ACML_MV is a library which contains fast and/or vectorized versions of some familar math library routines such as sin, cos and exp. The routines take advantage of the AMD64 architecture for performance, and so are currently only available with 64-bit versions of ACML. The routines in the library are very accurate over the range of acceptable input arguments.
Some of the performance is gained by sacrificing error handling or the acceptance of certain arguments. It is therefore the responsibility of the caller of these routines to ensure that their arguments are suitable. Furthermore, some of the routines are not callable from high-level languages at all, but must be called via assembly language; see the documentation of individual routines for details. Hence, these routines are intended to be utilized by knowledgeable users only.
The individual documentation for a routine states what outputs will be returned for special arguments, and also gives an indication of performance of the routine. In general, special case arguments for any routine will cause a return value in accordance with the C99 language standard [6].
Special case arguments include NaNs and infinities, as defined by the IEEE arithmetic standard [7]. In these documents, NaN means Not a Number, QNaN means Quiet NaN, and SNaN means Signalling NaN.
Performance of a routine is given in machine cycles, and is thus independent of processor speed.
Accuracy of a routine is quoted in ulps, where ulp stands for Unit in the Last Place. Since floating-point numbers on a computer are limited precision approximations of mathematical numbers, not all real numbers can be represented by machine numbers, and the machine number must in general be rounded to available precision. An ulp is the distance between the two machine numbers that bracket a real number.
In this document, the ulp is used as a measure of the error in a returned result when compared with the mathematically exact expected result. Because of the finite nature of machine arithmetic, a routine can never in general achieve accuracy of better than 0.5 ulps, and an accuracy of less than 1 ulp is good.
The following types are used to describe the functions contained in this chapter:
| __m128d | a pair of double precision values;
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| __m128 | four single precision values.
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