Numerical Precision Research Paper Example | Topics and Well Written Essays - 1250 words

Numerical Precision - Research Paper Example In order to be concerned with the right resulting solution, Goldberg (1991) asserts that we must consider the memory and the running time of the computer. This issue is further worsened because a lot of computer algorithms add approximations to house discrete computer. Goldberg (1991) adds that Java uses a small unit of IEEE 754 binary floating point standard to signify floating point numbers and explain the results of arithmetic operations. He says that a float is signified by 32 bits and that each mixture of possible bits signify an actual number, meaning that 232 possible real figures can be signified even though there are a lot of markedly actual numbers. IEEE standards do use the inner picture same as scientific code but in binary rather than base 10. This shelters a range from +/-1.40129846432481707e-45 to around +/-3.40282346638528860e+3 and with about 6 or 7 important decimal digits, plus or minus infinity as well as not a number. The number contains ‘s’ denoting plus or minus, 8 bits for advocate ’e’ and then 23 bits for a mantissa ’M.’ Goldberg (1991) adds that the decimal number is represented by the formula given as, (-1)s * m * 2(e-127) , Where; Sign bit ‘s’ (bit 31), Exponent field ‘e’ (bits 30 - 23) and, Mantissa ‘m’ (22 - 0). Floating-point arithmetic is the famous method of representing real figures in the contemporary computers. Faking an immeasurable, real figures with the machine figures is not a job that is forthright, negotiations that are a bit ingenious must be found amid correctness, swiftness, the ease of using it, lively range as well as application and memory. I therefore argue that floating-point arithmetic along well chosen precision, radix or any other limit is a very good negotiation for a lot of numerical implementations. Good memory performance of CPUs is mostly around the locality of the orientation and this is the same with the GPUs though with se veral significant alterations. The figure below shows a comparison of memory performance of the GPU and CPU. Buck (2005) argues that it is the role of cache that gives the difference between the performance in memory of a GPU and that of a CPU. He adds that the cache in the GPU hurries filtering of surface and therefore they need to be so big as the size of the sieve kernel for the surface sampler hat is a little it tiny and being seeded computation. On he other hand, Buck (2005) vows that the GPU cache formats are enhanced for two sizes and are not wanted. This unlike to the Pentium 4 caches that works at a great clock rate with megabytes of statistics. Moreover, he Pentium 4 cache has the ability to read as well as written memory operations unlike GPU cache for read-only surface statistics. Binary Code Decimal is an example of binary indoctrination of decimal figures where every decimal factor is denoted by a secure number of bits, it is always four to eight. The main asset of Bin ary Coded Decimal is a more perfect picture and rounding of decimal units and make it informal for human-readable picture. It with an advantage that one decimal numeral can be signified by the use of