"execution_count": 1,
"id": "08a49b81",
"metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "2147483648"
- ]
- }
- ],
+ "outputs": [],
"source": [
"1 31 << "
]
"execution_count": 2,
"id": "b34d58ef",
"metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": []
- }
- ],
+ "outputs": [],
"source": [
"unit [base] swoncat inscribe"
]
"execution_count": 3,
"id": "35476eac",
"metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": []
- }
- ],
+ "outputs": [],
"source": [
"[valid_digit [0 >] [base <] &&] inscribe"
]
"execution_count": 4,
"id": "02a48806",
"metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "32 true 1232147483648 false"
- ]
- }
- ],
+ "outputs": [],
"source": [
"32 valid_digit 1232147483648 valid_digit"
]
"execution_count": 5,
"id": "03a8fe65",
"metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": []
- }
- ],
+ "outputs": [],
"source": [
"clear"
]
"execution_count": 6,
"id": "3fc98ccd",
"metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "1797196498 5748904729"
- ]
- }
- ],
+ "outputs": [],
"source": [
"12345678901234567890 base divmod swap"
]
"execution_count": 7,
"id": "b838c4cb",
"metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "1797196498 1453937433 2"
- ]
- }
- ],
+ "outputs": [],
"source": [
"base divmod swap"
]
"execution_count": 8,
"id": "42c9d92d",
"metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "1797196498 1453937433 2 0"
- ]
- }
- ],
+ "outputs": [],
"source": [
"base divmod swap"
]
"execution_count": 9,
"id": "faaac9d6",
"metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "1312754386 1501085485 57659106 105448366 58"
- ]
- }
- ],
+ "outputs": [],
"source": [
"clear 1234567890123456789012345678901234567890\n",
"\n",
"execution_count": 10,
"id": "2a613f36",
"metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "[58 105448366 57659106 1501085485 1312754386]"
- ]
- }
- ],
+ "outputs": [],
"source": [
"clear [1234567890123456789012345678901234567890]\n",
"\n",
"id": "c89e6054",
"metadata": {},
"source": [
- "#### `to_bigint`"
+ "#### `to-bigint`"
]
},
{
}
],
"source": [
- "[to_bigint [!-] [abs digitalize] cleave cons] inscribe"
+ "[to-bigint [!-] [abs digitalize] cleave cons] inscribe"
]
},
{
}
],
"source": [
- "clear 1234567890123456789012345678901234567890 to_bigint"
+ "clear 1234567890123456789012345678901234567890 to-bigint"
]
},
{
}
],
"source": [
- "clear -1234567890123456789012345678901234567890 to_bigint"
+ "clear -1234567890123456789012345678901234567890 to-bigint"
]
},
{
"id": "7497680b",
"metadata": {},
"source": [
- "#### `prep` and `from_bigint'`"
+ "#### `prep` and `from-bigint'`"
]
},
{
],
"source": [
"[prep rest 1 0 rolldown] inscribe\n",
- "[from_bigint' [F] step popd] inscribe\n",
+ "[from-bigint' [F] step popd] inscribe\n",
"[F [G] [H] clop popdd] inscribe\n",
"[G popop base *] inscribe\n",
"[H rolldown * +] inscribe"
"source": [
"clear 1 0 [1312754386 1501085485 57659106 105448366 58]\n",
"\n",
- "from_bigint'"
+ "from-bigint'"
]
},
{
}
],
"source": [
- "to_bigint"
+ "to-bigint"
]
},
{
}
],
"source": [
- "from_bigint'"
+ "from-bigint'"
]
},
{
}
],
"source": [
- "to_bigint prep from_bigint'"
+ "to-bigint prep from-bigint'"
]
},
{
}
],
"source": [
- "to_bigint prep from_bigint'"
+ "to-bigint prep from-bigint'"
]
},
{
}
],
"source": [
- "to_bigint"
+ "to-bigint"
]
},
{
}
],
"source": [
- "[first] [prep from_bigint'] cleave"
+ "[first] [prep from-bigint'] cleave"
]
},
{
"source": [
"This gives:\n",
"\n",
- " foo == [first] [prep from_bigint'] cleave\n",
+ " foo == [first] [prep from-bigint'] cleave\n",
" bar == swap [] [neg] branch\n",
- " from_bigint == foo bar"
+ " from-bigint == foo bar"
]
},
{
"id": "8bffedec",
"metadata": {},
"source": [
- "#### `from_bigint`"
+ "#### `from-bigint`"
]
},
{
],
"source": [
"clear\n",
- "[foo [first] [prep from_bigint'] cleave] inscribe\n",
+ "[foo [first] [prep from-bigint'] cleave] inscribe\n",
"[bar swap [neg] [] branch] inscribe\n",
- "[from_bigint foo bar] inscribe"
+ "[from-bigint foo bar] inscribe"
]
},
{
}
],
"source": [
- "1234567890123456789012345678901234567890 to_bigint from_bigint"
+ "1234567890123456789012345678901234567890 to-bigint from-bigint"
]
},
{
}
],
"source": [
- "neg to_bigint from_bigint"
+ "neg to-bigint from-bigint"
]
},
{
"\n",
"Let's figure out how to add two lists of digits (we will assume that the signs are the same.) We need to put an inital `false` value for a carry flag, and then there's a `genrec`.\n",
"\n",
- " initial-carry ≡ false rollup\n",
