Elliptic curve arithmetic: Difference between revisions

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Also, some code was added to have the output better aligned   (for instance, negative and positive numbers).

<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)

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

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

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

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

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

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

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

cbrt: procedure; parse arg x; return root(x,3)

root: procedure; parse arg x,y; if x=0 | y=1 then return x/1; d=5; return rootI()

root: procedure; parse arg x,y; if x=0 | y=1 then return x/1; d=5; return rootI()/1

rootG: parse value format(x,2,1,,0) 'E0' with ? 'E' _ .; return (?/y'E'_%y) + (x>1)

func: procedure; parse arg y,k; if k=='' then k=7; return cbrt(y**2-k) y

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

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

~~numeric fuzz 3;~~ do until d==a; d=min(d+d,a); numeric digits d; o=0

do until d==a; d=min(d+d,a); numeric digits d; o=0

do until o=g; o=g; g=format((m*g**y+x)/y/g**m,,d-2); ~~end~~

do until o=g; o=g; g=format((m*g**y+x)/y/g**m,,d-2); end /*until o=g*/

~~end~~; _=g*sign(ox); if oy<0 then _=1/_; return _/1</lang>

end /*until d==a*/; _=g*sign(ox); if oy<0 then _=1/_; return _</lang>

'''output'''

<pre>