val volumeWithin: (Vec3, Vec3) -> List[Vec3] = (a: Vec3, b: Vec3) -> {
val Vec3(ax, ay, az) = a
val Vec3(bx, by, bz) = b
val (minX, maxX) =
if(ax <= bx) (ax, bx)
else (bx, ax)
val (minY, maxY) =
if(ay <= by) (ay, by)
else (by, ay)
val (minZ, maxZ) =
if(az <= bz) (az, bz)
else (bz, az)
val goI: (Int, List[Vec3]) => List[Vec3] = (i: Int, acci: List[Vec3]) => {
if(i > maxX) acci
else {
val goJ: (Int, List[Vec3]) => List[Vec3] = (j: Int, accj: List[Vec3]) => {
if(j > maxY) accj
else {
val goK: (Int, List[Vec3]) => List[Vec3] = (k: Int, acck: List[Vec3]) => {
if(k > maxZ) acck
else goK(k + 1, Vec3(i, j, k) :: acck)
}
goJ(j + 1, goK(minZ, accj))
}
}
goI(i + 1, goJ(minY, acci))
}
}
goI(minX, Nil)
}def volumeWithin = // a b -- vol
disintegrate // -- a bx by bz
4 // -- a bx by bz 4
fisherman // -- bx by bz a
disintegrate // -- bx by bz ax ay az
/*
I'm faced with `fedcba` on my stack, and would love to swindle it to
- `cfbead` (373, simple interleave)
- `fcbead` (61, interleave + swap first two)
- `cfebad` (363, interleave + swap middle two)
- `fcebad` (51, interleave + first two + middle two)
- `cfbeda` (372, interleave + swap last two)
- `fcbeda` (60, interleave + first two + last two)
- `cfebda` (362, interleave + middle two + last two)
- `fcebda` (50, interleave + all swaps)
What's important to note here:
- The "default" value is 373
- Swapping the first two is -312
- Swapping the middle two is -10
- Swapping the last two is -1
*/
373 // -- bx by bz ax ay az 373
3
fisherman2 // -- bx by bz ax ay az 373 ax
7
fisherman2 // -- bx by bz ax ay az 373 ax bx
lteq // -- bx by bz ax ay az 373 (ax<=bx)
0
-312
select
add // -- bx by bz ax ay az [interleave+swapAXBX?]
2
fisherman2
6
fisherman2 // -- bx by bz ax ay az [interleave+swapAXBX?] ay by
lteq // -- bx by bz ax ay az [...] (ay<=by)
0
-10
select
add // -- bx by bz ax ay az [interleave+swapAXBX?+swapAYBY?]
prospectors // -- bx by bz ax ay az [...] az
5
fisherman2 // -- bx by bz ax ay az [...] az bz
lteq
0
-1
select
add
swindle // -- minX maxX minY maxY minZ maxZ
// goI captures all of these except for minX. I'll pretend I planned that!
'goI // -- minX maxX minY maxY minZ maxZ 'goI
dup // -- minX maxX minY maxY minZ maxZ 'goI 'goI
empty_list // -- minX maxX minY maxY minZ maxZ 'goI 'goI Nil
/* Lehmer Code:
0 - maxX Nil - 7
1 - minY 'goI - 5
2 - maxY maxX - 0
3 - minZ minY - 1
4 - maxZ maxY - 2
5 - 'goI minZ - 3
6 - 'goI maxZ - 4
7 - Nil 'goI - 6
[7]5 0 1 2 3 4 6
7[5]0 1 2 3 4 6
7 5[0]1 2 3 4 5
7 5 0[0]1 2 3 4
7 5 0 0[0]1 2 3
7 5 0 0 0[0]1 2
7 5 0 0 0 0[0]1
7 5 0 0 0 0 0[0]
(7! * 7) + (6! * 5) = 38880
38880 = 108 * 360, both drawable literally
*/
108
360
mult
swindle
hermes
def goI = // i acci {'goI maxX minY maxY minZ maxZ}-- list
// pull maxX and i to the front
/*
0 1 2 3 4 5 6 7
1 2 4 5 6 7 0 3
1 1 3 4 5 6 0 2
1 1 2 3 4 5 0 1
1 1 2 2 3 4 0 1
1 1 2 2 2 3 0 1
1 1 2 2 2 2 0 1
1 1 2 2 2 2 0 1
1 1 2 2 2 2 0 0
(7! * 1) + (6! * 1) + (5! * 2) + (4! * 2) + (3! * 2) + (2! * 2) = 6064
6064 can be directly drawn
*/
6064
swindle // -- acci 'goI minY maxY minZ maxZ i maxX
dup2 // -- acci 'goI minY maxY minZ maxZ i maxX i maxX
gt // -- acci 'goI minY maxY minZ maxZ i maxX (i>maxX)
{
vvvvvvv // -- acci
}
{
swap // -- acci 'goI minY maxY minZ maxZ maxX i
dup // -- acci 'goI minY maxY minZ maxZ maxX i i
1
add // -- acci 'goI minY maxY minZ maxZ maxX i (i+1)
// desired stack for goJ call: minY acci* 'goJ maxY minZ maxZ i 'goJ
// many variables are duplicated = we cannot swindle
6
fisherman2 // -- acci 'goI minY maxY minZ maxZ maxX i (i+1) minY
10
fisherman // -- 'goI minY maxY minZ maxZ maxX i (i+1) minY acci
'goJ // -- 'goI minY maxY minZ maxZ maxX i (i+1) minY acci 'goJ
8
fisherman2 // -- 'goI minY maxY minZ maxZ maxX i (i+1) minY acci 'goJ maxY
8
fisherman2 // -- 'goI minY maxY minZ maxZ maxX i (i+1) minY acci 'goJ maxY minZ
8
fisherman2 // -- 'goI minY maxY minZ maxZ maxX i (i+1) minY acci 'goJ maxY minZ maxZ
8
fisherman // -- 'goI minY maxY minZ maxZ maxX (i+1) minY acci 'goJ maxY minZ maxZ i
4
fisherman2
hermes // -- 'goI minY maxY minZ maxZ maxX (i+1) goJ(minY, acci)
/*
0 1 2 3 4 5 6 7
6 7 0 5 1 2 3 4
6 6 0 5 1 2 3 4
6 6 0 5 1 2 3 4
6 6 0 4 0 1 2 3
...