+ " initial-carry == false rollup\n",
" add-digits' ≡ [P] [THEN] [R0] [R1] genrec\n",
" \n",
" add-digits ≡ initial-carry add-digits'"
"id": "223cee8e",
"metadata": {},
"source": [
- "#### `bool_to_int`"
+ "#### `bool-to-int`"
]
},
{
"source": [
"clear\n",
"\n",
- "[bool_to_int [0] [1] branch] inscribe"
+ "[bool-to-int [0] [1] branch] inscribe"
]
},
{
}
],
"source": [
- "false bool_to_int\n",
- "true bool_to_int"
+ "false bool-to-int\n",
+ "true bool-to-int"
]
},
{
"source": [
"clear\n",
"\n",
- "false 1 2 [bool_to_int] dipd + +"
+ "false 1 2 [bool-to-int] dipd + +"
]
},
{
"source": [
"clear\n",
"\n",
- "true 1 2 [bool_to_int] dipd + +"
+ "true 1 2 [bool-to-int] dipd + +"
]
},
{
"id": "89b971c9",
"metadata": {},
"source": [
- "So the first part of `F` is `[bool_to_int] dipd + +` to get the total, then we need to do\n",
+ "So the first part of `F` is `[bool-to-int] dipd + +` to get the total, then we need to do\n",
"\n",
"`base mod` to get the new digit and `base >=` to get the new carry flag:"
]
"source": [
"Put it all together and we have:\n",
"\n",
- " _add-with-carry0 ≡ [bool_to_int] dipd + +\n",
+ " _add-with-carry0 ≡ [bool-to-int] dipd + +\n",
" _add-with-carry1 ≡ base [mod] [>=] clop\n",
"\n",
" add-with-carry ≡ _add-with-carry0 _add-with-carry1\n"
],
"source": [
"clear\n",
- "[_add-with-carry0 [bool_to_int] dipd + +] inscribe\n",
+ "[_add-with-carry0 [bool-to-int] dipd + +] inscribe\n",
"[_add-with-carry1 base [mod] [>=] clop] inscribe\n",
"[add-with-carry _add-with-carry0 _add-with-carry1] inscribe"
]
},
{
"cell_type": "code",
- "execution_count": 91,
+ "execution_count": 57,
"id": "b46a62ba",
"metadata": {},
"outputs": [
"source": [
"clear\n",
"\n",
- "123 to_bigint 456 to_bigint"
+ "123 to-bigint 456 to-bigint"
]
},
{
"source": [
"clear\n",
"\n",
- "123 to_bigint 456 to_bigint"
+ "123 to-bigint 456 to-bigint"
]
},
{
}
],
"source": [
- "base -- to_bigint"
+ "base -- to-bigint"
]
},
{
},
{
"cell_type": "code",
- "execution_count": 95,
- "id": "d8832fda",
+ "execution_count": 90,
+ "id": "dac1c858",
"metadata": {},
"outputs": [
{
},
{
"cell_type": "markdown",
- "id": "fdc6fc09",
+ "id": "184f6b2e",
"metadata": {},
"source": [
"But this doesn't go quite far enough, I think.\n",
},
{
"cell_type": "markdown",
- "id": "94249f95",
+ "id": "7598e48c",
"metadata": {},
"source": [
"I think `R0` will pretty much always do:\n",
},
{
"cell_type": "markdown",
- "id": "ecc190e3",
+ "id": "b721354e",
"metadata": {},
"source": [
"And so it should be refactored further to something like:\n",
},
{
"cell_type": "markdown",
- "id": "c9fd7e21",
+ "id": "aa6e7586",
"metadata": {},
"source": [
"Let's figure out the new form.\n",
},
{
"cell_type": "markdown",
- "id": "64118784",
+ "id": "0a5e4669",
"metadata": {},
"source": [
"Let's not over think it.\n",
},
{
"cell_type": "markdown",
- "id": "90310271",
+ "id": "9d7aad63",
"metadata": {},
"source": [
"With:\n",
},
{
"cell_type": "code",
- "execution_count": 93,
+ "execution_count": 91,
"id": "55f64814",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 91,
+ "execution_count": 92,
"id": "04e2d0d0",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 92,
+ "execution_count": 93,
"id": "a28d9323",
"metadata": {},
"outputs": [
},
{
"cell_type": "markdown",
- "id": "e8433d46",
+ "id": "004b7aca",
"metadata": {},
"source": [
"So to get from \n",
},
{
"cell_type": "code",
- "execution_count": 103,
- "id": "77e6c03a",
+ "execution_count": 94,
+ "id": "bc16275c",
"metadata": {},
"outputs": [
{
},
{
"cell_type": "code",
- "execution_count": 104,
- "id": "1119f1e6",
+ "execution_count": 95,
+ "id": "c517da7a",
"metadata": {},
"outputs": [
{
},
{
"cell_type": "code",
- "execution_count": 105,
+ "execution_count": 96,
"id": "3f482224",
"metadata": {},
"outputs": [
{
"cell_type": "code",
"execution_count": null,
- "id": "02bfc247",
+ "id": "3a504505",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
- "execution_count": 106,
+ "execution_count": 97,
"id": "4b90e664",
"metadata": {},
"outputs": [
},
{
"cell_type": "markdown",
- "id": "089fc71c",
+ "id": "173bf5b7",
"metadata": {},
"source": [
"Compare the above with what we wanted:\n",
{
"cell_type": "code",
"execution_count": null,
- "id": "929366cc",
+ "id": "c816fa4b",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
- "execution_count": 107,
- "id": "a3b7e48a",
+ "execution_count": 98,
+ "id": "ff88e2c1",
"metadata": {},
"outputs": [
{
},
{
"cell_type": "code",
- "execution_count": 108,
- "id": "313ce113",
+ "execution_count": 99,
