perf: optimize reduceSelf for secp256k1, pre-allocate wNAF scratch
Two microoptimizations: 1. reduceSelf: exploit P's structure (P[1..3] = 0xFFFFFFFFFFFFFFFF). a >= P only if all top 3 limbs are max AND a[0] >= P[0]. The first check (a[3] == -1) fails >99.99% of the time, making this a single branch miss prediction instead of a 4-limb comparison loop. Called ~1,300× per verify, ~500× per ECDH. 2. Pre-allocate wNAF IntArrays and scratch MutablePoint/LongArray in PointScratch. Eliminates 8-12 IntArray(145) + 8-12 LongArray(4) allocations per mul/mulDoubleG call. Adds wnafInto() to Glv that writes into caller-provided arrays. https://claude.ai/code/session_01BhU63WUe9AhikZxRdw3Lpg
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Claude
@@ -293,7 +293,14 @@ internal object FieldP {
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// ==================== Reduction ====================
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fun reduceSelf(a: LongArray) {
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if (U256.cmp(a, P) >= 0) U256.subTo(a, a, P)
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// Exploit P's structure: P = [P0, -1, -1, -1] where P[1..3] = 0xFFFFFFFFFFFFFFFF.
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// a >= P only if a[3]==a[2]==a[1]==-1 AND a[0] >= P[0]. The first check (a[3]==-1)
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// fails >99.99% of the time for random field elements, making this a single branch.
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if (a[3] == -1L && a[2] == -1L && a[1] == -1L &&
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(a[0] xor Long.MIN_VALUE) >= (P[0] xor Long.MIN_VALUE)
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) {
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U256.subTo(a, a, P)
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}
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}
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/**
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@@ -85,25 +85,46 @@ internal object Glv {
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maxBits: Int,
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): IntArray {
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val totalBits = maxBits + w
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val sLimbs = maxOf((totalBits + 63) / 64, scalar.size)
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val result = IntArray(totalBits)
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val s = LongArray(sLimbs)
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scalar.copyInto(s)
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val s = LongArray(maxOf((totalBits + 63) / 64, scalar.size))
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wnafInto(result, s, scalar, w, maxBits)
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return result
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}
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/**
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* Encode scalar into wNAF using pre-allocated output and scratch arrays.
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* Returns the effective length (highest non-zero index + 1).
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*/
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fun wnafInto(
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result: IntArray,
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sTmp: LongArray,
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scalar: LongArray,
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w: Int,
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maxBits: Int,
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): Int {
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val totalBits = maxBits + w
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// Clear output and copy scalar into scratch
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for (i in 0 until totalBits.coerceAtMost(result.size)) result[i] = 0
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for (i in sTmp.indices) sTmp[i] = 0
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scalar.copyInto(sTmp)
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var bit = 0
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var highBit = 0
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while (bit < totalBits) {
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if ((s[bit / 64] ushr (bit % 64)) and 1L == 0L) {
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if ((sTmp[bit / 64] ushr (bit % 64)) and 1L == 0L) {
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bit++
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continue
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}
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var word = getBitsVar(s, bit, w.coerceAtMost(totalBits - bit))
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var word = getBitsVar(sTmp, bit, w.coerceAtMost(totalBits - bit))
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if (word >= (1 shl (w - 1))) {
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word -= (1 shl w)
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addBitTo(s, bit + w)
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addBitTo(sTmp, bit + w)
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}
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result[bit] = word
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highBit = bit + 1
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bit += w
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}
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return result
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return highBit
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}
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// ==================== Internal Helpers ====================
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@@ -320,6 +320,18 @@ internal object ECPoint {
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val t = Array(12) { LongArray(4) }
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val dblCopy = MutablePoint() // Copy buffer for in-place doubling (out === input)
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val w = LongArray(8) // Wide buffer for FieldP.mul/sqr — shared, avoids ThreadLocal
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// Pre-allocated scratch for wNAF encoding (avoids IntArray allocation per call).
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// Size 145 = 129 (max bits after GLV split) + 15 (max window) + 1 (headroom).
