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added some notes of constant selection

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as suggested in #151.
This commit is contained in:
Yann Collet
2018-10-11 17:07:38 -07:00
parent 74c2c63348
commit eec5700f4d
2 changed files with 27 additions and 22 deletions
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29
doc/xxhash_spec.md
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@@ -16,7 +16,7 @@ Distribution of this document is unlimited.
### Version
0.1.0 (15/01/18)
0.1.1 (10/10/18)
Table of Contents
@@ -63,13 +63,15 @@ The algorithm collect and transform input in _stripes_ of 16 bytes. The transfor
The algorithm uses 32-bits addition, multiplication, rotate, shift and xor operations. Many operations require some 32-bits prime number constants, all defined below :
static const u32 PRIME32_1 = 2654435761U;
static const u32 PRIME32_2 = 2246822519U;
static const u32 PRIME32_3 = 3266489917U;
static const u32 PRIME32_4 = 668265263U;
static const u32 PRIME32_5 = 374761393U;
static const u32 PRIME32_1 = 2654435761U; // 0b10011110001101110111100110110001
static const u32 PRIME32_2 = 2246822519U; // 0b10000101111010111100101001110111
static const u32 PRIME32_3 = 3266489917U; // 0b11000010101100101010111000111101
static const u32 PRIME32_4 = 668265263U; // 0b00100111110101001110101100101111
static const u32 PRIME32_5 = 374761393U; // 0b00010110010101100110011110110001
### Step 1. Initialise internal accumulators
These constants are prime numbers, and feature a good mix of bits 1 and 0, neither too regular, nor too dissymmetric. These properties help dispersion capabilities.
### Step 1. Initialize internal accumulators
Each accumulator gets an initial value based on optional `seed` input. Since the `seed` is optional, it can be `0`.
@@ -170,11 +172,13 @@ The algorithm collects and transforms input in _stripes_ of 32 bytes. The transf
The algorithm uses 64-bit addition, multiplication, rotate, shift and xor operations. Many operations require some 64-bit prime number constants, all defined below :
static const u64 PRIME64_1 = 11400714785074694791ULL;
static const u64 PRIME64_2 = 14029467366897019727ULL;
static const u64 PRIME64_3 = 1609587929392839161ULL;
static const u64 PRIME64_4 = 9650029242287828579ULL;
static const u64 PRIME64_5 = 2870177450012600261ULL;
static const u64 PRIME64_1 = 11400714785074694791ULL; // 0b1001111000110111011110011011000110000101111010111100101010000111
static const u64 PRIME64_2 = 14029467366897019727ULL; // 0b1100001010110010101011100011110100100111110101001110101101001111
static const u64 PRIME64_3 = 1609587929392839161ULL; // 0b0001011001010110011001111011000110011110001101110111100111111001
static const u64 PRIME64_4 = 9650029242287828579ULL; // 0b1000010111101011110010100111011111000010101100101010111001100011
static const u64 PRIME64_5 = 2870177450012600261ULL; // 0b0010011111010100111010110010111100010110010101100110011111000101
These constants are prime numbers, and feature a good mix of bits 1 and 0, neither too regular, nor too dissymmetric. These properties help dispersion capabilities.
### Step 1. Initialise internal accumulators
@@ -308,4 +312,5 @@ It links to the [github project page](https://github.com/Cyan4973/xxHash) where
Version changes
--------------------
v0.1.1 : added a note on rationale for selection of constants
v0.1.0 : initial release

20
xxhash.c
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@@ -260,11 +260,11 @@ XXH_PUBLIC_API unsigned XXH_versionNumber (void) { return XXH_VERSION_NUMBER; }
/* *******************************************************************
* 32-bit hash functions
*********************************************************************/
static const U32 PRIME32_1 = 2654435761U;
static const U32 PRIME32_2 = 2246822519U;
static const U32 PRIME32_3 = 3266489917U;
static const U32 PRIME32_4 = 668265263U;
static const U32 PRIME32_5 = 374761393U;
static const U32 PRIME32_1 = 2654435761U; /* 0b10011110001101110111100110110001 */
static const U32 PRIME32_2 = 2246822519U; /* 0b10000101111010111100101001110111 */
static const U32 PRIME32_3 = 3266489917U; /* 0b11000010101100101010111000111101 */
static const U32 PRIME32_4 = 668265263U; /* 0b00100111110101001110101100101111 */
static const U32 PRIME32_5 = 374761393U; /* 0b00010110010101100110011110110001 */
static U32 XXH32_round(U32 seed, U32 input)
{
@@ -663,11 +663,11 @@ static U64 XXH_readBE64(const void* ptr)
/*====== xxh64 ======*/
static const U64 PRIME64_1 = 11400714785074694791ULL;
static const U64 PRIME64_2 = 14029467366897019727ULL;
static const U64 PRIME64_3 = 1609587929392839161ULL;
static const U64 PRIME64_4 = 9650029242287828579ULL;
static const U64 PRIME64_5 = 2870177450012600261ULL;
static const U64 PRIME64_1 = 11400714785074694791ULL; /* 0b1001111000110111011110011011000110000101111010111100101010000111 */
static const U64 PRIME64_2 = 14029467366897019727ULL; /* 0b1100001010110010101011100011110100100111110101001110101101001111 */
static const U64 PRIME64_3 = 1609587929392839161ULL; /* 0b0001011001010110011001111011000110011110001101110111100111111001 */
static const U64 PRIME64_4 = 9650029242287828579ULL; /* 0b1000010111101011110010100111011111000010101100101010111001100011 */
static const U64 PRIME64_5 = 2870177450012600261ULL; /* 0b0010011111010100111010110010111100010110010101100110011111000101 */
static U64 XXH64_round(U64 acc, U64 input)
{