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Diffstat (limited to 'js/src/jit/ReciprocalMulConstants.cpp')
| -rw-r--r-- | js/src/jit/ReciprocalMulConstants.cpp | 94 |
1 files changed, 94 insertions, 0 deletions
diff --git a/js/src/jit/ReciprocalMulConstants.cpp b/js/src/jit/ReciprocalMulConstants.cpp new file mode 100644 index 0000000000..956c2e62d9 --- /dev/null +++ b/js/src/jit/ReciprocalMulConstants.cpp @@ -0,0 +1,94 @@ +/* -*- Mode: C++; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 2 -*- + * vim: set ts=8 sts=2 et sw=2 tw=80: + * This Source Code Form is subject to the terms of the Mozilla Public + * License, v. 2.0. If a copy of the MPL was not distributed with this + * file, You can obtain one at http://mozilla.org/MPL/2.0/. */ + +#include "jit/ReciprocalMulConstants.h" + +#include "mozilla/Assertions.h" + +using namespace js::jit; + +ReciprocalMulConstants ReciprocalMulConstants::computeDivisionConstants( + uint32_t d, int maxLog) { + MOZ_ASSERT(maxLog >= 2 && maxLog <= 32); + // In what follows, 0 < d < 2^maxLog and d is not a power of 2. + MOZ_ASSERT(d < (uint64_t(1) << maxLog) && (d & (d - 1)) != 0); + + // Speeding up division by non power-of-2 constants is possible by + // calculating, during compilation, a value M such that high-order + // bits of M*n correspond to the result of the division of n by d. + // No value of M can serve this purpose for arbitrarily big values + // of n but, for optimizing integer division, we're just concerned + // with values of n whose absolute value is bounded (by fitting in + // an integer type, say). With this in mind, we'll find a constant + // M as above that works for -2^maxLog <= n < 2^maxLog; maxLog can + // then be 31 for signed division or 32 for unsigned division. + // + // The original presentation of this technique appears in Hacker's + // Delight, a book by Henry S. Warren, Jr.. A proof of correctness + // for our version follows; we'll denote maxLog by L in the proof, + // for conciseness. + // + // Formally, for |d| < 2^L, we'll compute two magic values M and s + // in the ranges 0 <= M < 2^(L+1) and 0 <= s <= L such that + // (M * n) >> (32 + s) = floor(n/d) if 0 <= n < 2^L + // (M * n) >> (32 + s) = ceil(n/d) - 1 if -2^L <= n < 0. + // + // Define p = 32 + s, M = ceil(2^p/d), and assume that s satisfies + // M - 2^p/d <= 2^(p-L)/d. (1) + // (Observe that p = CeilLog32(d) + L satisfies this, as the right + // side of (1) is at least one in this case). Then, + // + // a) If p <= CeilLog32(d) + L, then M < 2^(L+1) - 1. + // Proof: Indeed, M is monotone in p and, for p equal to the above + // value, the bounds 2^L > d >= 2^(p-L-1) + 1 readily imply that + // 2^p / d < 2^p/(d - 1) * (d - 1)/d + // <= 2^(L+1) * (1 - 1/d) < 2^(L+1) - 2. + // The claim follows by applying the ceiling function. + // + // b) For any 0 <= n < 2^L, floor(Mn/2^p) = floor(n/d). + // Proof: Put x = floor(Mn/2^p); it's the unique integer for which + // Mn/2^p - 1 < x <= Mn/2^p. (2) + // Using M >= 2^p/d on the LHS and (1) on the RHS, we get + // n/d - 1 < x <= n/d + n/(2^L d) < n/d + 1/d. + // Since x is an integer, it's not in the interval (n/d, (n+1)/d), + // and so n/d - 1 < x <= n/d, which implies x = floor(n/d). + // + // c) For any -2^L <= n < 0, floor(Mn/2^p) + 1 = ceil(n/d). + // Proof: The proof is similar. Equation (2) holds as above. Using + // M > 2^p/d (d isn't a power of 2) on the RHS and (1) on the LHS, + // n/d + n/(2^L d) - 1 < x < n/d. + // Using n >= -2^L and summing 1, + // n/d - 1/d < x + 1 < n/d + 1. + // Since x + 1 is an integer, this implies n/d <= x + 1 < n/d + 1. + // In other words, x + 1 = ceil(n/d). + // + // Condition (1) isn't necessary for the existence of M and s with + // the properties above. Hacker's Delight provides a slightly less + // restrictive condition when d >= 196611, at the cost of a 3-page + // proof of correctness, for the case L = 31. + // + // Note that, since d*M - 2^p = d - (2^p)%d, (1) can be written as + // 2^(p-L) >= d - (2^p)%d. + // In order to avoid overflow in the (2^p) % d calculation, we can + // compute it as (2^p-1) % d + 1, where 2^p-1 can then be computed + // without overflow as UINT64_MAX >> (64-p). + + // We now compute the least p >= 32 with the property above... + int32_t p = 32; + while ((uint64_t(1) << (p - maxLog)) + (UINT64_MAX >> (64 - p)) % d + 1 < d) { + p++; + } + + // ...and the corresponding M. For either the signed (L=31) or the + // unsigned (L=32) case, this value can be too large (cf. item a). + // Codegen can still multiply by M by multiplying by (M - 2^L) and + // adjusting the value afterwards, if this is the case. + ReciprocalMulConstants rmc; + rmc.multiplier = (UINT64_MAX >> (64 - p)) / d + 1; + rmc.shiftAmount = p - 32; + + return rmc; +} |