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In contrast, one may need to perform less work to make part A perform twice as fast. This will make the computation much faster than by optimizing part B, even though part B's speedup is greater in terms of the ratio, (5 times versus 2 times). For example, with a serial program in two parts A and B for which T A = 3 s and T B = 1 s,
dc: "Desktop Calculator" arbitrary-precision RPN calculator that comes standard on most Unix-like systems. KCalc, Linux based scientific calculator; Maxima: a computer algebra system which bignum integers are directly inherited from its implementation language Common Lisp. In addition, it supports arbitrary-precision floating-point numbers ...
In computer science, arbitrary-precision arithmetic, also called bignum arithmetic, multiple-precision arithmetic, or sometimes infinite-precision arithmetic, indicates that calculations are performed on numbers whose digits of precision are potentially limited only by the available memory of the host system.
Denote the serial time as and the parallel time as , where + =. Denote the number of processors as N {\displaystyle N} . Hypothetically, when running the program on a serial system (only one processor), the serial part still takes s {\displaystyle s} , while the parallel part now takes N p {\displaystyle Np} .
Calculators that implement TI-BASIC have a built in editor for writing programs. While the considerably faster Z80 assembly language [2]: 120 is supported for the calculators, TI-BASIC's in-calculator editor and more user friendly syntax make it easier to use. TI-BASIC is interpreted. [2]: 155
Loop unrolling, also known as loop unwinding, is a loop transformation technique that attempts to optimize a program's execution speed at the expense of its binary size, which is an approach known as space–time tradeoff.
Example: 100P can be written as 2(2[P + 2(2[2(P + 2P)])]) and thus requires six point double operations and two point addition operations. 100P would be equal to f(P, 100). This algorithm requires log 2 (d) iterations of point doubling and addition to compute the full point multiplication. There are many variations of this algorithm such as ...
From a mathematician's point of view, this formula only works in limit where n goes to infinity, but very reasonable estimates can be found with just a few additional iterations after the main loop exits. Once b is found, by the Koebe 1/4-theorem, we know that there is no point of the Mandelbrot set with distance from c smaller than b/4.