Acosc.cin

// Acosc.cin is routine in [C++]] for evaluation of function ArcCosc with complex(double) precision. // ArcCosc is inverse function of Cosc; \(\text{cosc}(z) = \cos(z)/z\).

z_type cosc(z_type z) {return cos(z)/z;}
z_type cosp(z_type z) {return (-sin(z) - cos(z)/z)/z ;}
z_type cohc(z_type z) {return cosh(z)/z ;}
z_type cohp(z_type z) {return (sinh(z)-cosh(z)/z)/z ;}

z_type acoscL(z_type z){ int n; z_type s,q; z*=-I; q=I*sqrt(1.50887956153832-z);
  s=q*1.1512978931181814 + 1.199678640257734; DO(n,6) s+= (z-cohc(s))/cohp(s);
  return -I*s; }

z_type acoscR(z_type z) {int n; z_type s= (1.-0.5/(z*z))/z;
       DO(n,5) s+=(z-cosc(s))/cosp(s); return s;}

z_type acoscB(z_type z){ z_type t=0.33650841691839534+z, u=sqrt(t), s; int n;
s=    2.798386045783887
+u*(-2.437906425896532
+u*( 0.7079542331649882 
+u*(-0.5009330133042798
+u*( 0.5714459932734446    ))));
DO(n,6) s+=(z-cosc(s))/cosp(s); return s; }

z_type acosc(z_type z){ DB x1=-0.33650841691839534, x=Re(z), y=Im(z), yy=y*y, 
r=x-x1;r*=r;r+=yy; if(r < 1.8 )     return acoscB(z); 
r=x+2.;r*=r;r+=yy; if(r>8. && x>=0) return acoscR(z);
if(y >= 0) return acoscL(z);
      return conj(acoscL(conj(z))); }

// Copyleft 2012 by Dmitrii Kouznetsov.

//
//