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BinGen.kt
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BinGen.kt
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package ai.hypergraph.shipshape
import org.intellij.lang.annotations.Language
import kotlin.math.*
const val CONST = 6 // Constant by which addition and subtraction is always supported when defined, up to 2^POW + 1
const val POW = 7 // Maximum power
fun main() {
println(genBooleanTypeAliases())
}
@Language("kt")
fun genBinaryArithmetic() = """
// This file was generated by Shipshape
@file:Suppress("UNUSED_PARAMETER", "UNCHECKED_CAST")
package ai.hypergraph.kotlingrad.typelevel.binary
import kotlin.jvm.JvmName
sealed class B<X, P : B<X, P>>(open val x: X? = null) {
val T: T<P> get() = T(this as P)
val F: F<P> get() = F(this as P)
val U: U get() = U(toInt())
abstract fun flip(): B<X, *>
override fun equals(other: Any?) = toString() == other.toString()
override fun hashCode() = this::class.hashCode() + x.hashCode()
override fun toString() = "" + (x ?: "") + if (this is T) "1" else "0"
fun toInt(): Int = toInt(toString())
private tailrec fun toInt(s: String, sum: Int = 0): Int =
if (s.isEmpty()) sum else toInt(s.substring(1), (sum shl 1) + s[0].digitToInt())
}
open class T<X>(override val x: X = Ø as X) : B<X, T<X>>(x) {
companion object: T<Ø>(Ø)
override fun flip(): F<X> = F(x)
}
open class F<X>(override val x: X = Ø as X) : B<X, F<X>>(x) {
companion object: F<Ø>(Ø)
override fun flip(): T<X> = T(x)
}
// Unchecked / checked at runtime
open class U(val i: Int) : B<Any, U>() {
override fun flip(): U = TODO()
override fun equals(other: Any?) = (other as? U)?.let { i == it.i } ?: false
override fun hashCode() = i
}
@Suppress("NonAsciiCharacters", "ClassName")
object Ø: B<Ø, Ø>(null) { override fun flip() = Ø }
/**
* i │ 0 1 … k-1 k │ k+1 k+2 … k+c │ k+c+1 … k+c+k
* ───┼───────────────────┼────────────────────┼───────────────────┐ ┐
* 0 │ │ │ __/ │
* 1 │ │ │ __/XXX │
* … │ i ± i │ k ± i │ __/XXXXXX ├ ┐
* k-1 │ │ │ ___/XXXXXXXXX │ │
* k │ │ │ ___╱XXXXXXXXXXXXX │ │
* ────┼───────────────────┼────────────────────┴─┘XXXXXXXXXXXXXXXXX ┘ │
* k+1 │ │XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX │
* k+2 │ │XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX │
* … │ i ± k │XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX │
* … │ │XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX │
* k+c │ │XXXXXXXXXXXX XXXXXXXXXXXX │
* ─────┼───────────────────┤XXXXXXXXXXXX Run-time XXXXXXXXXXXX │
* k+c+1 │ ___/XXXXXXXXXXXXX type checked XXXXXXXXXXXX │
* … │ ___/XXXXXXXXXXXXXXXXX XXXXXXXXXXXX │
* … │ ___/XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX │
* … │ ___/XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX │
* k+c+k │__/XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX │
*
* └─────────┬─────────┘ Compile-time
* └───────────────────────────────────── type checked
*/
// Left padded with 0, B_0N indicates a binary string *0{B_0N}
// Enumerate (max(2ⁱ-k, 0), 2ⁱ+k) ∀0≤i≤⌊log₂(k+c+k)⌋
// i.e.: {0, 1, 2, *(4-k, 4+k), *(8-k, 8+k), *(16-k, 16+k),..., *(2^⌊log₂(k+c+k)⌋-k, 2^⌊log₂(k+c+k)⌋+k)}
${genBooleanTypeAliases()}
val B0: B_0<Ø> = F(Ø)
val B1: B_1<Ø> = T(Ø)
