While I am convinced that people are not supposed to live more than 50 years I'm still jogging on at the age of 62, so I decided to write a large(ish) programme.
The programme ecm takes a composite integer as input & returns a factor, found through the elliptic curve factorzing method.
ecm, while itself a short programme, has several sub-programmes integral to its functioning, as is my heart to my body, which qualify ecm to receive the attribute large
Code:
ecm
::
CK1&Dispatch
# FF
::
ID x00E
Z100_
ID x00D
;
;
x008
::
BINT0
4UNROLL
'
NULLLAM
BINT5
NDUPN
DOBIND
NULL{}
3GETLAM
Z1_
FPTR2 ^QSub
FPTR2 ^Z>R
% 999999999999.
%MIN
%RAN
%*
%IP
FPTR2 ^R>Z
1GETLAM
FPTR2 ^Z2BIN
ZERO_DO
INDEX@
DUP
BINT80h
#/
#1+
#>$
"Mul #: "
SWAP&$
BIGDISPROW2
DROP
FPTR2 ^#>Z
DUP
ZINT 128
FPTR2 ^QAdd
1GETLAM
FPTR2 ^ZNMin
DUP4PUTLAM
ID x00A
5GETLAM
3UNROLL
2GETLAM
3GETLAM
ID x009
IT
::
ExitAtLOOP
DUP
Z1_
Z>
OVER
3GETLAM
Z<
AND
NOT?SEMI
5GETLAM
2GETLAM
4GETLAM
BINT3
{}N
SWAP
;
BINT80h
+LOOP
ABND
OVER
NULLCOMP?
case2drop
Z0_
ROTDROP
;
x009
::
ROT
FPTR2 ^DupQIsZero?
case
::
4UNROLL3DROP
TRUE
;
FPTR2 ^Z>ZH
5UNROLL
3PICK
Z1_
5PICK
DUPDUP
FPTR2 ^RMULText
8PICK
FPTR2 ^RADDext
FPTR2 ^RMULText
5ROLL
FPTR2 ^RADDext
4PICK
FPTR2 ^ZMod
DUP
5PICK
ID x00F
ROTDUP
FPTR2 ^ZIsOne?
NOTcase
::
10UNROLL
BINT9
NDROP
TRUE
;
2DROP
'
NULLLAM
BINT7
NDUPN
DOBIND
FALSE
SWAP
FPTR2 ^ZBits
ONE_DO
::
3GETLAM
DUP
FPTR2 ^QAdd
5GETLAM
ID x00F
ROTDUP
FPTR2 ^ZIsOne?
NOTcase
::
5UNROLL
3DROPTRUE_
ExitAtLOOP
;
2DROP
Z3_
6GETLAM
FPTR2 ^ZSQ_
FPTR2 ^RMULText
7GETLAM
FPTR2 ^QAdd
1GETLAM
FPTR2 ^QMul
FPTR2 ^QMul
5GETLAM
FPTR2 ^ZMod
DUP
FPTR2 ^ZSQ_
2GETLAM
FPTR2 ^QMul
6GETLAM
DUP
FPTR2 ^QAdd
FPTR2 ^QSub
5GETLAM
FPTR2 ^ZMod
6GETLAM
OVER
6PUTLAM
FPTR2 ^RSUBext
FPTR2 ^QMul
3GETLAM
FPTR2 ^RNEGext
FPTR2 ^SWAPRSUB
5GETLAM
FPTR2 ^ZMod
3PUTLAM
ISTOP-INDEX
#1-
FPTR2 ^ZBit?
NOT?SEMI
6GETLAM
4GETLAM
FPTR2 ^QSub
5GETLAM
ID x00F
ROTDUP
FPTR2 ^ZIsOne?
