High-level Immutable Algorithm

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)
}

Reified Closures

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
  hermes

Hex Pattern

Vector 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.

s5bug/note.md

High-level Immutable Algorithm

Reified Closures

Hex Pattern

Sirius902 commented Jul 1, 2025

Uh oh!