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Update README.md
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周伯威 Po-Wei Chou
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README.md
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README.md
@ -104,13 +104,7 @@ sign = -(int)((unsigned int)((int)v) >> (sizeof(int) * CHAR_BIT - 1));
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sign = v >> (sizeof(int) * CHAR_BIT - 1);
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```
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The last expression above evaluates to sign = v >> 31
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for 32-bit integers.
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This is one operation faster than the obvious way, sign = -(v < 0).
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This trick works because when signed integers are shifted right, the value
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of the far left bit is copied to the other bits. The far left bit is 1
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when the value is negative and 0 otherwise; all 1 bits gives -1.
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Unfortunately, this behavior is architecture-specific.
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The last expression above evaluates to `sign = v >> 31` for 32-bit integers. This is one operation faster than the obvious way, `sign = -(v < 0)`. This trick works because when signed integers are shifted right, the value of the far left bit is copied to the other bits. The far left bit is 1 when the value is negative and 0 otherwise; all 1 bits gives -1. Unfortunately, this behavior is architecture-specific.
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Alternatively, if you prefer the result be either -1 or +1, then use:
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@ -127,27 +121,20 @@ sign = (v != 0) | (v >> (sizeof(int) * CHAR_BIT - 1)); // -1, 0, or +1
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// Or, for portability, brevity, and (perhaps) speed:
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sign = (v > 0) - (v < 0); // -1, 0, or +1
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```
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If instead you want to know if something is non-negative, resulting in +1 or
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else 0, then use:
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If instead you want to know if something is non-negative, resulting in +1 or else 0, then use:
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```c
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sign = 1 ^ ((unsigned int)v >> (sizeof(int) * CHAR_BIT - 1)); // if v < 0 then 0, else 1
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```
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Caveat: On March 7, 2003, Angus Duggan pointed out that the 1989 ANSI C
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specification leaves the result of signed right-shift implementation-defined,
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so on some systems this hack might not work. For greater portability,
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Toby Speight suggested on September 28, 2005 that CHAR_BIT be used here
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and throughout rather than assuming bytes were 8 bits long. Angus recommended
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the more portable versions above, involving casting on March 4, 2006.
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<a href="http://rpg-314.blogspot.com/">Rohit Garg</a> suggested the version
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for non-negative integers on September 12, 2009.
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Caveat: On March 7, 2003, Angus Duggan pointed out that the 1989 ANSI C specification leaves the result of signed right-shift implementation-defined, so on some systems this hack might not work. For greater portability, Toby Speight suggested on September 28, 2005 that CHAR_BIT be used here and throughout rather than assuming bytes were 8 bits long. Angus recommended the more portable versions above, involving casting on March 4, 2006. [Rohit Garg](http://rpg-314.blogspot.com/) suggested the version for non-negative integers on September 12, 2009.
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<hr>
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<a name="DetectOppositeSigns">### Detect if two integers have opposite signs
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<a name="DetectOppositeSigns">
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### Detect if two integers have opposite signs
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</a>
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@ -506,7 +493,9 @@ April 3, 2007 and alerted me to a typo 2 days later.
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<hr>
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<a name="ConditionalNegate">### Conditionally negate a value without branching</a>
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<a name="ConditionalNegate">
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### Conditionally negate a value without branching
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</a>
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If you need to negate only when a flag is false, then use the following
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@ -540,7 +529,8 @@ missing on November 26, 2009, and received a bug bounty.
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<a name="MaskedMerge">### Merge bits from two values according to a mask
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<a name="MaskedMerge">
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### Merge bits from two values according to a mask
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</a>
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@ -1748,7 +1738,8 @@ brought this oversight to my attention on December 12, 2003.
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<hr>
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<a name="IntegerLogDeBruijn">### Find the log base 2 of an N-bit integer in O(lg(N)) operations with multiply and lookup
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<a name="IntegerLogDeBruijn">
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### Find the log base 2 of an N-bit integer in O(lg(N)) operations with multiply and lookup
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</a>
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@ -1954,7 +1945,8 @@ and he suggested using memcpy.
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<hr>
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<a name="ZerosOnRightLinear">### Count the consecutive zero bits (trailing) on the right linearly
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<a name="ZerosOnRightLinear">
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### Count the consecutive zero bits (trailing) on the right linearly
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</a>
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@ -1986,7 +1978,8 @@ I had neglected to paste the unsigned modifier for v.
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<hr>
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<a name="ZerosOnRightParallel">### Count the consecutive zero bits (trailing) on the right in parallel
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<a name="ZerosOnRightParallel">
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### Count the consecutive zero bits (trailing) on the right in parallel
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</a>
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@ -2014,7 +2007,8 @@ February 4, 2011.
