scispace - formally typeset
Search or ask a question
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
More filters
Journal ArticleDOI
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

Journal ArticleDOI
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

Journal ArticleDOI
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

Proceedings ArticleDOI
16 May 1981
TL;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


Network Information
Related Topics (5)
Differential equation
88K papers, 2M citations
81% related
Matrix (mathematics)
105.5K papers, 1.9M citations
80% related
Bounded function
77.2K papers, 1.3M citations
79% related
Boundary value problem
145.3K papers, 2.7M citations
78% related
Nonlinear system
208.1K papers, 4M citations
77% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202335
202298
202134
202027
201918
201814