+ "id": "941a4426",
"metadata": {
"scrolled": true
},
},
{
"cell_type": "code",
- "execution_count": 110,
- "id": "aca55d10",
+ "execution_count": 100,
+ "id": "917600dd",
"metadata": {},
"outputs": [
{
]
},
{
- "cell_type": "markdown",
- "id": "92a471fa",
- "metadata": {},
- "source": [
- " combine-two-lists == build-two-list-combiner [i cons] genrec\n",
- " "
- ]
- },
- {
"cell_type": "code",
- "execution_count": 111,
- "id": "0fa2607d",
+ "execution_count": 101,
+ "id": "21f6b0e4",
"metadata": {},
"outputs": [
{
},
{
"cell_type": "code",
- "execution_count": 112,
- "id": "026095a5",
+ "execution_count": 102,
+ "id": "4a8819fc",
"metadata": {},
"outputs": [
{
},
{
"cell_type": "code",
- "execution_count": 113,
- "id": "15974737",
+ "execution_count": 103,
+ "id": "5d451c1e",
"metadata": {},
"outputs": [
{
},
{
"cell_type": "code",
- "execution_count": 114,
- "id": "525bc382",
+ "execution_count": 104,
+ "id": "28fefe8a",
"metadata": {},
"outputs": [
{
"source": [
"clear\n",
"\n",
- "123456 to_bigint\n",
+ "123456 to-bigint\n",
"\n",
"\n",
"\n"
},
{
"cell_type": "code",
- "execution_count": 117,
+ "execution_count": 105,
"id": "fa37c40c",
"metadata": {},
"outputs": [
]
},
{
- "cell_type": "markdown",
- "id": "5f739deb",
- "metadata": {},
- "source": [
- "\n",
- " combine-two-lists == build-two-list-combiner [i cons] genrec\n",
- " \n",
- " build-two-list-combiner == [[[ditch-empty-list] swoncat] dip [pop] swoncat] dip [uncons-two] [dipd] sandwich [[ifte] ccons [P'] swons [P] swap ] dip\n",
- " "
- ]
- },
- {
"cell_type": "code",
- "execution_count": 118,
+ "execution_count": 106,
"id": "850a1421",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 119,
- "id": "52bb5921",
+ "execution_count": 107,
+ "id": "4b6005fc",
"metadata": {},
"outputs": [
{
},
{
"cell_type": "code",
- "execution_count": 120,
+ "execution_count": 108,
"id": "c616033e",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 121,
+ "execution_count": 109,
"id": "1a18ddd7",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 122,
+ "execution_count": 110,
"id": "3c639487",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 123,
+ "execution_count": 111,
"id": "c9222cab",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 124,
+ "execution_count": 112,
"id": "f3bc8d28",
"metadata": {},
"outputs": [
},
{
"cell_type": "markdown",
- "id": "c85d6fe6",
+ "id": "82b7bf9a",
"metadata": {},
"source": [
"#### Demonstrate `add-bigints`"
},
{
"cell_type": "code",
- "execution_count": 125,
- "id": "3da6266b",
+ "execution_count": 113,
+ "id": "b4a71b70",
"metadata": {},
"outputs": [
{
}
],
"source": [
- "1234 999 [to_bigint] ii "
+ "1234 999 [to-bigint] ii "
]
},
{
"cell_type": "code",
- "execution_count": 126,
- "id": "7d38dbaa",
+ "execution_count": 114,
+ "id": "6aba84ae",
"metadata": {},
"outputs": [
{
},
{
"cell_type": "code",
- "execution_count": 127,
- "id": "e65f7ff9",
+ "execution_count": 115,
+ "id": "d5dc4dce",
"metadata": {},
"outputs": [
{
}
],
"source": [
- "from_bigint"
+ "from-bigint"
]
},
{
"cell_type": "code",
- "execution_count": 128,
- "id": "5d385f35",
+ "execution_count": 116,
+ "id": "2e9ab2c2",
"metadata": {},
"outputs": [
{
},
{
"cell_type": "code",
- "execution_count": null,
- "id": "fb7da91a",
+ "execution_count": 117,
+ "id": "080d81a3",
"metadata": {},
- "outputs": [],
- "source": []
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": []
+ }
+ ],
+ "source": [
+ "clear"
+ ]
},
{
"cell_type": "code",
"execution_count": null,
- "id": "679e9df6",
+ "id": "7b237ca8",
"metadata": {},
"outputs": [],
"source": []
{
"cell_type": "code",
"execution_count": null,
- "id": "d4d2850a",
+ "id": "46f50f12",
"metadata": {},
"outputs": [],
"source": []
{
"cell_type": "code",
"execution_count": null,
- "id": "c4da9da4",
+ "id": "7e035a2c",
"metadata": {},
"outputs": [],
"source": []
{
"cell_type": "code",
"execution_count": null,
- "id": "55a37610",
+ "id": "f2492e55",
"metadata": {},
"outputs": [],
"source": []
{
"cell_type": "code",
"execution_count": null,
- "id": "c637a7ea",
+ "id": "8dfddc89",
"metadata": {},
"outputs": [],
"source": []
{
"cell_type": "code",
"execution_count": null,
- "id": "b56cf709",
+ "id": "7f2bf0e5",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
- "execution_count": 112,
+ "execution_count": 118,
"id": "9c50bd24",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 113,
+ "execution_count": 119,
"id": "4c1dbabd",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 114,
