lib_trig_basic.nolol

include "std/math"
include "std/logic"

define rad_to_deg=180/math_pi
define math_half_rot=180
define math_full_rot=360
define math_tau=2*math_pi
define math_quater_rot=90
define deg_to_rad=math_pi/180

//angle betwen -180 and 180
macro angle_mod(x) expr
	math_mod(math_mod(x,math_full_rot)+(math_full_rot+math_half_rot),math_full_rot)-math_half_rot
end

// acurate to within 2.123 degrees
macro math_acos(out, x) block
	out=(-356.719+x*(222.021+90*x))/(-3.964+x*x)
end

// acurate to within 2.123 degrees
macro math_asin(out, x) block
	out=-244.343*x/(-4.3+x*x)
end

// economized rational approximation
// acurate to within 0.109 degrees
macro math_atan(out, y) block
	//out = 0.9724*x−0.1919*x^3
	sign=math_sign(y)
	
	didFlip=y<1 and y>-1
	flip=1-2*didFlip
	if didFlip then
		y=1/y
	end
	out=90*didFlip*sign+flip*215.814*y/(3.8+y*y)
end


macro math_tan(out, x) block
	o=math_mod(math_mod(x,math_half_rot)+math_half_rot+math_quater_rot,math_half_rot)-math_quater_rot
	out=-140.706*o/(-8228.419+o*o)
end

// Bhaskara I method, acurate within 0.002
macro math_sin(out, x) block
	o=angle_mod(x)
	s=math_sign(o)
	o=math_abs(o)
	t=180-o
	out=s*4*o*t/(40500-o*t)
end

// acurate within 0.002
macro math_cos(out, x) block
	math_sin(out,x+math_quater_rot)	
end


// really need to optimize this.
macro math_atan2(out, y, x) block
	sgny=math_sign(y)
	atanyx=0
	t=0 // need this becuse compiler shinanigans
	t=y/x
	math_atan(atanyx,t)	
	$ out=atanyx+(1-math_sign(x))/2*(1+sgny-sgny*sgny)*180
end