NOTcase
::
5UNROLL
3DROPTRUE_
ExitAtLOOP
;
2DROP
Z-1_
3GETLAM
Z1_
FPTR2 ^QSub
ROT
FPTR2 ^QMul
5GETLAM
FPTR2 ^ZMod
DUPDUP
FPTR2 ^QMul
2GETLAM
FPTR2 ^QMul
6GETLAM
FPTR2 ^QSub
4GETLAM
FPTR2 ^QSub
5GETLAM
FPTR2 ^ZMod
DUP
6PUTLAM
4GETLAM
FPTR2 ^QSub
FPTR2 ^QMul
FPTR2 ^QSub
5GETLAM
FPTR2 ^ZMod
3PUTLAM
;
LOOP
SWAPDROPDUP
?SKIP
::
6GETLAM
SWAP
;
ABND
;
x00A
::
Z1_
OVER
ID x00C
4PICK
ID x00C
Z1_
FPTR2 ^QAdd
Z2_
FPTR2 ^ZNMax
::
BEGIN
2DUP
Z<
case
COLA_EVAL
::
DUP
4ROLL
FPTR2 ^RMULText
3UNROLL
Z1_
FPTR2 ^RADDext
;
AGAIN
;
2DROP
SWAPROT
Z2_
FPTR2 ^ZNMax
::
BEGIN
FPTR2 ^Prime+
2DUP
Z<
case
COLA_EVAL
::
DUP
4ROLL
FPTR2 ^RMULText
3UNROLL
;
AGAIN
;
2DROP
;
x00B
::
%ABS
%3
%MAX
%LN
DUP
%LN
%*
%SQRT
%EXP
;
x00C
::
DUP
Z2_
Z<
?SEMI
Z2_
OVER
FPTR2 ^Z>ZH
FPTR2 ^ZBits
SWAPDROP
#2/
#1+
FPTR2 ^RP#
ZEROSWAP
BEGIN
SWAPDROPDUP
3PICKOVER
FPTR2 ^ZDIVext
DROP
FPTR2 ^QAdd
Z2_
FPTR2 ^ZDIVext
DROP
2DUP
Z>
NOT_UNTIL
DROPSWAPDROP
;
x00D
::
FPTR2 ^3LAMBIND
Z0_
1GETLAM
FPTR2 ^Z2BIN
#1+_ONE_DO
"Curve #: "
INDEX@
#>$
&$
BIGDISPROW3
3GETLAM
BINT2
ZERO_DO
%RAN
% 999999999999.
%*
%IP
FPTR2 ^R>Z
OVER
FPTR2 ^ZMod
SWAPLOOP
3UNROLL
ZINT 27
OVER
BINT2
FPTR2 ^RP#
FPTR2 ^QMul
Z4_
4PICK
BINT3
FPTR2 ^RP#
FPTR2 ^RMULText
FPTR2 ^QAdd
4PICK
FPTR2 ^ZGcd
FPTR2 ^DupZIsOne?
ITE
::
DROPSWAP
3UNROLL
2GETLAM
ID x008
DUP
Z1_
Z>
OVER
3GETLAM
Z<
ANDcase
ExitAtLOOP
DROP
;
::
ROTROT2DROP
ExitAtLOOP
;
LOOP
ABND
FPTR2 ^DupQIsZero?
?SEMI
ROTDROP
;
x00E
::
DUP
FPTR2 ^Z>R
ID x00B
%2
%SQRT
%NROOT
%CEIL
FPTR2 ^R>Z
;
x00F
::
BINT0
3UNROLL
BEGIN
ROT#1+UNROT
DUPUNROT
FPTR2 ^ZDIVext
SWAP
4UNROLLDUP
Z0_
EQUAL
UNTIL
DROP
ZINT1_0_
4ROLL
ZERO_DO
DUPUNROT
5ROLL
FPTR2 ^QMul
FPTR2 ^QSub
LOOP
3PICK
FPTR2 ^ZIsNeg?
NOT?SEMI
BINT3
ZERO_DO
ROT
FPTR 6 4FB
LOOP
;
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(50G) Elliptic Curve Integer Factorization Programme
