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  1. // +build !go1.9
  2. package roaring
  3. // Reuse of portions of go/src/math/big standard lib code
  4. // under this license:
  5. /*
  6. Copyright (c) 2009 The Go Authors. All rights reserved.
  7. Redistribution and use in source and binary forms, with or without
  8. modification, are permitted provided that the following conditions are
  9. met:
  10. * Redistributions of source code must retain the above copyright
  11. notice, this list of conditions and the following disclaimer.
  12. * Redistributions in binary form must reproduce the above
  13. copyright notice, this list of conditions and the following disclaimer
  14. in the documentation and/or other materials provided with the
  15. distribution.
  16. * Neither the name of Google Inc. nor the names of its
  17. contributors may be used to endorse or promote products derived from
  18. this software without specific prior written permission.
  19. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
  20. "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
  21. LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
  22. A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
  23. OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
  24. SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
  25. LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
  26. DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
  27. THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
  28. (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
  29. OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  30. */
  31. const deBruijn32 = 0x077CB531
  32. var deBruijn32Lookup = []byte{
  33. 0, 1, 28, 2, 29, 14, 24, 3, 30, 22, 20, 15, 25, 17, 4, 8,
  34. 31, 27, 13, 23, 21, 19, 16, 7, 26, 12, 18, 6, 11, 5, 10, 9,
  35. }
  36. const deBruijn64 = 0x03f79d71b4ca8b09
  37. var deBruijn64Lookup = []byte{
  38. 0, 1, 56, 2, 57, 49, 28, 3, 61, 58, 42, 50, 38, 29, 17, 4,
  39. 62, 47, 59, 36, 45, 43, 51, 22, 53, 39, 33, 30, 24, 18, 12, 5,
  40. 63, 55, 48, 27, 60, 41, 37, 16, 46, 35, 44, 21, 52, 32, 23, 11,
  41. 54, 26, 40, 15, 34, 20, 31, 10, 25, 14, 19, 9, 13, 8, 7, 6,
  42. }
  43. // trailingZeroBits returns the number of consecutive least significant zero
  44. // bits of x.
  45. func countTrailingZeros(x uint64) int {
  46. // x & -x leaves only the right-most bit set in the word. Let k be the
  47. // index of that bit. Since only a single bit is set, the value is two
  48. // to the power of k. Multiplying by a power of two is equivalent to
  49. // left shifting, in this case by k bits. The de Bruijn constant is
  50. // such that all six bit, consecutive substrings are distinct.
  51. // Therefore, if we have a left shifted version of this constant we can
  52. // find by how many bits it was shifted by looking at which six bit
  53. // substring ended up at the top of the word.
  54. // (Knuth, volume 4, section 7.3.1)
  55. if x == 0 {
  56. // We have to special case 0; the fomula
  57. // below doesn't work for 0.
  58. return 64
  59. }
  60. return int(deBruijn64Lookup[((x&-x)*(deBruijn64))>>58])
  61. }
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