Topic
Inverse trigonometric functions
About: Inverse trigonometric functions is a research topic. Over the lifetime, 854 publications have been published within this topic receiving 11141 citations. The topic is also known as: arcus function & antitrigonometric function.
Papers published on a yearly basis
Papers
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TL;DR: By induction, the Faa di Bruno formula, and some techniques in the theory of complex functions, the author finds explicit formulas for higher order derivatives of the tangent and cotangent functions as well as powers of the sine and cosine functions.
75 citations
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TL;DR: A new method for the fast evaluation of the elementary functions in single precision based on the evaluation of truncated Taylor series using a difference method, which can calculate the basic elementary functions, namely reciprocal, square root, logarithm, exponential, trig onometric and inverse trigonometric functions, within the latency of two to four floating point multiplies.
Abstract: In this paper we introduce a new method for the fast evaluation of the elementary functions in single precision based on the evaluation of truncated Taylor series using a difference method. We assume the availability of large and fast (at least for read purposes) memory. We call this method the ATA (Add-Table lookup-Add) method. As the name implies, the hardware required for the method are adders (both two/ and multi/operand adders) and fast tables. For IEEE single precision numbers our initial estimates indicate that we can calculate the basic elementary functions, namely reciprocal, square root, logarithm, exponential, trigonometric and inverse trigonometric functions, within the latency of two to four floating point multiplies. >
72 citations
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TL;DR: Algorithms for the approximation of multivariate periodic functions by trigonometric polynomials and an algorithm for sampling multivariate functions on perturbed rank-1 lattices are presented and numerical stability of the suggested method is shown.
69 citations
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16 May 1981TL;DR: This paper elaborate on a technique for computing piecewise quadratric approximations to many elementary functions, which permits the effective use of large RAMs or ROMs and parallel multipliers for rapidly generating single-precision floating-point function values.
Abstract: Among the requirements currently being imposed on high-performance digital computers to an increasing extent are the high-bandwidth computations of elementary functions, which are relatively time-consuming procedures when conducted in software. In this paper, we elaborate on a technique for computing piecewise quadratric approximations to many elementary functions. This method permits the effective use of large RAMs or ROMs and parallel multipliers for rapidly generating single-precision floating-point function values (e.g., 30–45 bits of fraction, with current RAM and ROM technology). The technique, based on the use of Taylor series, may be readily pipelined. Its use for calculating values for floating-point reciprocal, square root, sine, cosine, arctangent, logarithm, exponential and error functions is discussed.
68 citations