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Processors typically provide only a subset of the useful bit operators. Programming languages don't directly support most bit operations, so idioms must be used to code them. The 'C' programming language, for example provides only bit-wise AND(&), OR(|), XOR(^) and NOT(~). Fortran provides AND(.and.), OR (.or.), XOR (.neqv.) and EQV(.eqv.). Algol provides syntactic bitfield extract and insert. When languages provide bit operations that don't directly map to hardware instructions, compilers must synthesize the operation from available operators.
An especially useful bit operation is ''count leading zeros'' used to find the high set bit of a machine word, though it may have different names on various architectures<ref>On most Intel chips, it's BSR (bitscan reverse), though newer SoCs also have LZCNT (count leading zeros)</ref>. There's no simple programming language idiom, so it must be provided by a compiler intrinsic or system library routine. Without that operator, it is ''very'' expensive (see [[Find first set#CLZ]]) to do any operations with regard to the high bit of a word, due to the asymmetric carry-propagate of arithmetic operations. Fortunately, most cpu architectures have provided that since the middle 1980's. An accompanying operation ''count ones'', also called POPCOUNT, which counts the number of set bits in a machine word, is also usually provided as a hardware operator. Simpler bit operations like bit set, reset, test and toggle are often provided as hardware operators, but are easily simulated if they aren't - for example
Some of the more useful and complex bit operations that must be coded as idioms in the programming language and synthesized by compilers include:
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