+ "execution_count": 120,
"id": "ef683ade",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 115,
+ "execution_count": 121,
"id": "ff52920a",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 116,
+ "execution_count": 122,
"id": "be946f53",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 117,
+ "execution_count": 123,
"id": "056e3072",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 118,
+ "execution_count": 124,
"id": "02d4e38e",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 119,
+ "execution_count": 125,
"id": "5683eb84",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 120,
+ "execution_count": 126,
"id": "a4e1f728",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 121,
+ "execution_count": 127,
"id": "dc7c151a",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 122,
+ "execution_count": 128,
"id": "50c2669a",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 123,
+ "execution_count": 129,
"id": "1bbf3465",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 124,
+ "execution_count": 130,
"id": "5a9347f6",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 125,
+ "execution_count": 131,
"id": "69b18847",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 126,
+ "execution_count": 132,
"id": "0b29370d",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 127,
+ "execution_count": 133,
"id": "32ce148e",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 128,
+ "execution_count": 134,
"id": "4efc8f76",
"metadata": {},
"outputs": [
"\n",
"we have three lists. The first is a possibly-empty list of pairs to compare.\n",
"\n",
- "THe second two are the tails of the original lists.\n",
+ "The second two are the tails of the original lists.\n",
"\n",
"if the first list is non-empty then the second list must be empty so the whole function should return true\n",
"\n",
},
{
"cell_type": "code",
- "execution_count": 129,
+ "execution_count": 135,
"id": "7d973f7f",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 130,
+ "execution_count": 136,
"id": "9239e0c4",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 131,
+ "execution_count": 137,
"id": "0c58a6e0",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 132,
+ "execution_count": 138,
"id": "7f302157",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 133,
+ "execution_count": 139,
"id": "d25ef02e",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 134,
+ "execution_count": 140,
"id": "06e0ffcb",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 135,
+ "execution_count": 141,
"id": "b2428f49",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 136,
+ "execution_count": 142,
"id": "4ef5f503",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 246,
+ "execution_count": 143,
"id": "7f060f83",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 138,
+ "execution_count": 144,
"id": "8d74a801",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 139,
+ "execution_count": 145,
"id": "0104d2b0",
"metadata": {},
"outputs": [
"name": "stdout",
"output_type": "stream",
"text": [
- "false"
+ "true"
]
}
],
},
{
"cell_type": "code",
- "execution_count": 140,
+ "execution_count": 146,
"id": "4728d141",
"metadata": {},
"outputs": [
"name": "stdout",
"output_type": "stream",
"text": [
- "false"
+ "true"
]
}
],
},
{
"cell_type": "code",
- "execution_count": 141,
+ "execution_count": 147,
"id": "bfb5e62c",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 142,
+ "execution_count": 148,
"id": "7983881c",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 143,
+ "execution_count": 149,
"id": "677757c5",
"metadata": {},
"outputs": [
"name": "stdout",
"output_type": "stream",
"text": [
- "false"
+ "true"
]
}
],
},
{
"cell_type": "code",
- "execution_count": 144,
+ "execution_count": 150,
"id": "5691f813",
"metadata": {},
"outputs": [
"name": "stdout",
"output_type": "stream",
"text": [
- "false"
+ "true"
]
}
],
},
{
"cell_type": "code",
- "execution_count": 145,
+ "execution_count": 151,
"id": "b95fe984",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 146,
+ "execution_count": 152,
"id": "b5ddac15",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 147,
+ "execution_count": 153,
"id": "d4077376",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 148,
+ "execution_count": 154,
"id": "ac840996",
"metadata": {},
"outputs": [
"name": "stdout",
"output_type": "stream",
"text": [
- "false"
+ "true"
]
}
],
},
{
"cell_type": "code",
- "execution_count": 149,
+ "execution_count": 155,