${genBooleanLiterals()}
@JvmName("bnp1") operator fun Ø.plus(t: T<Ø>) = B1
@JvmName("b0p1") operator fun B_0<Ø>.plus(t: T<Ø>) = B1
@JvmName("b1m1") operator fun B_1<Ø>.minus(t: T<Ø>): B_0<Ø> = B0
@JvmName("b2m1") operator fun B_2<Ø>.minus(t: T<Ø>): B_1<Ø> = B1
${genBooleanPlusMinusOne(maxPow = POW)}
${genBooleanPlusMinus()}
@JvmName("b_t0") operator fun <K: B<*, *>> K.times(t: F<Ø>) = t
@JvmName("b0t_") operator fun <K: B<*, *>> F<Ø>.times(t: K) = this
@JvmName("b_t1") operator fun <K: B<*, *>> K.times(t: T<Ø>) = this
@JvmName("b1t_") operator fun <K: B<*, *>> T<Ø>.times(t: K) = t
${genMultiplicationTable()}
@JvmName("b_d1") operator fun <K: B<*, *>> K.div(t: T<Ø>) = this
${genDivisionTable()}
${genUnchecked()}
"""
@Language("kt")
fun genUnchecked() =
"""
@JvmName("b_p_") operator fun <K: B<*, *>, Y: B<*, *>> K.plus(y: Y) = U(toInt() + y.toInt())
@JvmName("b_m_") operator fun <K: B<*, *>, Y: B<*, *>> K.minus(y: Y) = U(toInt() - y.toInt())
@JvmName("b_t_") operator fun <K: B<*, *>, Y: B<*, *>> K.times(y: Y) = U(toInt() * y.toInt())
@JvmName("b_d_") operator fun <K: B<*, *>, Y: B<*, *>> K.div(y: Y) = U(toInt() / y.toInt())
// Would be nice if it worked, but cannot match the same K twice
// @JvmName("b_d_") operator fun <K: B<*, *>> K.div(t: K) = T(Ø)
// @JvmName("b_p_") operator fun <K: B<*, *>> K.plus(k: K) = F(k)
// @JvmName("b_m_") operator fun <K: B<*, *>> K.minus(k: K) = F(Ø)
""".trimIndent()
fun genBooleanTypeAliases(maxPow: Int = POW, const: Int = CONST): String =
(0..maxPow).asSequence().map { 2.0.pow(it).toInt() }
.map { (it - const).coerceAtLeast(0) until (it + const) }
.flatten().distinct().joinToString("\n") { "typealias B_$it<B> = ${it.toBigEndian("B")}" }
fun genBooleanLiterals(const: Int = CONST): String =
(2..const).joinToString("\n") { "val B$it: B_$it<Ø> = ${it.toBigEndianVal()}" }
fun genBooleanPlusMinus(maxPow: Int = POW, const: Int = CONST): String =
(2..const).joinToString("\n", "\n") { k ->
val (p1, p2) = balancedPartition(k)
val (v1, v2) = "B$p1" to "B$p2"
val range = (0..maxPow).asSequence().map { 2.0.pow(it).toInt() }
.map { ((it - k).coerceAtLeast(0) until it).toList() }
.flatten().distinct()
range.joinToString("\n", "\n", "\n") {
val result = it + k
"""@JvmName("bop${it}p$k") operator fun B_${it}<Ø>.plus(r: B_${k}<Ø>): B_$result<Ø> = plus($v2) + $v1"""
} + range.joinToString("\n", "\n", "\n") {
val lpad = (it + k).toString(2).length - it.toString(2).length
val fpad = "F".repeat(lpad).toBigEndian("K")
"""@JvmName("bop?0${it}p$k") operator fun <K: B<*, *>> B_${it}<$fpad>.plus(r: B_${k}<Ø>) = plus($v2) + $v1"""
} + range.map { it + k }.joinToString("\n", "\n", "\n") {
val result = it - k
"""@JvmName("bop${it}m$k") operator fun B_${it}<Ø>.minus(r: B_${k}<Ø>): B_$result<Ø> = minus($v2) - $v1"""
} + range.map { it + k }.joinToString("\n", "\n", "\n") {
val result = it - k
"""@JvmName("bop?${it}m$k") operator fun <K: B<*, *>> B_${it}<K>.minus(r: B_${k}<Ø>) = minus($v2) - $v1"""
}
}
fun genBooleanPlusMinusOne(maxPow: Int, range: Sequence<Int> = (1..maxPow).asSequence().map { 2.0.pow(it).toInt() }) =
range.joinToString("\n", "\n", "\n") {
"""@JvmName("b${it - 1}p1") operator fun B_${it - 1}<Ø>.plus(t: T<Ø>): B_$it<Ø> = F(x + B1)"""
