剰余

[具体的な関数]

• float fmod(float x, float y);
• double fmod(double x, double y);
• long double fmod(long double x, long double y);
• float fmodf(float x, float y); // C++17
• long double fmodl(long double x, long double y); // C++17
  浮動小数点数の除算に対する剰余を得る．以下に示す計算結果が返される．ただし，n は，x を y で割った結果の小数点以下を切り捨てて，整数に変換した値である．

  	x - n * y			

• float remainder(float x, float y); // C++11
• double remainder(double x, double y); // C++11
• long double remainder(long double x, long double y); // C++11
• float remainderf(float x, float y); // C++17
• long double remainderl(long double x, long double y); // C++17
  浮動小数点数の除算に対する剰余を得る．以下に示す計算結果が返される．ただし，n は，x を y で割った結果の小数点以下を四捨五入して，整数に変換した値である（次に示す関数 remquo の quo と同じ)．

  	x - n * y			

• float remquo(float x, float y, int* quo); // C++11
• double remquo(double x, double y, int* quo); // C++11
• long double remquo(long double x, long double y, int* quo); // C++11
• float remquof(float x, float y, int* quo); // C++17
• long double remquol(long double x, long double y, int* quo); // C++17
  浮動小数点数の除算に対する商と剰余を得る．以下に示す計算結果が剰余，quo が商となる．ただし，quo は，x を y で割った結果の小数点以下を四捨五入して，整数に変換した値である．

  	x - quo * y			

[使用例]

1. fmod，remainder，remquo の使用方法です．

   #include <iostream>
   #include <cmath>
   
   using namespace std;
   
   int main()
   {
   			// b = 1.5 
   	double s = 3.14, b = 1.5;
   	cout << "***s : " << s << "， b : " << b <<  "， s/b : " << s/b << endl;
   	cout << "  fmod : (s, b) " << fmod(s, b) << " (s, -b) " << fmod(s, -b) << " (-s, b) " << fmod(-s, b) << " (-s, -b) " << fmod(-s, -b) << endl;
   	cout << "  remainder : (s, b) " << remainder(s, b) << " (s, -b) " << remainder(s, -b) << " (-s, b) " << remainder(-s, b) << " (-s, -b) " << remainder(-s, -b) << endl;
   	int q1, q2, q3, q4;
   	double r1 = remquo(s, b, &q1);
   	double r2 = remquo(s, -b, &q2);
   	double r3 = remquo(-s, b, &q3);
   	double r4 = remquo(-s, -b, &q4);
   	cout << "  remquo : (s,b,&q1) (" << r1 << ", " << q1 << ") (s,-b,&q2) (" << r2 << ", " << q2 << ") (-s,b,&q3) (" << r3 << ", " << q3 << ") (-s,-b,&q4) (" << r4 << ", " << q4 << ")" << endl;
   			// b = 1.2 
   	b = 1.2;
   	cout << "***s : " << s << "， b : " << b <<  "， s/b : " << s/b << endl;
   	cout << "  fmod : (s, b) " << fmod(s, b) << " (s, -b) " << fmod(s, -b) << " (-s, b) " << fmod(-s, b) << " (-s, -b) " << fmod(-s, -b) << endl;
   	cout << "  remainder : (s, b) " << remainder(s, b) << " (s, -b) " << remainder(s, -b) << " (-s, b) " << remainder(-s, b) << " (-s, -b) " << remainder(-s, -b) << endl;
   	r1 = remquo(s, b, &q1);
   	r2 = remquo(s, -b, &q2);
   	r3 = remquo(-s, b, &q3);
   	r4 = remquo(-s, -b, &q4);
   	cout << "  remquo : (s,b,&q1) (" << r1 << ", " << q1 << ") (s,-b,&q2) (" << r2 << ", " << q2 << ") (-s,b,&q3) (" << r3 << ", " << q3 << ") (-s,-b,&q4) (" << r4 << ", " << q4 << ")" << endl;
   
   	return 0;
   }
   			

   （出力）

   ***s : 3.14， b : 1.5， s/b : 2.09333
     fmod : (s, b) 0.14 (s, -b) 0.14 (-s, b) -0.14 (-s, -b) -0.14
     remainder : (s, b) 0.14 (s, -b) 0.14 (-s, b) -0.14 (-s, -b) -0.14
     remquo : (s,b,&q1) (0.14, 2) (s,-b,&q2) (0.14, -2) (-s,b,&q3) (-0.14, -2) (-s,-b,&q4) (-0.14, 2)
   ***s : 3.14， b : 1.2， s/b : 2.61667
     fmod : (s, b) 0.74 (s, -b) 0.74 (-s, b) -0.74 (-s, -b) -0.74
     remainder : (s, b) -0.46 (s, -b) -0.46 (-s, b) 0.46 (-s, -b) 0.46
     remquo : (s,b,&q1) (-0.46, 3) (s,-b,&q2) (-0.46, -3) (-s,b,&q3) (0.46, -3) (-s,-b,&q4) (0.46, 3)