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Optimize RemoveCrc32cSuffix. · 4b34e197
The implementation can be optimized to not having to perform an ExtendByZero operation. `RemoveCrc32cSuffix` can simply be implemented as uint32_t result = static_cast<uint32_t>(full_string_crc) ^ static_cast<uint32_t>(suffix_crc); CrcEngine()->UnextendByZeroes(&result, suffix_len); return crc32c_t{result}; Math proof that this change is correct: `ComputeCrc32c` actually computes the following: ConditionedCRC(data) = UnconditionedCRC(data) + StartValue(data) + ~0 with: StartValue(data) = ~0 * x**BitLength(data) mod P (with `+` being a carry-less add, ie an xor). ``UnconditionedCRC` in the context of this description means: no initial or final xor with ~0 and a starting value of zero - ie the result that `CrcEngine()->Extend` would give you with a starting value of 0. Given `full_string_crc` and `suffix_crc` (both conditioned CRCs), xoring them together results in: (1): full_string_crc + suffix_crc = UnconditionedCRC(full_string) + StartValue(full_string) + ~0 + UnconditionedCRC(suffix) + StartValue(suffix) + ~0 Since `+` is carry-less addition (ie an XOR), the two ~0 cancel each other out. (2) full_string_crc + suffix_crc = UnconditionedCRC(full_string) + StartValue(full_string) + UnconditionedCRC(suffix) + StartValue(suffix) We can make use of the fact that: (3) UnconditionedCRC(full_string) + UnConditionedCRC(suffix) = UnconditionedCRC(full_string_with_suffix_replaced_by_zeros). Ie, UnconditionedCRC("AABBB") + UnconditionedCRC("BBB") = UnconditionedCRC("AA\0\0\0") Putting (3) into (2) yields: (4) full_string_crc + suffix_crc = UnconditionedCRC(full_string_with_suffix_replaced_by_zeros) + StartValue(full_string) + StartValue(suffix) Using: (5) UnconditionedCRC(full_string_with_suffix_replaced_by_zeros) = UnconditionedCRC(full_string_without_suffix) * x**Bitlength(suffix) mod P and putting (5) into (4) (6) full_string_crc + suffix_crc = UnconditionedCRC(full_string_without_suffix) * x**Bitlength(suffix) mod P + StartValue(full_string) + StartValue(suffix) Using (7) StartValue(full_string) = ~0 * x ** Bitlength(full_string) mod P and (8) StartValue(suffix) = ~0 * x**BitLength(suffix) mod P Putting (7) and (8) in (6): (9): full_string_crc + suffix_crc = UnconditionedCRC(full_string_without_suffix) * x**(Bitlength(suffix)) mod P + ~0 * x ** Bitlength(full_string) mod P + ~0 * x ** BitLength(suffix) mod P Using: (10) Bitlength(full_string) = Bitlength(full_string_without_suffix) + Bitlength(suffix) And putting (10) in (9): (11) full_string_crc + suffix_crc = UnconditionedCRC(full_string_without_suffix) * x**(Bitlength(suffix)) mod P + ~0 * x ** (Bitlength(full_string_without_suffix) + Bitlength(suffix)) mod P + ~0 * x ** BitLength(suffix) mod P using x**(A+B) = x**A * x**B results in: (12) full_string_crc + suffix_crc = UnconditionedCRC(full_string_without_suffix) * x**(Bitlength(suffix)) mod P + [ ~0 * x ** Bitlength(full_string_without_suffix) * x**Bitlength(suffix)] mod P + ~0 * x ** BitLength(suffix) mod P using A mod P + B mod P + C mod P = (A + B + C) mod P: (this works in carry-less arithmetic) (13) full_string_crc + suffix_crc = [ UnconditionedCRC(full_string_without_suffix) * x**(Bitlength(suffix)) + [ ~0 * x ** Bitlength(full_string_without_suffix) * x**Bitlength(suffix)] + ~0 * x ** BitLength(suffix) ] mod P Factor out x**Bitlength(suffix): (14) full_string_crc + suffix_crc = [ x**(Bitlength(suffix)) * [ UnconditionedCRC(full_string_without_suffix) + ~0 * x ** Bitlength(full_string_without_suffix) + ~0 ] mod P Using: (15) ConditionedCRC(full_string_without_suffix) = [ UnconditionedCRC(full_string_without_suffix) + ~0 * x ** Bitlength(full_string_without_suffix) ] mod P + ~0 = [ UnconditionedCRC(full_string_without_suffix) + ~0 * x ** Bitlength(full_string_without_suffix) + ~0] mod P (~0 is less than x**32, so ~0 mod P = ~0) Putting (15) in (14) results in: full_string_crc + suffix_crc = [ x**(Bitlength(suffix)) * ConditionedCRC(full_string_without_suffix)] mod P Or: (16) ConditionedCRC(full_string_without_suffix) = (full_string_crc + suffix_crc) * x**(-Bitlength(suffix)) mod P A multiplication by x**(-8*bytelength) mod P is implemented by `CrcEngine()->UnextendByZeros`. PiperOrigin-RevId: 502659140 Change-Id: I66b0700d258f948be0885f691370b73d7fad56e3Abseil Team committed
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