} + """@JvmName("b?0p1") operator fun <K: B<*, *>> B_0<K>.plus(t: T<Ø>) = T(x)""" +
range.joinToString("\n", "\n", "\n\n") {
"""@JvmName("b?0${it - 1}p1") operator fun <K: B<*, *>> B_${it - 1}<F<K>>.plus(t: T<Ø>) = F(x + B1)"""
} + range.drop(1).joinToString("\n", "\n", "\n") {
val result = it - 1
"""@JvmName("b${it}m1") operator fun B_${it}<Ø>.minus(t: T<Ø>): B_$result<Ø> = T(x - B1)"""
} + """@JvmName("b?1p1") operator fun <K: B<*, *>> B_1<K>.minus(t: T<Ø>) = F(x)""" +
range.joinToString("\n", "\n") {
val result = it - 1
"""@JvmName("b?${it}m1") operator fun <K: B<*, *>> B_${it}<K>.minus(t: T<Ø>) = T(x - B1)"""
}
@Language("kt")
fun genMultiplicationTable(
range: IntRange = 2..16,
easy: Set<Int> = range.filter { log2(it.toFloat()).let { ceil(it) == floor(it) } }.toSet(),
hard: Set<Int> = range.filter { log2(it.toFloat()).let { ceil(it) != floor(it) } }.toSet()
) =
easy.joinToString("\n","\n","\n") {
val pow = log2(it.toFloat()).toInt()
val padthis = "F".repeat(pow).toBigEndianVal("this")
val padarg = "F".repeat(pow).toBigEndianVal("t")
"""
@JvmName("b_t${it}") operator fun <K: B<*, *>> K.times(t: B_$it<Ø>) = $padthis
@JvmName("b${it}t_") operator fun <K: B<*, *>> B_$it<Ø>.times(t: K) = $padarg
""".trimIndent()
} + (hard * hard).joinToString("\n", "\n") { (a, b) ->
val result = (a * b).toBigEndian("Ø", "(", ")")
"""
@JvmName("b${a}t${b}") operator fun B_$a<Ø>.times(t: B_$b<Ø>) = $result
""".trimIndent()
}
fun genDivisionTable(
maxPow: Int = POW,
range: IntRange = 1..maxPow,
easy: Set<Int> = range.map { 2.0.pow(it).toInt() }.toSet(),
hard: Set<Triple<Int, Int, Int>> = (2..2.0.pow(maxPow).toInt()).map { it.nontrivialDivisors() }.flatten().toSet()
) =
easy.joinToString("\n", "", "\n") {
val pow = log2(it.toFloat()).toInt()
val pad = "F".repeat(pow).toBigEndian("K")
val divisor = "x".repeat(pow).toCharArray().joinToString(".").ifEmpty { "this" }
"""@JvmName("b_d$it") operator fun <K: B<*, *>> $pad.div(d: ${it.toBigEndian("Ø")}) = $divisor""".trimIndent()
} + hard.joinToString("\n", "\n", "\n") { (a, b, c) ->
val dividend = a.toBigEndian("Ø")
val divisor = b.toBigEndian("Ø")
val quotient = c.toBigEndian("Ø", "(", ")")
"""
@JvmName("b${a}d${b}") operator fun $dividend.div(d: $divisor) = $quotient
""".trimIndent()
}
fun Int.nontrivialDivisors(
maxPerDividend: Int = 20,
criteria: (Int) -> Boolean = { !it.isPowerOfTwo() && (this % it) == 0 }
): List<Triple<Int, Int, Int>> =
(1..(this / 2 + 1)).filter(criteria).take(maxPerDividend)
.map { Triple(this, it, this / it) }.toList()
fun Int.isPowerOfTwo() = log2(toFloat()).let { ceil(it) == floor(it) }
fun Int.toBigEndianVal() =
// toString(2).fold("Ø") { a, b -> if(b == '0') "F($a)" else "T($a)" }
toString(2).toCharArray().joinToString(".") { if (it == '1') "T" else "F" }
// toString(2).fold("") { a, b -> (if(a.isEmpty()) "" else "$a.") + if(b == '0') "F" else "T" }
fun Int.toBigEndian(typeParam: String, lp: String = "<", rp: String = ">") =
toString(2).fold(typeParam) { a, b -> if(b == '0') "F$lp$a$rp" else "T$lp$a$rp" }
fun String.toBigEndian(typeParam: String) = fold(typeParam) { a, b -> "$b<$a>" }
fun String.toBigEndianVal(typeParam: String) = fold(typeParam) { a, b -> "$b($a)" }