C++ 什么'；在计算多项式时，跳过0系数是一种有效的方法吗？
我正在研究一个单核的微芯片（stm32f103c8t6），我想计算一些多项式，使其达到预定的指数，因此C++ 什么'；在计算多项式时，跳过0系数是一种有效的方法吗？,c++,performance,polynomials,C++,Performance,Polynomials,我正在研究一个单核的微芯片（stm32f103c8t6），我想计算一些多项式，使其达到预定的指数，因此f（x）=a0+a1*x+a2*x^2+…+an*x^n其中n在编译时已知 系数a0…an将在运行期间发生变化，其中一些很可能变为零，我想找到一种方法，在计算f（x）时跳过这些系数。注意，大多数将是非零的。理想情况下，我希望在运行时重写f（x），这样零的系数就不再存在于函数中，但我不想进入自修改代码领域（除非有一些简单的方法在C++中实现）。微芯片能够进行单指令乘法，因此，任何等效于使用if语句
f（x）=a0+a1*x+a2*x^2+…+an*x^n我正在用C++编写微芯片，虽然我现在正在研究Python中的算法，因为它更容易绘制结果，所以我没有任何代码来解决这个问题。< P>使用有限状态机。您需要为每个可能的状态编写代码。但这可能是最快的计算方法 这是一个示例，它使用示例数学函数和迭代的示例值。OP必须为每个状态提供自己的数学函数和迭代值
#include <iostream>
int main(int argc, char *argv[]){
/* MAX_COEFFICIENTS <-- states == 2^coefficients */
const int MAX_COEFFICIENTS = 3;
int coefficientsv[] = {1, 0, 3}; /* {A, B, C} */
int coefficientsc = sizeof coefficientsv / sizeof coefficientsv[0];
if(coefficientsc > MAX_COEFFICIENTS) return -1; /* Out of bounds! */
register int A = 0, B = 0, C = 0;
for(int i = 0; i < coefficientsc; i++){
if(i == 0) A = coefficientsv[i];
else if(i == 1) B = coefficientsv[i];
else if(i == 2) C = coefficientsv[i];
}
register long polycalc = 0; /* or use just int, if int is big enough */
register int iteration = 1000; /* example value */
/* state truth table */
/* A B C */
/* 0 0 0 goto STATE_0 */
/* 1 0 0 goto STATE_A */
/* 0 1 0 goto STATE_B */
/* 1 1 0 goto STATE_AB */
/* 0 0 1 goto STATE_C */
/* 1 0 1 goto STATE_AC */
/* 0 1 1 goto STATE_BC */
/* 1 1 1 goto STATE_ABC */
STATE_SELECT:
if(!A && !B && !C) goto STATE_0;
if( A && !B && !C) goto STATE_A;
if(!A && B && !C) goto STATE_B;
if( A && B && !C) goto STATE_AB;
if(!A && !B && C) goto STATE_C;
if( A && !B && C) goto STATE_AC;
if(!A && B && C) goto STATE_BC;
if( A && B && C) goto STATE_ABC;
STATE_0:
while(iteration){
polycalc = 0;
iteration--;
}
goto END;
STATE_A:
while(iteration){
polycalc = A;
iteration--;
}
goto END;
STATE_B:
while(iteration){
polycalc = B * B;
iteration--;
}
goto END;
STATE_AB:
while(iteration){
polycalc = A + B * B;;
iteration--;
}
goto END;
STATE_C:
while(iteration){
polycalc = C * C * C;
iteration--;
}
goto END;
STATE_AC:
while(iteration){
polycalc = A + C * C * C;
iteration--;
}
goto END;
STATE_BC:
while(iteration){
polycalc = B * B + C * C * C;
iteration--;
}
goto END;
STATE_ABC:
while(iteration){
polycalc = A + B * B + C * C * C;
iteration--;
}
/* Example: Pseudo-Code */
/* Maybe your first calculation has shown that C becomes 0. */
/* So simply use "goto STATE_AB", maybe set some variables. */
/* In another example, you only know that some coefficient */
/* has become 0, but you don't know which one, */
/* so use "goto STATE_SELECT", maybe set some variables too. */
goto END;
END:
std::cout << polycalc << std::endl;
return 0;
}
#包括
int main（int argc，char*argv[]）{
/*MAX_系数MAX_系数）返回-1；/*超出范围*/
寄存器int A=0，B=0，C=0；
对于（int i=0；i#include <iostream>
int main(int argc, char *argv[]){
/* MAX_COEFFICIENTS <-- states == 2^coefficients */
const int MAX_COEFFICIENTS = 3;
int coefficientsv[] = {1, 0, 3}; /* {A, B, C} */
