Matlab Portable 64 Bits Full 1 Link 1l
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Some compiler writers view restrictions which prohibit converting (x + y) + z to x + (y + z) as irrelevant, of interest only to programmers who use unportable tricks. Perhaps they have in mind that floating-point numbers model real numbers and should obey the same laws that real numbers do. The problem with real number semantics is that they are extremely expensive to implement. Every time two n bit numbers are multiplied, the product will have 2n bits. Every time two n bit numbers with widely spaced exponents are added, the number of bits in the sum is n + the space between the exponents. The sum could have up to (emax - emin) + n bits, or roughly 2·emax + n bits. An algorithm that involves thousands of operations (such as solving a linear system) will soon be operating on numbers with many significant bits, and be hopelessly slow. The implementation of library functions such as sin and cos is even more difficult, because the value of these transcendental functions aren't rational numbers. Exact integer arithmetic is often provided by lisp systems and is handy for some problems. However, exact floating-point arithmetic is rarely useful.
The preceding paper has shown that floating-point arithmetic must be implemented carefully, since programmers may depend on its properties for the correctness and accuracy of their programs. In particular, the IEEE standard requires a careful implementation, and it is possible to write useful programs that work correctly and deliver accurate results only on systems that conform to the standard. The reader might be tempted to conclude that such programs should be portable to all IEEE systems. Indeed, portable software would be easier to write if the remark "When a program is moved between two machines and both support IEEE arithmetic, then if any intermediate result differs, it must be because of software bugs, not from differences in arithmetic," were true.
Some algorithms that depend on correct rounding can fail with double-rounding. In fact, even some algorithms that don't require correct rounding and work correctly on a variety of machines that don't conform to IEEE 754 can fail with double-rounding. The most useful of these are the portable algorithms for performing simulated multiple precision arithmetic mentioned in the section Exactly Rounded Operations. For example, the procedure described in Theorem 6 for splitting a floating-point number into high and low parts doesn't work correctly in double-rounding arithmetic: try to split the double precision number 252 + 3 × 226 - 1 into two parts each with at most 26 bits. When each operation is rounded correctly to double precision, the high order part is 252 + 227 and the low order part is 226 - 1, but when each operation is rounded first to extended double precision and then to double precision, the procedure produces a high order part of 252 + 228 and a low order part of -226 - 1. The latter number occupies 27 bits, so its square can't be computed exactly in double precision. Of course, it would still be possible to compute the square of this number in extended double precision, but the resulting algorithm would no longer be portable to single/double systems. Also, later steps in the multiple precision multiplication algorithm assume that all partial products have been computed in double precision. Handling a mixture of double and extended double variables correctly would make the implementation significantly more expensive.
defined on 48-bit unsigned integers with, and.The seed specifies the upper 32 bits of the initial value, ,with the lower 16 bits set to 0x330E. The functiongsl_rng_get() returns the upper 32 bits from each term of thesequence. This does not have a direct parallel in the originalrand48 functions, but forcing the result to type long intreproduces the output of mrand48. The functiongsl_rng_uniform() uses the full 48 bits of internal state to returnthe double precision number , which is equivalent to thefunction drand48. Note that some versions of the GNU C Librarycontained a bug in mrand48 function which caused it to producedifferent results (only the lower 16-bits of the return value were set).
R CMD check performs some checks for non-portable compiler/linker flags in src/Makevars. However, it cannot check the meaning of such flags, and some are commonly accepted but with compiler-specific meanings. There are other non-portable flags which are not checked, nor are src/Makefile files and makefiles in sub-directories. As a comment in the code says
Headers in subdirectories are often not portable. For C++, this includes bits/, tr1/ and tr2/, none of which exist on macOS (and ext/ exists there but with different content from g++-based platforms). Header bits/stdc++.h is both not portable and not recommended for end-user code even on platforms which include it. 2b1af7f3a8