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By Arndt J.

This can be a draft of a ebook approximately chosen algorithms. The viewers in brain are programmers who're drawn to the handled algorithms and truly are looking to create and comprehend operating and fairly optimized code.

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11......................... 11111111111111111111111111 = inverse_gray_code 1111111......................... 11........................ 15-D: Four examples of the Gray code, reversed Gray code and their inverses with 32-bit words. We define the reversed Gray code to be the bit-reversed word of the Gray code of the bit-reversed word. That is, rev_gray_code(x) := revbin(gray_code(revbin(x))) It turns out that the corresponding functions are identical to the Gray code versions up to the reversed shift operations (C-language operators ‘>>’ replaced by ‘<<’).

BITS_PER_LONG−1}. As an example, in order to determine whether x is a prime less than 32, one can use the function ulong m = (1UL<<2) | (1UL<<3) | (1UL<<5) | ... 6 on page 152. 10 Avoiding branches Branches are expensive operations with many CPUs, especially if the CPU pipeline is very long. h]. The following function returns max(0, x). That is, zero is returned for negative input, else the unmodified input: static inline long max0(long x) { return x & ~(x >> (BITS_PER_LONG-1)); } There is no restriction on input range.

11.. 11. 11 E**1=E 1....... 1...... 1..... 1.... 1... 1.. 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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