Download e-book for iPad: Algorithms for programmers: ideas and source code by Arndt J.

By Arndt J.

It is a draft of a publication approximately chosen algorithms. The viewers in brain are programmers who're attracted to the taken care of algorithms and really are looking to create and comprehend operating and fairly optimized code.

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The following upos_*() functions only work for a limited range. The highest bit must not be set in order to have the highest bit emulate the carry flag. 10: Avoiding branches 23 static inline ulong upos_abs_diff(ulong a, ulong b) { long d1 = b - a; long d2 = (d1 & (d1>>(BITS_PER_LONG-1)))<<1; return d1 - d2; // == (b - d) - (a + d); } Sorting of the arguments: static inline void upos_sort2(ulong &a, ulong &b) // Set {a, b} := {min(a, b), max(a,b)} // Both a and b must not have the most significant bit set { long d = b - a; d &= (d>>(BITS_PER_LONG-1)); a += d; b -= d; } The following two functions adjust a given values when it lies outside a given range.

1. 1.. 11. 11... 1. 111.. 1111. 11111 37 g(k) ....... 1. 11. 1.. 11.. 111. 1. 1... 11... 1. 1111. 111.. 1.. 11. 1. 1.... g(g(k)) ....... 1. 1.. 11. 1. 1... 111. 11.. 1.. 11. 1.... 1. 1111. 111.. 1. 11... g(2*k) ....... 11. 11.. 1. 11... 1111. 1.. 1. 11.... 11. 1111.. 1. 1... 111. 1.. 1. 1. 1.. 111. 1... 1. 111.. 11. 1.... 1. 1.. 11111. 111... 1. 11.. 11. 1..... 15-A: Binary words, their Gray code, squared Gray code, and Gray codes of even and odd values. return r; } For n-bit words, n-fold application of the Gray code gives back the original word.

1. 1 E**2 1....... 11...... 111..... 1111.... 1111... 1111.. 1111. 1111 E**3 1....... 1...... 1..... 1.... 1... 1.. 1. 1 E**4 We just have to reverse the shift operator in the functions: inline ulong rev_gray_pow(ulong x, ulong e) // Return (rev_gray_code**e)(x) { e &= (BITS_PER_LONG-1); // modulo BITS_PER_LONG ulong s = 1; while ( e ) { if ( e & 1 ) x ^= x << s; // rev_gray ** s s <<= 1; e >>= 1; } return x; } The inverse function is inline ulong inverse_rev_gray_pow(ulong x, ulong e) // Return (inverse_rev_gray_code**(e))(x) { return rev_gray_pow(x, -e); } [fxtbook draft of 2008-January-19] 1.......

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Algorithms for programmers: ideas and source code by Arndt J.


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