{ 
    Subroutine to compute the tangent of
    a floating point input.

	    Y=TAN(X) 

	Calling Registers
    F0 = Input Value X=[6E-20, 6E20] 
    l_reg = 0 (usually L3)

	Result Registers
    F0 = tangent of input X

	Altered Registers
    F0, F1, F2, F4, F7, F8, F12
    i_reg (usually I3)

	Computation Time
    38 Cycles

    Version 0.03    7/5/90	Gordon A. Sterling
 }

#include "asm_glob.h"

.SEGMENT/PM	Assembly_Library_Code_Space;

.PRECISION=MACHINE_PRECISION;

.GLOBAL	tan;

tan:		i_reg=tangent_data;
		F8=PASS F0, F2=mem(i_reg,1);  { Use absolute value of input }

compute_modulo:	F4=F8*F2, F1=F0;	    { Compute fp modulo value }
		R2=FIX F4, F12=mem(i_reg,1); { Rnd nearest fractional portion }
		F4=FLOAT R2, R0=R2;	    { Return to fp }

compute_f:	F12=F12*F4, F2=mem(i_reg,1); { Compute XN*C1 }
		F2=F2*F4, F12=F8-F12;	    { Compute X-XN*C1, and XN*C2 }
		F8=F12-F2, F4=mem(i_reg,1);  { Compute f=(X-XN*C1)-XN*C2 }
		F12=ABS F8, F7=F8;
		F4=F12-F4, F12=mem(i_reg,1); { Check for TAN(x)=x }		    
		IF LT JUMP compute_quot;    { Compute quotient with NUM=f DEN=1 }

compute_P:	F12=F8*F8, F4=mem(i_reg,1);  { g=f*f }
		F4=F12*F4, F2=mem(i_reg,1);  { Compute p3*g }
		F4=F2+F4;		    { Compute (p3*g + p2) }
		F4=F12*F4, F2=mem(i_reg,1);  { Compute (p3*g + p2)*g }
		F4=F2+F4;		    { Compute (p3*g + p2)*g + p1 }
		F4=F12*F4;		    { Compute ((p3*g + p2)*g + p1)*g }
		F4=F4*F8;		    { Compute ((p3*g + p2)*g + p1)*g*f }
		F8=F4+F8, F4=mem(i_reg,1);   { Compute f*P(g) }

compute_Q:	F4=F12*F4, F2=mem(i_reg,1);  { Compute sum*g }
		F4=F2+F4;		    { Compute sum=sum+next q }
		F4=F12*F4, F2=mem(i_reg,1);  { Compute sum*g }
		F4=F2+F4;		    { Compute sum=sum+next q }
		F4=F12*F4, F2=mem(i_reg,1);  { Compute sum*g }
		F12=F2+F4, F7=F8;	    { Compute sum=sum+next q }

compute_quot:	BTST R0 BY 0;
		IF NOT SZ F12=-F7, F7=F12;
		F0=RECIPS F12;		    { Get 4 bit seed R0=1/D }
		F12=F0*F12, F11=mem(i_reg,1); { D(prime) = D*R0 }
		F7=F0*F7, F0=F11-F12;	    { F0=R1=2-D(prime), F7=N*R0 }
		F12=F0*F12;		    { F12=D(prime)=D(prime)*R1 }
		F7=F0*F7, F0=F11-F12;	    { F7=N*R0*R1, F0=R2=2-D(prime) }
		RTS (DB), F12=F0*F12;	    { F12=D(prime)=D(prime)*R2 }
		F7=F0*F7, F0=F11-F12;	    { F7=N*R0*R1*R2, F0=R3=2-D(prime) }
		F0=F0*F7;		    { F7=N*R0*R1*R2*R3 }

.ENDSEG;

.SEGMENT/SPACE Assembly_Library_Data_Space;

.PRECISION=MEMORY_PRECISION;

.VAR tangent_data[13] =	 0.6366197723675834308,		{ 2/PI }
			 1.57080078125,			{ C1, almost PI/2 }
			-4.454455103380768678308E-6,	{ C2, PI/2=C1+C2 }
			 9.536743164E-7,		{ eps, TAN(eps)=eps }
			 1.0,				{ Used in one path }
			-0.7483634966612065149E-5,	{ P3 }
			 0.2805918241169988906E-2,	{ P2 }
			-0.1282834704095743847,		{ P1 }
			-0.2084480442203870948E-3,	{ Q3 }
			 0.2334485282206872802E-1,	{ Q2 }
			-0.4616168037429048840,		{ Q1 }
			 1.0,				{ Q0 }
			 2.0;				{ Used in divide }

.ENDSEG;