add: 头歌上的隐藏测试集 (#82)

Reviewed-on: PostGuard/Canon#82

open_set/92_math.pas

@@ -0,0 +1,163 @@
+program main;
+const e = 2.1718281828459045;
+split = '--';
+var
+x,y:real;
+num,i:integer;
+
+function my_fabs(x: real):real;
+begin
+    if x > 0 then
+        my_fabs := x
+    else
+        my_fabs := -x;
+end;
+
+function my_pow(a:real; n: integer):real;
+var i:integer; res: real;
+begin
+    if n < 0 then
+        my_pow := 1 / (my_pow(a, -n))
+    else
+    begin
+        res := 1.0;
+        for i := 0 to n - 1 do
+            res := res * a;
+        my_pow := res;
+    end;
+end;
+
+function my_sqrt(x:real):real;
+var t:real; c:integer;
+begin
+    if x > 100 then
+        my_sqrt := 10.0 * my_sqrt(x / 100)
+    else
+    begin
+        t := x / 8 + 0.5 + 2 * x / (4 + x);
+        for c := 0 to 9 do
+            t := (t + x / t) / 2;
+        my_sqrt := t;
+    end
+end;
+
+function F1(x:real):real;
+begin
+    F1 := 1 / x;
+end;
+
+function F2(x:real):real;
+begin
+    F2 := 1 / my_sqrt(1 - x * x);
+end;
+
+function simpson(a,b: real; flag: integer): real;
+var c:real;
+begin
+    c := a + (b - a) / 2;
+    simpson := 0;
+    if flag = 1 then
+        simpson := (F1(a) + 4 * F1(c) + F1(b)) * (b - a) / 6
+    else
+        simpson := (F2(a) + 4 * F2(c) + F2(b)) * (b - a) / 6;
+end;
+
+function asr5(a,b,eps,AA: real; flag:integer):real;
+var c,L,R:real;
+begin
+    c := a + (b - a) / 2;
+    L := simpson(a, c, flag);
+    R := simpson(c, b, flag);
+    if my_fabs(L + R - AA) <= (15 * eps) then
+        asr5 := L + R + (L + R - AA) / 15.0
+    else
+        asr5 := asr5(a, c, eps/2, L, flag) + asr5(c, b, eps/2, R, flag);
+end;
+
+function asr4(a,b,eps:real; flag: integer):real;
+begin
+    asr4 := asr5(a, b, eps, simpson(a, b, flag), flag);
+end;
+
+function eee(x:real):real;
+var ee: real;
+begin
+    if x > 0.001 then
+    begin
+        ee := eee(x / 2);
+        eee := ee * ee;
+    end
+    else
+        eee := 1 + x + x * x / 2 + my_pow(x, 3) / 6 + my_pow(x, 4) / 24 + my_pow(x, 5) / 120;
+end;
+
+function my_exp(x:real):real;
+var e1,e2: real; n: integer;
+begin
+    if x < 0 then
+        my_exp := 1 / my_exp(-x)
+    else
+    begin
+    //pascal no cut the integer part and float part
+        n := 1;
+        x := x - 1.0;
+        e1 := my_pow(e, n);
+        e2 := eee(x);
+        my_exp := e1 * e2;
+    end;
+end;
+
+function my_ln(x:real):real;
+begin
+    my_ln := asr4(1, x, 0.00000001, 1);
+end;
+
+function my_log(a,N: real):real;
+begin
+    my_log := my_ln(N) / my_ln(a);
+end;
+
+function my_powf(a,x:real):real;
+begin
+    my_powf := my_exp(x * my_ln(a));
+end;
+
+procedure putfloat(f:real);
+begin
+    write(f);
+end;
+
+
+function getfloat():real;
+begin
+    read(getfloat);
+end;
+
+begin
+    num := 2;
+    for i := 0 to num - 1 do
+    begin
+        x := getfloat;
+        y := getfloat;
+        putfloat(my_fabs(x));
+        putfloat(my_pow(x, 2));
+        putfloat(my_sqrt(x));
+        putfloat(my_exp(x));
+
+        if x > 0.0 then
+            putfloat(my_ln(x))
+        else
+            write(split);
+
+        if (x > 0.0) and (y > 0.0) then
+            putfloat(my_log(x, y))
+        else
+            write(split);
+        
+        if x > 0.0 then
+            putfloat(my_powf(x, y))
+        else
+            write(split);
+    end;
+    read(num);
+end.