"id": "e7c3b141",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 150,
+ "execution_count": 156,
"id": "95c7308d",
"metadata": {},
"outputs": [
"name": "stdout",
"output_type": "stream",
"text": [
- "true"
+ "false"
]
}
],
},
{
"cell_type": "code",
- "execution_count": 151,
+ "execution_count": 157,
"id": "5e43ba80",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 152,
+ "execution_count": 158,
"id": "20070426",
"metadata": {},
"outputs": [
"name": "stdout",
"output_type": "stream",
"text": [
- "false"
+ "true"
]
}
],
},
{
"cell_type": "code",
- "execution_count": 154,
+ "execution_count": 159,
"id": "c97b0df9",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 155,
+ "execution_count": 160,
"id": "980a1bbf",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 199,
+ "execution_count": 161,
"id": "4f429421",
"metadata": {},
"outputs": [
"name": "stdout",
"output_type": "stream",
"text": [
- "false"
+ "true"
]
}
],
},
{
"cell_type": "code",
- "execution_count": 158,
+ "execution_count": 162,
"id": "5a6419ee",
"metadata": {},
"outputs": [
"name": "stdout",
"output_type": "stream",
"text": [
- "true"
+ "false"
]
}
],
},
{
"cell_type": "code",
- "execution_count": 159,
+ "execution_count": 163,
"id": "cd586291",
"metadata": {},
"outputs": [
"name": "stdout",
"output_type": "stream",
"text": [
- "false"
+ "true"
]
}
],
},
{
"cell_type": "code",
- "execution_count": 160,
+ "execution_count": 164,
"id": "35fb22d2",
"metadata": {},
"outputs": [
"name": "stdout",
"output_type": "stream",
"text": [
- "[3 2 1] [4 5 6]"
+ "[4 5 6] [3 2 1]"
]
}
],
},
{
"cell_type": "code",
- "execution_count": 161,
+ "execution_count": 165,
"id": "36d74e5b",
"metadata": {},
"outputs": [
"name": "stdout",
"output_type": "stream",
"text": [
- "[3 2 1] [4 5 6]"
+ "[4 5 6] [3 2 1]"
]
}
],
},
{
"cell_type": "code",
- "execution_count": 202,
+ "execution_count": 166,
"id": "dd645337",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 203,
+ "execution_count": 167,
"id": "935552d4",
"metadata": {},
"outputs": [
},
{
"cell_type": "code",
- "execution_count": 204,
+ "execution_count": 168,
"id": "05100765",
"metadata": {},
"outputs": [
"name": "stdout",
"output_type": "stream",
"text": [
- "true [3 2 1] [4 5 6]"
+ "false [4 5 6] [3 2 1]"
]
}
],
},
{
"cell_type": "code",
- "execution_count": 134,
- "id": "187c0381",
+ "execution_count": 169,
+ "id": "7ac873d4",
"metadata": {},
"outputs": [
{
},
{
"cell_type": "markdown",
- "id": "1a8a8196",
+ "id": "7ef0f655",
"metadata": {},
"source": [
"### Subtraction, at last...\n",
},
{
"cell_type": "markdown",
- "id": "9751fd65",
+ "id": "173aa582",
"metadata": {},
"source": [
"We want to use `check-gt` here:\n",
},
{
"cell_type": "markdown",
- "id": "df2ae839",
+ "id": "242e863f",
"metadata": {},
"source": [
"It seems we should just flip the sign bit if we swap, eh?\n",
},
{
"cell_type": "markdown",
- "id": "c775c3a4",
+ "id": "37ed39c6",
"metadata": {},
"source": [
"Now we subtract the digits:\n",
" [swap sub-carry]\n",
" [sub-with-carry]\n",
" build-two-list-combiner\n",
- " [i cons] genrec\n",
+ " genrec\n",
"\n",
"We just need to define the pieces."
]
},
{
"cell_type": "markdown",
- "id": "32eeaf38",
+ "id": "844210e4",
"metadata": {},
"source": [
"#### `sub-with-carry`\n",
},
{
"cell_type": "markdown",
- "id": "3b47df3b",
+ "id": "3c10e256",
"metadata": {},
"source": [
" carry a b sub-with-carry\n",
" ------------------------------\n",
" (a-b-carry) new-carry\n",
"\n",
- " _sub-with-carry0 ≡ [bool_to_int] dipd - -\n",
+ " _sub-with-carry0 ≡ [bool-to-int] dipd - -\n",
" _sub-with-carry1 ≡ [base + base mod] [0 <] clop\n",
"\n",
" sub-with-carry ≡ _sub-with-carry0 _sub-with-carry1\n"
},
{
"cell_type": "code",
- "execution_count": 135,
- "id": "880dc3da",
+ "execution_count": 170,
+ "id": "c360cc7b",
"metadata": {},
"outputs": [
{
}
],
"source": [
- "[_sub-with-carry0 rolldown bool_to_int [-] ii] inscribe\n",
+ "[_sub-with-carry0 rolldown bool-to-int [-] ii] inscribe\n",
"[_sub-with-carry1 [base + base mod] [0 <] cleave] inscribe\n",
"[sub-with-carry _sub-with-carry0 _sub-with-carry1] inscribe"
]
},
{
"cell_type": "code",
- "execution_count": 139,
- "id": "bae53ad4",
+ "execution_count": 171,
+ "id": "3a84adff",
"metadata": {
"scrolled": true
},
},
{
"cell_type": "code",
- "execution_count": 140,
- "id": "f54d93bc",
+ "execution_count": 172,
+ "id": "0dcdc968",
"metadata": {},
"outputs": [
{
},
{
"cell_type": "code",
- "execution_count": 141,
- "id": "740034d8",
+ "execution_count": 173,
+ "id": "2d60492d",