int coefficientsc = sizeof coefficientsv / sizeof coefficientsv[0];
if(coefficientsc > MAX_COEFFICIENTS) return -1; /* Out of bounds! */
register int A = 0, B = 0, C = 0;
for(int i = 0; i < coefficientsc; i++){
if(i == 0) A = coefficientsv[i];
else if(i == 1) B = coefficientsv[i];
else if(i == 2) C = coefficientsv[i];
}
register long polycalc = 0; /* or use just int, if int is big enough */
register int iteration = 1000; /* example value */
/* state truth table */
/* A B C */
/* 0 0 0 goto STATE_0 */
/* 1 0 0 goto STATE_A */
/* 0 1 0 goto STATE_B */
/* 1 1 0 goto STATE_AB */
/* 0 0 1 goto STATE_C */
/* 1 0 1 goto STATE_AC */
/* 0 1 1 goto STATE_BC */
/* 1 1 1 goto STATE_ABC */
STATE_SELECT:
if(!A && !B && !C) goto STATE_0;
if( A && !B && !C) goto STATE_A;
if(!A && B && !C) goto STATE_B;
if( A && B && !C) goto STATE_AB;
if(!A && !B && C) goto STATE_C;
if( A && !B && C) goto STATE_AC;
if(!A && B && C) goto STATE_BC;
if( A && B && C) goto STATE_ABC;
STATE_0:
while(iteration){
polycalc = 0;
iteration--;
}
goto END;
STATE_A:
while(iteration){
polycalc = A;
iteration--;
}
goto END;
STATE_B:
while(iteration){
polycalc = B * B;
iteration--;
}
goto END;
STATE_AB:
while(iteration){
polycalc = A + B * B;;
iteration--;
}
goto END;
STATE_C:
while(iteration){
polycalc = C * C * C;
iteration--;
}
goto END;
STATE_AC:
while(iteration){
polycalc = A + C * C * C;
iteration--;
}
goto END;
STATE_BC:
while(iteration){
polycalc = B * B + C * C * C;
iteration--;
}
goto END;
STATE_ABC:
while(iteration){
polycalc = A + B * B + C * C * C;
iteration--;
}
/* Example: Pseudo-Code */
/* Maybe your first calculation has shown that C becomes 0. */
/* So simply use "goto STATE_AB", maybe set some variables. */
/* In another example, you only know that some coefficient */
/* has become 0, but you don't know which one, */
/* so use "goto STATE_SELECT", maybe set some variables too. */
goto END;
END:
std::cout << polycalc << std::endl;
return 0;
}
#包括
int main（int argc，char*argv[]）{
/*MAX_系数MAX_系数）返回-1；/*超出范围*/
寄存器int A=0，B=0，C=0；
对于（int i=0；iint max_idx = a.size() - 1;
float result = a[max_idx];
int i = max_idx;
while (i > 0) {
-- i;
result = a[i] + x * result;
}
return result;
// compute powers between nonzero coefficients
int max_idx = a.size() - 1;
assert(a[max_idx] != 0); // you should not have leading zeroes in the first place
std::vector<int> inc_powers;
std::vector<int> inc_indices;
int inc_pow = 0;
int i = max_idx;
while (i > 0) {
-- i;
++ inc_pow;
if (a[i] != 0 || i == 0) {
inc_powers.push_back(inc_pow);
inc_indices.push_back(i);
inc_pow = 0;
}
}
int i = a.size() - 1;
float result = a[i];
for (int i = 0; i < inc_powers.size(); ++i) {
result = a[inc_indices[i]] + x_powers[inc_powers[i]] * result;
}
return result;
int max_powers = 0;
for (power: inc_powers) {
if (power > max_powers) { max_powers = power; }
}
std::vector<float> x_powers(max_powers + 1);
float value = x;
for (int i = 1; i < max_powers; ++i) {
x_powers[i] = value;
value *= x;
}
x_powers[max_powers] = value;