sysy-data/hidden_functional_c/sy/35_math.sy

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2024-04-14 22:20:29 +08:00
#include "sylib.h"
// reference: https://zhuanlan.zhihu.com/p/20085048
const float e = 2.718281828459045;
float my_fabs(float x) {
if (x > 0) return x;
return -x;
}
float my_pow(float a, int n) {
if (n < 0) return 1 / my_pow(a, -n);
float res = 1.0;
while (n) {
if (n % 2) res = res * a;
a = a * a;
n = n / 2;
}
return res;
}
float my_sqrt(float x) {
if (x > 100) return 10.0 * my_sqrt(x / 100);
float t = x / 8 + 0.5 + 2 * x / (4 + x);
int c = 10;
while (c) {
t = (t + x / t) / 2;
c = c - 1;
}
return t;
}
float F1(float x) { return 1 / x; }
float F2(float x) { return 1 / my_sqrt(1 - x * x); }
float simpson(float a, float b, int flag) {
float c = a + (b - a) / 2;
if (flag == 1) return (F1(a) + 4 * F1(c) + F1(b)) * (b - a) / 6;
if (flag == 2) return (F2(a) + 4 * F2(c) + F2(b)) * (b - a) / 6;
return 0;
}
float asr5(float a, float b, float eps, float A, int flag) {
float c = a + (b - a) / 2;
float L = simpson(a, c, flag), R = simpson(c, b, flag);
if (my_fabs(L + R - A) <= 15 * eps) return L + R + (L + R - A) / 15.0;
return asr5(a, c, eps / 2, L, flag) + asr5(c, b, eps / 2, R, flag);
}
float asr4(float a, float b, float eps, int flag) {
return asr5(a, b, eps, simpson(a, b, flag), flag);
}
float eee(float x) {
if (x > 1e-3) {
float ee = eee(x / 2);
return ee * ee;
}
return 1 + x + x * x / 2 + my_pow(x, 3) / 6 + my_pow(x, 4) / 24 +
my_pow(x, 5) / 120;
}
float my_exp(float x) {
if (x < 0) return 1 / my_exp(-x);
int n = x;
x = x - n;
float e1 = my_pow(e, n);
float e2 = eee(x);
return e1 * e2;
}
float my_ln(float x) { return asr4(1, x, 1e-8, 1); }
float my_log(float a, float N) { return my_ln(N) / my_ln(a); }
float my_powf(float a, float x) { return my_exp(x * my_ln(a)); }
int main() {
int num = getint();
while (num) {
float x = getfloat(), y = getfloat();
putfloat(my_fabs(x));
putch(32);
putfloat(my_pow(x, 2));
putch(32);
putfloat(my_sqrt(x));
putch(32);
putfloat(my_exp(x));
putch(32);
if (x > 0) {
putfloat(my_ln(x));
} else {
putch(45);
}
putch(32);
if (x > 0 && y > 0) {
putfloat(my_log(x, y));
} else {
putch(45);
}
putch(32);
if (x > 0) {
putfloat(my_powf(x, y));
} else {
putch(45);
}
putch(10);
num = num - 1;
}
return 0;
}