Elliptic curve arithmetic: Difference between revisions

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<lang rexx>/*REXX program defines (for any 2 points on the curve), returns the sum of the 2 points.*/

numeric digits 100 /*try to ensure a min. of accuracy loss*/

a=func(1) ; say ' a = ' show(a)

a= func(1) ; say ' a = ' show(a)

b=func(2) ; say ' b = ' show(b)

b= func(2) ; say ' b = ' show(b)

c=add(a, b) ; say ' c = (a+b) =' show(c)

c= add(a, b) ; say ' c = (a+b) =' show(c)

d=neg(c) ; say ' d = -c =' show(d)

d= neg(c) ; say ' d = -c =' show(d)

e=add(c, d) ; say ' e = (c+d) =' show(e)

e= add(c, d) ; say ' e = (c+d) =' show(e)

g=add(a, add(b, d)) ; say ' g = (a+b+d) =' show(g)

g= add(a, add(b, d)) ; say ' g = (a+b+d) =' show(g)

exit /*stick a fork in it, we're all done. */

/*──────────────────────────────────────────────────────────────────────────────────────*/

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add: procedure; parse arg px py, qx qy; if px=qx & py=qy then return dbl(px py)

if isZ(px py) then return qx qy; if isZ(qx qy) then return px py

z=qx - px; if z=0 then do; $=inf(); rx=inf(); end

z= qx - px; if z=0 then do; $= inf(); rx= inf(); end

else do; $=(qy-py) / z; rx=$*$ - px - qx; end

else do; $= (qy-py) / z; rx= $*$ - px - qx; end

ry=$ * (px-rx) - py; return rx ry

ry= $ * (px-rx) - py; return rx ry

/*──────────────────────────────────────────────────────────────────────────────────────*/

dbl: procedure; parse arg px py; if isZ(px py) then return px py; z=py+py

dbl: procedure; parse arg px py; if isZ(px py) then return px py; z= py+py

if z=0 then $=inf()

if z=0 then $= inf()

else $=(3*px*py) / (py+py)

else $= (3*px*py) / (py+py)

rx=$*$ - px*px; ry=$ * (px-rx) - py; return rx ry

rx= $*$ - px*px; ry= $ * (px-rx) - py; return rx ry

/*──────────────────────────────────────────────────────────────────────────────────────*/

rootI: ox=x; oy=y; x=abs(x); y=abs(y); a=digits()+5; numeric form; g=rootG(); m=y-1