"metadata": {},
"outputs": [
{
},
{
"cell_type": "markdown",
- "id": "d29e6193",
+ "id": "fc4ff7c6",
"metadata": {},
"source": [
"That leaves the recursive branch:\n",
},
{
"cell_type": "markdown",
- "id": "d31868ab",
+ "id": "984f1bf4",
"metadata": {},
"source": [
" \n",
},
{
"cell_type": "markdown",
- "id": "5c4404a8",
+ "id": "845abba7",
"metadata": {},
"source": [
"But there's a problem! This winds up subtracting `a` from 0 rather than the other way around:\n",
},
{
"cell_type": "code",
- "execution_count": 147,
- "id": "be093900",
+ "execution_count": 174,
+ "id": "20c8ad40",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
- "text": [
- "[3 2 1]"
- ]
+ "text": []
}
],
"source": [
},
{
"cell_type": "markdown",
- "id": "253538a4",
+ "id": "77e427f9",
"metadata": {},
"source": [
"Try it out:"
},
{
"cell_type": "code",
- "execution_count": 148,
- "id": "ce9f01e2",
+ "execution_count": 175,
+ "id": "92201303",
"metadata": {},
"outputs": [
{
},
{
"cell_type": "code",
- "execution_count": 160,
- "id": "2120af39",
+ "execution_count": 176,
+ "id": "1a1d7cdc",
"metadata": {},
"outputs": [
{
},
{
"cell_type": "code",
- "execution_count": 161,
- "id": "55fc1f59",
+ "execution_count": 177,
+ "id": "39ce9c6a",
"metadata": {},
"outputs": [
{
},
{
"cell_type": "code",
- "execution_count": 162,
- "id": "1db3eaeb",
+ "execution_count": 178,
+ "id": "a93e916e",
"metadata": {},
"outputs": [
{
},
{
"cell_type": "code",
- "execution_count": 163,
- "id": "ededec7b",
+ "execution_count": 179,
+ "id": "c2273ff3",
"metadata": {},
"outputs": [
{
},
{
"cell_type": "markdown",
- "id": "ffc08bef",
+ "id": "7c609313",
"metadata": {},
"source": [
"But what about those leading zeroes?\n",
},
{
"cell_type": "code",
- "execution_count": 165,
- "id": "fe557598",
+ "execution_count": 180,
+ "id": "d8c7f7a5",
"metadata": {},
"outputs": [
{
},
{
"cell_type": "code",
- "execution_count": null,
- "id": "f7275cd6",
- "metadata": {},
- "outputs": [],
- "source": []
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "740a5c97",
- "metadata": {},
- "outputs": [],
- "source": []
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "9ea8ba1c",
- "metadata": {},
- "outputs": [],
- "source": []
- },
- {
- "cell_type": "code",
- "execution_count": 164,
- "id": "b6c2e9ee",
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": []
- }
- ],
- "source": [
- "[sub-carry-from-digits popd] inscribe"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "32cef119",
- "metadata": {},
- "source": [
- " sub-carry == pop"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 230,
- "id": "c22775e9",
+ "execution_count": 181,
+ "id": "875aaafa",
"metadata": {},
"outputs": [
{
}
],
"source": [
- "[sub-like-bigints [uncons] dip rest check-gt sub-digits cons] inscribe\n",
- "[sub-digits initial-carry sub-digits'] inscribe\n",
- "[sub-digits'\n",
- " [sub-carry-from-digits]\n",
- " [swap sub-carry]\n",
- " [sub-with-carry]\n",
- " build-two-list-combiner\n",
- " \n",
+ "[sub-carry-from-digits\n",
+ " [pop not]\n",
+ " [popd]\n",
+ " [_scfd_R0]\n",
+ " [i cons-but-not-leading-zeroes]\n",
+ " genrec\n",
"] inscribe"
]
},
{
"cell_type": "code",
- "execution_count": 231,
- "id": "ac670030",
+ "execution_count": 182,
+ "id": "bd2447b6",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
- "text": [
- "false [3 2 1] [6 5 4] [P] [[P'] [ditch-empty-list sub-carry-from-digits] [pop swap sub-carry] ifte] [uncons-two [sub-with-carry] dipd]"
- ]
+ "text": []
}
],
"source": [
- "clear\n",
- "false\n",
- "[3 2 1] [6 5 4]\n",
- "[sub-carry-from-digits]\n",
- " [swap sub-carry]\n",
- " [sub-with-carry]\n",
- " build-two-list-combiner"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "8fbba815",
- "metadata": {},
- "outputs": [],
- "source": [
- "[i cons] genrec\n"
+ "[_scfd_R0 uncons 0 swap [sub-with-carry] dip] inscribe"
]
},
{
"cell_type": "code",
- "execution_count": null,
- "id": "cce0cc68",
- "metadata": {},
- "outputs": [],
- "source": []
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "9163ad94",
- "metadata": {},
- "outputs": [],
- "source": []
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "d862f5a8",
- "metadata": {},
- "outputs": [],
- "source": []
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "976c4d53",
- "metadata": {},
- "outputs": [],
- "source": []
- },
- {
- "cell_type": "code",
- "execution_count": 212,
- "id": "3b05693f",
+ "execution_count": 183,
+ "id": "ffaf1fcc",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
- "[true 12345] [true 109]"
