-- 3e Essais de faire des fonctions trigos qui manque dans NodeMCU
-- source pour arctan,arcsin et arccos: http://mathonweb.com/help_ebook/html/algorithms.htm
-- source pour sin&cos: https://www.esp8266.com/viewtopic.php?p=64415#
-- source pour arcsin&arctan: http://www.electronicwings.com/nodemcu/magnetometer-hmc5883l-interfacing-with-nodemcu
print("\ntrigo3.lua   zf180819.1745   \n")

pi = 3.14159265358979323846

function zsin(x)
   local p=-x*x*x   local f=6   local r=x+p/f
   for j=1,60 do
      p=-p*x*x   f=f*2*(j+1)*(j+j+3)   r=r+p/f
   end
   return r
end

function zcos(x)
   return zsin(math.pi/2-x)
end

function ztan(x)
   return zsin(x)/zcos(x)
end




function zatan(x)
  local y=1  local z
  if x<0 then
    y=-1  x=y*x
  end
  if x<1 then
    z=zzatan(x)
  else
    z=pi/2-zatan(1/x)
  end
  return y*z
end

function zzatan(x)
  return x-x^3/3+x^5/5-x^7/7
end




--[[
--print("On voit que l'arc sinus est précis au 1/2% prêt !")
a=0.9
print("théorique tan("..a.."): "..math.tan(a))
print("calculée  tan("..a.."): "..ztan(a))
b=math.tan(a)
print("théorique atan("..b.."): "..math.atan(b))
print("calculée  atan("..b.."): "..zatan(b)..", "..pi/2-zatan(1/b))
--print("pi/(arcsin(1)*2): "..pi/(arcsin(1)*2))
]]


--[[
print("On voit que l'arc sinus est précis au 1/2% prêt !")
print("sin(3.14/2): "..sin(3.14/2))
print("pi/(arcsin(1)*2): "..pi/(arcsin(1)*2))
]]


--[[
function arcsin(value)
    local val = value
    local sum = value
    if(value == nil) then
        return 0
    end
-- as per equation it needs infinite iterations to reach upto 100% accuracy
-- but due to technical limitations we are using
-- only 10000 iterations to acquire reliable accuracy
    for i = 1,10000, 2 do
        val = (val*(value*value)*(i*i)) / ((i+1)*(i+2))
        sum = sum + val;
    end
    return sum
end

function arctan(value)
    if(value == nil) then
        return 0
    end
    local _value = value/math.sqrt((value*value)+1)
    return arcsin(_value)
end

function atan2(y, x)
    if(x == nil or y == nil) then
        return 0
    end

    if(x > 0) then
        return arctan(y/x)
    end
    if(x < 0 and 0 <= y) then
        return arctan(y/x) + pi
    end
    if(x < 0 and y < 0) then
        return arctan(y/x) - pi
    end
    if(x == 0 and y > 0) then
        return pi/2
    end
    if(x == 0 and y < 0) then
        return -pi/2
    end
    if(x == 0 and y == 0) then
        return 0
    end
    return 0
end
]]