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Minor cleanup.

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Simon Forman 2022-10-10 22:23:19 -07:00
parent b48419ec1a
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1 changed files with 49 additions and 39 deletions
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docs/notebooks/BigInts.ipynb
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@ -484,7 +484,7 @@
"- We're tearing down two lists simultaneously.\n",
"- They might not be the same length.\n",
"\n",
"There are two base cases: two empty lists or one empty list, the recursive branch is taken only if both lists at non-empty.\n",
"There are two base cases: two empty lists or one empty list, the recursive branch is taken only if both lists are non-empty.\n",
"\n",
" bool [a ...] [b ...] P\n",
"\n",
@ -955,7 +955,7 @@
" carry [n ...] add-carry-to-digits\n",
" carry [n ...] [_actd_P] [_actd_THEN] [_actd_R0] [_actd_R1] genrec\n",
"\n",
"The predicate is the carry flag itself inverted, but when we recur we need to check if the list is non-empty because it will eventually be empty or the carry flag will be false:\n",
"The predicate is the carry flag itself inverted (but when we recur we will need to check if the list is non-empty because it may eventually be empty):\n",
"\n",
" _actd_P ≡ pop not\n",
"\n",
@ -992,52 +992,22 @@
},
{
"cell_type": "markdown",
"id": "379d88db",
"id": "d5898c6a",
"metadata": {},
"source": [
"If it's empty...\n",
"\n",
" true [] R0.else [add-carry-to-digits] R1\n",
" ----------------------------------------------\n",
" false [1] [add-carry-to-digits] R1\n",
"\n",
" R0.else ≡ 1 swons popd false swap"
]
},
{
"cell_type": "markdown",
"id": "9f1e5b30",
"metadata": {},
"source": [
"If it's not empty...\n",
"\n",
" true [a ...] R0.then [add-carry-to-digits] R1\n",
" -------------------------------------------------------------\n",
" true 0 a add-with-carry [...1] [add-carry-to-digits] R1\n",
" -------------------------------------------------------------\n",
" (a+1) carry [...1] [add-carry-to-digits] R1"
]
},
{
"cell_type": "markdown",
"id": "d5898c6a",
"metadata": {},
"source": [
"Ah ha!? How to get that `(a+1)` back into the list!?\n",
"\n",
"If it's empty...\n",
"\n",
" true [] R0.else [add-carry-to-digits] R1\n",
" ------------------------------------------------\n",
" 1 false [] [add-carry-to-digits] i cons\n",
" 1 false [] [add-carry-to-digits] i cons\n",
"\n",
"and\n",
"\n",
" true [a ...] R0.then [add-carry-to-digits] i cons\n",
" -------------------------------------------------------------\n",
" true 0 a add-with-carry [...1] [add-carry-to-digits] i cons\n",
" -------------------------------------------------------------\n",
" (a+1) carry [...1] [add-carry-to-digits] i cons"
" true [a ...] R0.then [add-carry-to-digits] i cons\n",
" ----------------------------------------------------------------\n",
" true 0 a add-with-carry [...] [add-carry-to-digits] i cons\n",
" ----------------------------------------------------------------\n",
" (a+1) carry [...] [add-carry-to-digits] i cons"
]
},
{
@ -1546,6 +1516,46 @@
"source": [
"Bitchin'"
]
},
{
"cell_type": "markdown",
"id": "f2b707c1",
"metadata": {},
"source": [
"## Appendix: Source Code\n",
"\n",
" base 2147483648\n",
" ditch-empty-list [bool] [popd] [pop] ifte\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",
" _a1 base [mod] [>=] clop\n",
"\n",
" add-carry-to-digits [pop not] [popd] [_actd_R0] [i cons] genrec\n",
" _actd_R0 [bool] [_actd_R0.then] [_actd_R0.else] ifte\n",
" _actd_R0.else popd 1 false rolldown\n",
" _actd_R0.then 0 swap uncons [add-with-carry] dip\n",
"\n",
" add-digits initial-carry add-digits'\n",
" initial-carry false rollup\n",
" add-digits' [P] [THEN] [R0] [i cons] genrec\n",
" P [bool] ii & not\n",
" THEN [P'] [THEN'] [ELSE] ifte\n",
" R0 uncons-two [add-with-carry] dipd\n",
" P' [bool] ii |\n",
" THEN' ditch-empty-list add-carry-to-digits\n",
" ELSE pop swap [] [1 swons] branch\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "84affe68",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {