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BigInteger.sqrtRem(result, remainder, n); Unknown Common Lisp (isqrt n) [4] Unknown Crystal: Math.isqrt(n) [5] 1.2 Java: n.sqrt() [6] (BigInteger only) 9 Julia: isqrt(n) [7] 0.3 Maple: isqrt(n) [8] Unknown PARI/GP: sqrtint(n) [9] 1.35a [10] (as isqrt) or before Python: math.isqrt(n) [11] 3.8 Racket (integer-sqrt n) [12] (integer-sqrt/remainder ...
To factorize the integer n, Fermat's method entails a search for a single number a, n 1/2 < a < n−1, such that the remainder of a 2 divided by n is a square. But these a are hard to find. The quadratic sieve consists of computing the remainder of a 2 /n for several a, then finding a subset of these whose product is a square. This will yield a ...
The IEEE 754 floating-point standard guarantees that add, subtract, multiply, divide, fused multiply–add, square root, and floating-point remainder will give the correctly rounded result of the infinite-precision operation. No such guarantee was given in the 1985 standard for more complex functions and they are typically only accurate to ...
[8] During the Dutch East Indies campaign of 1941–42, by forces of the Empire of Japan, most of the KNIL and other Allied forces were quickly defeated. [9] Most European soldiers, which in practice included all able bodied Indo-European males, were interned by the Japanese as POWs. 25% of the POWs did not survive their internment.
[5] [6] [7] Brooklyn, at 37,339.9 inhabitants per square mile (14,417.0/km 2), is the second most densely populated county in the U.S. after Manhattan (New York County), as of 2022. [8] Had Brooklyn remained an independent city, it would now be the fourth most populous American city after the rest of New York City, Los Angeles , and Chicago .
The Bombing of Darwin, also known as the Battle of Darwin, [4] on 19 February 1942 was the largest single attack ever mounted by a foreign power on Australia. [5] On that day, 242 Japanese aircraft, in two separate raids, attacked the town, ships in Darwin Harbour and the town's two airfields in an attempt to prevent the Allies from using them as bases to contest the invasion of Timor and Java ...
With the departure of the Sailendras and the fall of Singhasari, a new Majapahit kingdom appeared in eastern Java, which reverted from Buddhism to Hinduism. By the middle of the 14th century, Majapahit controlled most of Java, Sumatra and the Malay Peninsula, part of Borneo, the southern Celebes and the Moluccas. It also exerted considerable ...