6 6 0 4 0 0 0 0
(7! * 6) + (6! * 6) + (4! * 4) = 34656 = 152 * 228
*/
152
228
mult
swindle // -- (i+1) goJ(minY, acci) 'goI maxX minY maxY minZ maxZ
5
fisherman2
hermes
}
select
hermes
def goJ = // j accj {'goJ maxY minZ maxZ i}-- list
// pull j, maxY to the front
/*
0 1 2 3 4 5 6
1 2 4 5 6 0 3
1 1 3 4 5 0 2
1 1 2 3 4 0 1
1 1 2 2 3 0 1
1 1 2 2 2 0 1
1 1 2 2 2 0 1
1 1 2 2 2 0 0
(6! * 1) + (5! * 1) + (4! * 2) + (3! * 2) + (2! * 2) = 904
*/
904
swindle // -- accj 'goJ minZ maxZ i j maxY
dup2 // -- accj 'goJ minZ maxZ i j maxY j maxY
gt // -- accj 'goJ minZ maxZ i j maxY (j>maxY)
{
vvvvvv // -- accj
}
{
swap
dup
1
add // -- accj 'goJ minZ maxZ i maxY j (j+1)
// desired stack for goK call: minZ accj* 'goK maxZ i j 'goK
5
fisherman2 // -- accj 'goJ minZ maxZ i maxY j (j+1) minZ
9
fisherman // -- 'goJ minZ maxZ i maxY j (j+1) minZ accj
'goK // -- 'goJ minZ maxZ i maxY j (j+1) minZ accj 'goK
7
fisherman2 // -- 'goJ minZ maxZ i maxY j (j+1) minZ accj 'goK maxZ
7
fisherman2 // -- 'goJ minZ maxZ i maxY j (j+1) minZ accj 'goK maxZ i
7
fisherman // -- 'goJ minZ maxZ i maxY (j+1) minZ accj 'goK maxZ i j
3
fisherman2 // -- 'goJ minZ maxZ i maxY (j+1) minZ accj 'goK maxZ i j 'goK
hermes // -- 'goJ minZ maxZ i maxY (j+1) goK(minZ, accj)
// we can't combine the swindles due to our inability to push goK down the stack in 0.10.3
// we could possibly combine both the 'goJ duplication and 'goK duplication into one dioscuri gambit
// but the resulting swindle numbers might be too large as to require two extra ops, negating the benefit
/*
0 1 2 3 4 5 6
5 6 0 4 1 2 3
5 5 0 4 1 2 3
5 5 0 4 1 2 3
5 5 0 3 0 1 2
5 5 0 3 0 1 2
5 5 0 3 0 0 1
5 5 0 3 0 0 0
(6! * 5) + (5! * 5) + (3! * 3) = 4218
*/
4218
swindle // -- (j+1) goK(minZ, accj) 'goJ maxY minZ maxZ i
4
fisherman2
hermes
}
select
hermes
def goK = // k acck {'goK maxZ i j}-- list
dup2 // -- k acck 'goK maxZ i j i j
/*
0 1 2 3 4 5 6 7
1 2 4 5 6 7 0 3
1 1 3 4 5 6 0 2
1 1 2 3 4 5 0 1
1 1 2 2 3 4 0 1
1 1 2 2 2 3 0 1
1 1 2 2 2 2 0 1
1 1 2 2 2 2 0 0
(7! * 1) + (6! * 1) + (5! * 2) + (4! * 2) + (3! * 2) + (2! * 2) = 6064
*/
6304
swindle // -- acck 'goK i j i j k maxZ
dup2
gt // -- acck 'goK i j i j k maxZ (k>maxZ)
{
vvvvvvv
}
{
swap // -- acck 'goK i j i j maxZ k
dup
1
add // -- acck 'goK i j i j maxZ k (k+1)
// we want (k+1) 'goK maxZ i j acck i j k
/*
0 1 2 3 4 5 6 7 8
8 1 6 2 3 0 4 5 7
8 1 6 2 3 0 4 5 7
8 1 5 1 2 0 3 4 6
8 1 5 1 2 0 3 4 5
8 1 5 1 1 0 2 3 4
8 1 5 1 1 0 1 2 3
...
