#
# canola - canon canola 1614p emulator
# Copyright (C) 2011 Peter Miller
#
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License, version 3, as
# published by the Free Software Foundation.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
# General Public License for more details.
#
# You should have received a copy of the GNU General Public License along
# with this program. If not, see <http://www.gnu.org/licenses/>.
#
;
; ----------  Card-Pocket-Begin  -------------------------------------------
; Title: Cube Root by Halley's Method, by P. Miller
; Style: aus
; Disassemble: true
; ----------  Card-Pocket-End  ---------------------------------------------
;
; The method used here is actually an application of a method devised by
; comet discoverer Edmond Halley (see Halley's Method).  Over the years
; it has been repeatedly rediscovered and attributed to others including
; Lambert and Bailey.  It has cubic convergence, which is better than
; Newton-Raphson quadratic convergence.
;
;     solve:  x**3 - a = 0
;
;     x2 = x1 * ((x1**3 + a) + a) / (x1**3 + (x1**3 + a))
;
; See Also
; https://en.wikipedia.org/wiki/Halley%27s_method
;
sfj $210
    sm14        ; a => m14
    sqrt
    sqrt        ; first approximation is 4th root
    sm13        ; x1 => m13
fj $210
    rm13
    *
    +=
    *
    rm13
    +=
    sm12        ; x1**3 => m12

    rm14
    +=
    sm11        ; x1**3 + a => m11

    rm12
    +=
    sm10        ; (x1**3 + (x1**3 + a)) => m10

    rm11
    rm14
    +=          ; ((x1**3 + a) + a)
    *
    rm13
    /           ; x1 * ((x1**3 + a) + a)
    rm10
    +=          ; x2
    rm13
    rv
    sm13
    -=          ; x2 - x1
    *
    .1
    +=
    mj $210
    sc
    mj $210
    rm13
    srj