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<hr>
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<a name="ZerosOnRightBinSearch">### Count the consecutive zero bits (trailing) on the right by binary search
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<a name="ZerosOnRightBinSearch">
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### Count the consecutive zero bits (trailing) on the right by binary search
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</a>
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@ -2072,7 +2066,8 @@ subtracting at the end).
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<hr>
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<a name="ZerosOnRightFloatCast">### Count the consecutive zero bits (trailing)
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<a name="ZerosOnRightFloatCast">
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### Count the consecutive zero bits (trailing)
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on the right by casting to a float
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</a>
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@ -2095,7 +2090,8 @@ If v is zero, then the result is -127.
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<hr>
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<a name="ZerosOnRightModLookup">### Count the consecutive zero bits (trailing)
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<a name="ZerosOnRightModLookup">
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### Count the consecutive zero bits (trailing)
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on the right with modulus division and lookup
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</a>
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@ -2127,7 +2123,8 @@ the table values, and found it was invented earlier by Reiser, according to
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<hr>
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<a name="ZerosOnRightMultLookup">### Count the consecutive zero bits (trailing)
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<a name="ZerosOnRightMultLookup">
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### Count the consecutive zero bits (trailing)
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on the right with multiply and lookup
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</a>
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@ -2164,7 +2161,8 @@ compiled with 64-bit ints.
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<hr>
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<a name="RoundUpPowerOf2Float">### Round up to the next highest power of 2 by float casting
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<a name="RoundUpPowerOf2Float">
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### Round up to the next highest power of 2 by float casting
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</a>
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@ -2208,7 +2206,8 @@ rounding, but it used one more operation.
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<hr>
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<a name="RoundUpPowerOf2">### Round up to the next highest power of 2
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<a name="RoundUpPowerOf2">
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### Round up to the next highest power of 2
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</a>
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@ -2258,7 +2257,8 @@ where they arrive at the same algorithm.
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<hr>
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<a name="InterleaveTableObvious">### Interleave bits the obvious way
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<a name="InterleaveTableObvious">
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### Interleave bits the obvious way
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</a>
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@ -2282,7 +2282,8 @@ another if their x and y values are close.
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<hr>
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<a name="InterleaveTableLookup">### Interleave bits by table lookup
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<a name="InterleaveTableLookup">
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### Interleave bits by table lookup
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</a>
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@ -2343,7 +2344,8 @@ only need 11 operations total.
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<hr>
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<a name="Interleave64bitOps">### Interleave bits with 64-bit multiply</a>
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<a name="Interleave64bitOps">
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### Interleave bits with 64-bit multiply</a>
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In 11 operations, this version interleaves bits of two bytes
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@ -2370,7 +2372,8 @@ October 10, 2004 after reading the multiply-based bit reversals here.
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<hr>
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<a name="InterleaveBMN">### Interleave bits by Binary Magic Numbers
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<a name="InterleaveBMN">
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### Interleave bits by Binary Magic Numbers
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</a>
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@ -2400,7 +2403,8 @@ z = x | (y << 1);
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<hr>
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<a name="ZeroInWord">### Determine if a word has a zero byte
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<a name="ZeroInWord">
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### Determine if a word has a zero byte
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</a>
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@ -2478,7 +2482,8 @@ on April 27, 1987 by Alan Mycroft.
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<hr>
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<a name="#ValueInWord">### Determine if a word has a byte equal to n
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<a name="#ValueInWord">
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### Determine if a word has a byte equal to n
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</a>
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@ -2500,7 +2505,8 @@ for `haszero`.
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<hr>
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<a name="HasLessInWord">### Determine if a word has a byte less than n
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<a name="HasLessInWord">
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### Determine if a word has a byte less than n
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</a>
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@ -2531,7 +2537,8 @@ April 10, 2005, inspired by Juha's `countmore`, below.
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<hr>
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<a name="HasMoreInWord">### Determine if a word has a byte greater than n
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<a name="HasMoreInWord">
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### Determine if a word has a byte greater than n
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</a>
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@ -2556,7 +2563,8 @@ April 6, 2005, and he added `countmore` on April 8, 2005.
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<hr>
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<a name="HasBetweenInWord">### Determine if a word has a byte between m and n
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<a name="HasBetweenInWord">
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### Determine if a word has a byte between m and n
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</a>
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@ -2599,7 +2607,8 @@ Sean Anderson created `hasbetween` and
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<hr>
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<a name="NextBitPermutation">### Compute the lexicographically next bit permutation
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<a name="NextBitPermutation">
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### Compute the lexicographically next bit permutation
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</a>
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