8 1 5 1 1 0 0 0 0
(8! * 8) + (7! * 1) + (6! * 5) + (5! * 1) + (4! * 1) = 331344 = 708 * 468
*/
708
468
mult
swindle // -- (k+1) 'goK maxZ i j acck i j k
exalt // -- (k+1) 'goK maxZ i j acck <i, j, k>
integrate // -- (k+1) 'goK maxZ i j [...acck, <i, j, k>]
/*
0 1 2 3 4
4 0 1 2 3
*/
96
swindle // -- (k+1) [...acck, <i, j, k>] 'goK maxZ i j
3
fisherman2
hermes
}
select
hermesVector Disintegration
Numerical Reflection: 4
Fisherman's Gambit
Vector Disintegration
Numerical Reflection: 373
Numerical Reflection: 3
Fisherman's Gambit II
Numerical Reflection: 7
Fisherman's Gambit II
Minimus Distillation II
Numerical Reflection: 0
Numerical Reflection: -312
Augur's Exaltation
Additive Distillation
Numerical Reflection: 2
Fisherman's Gambit II
Numerical Reflection: 6
Fisherman's Gambit II
Minimus Distillation II
Numerical Reflection: 0
Numerical Reflection: -10
Augur's Exaltation
Additive Distillation
Prospector's Gambit
Numerical Reflection: 5
Fisherman's Gambit II
Minimus Distillation II
Numerical Reflection: 0
Numerical Reflection: -1
Augur's Exaltation
Additive Distillation
Swindler's Gambit
{
Numerical Reflection: 6064
Swindler's Gambit
Dioscuri Gambit
Maximus Distillation
{
Bookkeeper's Gambit: vvvvvvv
}
{
Jester's Gambit
Gemini Decomposition
Numerical Reflection: 1
Additive Distillation
Numerical Reflection: 6
Fisherman's Gambit II
Numerical Reflection: 10
Fisherman's Gambit
{
Numerical Reflection: 904
Swindler's Gambit
Dioscuri Gambit
Maximus Distillation
{
Bookkeeper's Gambit: vvvvvv
}
{
Jester's Gambit
Gemini Decomposition
Numerical Reflection: 1
Additive Distillation
Numerical Reflection: 5
Fisherman's Gambit II
Numerical Reflection: 9
Fisherman's Gambit
{
Dioscuri Gambit
Numerical Reflection: 6064
Swindler's Gambit
Dioscuri Gambit
Maximus Distillation
{
Bookkeeper's Gambit: vvvvvvv
}
{
Jester's Gambit
Gemini Decomposition
Numerical Reflection: 1
Additive Distillation
Numerical Reflection: 708
Numerical Reflection: 468
Multiplicative Distillation
Swindler's Gambit
Vector Exaltation
Integration Distillation
Numerical Reflection: 96
Swindler's Gambit
Numerical Reflection: 3
Fisherman's Gambit II
Hermes' Gambit
}
Augur's Exaltation
Hermes' Gambit
}
Numerical Reflection: 7
Fisherman's Gambit II
Numerical Reflection: 7
Fisherman's Gambit II
Numerical Reflection: 7
Fisherman's Gambit
Numerical Reflection: 3
Fisherman's Gambit II
Hermes' Gambit
Numerical Reflection: 4218
Swindler's Gambit
Numerical Reflection: 4
Fisherman's Gambit II
Hermes' Gambit
}
Augur's Exaltation
Hermes' Gambit
}
Numerical Reflection: 8
Fisherman's Gambit II
Numerical Reflection: 8
Fisherman's Gambit II
Numerical Reflection: 8
Fisherman's Gambit II
Numerical Reflection: 8
Fisherman's Gambit
Numerical Reflection: 4
Fisherman's Gambit II
Hermes' Gambit
Numerical Reflection: 152
Numerical Reflection: 228
Multiplicative Distillation
Swindler's Gambit
Numerical Reflection: 5
Fisherman's Gambit II
Hermes' Gambit
}
Augur's Exaltation
Hermes' Gambit
}
Gemini Decomposition
Vacant Reflection
Numerical Reflection: 108
Numerical Reflection: 360
Multiplicative Distillation
Swindler's Gambit
Hermes' Gambit
Requires two Vec3s on the stack beforehand.