+ "[9 9]"
]
}
],
"source": [
"clear\n",
- "12345 to_bigint 109 to_bigint"
+ "\n",
+ "true [0 0 1] sub-carry-from-digits"
]
},
{
"cell_type": "code",
- "execution_count": 213,
- "id": "fc69485b",
+ "execution_count": 184,
+ "id": "8a2b2165",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
- "text": [
- "false false [109] [12345] [P] [[[P'] [ditch-empty-list sub-carry-from-digits] [pop swap sub-carry] ifte] uncons-two [sub-with-carry] dipd]"
- ]
+ "text": []
}
],
"source": [
- "sub-like-bigints"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "ca954866",
- "metadata": {},
- "source": [
- " false false [109] [12345]\n",
- " [P]\n",
- " [\n",
- " [P']\n",
- " [ditch-empty-list sub-carry-from-digits]\n",
- " [pop swap sub-carry]\n",
- " ifte\n",
- " ]\n",
- " [\n",
- " [uncons-two [sub-with-carry] dipd]\n",
- " i cons\n",
- " ]"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "45a744b7",
- "metadata": {},
- "outputs": [],
- "source": [
- "[i cons] genrec"
+ "clear"
]
},
{
"cell_type": "markdown",
- "id": "bc354239",
- "metadata": {},
- "source": [
- "- Did I redefine something?\n",
- "- Did a definition not make it into the dictionary?\n",
- "- Trace in the Notebooks should show a trace even if an exception is encountered.\n"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 215,
- "id": "9b2fd2fb",
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "\n",
- "==== Help on P ====\n",
- "\n",
- "P ≡ [bool] ii & not\n",
- "\n",
- "---- end ( P )\n",
- "\n",
- "\n",
- "false false [109] [12345] [P] [[[P'] [ditch-empty-list sub-carry-from-digits] [pop swap sub-carry] ifte] uncons-two [sub-with-carry] dipd]"
- ]
- }
- ],
- "source": [
- "[P] help"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 216,
- "id": "3a69a1a2",
+ "id": "73180c15",
"metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "\n",
- "==== Help on P' ====\n",
- "\n",
- "P' ≡ [bool] ii |\n",
- "\n",
- "---- end ( P' )\n",
- "\n",
- "\n",
- "false false [109] [12345] [P] [[[P'] [ditch-empty-list sub-carry-from-digits] [pop swap sub-carry] ifte] uncons-two [sub-with-carry] dipd]"
- ]
- }
- ],
"source": [
- "[P'] help"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 224,
- "id": "e29a136f",
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "false false [109] [12345]"
- ]
- }
- ],
- "source": [
- "pop"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 220,
- "id": "7499c430",
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "false false [109] [12345]"
- ]
- }
- ],
- "source": [
- " [109] [12345] "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 225,
- "id": "1f38a3a1",
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "false false [109] [12345] true"
- ]
- }
- ],
- "source": [
- "[P'] nullary\n",
- " "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 221,
- "id": "31103274",
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "false false [109] [12345] [[P'] [ditch-empty-list sub-carry-from-digits] [pop swap sub-carry] ifte]"
- ]
- }
- ],
- "source": [
- " [[P'] [ditch-empty-list sub-carry-from-digits] [pop swap sub-carry] ifte]\n",
- " "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 221,
- "id": "9f3e739d",
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "false false [109] [12345] [[P'] [ditch-empty-list sub-carry-from-digits] [pop swap sub-carry] ifte]"
- ]
- }
- ],
- "source": [
- " [[P'] [ditch-empty-list sub-carry-from-digits] [pop swap sub-carry] ifte]\n",
- " "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "11639f03",
- "metadata": {},
- "outputs": [],
- "source": [
- " uncons-two [sub-with-carry] dipd"
+ "#### `sub-carry`\n",
+ "\n",
+ " sub-carry == pop"
]
},
{
"cell_type": "code",
- "execution_count": null,
- "id": "2889ee5e",
- "metadata": {},
- "outputs": [],
- "source": []
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "328334db",
- "metadata": {},
- "outputs": [],
- "source": []
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "76e3a1ca",
- "metadata": {},
- "outputs": [],
- "source": []
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "93d70133",
- "metadata": {},
- "outputs": [],
- "source": []
- },
- {
- "cell_type": "code",
- "execution_count": 240,
- "id": "f2bc1f16",
+ "execution_count": 185,
+ "id": "c22775e9",
"metadata": {},
"outputs": [
{
}
],
"source": [
- "clear"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 241,
- "id": "c404eb99",
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "false [3 2 1] [6 5 4] [P] [[P'] [ditch-empty-list sub-carry-from-digits] [pop swap pop] ifte] [uncons-two [sub-with-carry] dipd]"
