SCIP in C++11 ― 1.1節

1.1節　プログラムの要素

問題1.1～1.6はSchemeの練習なのでパス。

問題1.7～1.8：平方根計算の改善と立方根

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//ヘッダincludeと関数プロトタイプ宣言は略

int main(int argc, char** argv)

{

    cout<<"Excersize 1.7:"<<endl;

    const double r1(calculateSquareRoot(2.0));

    cout<<setprecision(16)<<"sqrt(2)="<<r1<<endl

        <<"sqrt(2)^2="<<r1*r1<<endl;

    const double r2(calculateSquareRoot(10000));

    cout<<endl<<setprecision(16)<<"sqrt(10000)="<<r2<<endl

        <<"sqrt(10000)^2="<<r2*r2<<endl;

    const double r3(calculateSquareRoot(0.0001));

    cout<<endl<<setprecision(16)<<"sqrt(0.0001)="<<r3<<endl

        <<"sqrt(0.0001)^2="<<r3*r3<<endl;

    cout<<endl<<"Excersize 1.8:"<<endl;

    const double c1(calculateCubicRoot(2.0));

    cout<<setprecision(16)<<"cbrt(2)="<<c1<<endl

        <<"cbrt(2)^3="<<c1*c1*c1<<endl;

   

   

    return(0);

}

const double calculateSquareRoot(const double x)

{

    return(squareRootIteration2(1.0,x,x));

}

const bool isGoodEnoughSquareRoot(const double guess, const double x)

{

    if (abs(x-guess*guess)<0.001){

        return(true);

    }

    return(false);

}

const double average(const double x, const double y)

{

    return((x+y)/2.0);

}

const double improveGuessSquareRoot(const double guess,const double x)

{

    return(average(guess, x/guess));

}

const double squareRootIteration(const double guess, const double x)

{

    if(isGoodEnoughSquareRoot(guess,x)){

        return(guess);

    }else{

        return(squareRootIteration(improveGuessSquareRoot(guess,x),x));

    }

}

const bool isGoodEnoughSquareRoot2(const double guess, const double oldGuess)

{

    if (abs((guess-oldGuess)/guess)<0.001){

        return(true);

    }

    return(false);

}

const double squareRootIteration2(const double guess, const double oldGuess, const double x)

{

    if(isGoodEnoughSquareRoot2(guess,oldGuess)){

        return(guess);

    }else{

        return(squareRootIteration2(improveGuessSquareRoot(guess,x),guess,x));

    }

}

const double calculateCubicRoot(const double x)

{

    return(cubicRootIteration(1.0,x));

}

const bool isGoodEnoughCubicRoot(const double guess, const double x)

{

    if (abs(x-guess*guess*guess)<0.001){

        return(true);

    }

    return(false);

}

const double improveGuessCubicRoot(const double guess,const double x)

{

    return(average(guess, (x/guess/guess+2*guess)/3.0));

}

const double cubicRootIteration(const double guess, const double x)

{

    if(isGoodEnoughCubicRoot(guess,x)){

        return(guess);

    }else{

        return(cubicRootIteration(improveGuessCubicRoot(guess,x),x));

    }

}

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出力

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Excersize 1.7:

sqrt(2)=1.41421356237469

sqrt(2)^2=2.000000000004511

sqrt(10000)=100.0000002549074

sqrt(10000)^2=10000.00005098149

sqrt(0.0001)=0.01000000002549074

sqrt(0.0001)^2=0.0001000000005098149

Excersize 1.8:

cbrt(2)=1.259765013452635

cbrt(2)^3=1.999257014785836