout << " =" << inner_product(a, b, N) << endl; /* a, b * */ delete [] a; delete [] b; ( ) ( ) 2 C C99 C Fortran C11 GCC LLVM 2 2 malloc() C++ Eigen 7 C

23 prog12.c 2 /* * prog12.c */ void display(double A[2][2]) int i, j; for (i = 0; i < 2; i++) for (j = 0; j < 2; j++) printf("%7.2f ", A[i][j]); printf("\n"); int i, j; double a[2][2] = 1,2,3,4; double b[2][2], c[2][2]; /* b */ for (i = 0; i < 2; i++) for (j = 0; j < 2; j++) printf("b[%d][%d]=", i, j); scanf("%lf", &b[i][j]); /* c:=a+b */ for (i = 0; i < 2; i++) for (j = 0; j < 2; j++) c[i][j] = a[i][j] + b[i][j]; /* a,b,c */ printf("a=\n"); display(a); printf("b=\n"); display(b); printf("c=\n"); display(c); prog12 oyabun% gcc prog12.c oyabun%./a.out b[0][0]=4 b[0][1]=3 b[1][0]=2 b[1][1]=1 a= b= c= oyabun% 23

24 prog12a.c 2 /* * prog12a-new.c --- C99 */ /* --- */ void display(int m, int n, double A[m][n]) int i, j; for (i = 0; i < m; i++) for (j = 0; j < n; j++) printf("%7.2f ", A[i][j]); printf("\n"); int i, j, k, m, n; /* */ printf("m= "); scanf("%d", &m); n = m; double a[m][n], b[m][n], c[m][n]; // : m*n /* a */ k = 0; for (i = 0; i < m; i++) for (j = 0; j < n; j++) a[i][j] = k++; /* b */ for (i = 0; i < m; i++) for (j = 0; j < n; j++) printf("b[%d][%d]=", i, j); scanf("%lf", &b[i][j]); /* c:=a+b */ for (i = 0; i < m; i++) for (j = 0; j < n; j++) c[i][j] = a[i][j] + b[i][j]; /* a,b,c */ printf("a=\n"); display(m, n, a); printf("b=\n"); display(m, n, b); printf("c=\n"); display(m, n, c); 24

25 $./prog12a-new m= 2 b[0][0]=1 b[0][1]=2 b[1][0]=3 b[1][1]=4 a= b= c= $ prog12b.c double malloc() /* * prog12b.c --- */ #include <stdlib.h> /* double vector, vector matrix */ typedef double *vector; typedef vector *matrix; /* matrix */ void display(int m, int n, matrix A) int i, j; for (i = 0; i < m; i++) for (j = 0; j < n; j++) printf("%7.2f ", A[i][j]); printf("\n"); /* matrix ( ) */ matrix new_matrix(int m, int n) int i; vector ap; matrix a; if ((a = malloc(sizeof(vector) * m)) == NULL) return NULL; 25

26 if ((ap = malloc(sizeof(double) * (m * n))) == NULL) free(a); return NULL; for (i = 0; i < m; i++) a[i] = ap + i * n; return a; /* matrix */ void free_matrix(matrix a) free(a[0]); free(a); int i, j, m, n; matrix a, b, c; m = 2; n = 2; a = new_matrix(m, n); b = new_matrix(m, n); c = new_matrix(m, n); if (a == NULL b == NULL c == NULL) fprintf(stderr, " \n"); exit(1); /* a */ a[0][0] = 1; a[0][1] = 2; a[1][0] = 3; a[1][1] = 4; /* b */ for (i = 0; i < m; i++) for (j = 0; j < n; j++) printf("b[%d][%d]=", i, j); scanf("%lf", &b[i][j]); /* c:=a+b */ for (i = 0; i < m; i++) for (j = 0; j < n; j++) c[i][j] = a[i][j] + b[i][j]; /* a,b,c */ printf("a=\n"); display(m, n, a); printf("b=\n"); display(m, n, b); printf("c=\n"); display(m, n, c); 4 26

27 4.1 [1] n n 8 [2] a, n a n 9 [3] k, n 1 k, 2 k,, n k 10 [4] a 1 = 1, a n+1 = 3a n + 2 (n 1) 100 (n ) [5] a 0 = 1, a 1 = 1, a n+2 = a n+1 + a n (n 0) ( ) a n n = 1, 2,..., 100 a n a n /a n 1 (n ) [ ] a n /a n 1 ( ) [6] n S 1 (n) := n k=1 1 k, S 2(n) := double [ ] lim n S 2 (n) = π 2 /6 (n, π 2 /6 S 2 (n)) [7] n S n = ) n k=0 1 k! n k=1 1 k 2 (1/k! [8] f : [a, b] R f x (0 x 1/2) f(x) := 1 x (1/2 x 1) 0 ( ) 0.2 x 1.2 [9] ( ) n, x s n (x) := n k=1 ( 1) k+1 (2k 1)! x2k 1 n = 1, 2, 3,, 10 s n (x) (0 x 2π) ( Taylor ) [10] R 3 ( ) 8 n(n + 1)/2 1 n 9 pow() 10 for 27

