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#pragma once |
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#include "../Common.h" |
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#include <cstdint> |
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namespace Feather::Math |
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{ |
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// de Bruijn Sequence: B(2, 5) = 0000 0111 0111 1100 1011 0101 0011 0001. Contains all 32 distinct 5-bit strings. |
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constexpr uint32_t DE_BRUIJN_SEQ = 0x077CB531U; |
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constexpr int MULTIPLY_DE_BRUIJN_BIT_POSITION[32] = {0, 1, 28, 2, 29, 14, 24, 3, 30, 22, 20, 15, 25, 17, 4, 8, 31, 27, 13, 23, 21, 19, 16, 7, 26, 12, 18, 6, 11, 5, 10, 9}; |
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// Is x a power of two? |
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inline constexpr bool IsPowerOf2(int x) |
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{ |
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return x != 0 && (x & (x - 1)) == 0; |
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} |
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// Smallest number 2^z that is greater than or equal to x |
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// Precondition: x > 0 |
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inline constexpr int RoundToPowerOf2(int x) |
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{ |
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x--; |
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x |= x >> 1; |
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x |= x >> 2; |
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x |= x >> 4; |
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x |= x >> 8; |
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x |= x >> 16; |
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return x + 1; |
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} |
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inline constexpr int CeilLog2(int x) |
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{ |
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// Ensure x is power of 2 |
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x = IsPowerOf2(x) ? x : RoundToPowerOf2(x); |
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// The de Bruijn sequence contains all 32 distinct 5-bit strings |
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// 27 is 32 - 5 and 0x1F (31) is the lower 5 bits 0001 1111 |
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return MULTIPLY_DE_BRUIJN_BIT_POSITION[(int)((int64_t)x * DE_BRUIJN_SEQ >> 27) & 0x1F]; |
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} |
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// log base 2 |
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inline constexpr int Log2(int x) |
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{ |
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return CeilLog2(x) - (IsPowerOf2(x) ? 0 : 1); |
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} |
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// Divide and round up |
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template<typename T> |
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inline constexpr T CeilDiv(const T a, const T b) |
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{ |
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return (a / b) + (a % b != 0); |
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} |
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}
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