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val wnaf1 = IntArray(145)
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val wnaf2 = IntArray(145)
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val wnaf3 = IntArray(145) // mulDoubleG needs 4 wNAF arrays
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val wnaf4 = IntArray(145)
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val wnafTmp = LongArray(4) // scratch for wnaf scalar copy (GLV scalars are up to 4 limbs)
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// Pre-allocated scratch for wNAF mixed addition
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val mixTmp = MutablePoint()
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val mixNegY = LongArray(4)
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}
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private val scratch = ThreadLocal.withInitial { PointScratch() }
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@@ -540,8 +552,10 @@ internal object ECPoint {
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// Split scalar via GLV: scalar = k₁ + k₂·λ
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val split = Glv.splitScalar(scalar)
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val wnaf1 = Glv.wnaf(split.k1, wnd, 129)
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val wnaf2 = Glv.wnaf(split.k2, wnd, 129)
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Glv.wnafInto(s.wnaf1, s.wnafTmp, split.k1, wnd, 129)
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Glv.wnafInto(s.wnaf2, s.wnafTmp, split.k2, wnd, 129)
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val wnaf1 = s.wnaf1
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val wnaf2 = s.wnaf2
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// P odd-multiples [1P, 3P, 5P, ..., 15P] via 2P stepping (Jacobian)
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val p2 = MutablePoint()
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@@ -568,16 +582,14 @@ internal object ECPoint {
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batchToAffinePair(pOddJac, pLamOddJac, pOdd, pLamOdd, s)
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// Find highest non-zero digit
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var bits = maxOf(wnaf1.size, wnaf2.size)
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while (bits > 0) {
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val b = bits - 1
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if ((b < wnaf1.size && wnaf1[b] != 0) || (b < wnaf2.size && wnaf2[b] != 0)) break
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var bits = 129 + wnd
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while (bits > 0 && wnaf1[bits - 1] == 0 && wnaf2[bits - 1] == 0) {
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bits--
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}
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out.setInfinity()
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val tmp = MutablePoint()
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val negY = LongArray(4)
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val tmp = s.mixTmp
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val negY = s.mixNegY
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for (i in bits - 1 downTo 0) {
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doublePoint(out, out, s)
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@@ -658,10 +670,14 @@ internal object ECPoint {
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val eSplit = Glv.splitScalar(e)
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// Build wNAF: G-side uses wider window (cached table), P-side uses w=5
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val wnafS1 = Glv.wnaf(sSplit.k1, WINDOW_G, 129)
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val wnafS2 = Glv.wnaf(sSplit.k2, WINDOW_G, 129)
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val wnafE1 = Glv.wnaf(eSplit.k1, wP, 129)
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val wnafE2 = Glv.wnaf(eSplit.k2, wP, 129)
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Glv.wnafInto(sc.wnaf1, sc.wnafTmp, sSplit.k1, WINDOW_G, 129)
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Glv.wnafInto(sc.wnaf2, sc.wnafTmp, sSplit.k2, WINDOW_G, 129)
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Glv.wnafInto(sc.wnaf3, sc.wnafTmp, eSplit.k1, wP, 129)
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Glv.wnafInto(sc.wnaf4, sc.wnafTmp, eSplit.k2, wP, 129)
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val wnafS1 = sc.wnaf1
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val wnafS2 = sc.wnaf2
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val wnafE1 = sc.wnaf3
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val wnafE2 = sc.wnaf4
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// G tables: precomputed and cached (no per-verify allocation)
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val gOdd = gOddTable
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@@ -689,17 +705,16 @@ internal object ECPoint {
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batchToAffinePair(pOddJac, pLamOddJac, pOdd, pLamOdd, sc)
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// Find highest non-zero digit across all 4 streams
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val allWnaf = arrayOf(wnafS1, wnafS2, wnafE1, wnafE2)
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var bits = allWnaf.maxOf { it.size }
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while (bits > 0) {
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val b = bits - 1
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if (allWnaf.any { b < it.size && it[b] != 0 }) break
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var bits = 129 + WINDOW_G // max possible wNAF length
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while (bits > 0 && wnafS1[bits - 1] == 0 && wnafS2[bits - 1] == 0 &&
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wnafE1[bits - 1] == 0 && wnafE2[bits - 1] == 0
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) {
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bits--
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}
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out.setInfinity()
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val tmp = MutablePoint()
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val negY = LongArray(4)
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val tmp = sc.mixTmp
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val negY = sc.mixNegY
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for (i in bits - 1 downTo 0) {
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doublePoint(out, out, sc)
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