28 x = r * sin(theta) * cos(phi); y = r * sin(theta) * sin(phi); z = r * cos(theta); ( ) d2p() 11 d2p(x, y, z, &r, &theta, &phi); [11] Euler Runge-Kutta (1) x (t) = x(t), x(0) = 1. x(1) = e (2) x (t) = g γx (t), x(0) = H, x (0) = 0. g > 0, γ 0 ( ) x (t) = g γx (t) 2 (3) d dt ( x y ) ( a = c ) ( b d x y ) (x 0, y 0 ), x(0) = x 0, y(0) = y 0. a, b, c, d [12] cos x x = 0 Newton (f(x) := cos x x f(0) = 1 > 0, f(1) = cos 1 1 < 0 (0, 1) 1 ) 4.2 ( ) [5] n n n a = (a 1, a 2,, a n ) a := max a i i=1,2,,n 3 maxnorm0() 11 Decartes to Polar 28

29 #define N 3 int i; double a[n], maxnorm0(); for (i = 0; i < N; i++) scanf("%lf", &a[i]); printf("maxnorm=%g\n", maxnorm0(a)); double maxnorm0(... ( ) [6] ( ) n maxnorm() #define MAXN 1000 int i, n; double a[maxn], maxnorm(); printf("input n (<= %d): ", MAXN); scanf("%d", &n); if (n > MAXN) exit(1); for (i = 0; i < n; i++) scanf("%lf", &a[i]); printf("maxnorm=%g\n", maxnorm(a, n)); double maxnorm(... maxnorm() ( ) [7] MAXN MAXN n malloc() 29

30 #include <stdlib.h> int i, n; double *a, maxnorm(); printf("input n: "); scanf("%d", &n); a = malloc(n * sizeof(double)); if (a == NULL) fprintf(stderr, " \n"); exit(1); /* OK */ for (i = 0; i < n; i++) scanf("%lf", &a[i]); printf("maxnorm=%g\n", maxnorm(a, n)); double maxnorm(... (C++ C++ ) n addvector(), dotproduct(), norm(), angle() [8] a[0], a[100] a[0], a[1], a[2],, a[100] a[1], a[2],, a[99] maxnorm() A A.1 I(f, a, b) := b a f(x) dx f trapezoidal() 30

31 /* * ex1.c --- 1/x [1,2] */ #include <math.h> typedef double rrfunction(double); rrfunction f; double trapezoidal(rrfunction, double, double, int); int main() int N; double I, T; I = log(2.0); printf(" \n"); printf(" N \n"); for (N = 1; N <= (1 << 16); N *= 2) T = trapezoidal(f, 1.0, 2.0, N); printf("%5d\t%25.18f\t%e\n", N, T, I - T); double trapezoidal(rrfunction f, double a, double b, int N) int j; double h, T; h = (b - a) / N; T = (f(a) + f(b)) / 2; for (j = 1; j < N; j++) T += f(a + j * h); T *= h; return T; double f(double x) return 1 / x; A.2 31

32 /* void vvfunc */ typedef void vvfunc(void); /* vvfunc a */ vvfunc *a = NULL; void f(void) printf("hello\n"); void g(void) printf("bye\n"); int main() a = f; a(); a = g; a(); oyabun% cc -o prog1 prog1.c oyabun%./prog1 Hello Bye oyabun% /* void vvfunc */ typedef void vvfunc(void); void f(void) printf("hello\n"); void g(void) printf("bye\n"); int n = 0; vvfunc *commands[10]; void register_command(vvfunc *F) commands[n++] = F; void all_commands(void) int i; for (i = 0; i < n; i++) commands[i](); int main() register_command(f); register_command(g); all_commands(); 32

33 oyabun% cc -o prog2 prog2.c oyabun%./prog2 Hello Bye oyabun% ( ) /* void vvfunc */ typedef void vvfunc(void); void f(void) printf("hello\n"); void g(void) printf("bye\n"); /* */ int n = 0; vvfunc *commands[10]; char keys[10]; void register_command(vvfunc *F, char c) keys[n] = c; commands[n++] = F; void command(char c) int i; for (i = 0; i < n; i++) if (c == keys[i]) commands[i](); return; /* */ int main() register_command(f, H ); register_command(g, B ); command( H ); command( B ); oyabun% cc -o prog3 prog3.c oyabun%./prog3 Hello Bye oyabun% 33

[1] #include<stdio.h> main() { printf("hello, world."); return 0; } (G1) int long int float ± ±

[1] #include<stdio.h> main() { printf(hello, world.); return 0; } (G1) int long int float ± ± [1] #include printf("hello, world."); (G1) int -32768 32767 long int -2147483648 2147483647 float ±3.4 10 38 ±3.4 10 38 double ±1.7 10 308 ±1.7 10 308 char [2] #include int a, b, c, d,