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Распараллеливание программ. Учебник

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              
   
2
                
   
                  
   
        
2

Доказательство.     
                    
Пример 87
   
for(i=1; i <= N; ++i) for(j=1; j <= M; ++j) { { X[j] = Y[i-1,j]*Z[i-1] } { Y[i,j] = Y[i,j-1]*D[j]; Z[i] = 1 } }
Конец примера.
82


             
   
         
  
        
Пример 88.

for(i=1; i <= N; ++i) for(j=1; j <= M; ++j) { a[j] = b[i,j]*c[i,j]
x[i,j] = a[j]*d[i,j];
}
 
for(i=1; i <= N; ++i) for(j=1; j <= M; ++j) { aa[i,j] = b[i,j]*c[i,j]
x[i,j] = aa[i,j]*d[i,j];
} for(j=1; j <= M; ++j) { a[j] = aa[N,j];
}
Конец примера.
83
      
Пример 89.
 
for(i=1; i <= N; ++i) for(j=1; j <= M; ++j) { a[j] = a[j]+b[i,j]*c[i,j]
x[i,j] = a[j]*d[i,j];
}

for(k=1; k <= p; ++k) for(l=1; l <= R; ++l)
for(j=1; j <= M; ++j) {
i = (k-1)*R+l
a[j] = a[j]+b[i,j]*c[i,j]
x[i,j] = a[j]*d[i,j];
}
 
for(k=1; k <= p; ++k) for(l=1; l <= R; ++l)
for(j=1; j <= M; ++j) {
i = (k-1)*R+l
aa[k,j] = aa[k,j]+b[i,j]*c[i,j]
x[i,j] = aa[k,j]*d[i,j];
}
 
Конец примера.


                      uv
84
u vu v
Пример 90.
{ for(i=1; i <= N; ++i) for(j=1; j <= N; ++j) { a[i+j] = … = … a[i+j-1]; } }
Рис. 4. Решетчатый граф, построенный с помощью ОРС. Зеленые дуги – истинная
зависимость, красные – антизависимость, синие – выходная самозависимость
Конец примера.
Пример 91.


{ for(i=1; i <= M; ++i) for(j=1; j <= N; ++j) { = … a;
85
a = … } }
 
{ for(i=1; i <= M; ++i) { aa[0] = a for(j=1; j <= N; ++j) { = … aa[j-1]; aa[j] = … } a = aa[N] } }
 
{
aaa[0] = a
for(i=1; i <= M; ++i)
{
aa[0] = aaa[i-1]
for(j=1; j <= N; ++j)
{
= … aa[j-1];
aa[j] = …
}
aaa[i] = aa[N]
}
a = aaa[M]
}
Конец примера.
  

    
86
   
        
Пример 92. 
DO 99 I = 1, N X(I) = A(I)+B(I) A(I) = C(I)+D(I). Y(I) = X(I)*Z(I) V(I) = A(I)*U(I). W(I) = C(I)*D(I) B(I) = Z(I)+D(I).
99 CONTINUE
 
DO 99 I = 1, N X(I) = A(I)+B(I) ; W(I) = C(I)*D(I) A(I) = C(I)+D(I); Y(I) = X(I)*Z(I) V(I) = A(I)*U(I); B(I) = Z(I)+D(I).
99 CONTINUE
Конец примера.
Пример 93.


DO 99 I = 1, N X(I) = A(I)+B(I) Y(I) = X(I)*D(I).
99 CONTINUE
   
DO 99 I = 1, N, 3 1 X(I) = A(I)+B(I) 2 Y(I) = X(I)*D(I). 3 X(I) = A(I+1)+B(I+1) 4 Y(I) = X(I+1)*D(I+1). 5 X(I) = A(I+2)+B(I+2) 6 Y(I) = X(I+2)*D(I+2).
87
99 CONTINUE
DO 999 I = (N//3)*3+1, N X(I) = A(I)+B(I) Y(I) = X(I)*D(I).
999 CONTINUE
   
Конец примера.
Пример 94.


DO 77 I = 1, N X(I) = A(I)+B(I)
Y(I) = С(I)-D(I).
77 CONTINUE
DO 99 I = 1, N Z(I) = A(I)*B(I) T(I) = X(I)*Z(I).
99 CONTINUE
    
DO 77 I = 1, N X(I) = A(I)+B(I); Z(I) = A(I)*B(I)
Y(I) = С(I)-D(I);
T(I) = X(I)*Z(I).
99 CONTINUE
Конец примера.
                

    
88
              
Пример 95.
  
DO 99 I = 1, N X(I) = C(I)+B(I); DO 99 J = 1, N A(J) = A(J) + D(I,J)*X(I);
99 CONTINUE
Конец примера.
                          
               
Пример 96.  
 
DO 99 I = 1, N X(I) = A(I)+B(I); A(I) = C(I+1)+X(I);
89
A(I-1) = X(I-1)*B(I+3);
99 CONTINUE
     
Конец примера.
     
КОНВЕЙЕРНЫЕ ВЫЧИСЛЕНИЯ
  
    
          
         
        
    
90

                 
      
Пример 97. 
X = (X*A(I)+B(I))+C(I)

X * + + X
A(I) B(I) C(I)
Рис. 5. Дерево вычислений
 
        

DO 99 I=1, N
99 ТЕЛОЦИКЛА(I) (14)
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