- ]
- }
- ],
- "source": [
- "clear\n",
- "false\n",
- "[3 2 1] [6 5 4]\n",
- "[sub-carry-from-digits]\n",
+ "[sub-like-bigints [uncons] dip rest check-gt sub-digits cons] inscribe\n",
+ "[sub-digits initial-carry sub-digits'] inscribe\n",
+ "[sub-digits'\n",
+ " [sub-carry-from-digits]\n",
" [swap pop]\n",
" [sub-with-carry]\n",
- " build-two-list-combiner"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 242,
- "id": "74502c4c",
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "[2147483645 2147483644 2147483644]"
- ]
- }
- ],
- "source": [
- "[i cons] genrec\n"
+ " build-two-list-combiner\n",
+ " genrec\n",
+ "] inscribe"
]
},
{
"cell_type": "code",
- "execution_count": null,
- "id": "39a842e5",
- "metadata": {},
- "outputs": [],
- "source": []
- },
- {
- "cell_type": "code",
- "execution_count": 243,
- "id": "ecb3de02",
+ "execution_count": 186,
+ "id": "ac670030",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
- "false [6 5 4] [3 2 1] [P] [[P'] [ditch-empty-list sub-carry-from-digits] [pop swap pop] ifte] [uncons-two [sub-with-carry] dipd]"
+ "true [3 2 1] [6 5 4]"
]
}
],
"source": [
"clear\n",
- "false\n",
- "[3 2 1] [6 5 4] swap\n",
- "[sub-carry-from-digits]\n",
- " [swap pop]\n",
- " [sub-with-carry]\n",
- " build-two-list-combiner"
+ "true [3 2 1] [6 5 4]"
]
},
{
"cell_type": "code",
- "execution_count": 244,
- "id": "0bf21e08",
+ "execution_count": 187,
+ "id": "c19ff340",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
- "[3 3 3]"
+ "false false [6 5 4] [3 2 1]"
]
}
],
"source": [
- "[i cons] genrec\n"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "74054f2f",
- "metadata": {},
- "source": [
- "That sure fucking *looks* like it works."
+ "check-gt initial-carry"
]
},
{
"cell_type": "code",
- "execution_count": null,
- "id": "20462cd5",
- "metadata": {},
- "outputs": [],
- "source": []
- },
- {
- "cell_type": "code",
- "execution_count": 247,
- "id": "2ab1031c",
+ "execution_count": 188,
+ "id": "8fbba815",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
- "true [6 5 4] [3 2 1]"
+ "false [3 3 3]"
]
}
],
"source": [
- "clear\n",
- "false\n",
- "[3 2 1] [6 5 4] check-gt"
+ "sub-digits'"
]
},
{
"cell_type": "code",
- "execution_count": 248,
- "id": "1b908ee7",
+ "execution_count": 189,
+ "id": "3b05693f",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
- "true [6 5 4] [3 2 1] [P] [[P'] [ditch-empty-list sub-carry-from-digits] [pop swap pop] ifte] [uncons-two [sub-with-carry] dipd]"
+ "[true 5 4 3 2 1] [true 9 0 1]"
]
}
],
"source": [
- "[sub-carry-from-digits]\n",
- " [swap pop]\n",
- " [sub-with-carry]\n",
- " build-two-list-combiner"
+ "clear\n",
+ "12345 to-bigint 109 to-bigint"
]
},
{
"cell_type": "code",
- "execution_count": 249,
- "id": "e223937e",
+ "execution_count": 190,
+ "id": "fc69485b",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
- "[2 3 3]"
+ "[true 6 3 2 2 1]"
]
}
],
"source": [
- "[i cons] genrec\n"
+ "sub-like-bigints"
]
},
{
"cell_type": "code",
- "execution_count": 251,
- "id": "a5747b29",
+ "execution_count": 191,
+ "id": "c992d25a",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
- "-333"
+ "12236"
]
}
],
"source": [
- "clear 123 456 -"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "64c14e67",
- "metadata": {},
- "source": [
- "Almost."
+ "from-bigint"
]
},
{
- "cell_type": "code",
- "execution_count": null,
- "id": "c9999912",
- "metadata": {},
- "outputs": [],
- "source": []
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "29a0586c",
- "metadata": {},
- "outputs": [],
- "source": []
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "bb8cb15e",
- "metadata": {},
- "outputs": [],
- "source": []
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "6a5b3ace",
- "metadata": {},
- "outputs": [],
- "source": []
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "417e2d45",
- "metadata": {},
- "outputs": [],
- "source": []
- },
- {
"cell_type": "markdown",
"id": "f2b707c1",
"metadata": {},
"\n",
" base 2147483648\n",
" ditch-empty-list [bool] [popd] [pop] ifte\n",
- " bool_to_int [0] [1] branch\n",
+ " bool-to-int [0] [1] branch\n",
" uncons-two [uncons] ii swapd\n",
"\n",
" add-with-carry _a0 _a1\n",
- " _a0 [bool_to_int] dipd + +\n",
+ " _a0 [bool-to-int] dipd + +\n",
" _a1 base [mod] [>=] clop\n",
"\n",
" add-carry-to-digits [pop not] [popd] [_actd_R0] [i cons] genrec\n",
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