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returns the nearest integer not greater in magnitude than the given value round lround llround: returns the nearest integer, rounding away from zero in halfway cases nearbyint: returns the nearest integer using current rounding mode rint lrint llrint: returns the nearest integer using current rounding mode with exception if the result differs ...
Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.
Names and symbols used for integer division include div, /, \, and %. Definitions vary regarding integer division when the dividend or the divisor is negative: rounding may be toward zero (so called T-division) or toward −∞ (F-division); rarer styles can occur – see modulo operation for the details.
In the example from "Double rounding" section, rounding 9.46 to one decimal gives 9.4, which rounding to integer in turn gives 9. With binary arithmetic, this rounding is also called "round to odd" (not to be confused with "round half to odd"). For example, when rounding to 1/4 (0.01 in binary), x = 2.0 ⇒ result is 2 (10.00 in binary)
Shifting right by 1 bit will divide by two, always rounding down. However, in some languages, division of signed binary numbers round towards 0 (which, if the result is negative, means it rounds up). For example, Java is one such language: in Java, -3 / 2 evaluates to -1, whereas -3 >> 1 evaluates to -2.
For to be an integer, we need to round / somehow. Rounding to the nearest integer will give the best approximation but can result in m / 2 k {\displaystyle m/2^{k}} being larger than 1 / n {\displaystyle 1/n} , which can cause underflows.
This is different from the way rounding is usually done in signed integer division (which rounds towards 0). This discrepancy has led to bugs in a number of compilers. [8] For example, in the x86 instruction set, the SAR instruction (arithmetic right shift) divides a signed number by a power of two, rounding towards negative infinity. [9]
Rounding up and down to a multiple of a known power of 2, the next power of 2 and for detecting whether an operation crossed a power-of-2 boundary; Checking bounds; Counting total, leading and trailing zeros; Searching for bit strings; Permutations of bits and bytes in a word; Software algorithms for multiplication; Integer division