TempleOSCD_150216.ISO

Adam/AMath.CPP

@@ -0,0 +1,136 @@
+#help_index "Math"
+public U0 R2P(F64 *_mag=NULL,F64 *_arg=NULL,F64 x,F64 y)
+{//Rect to polar
+  //Returns angle in range (-ã,ã]
+  if (_arg)
+    *_arg=Arg(x,y);
+  if (_mag)
+    *_mag=Sqrt(x*x+y*y);
+}
+
+public U0 P2R(F64 *_x=NULL,F64 *_y=NULL,F64 mag,F64 arg)
+{//Polar to Rect
+  if (_x)
+    *_x=mag*Cos(arg);
+  if (_y)
+    *_y=mag*Sin(arg);
+}
+
+public F64 Wrap(F64 é,F64 base=-ã)
+{//Returns angle in range [base,base+2*ã)
+  F64 result=é%(2*ã);
+  if (result>=base+2*ã)
+    result-=2*ã;
+  else if (result<base)
+    result+=2*ã;
+  return result;
+}
+
+public I64 DistSqrI64(I64 x1,I64 y1,I64 x2,I64 y2)
+{//Distance-squared between 2 points.
+  I64 dx=x1-x2,dy=y1-y2;
+  return dx*dx+dy*dy;
+}
+
+public F64 ASin(F64 s)
+{//Arc Sin (Inverse Sin).
+  F64 c;
+  c=s*s;
+  if (c>=1.0)
+    return ã/2.0;
+  c=Sqrt(1.0-c);
+  return ATan(s/c);
+}
+
+public F64 ACos(F64 c)
+{//Arc Cos (Inverse Cos).
+  F64 s;
+  if (!c)
+    return ã/2.0;
+  s=c*c;
+  if (s>=1.0)
+    return 0.0;
+  s=Sqrt(1.0-s);
+  return ATan(s/c);
+}
+
+public F64 Sinh(F64 x)
+{//Hyperbolic Sine.
+  return 0.5*(Exp(x)-Exp(-x));
+}
+
+public F64 Cosh(F64 x)
+{//Hyperbolic Cosine.
+  return 0.5*(Exp(x)+Exp(-x));
+}
+
+#help_index "Math/Complex"
+public Complex *CAdd(Complex *n1,Complex *n2,Complex *sum)
+{//n1 + n2 -->sum
+  sum->x=n1->x+n2->x;
+  sum->y=n1->y+n2->y;
+  return sum;
+}
+
+public Complex *CSub(Complex *n1,Complex *n2,Complex *diff)
+{//n1 - n2 -->diff
+  diff->x=n1->x-n2->x;
+  diff->y=n1->y-n2->y;
+  return diff;
+}
+
+public Complex *CMul(Complex *n1,Complex *n2,Complex *prod)
+{//n1 * n2 -->prod
+  prod->x=n1->x*n2->x-n1->y*n2->y;
+  prod->y=n1->x*n2->y+n1->y*n2->x;
+  return prod;
+}
+
+public Complex *CDiv(Complex *n1,Complex *n2,Complex *quot)
+{//n1 / n2 -->quot
+  F64 m1,a1,m2,a2;
+  R2P(&m1,&a1,n1->x,n1->y);
+  R2P(&m2,&a2,n2->x,n2->y);
+  m1/=m2;
+  a1-=a2;
+  quot->x=m1*Cos(a1);
+  quot->y=m1*Sin(a1);
+  return quot;
+}
+
+public Complex *CScale(Complex *dst,F64 s)
+{//dst *= s
+  dst->x*=s;
+  dst->y*=s;
+  return dst;
+}
+
+public Complex *CCopy(Complex *dst,Complex *src)
+{//dst=src
+  dst->x=src->x;
+  dst->y=src->y;
+  return dst;
+}
+
+public Complex *CEqu(Complex *dst,F64 x,F64 y)
+{//dst=x,y
+  dst->x=x;
+  dst->y=y;
+  return dst;
+}
+
+public Complex *CPoly(Complex *dst,Complex *x,Complex *zeros,I64 n)
+{//Eval complex polynomial.
+  I64 i;
+  Complex n1,n2;
+  if (n>0) {
+    CSub(x,&zeros[0],dst);
+    for (i=1;i<n;i++) {
+      CCopy(&n1,dst);
+      CSub(x,&zeros[i],&n2);
+      CMul(&n1,&n2,dst);
+    }
+  } else
+    CEqu(dst,1.0,0.0);
+  return dst;
+}