You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
112 lines
2.3 KiB
112 lines
2.3 KiB
// 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;
|
|
}
|