Hardware Efficient Algorithms for Trigonometric Functions

  title={Hardware Efficient Algorithms for Trigonometric Functions},
  author={Raymond E. Fowkes},
  journal={IEEE Trans. Computers},
A new algorithm is presented which significantly reduces the minimum amount of logic required to calculate sine, cosine, and square root. It is derived from an old method for computing certain inverse functions which was once considered for use in software, but then abandoned because of efficiency concerns. However, when reversed and combined with a restoring square root algorithm, a unique new design emerges which performs trigonometric calculations without the use of pre-stored constants or… 
A Bibliography of Publications on Floating-Point Arithmetic
This is a bibliography of material on floating-point arithmetic that I came up with while doing research on a floating-point package of my own. I don’t claim it to be anywhere near complete. The
Design-for-testability techniques for CORDIC design
Two C-testable design-for-testability (DFT) architectures for coordinate rotation digital computer (CORDIC) design are proposed, one connected into a non-homogenous ILA for saving lot of test pins and built-in self-test (BIST) area; in the second, the special properties of the sequences reduce HO/NTP significantly.
Trignometric Function Generator Implementation on FPGA
This paper aims to demonstrate the efforts towards in-situ applicability of EMMARM, as to provide real-time information about the physical properties of E-modulus and its applications in the environment.
An on-line approach for evaluating trigonometric functions
An On-Line approach for Evaluating Trigonometric Functions and an on-line approach for evaluating trigonometric functions are presented.
A VLSI chip for 3-D camera calibration
This paper presents the preliminary design of a VLSI chip to support and efficiently implement the calibration operations of a 3-D camera based on the principle of autosynchronized triangulation.
Fuzzy-Based Torque Ripple Optimization and Digitalized Sector Selection in DTC Scheme
This paper presents an efficient method of torque ripple optimization in Direct Torque Control (DTC) scheme for an induction motor drive (IMD), where the optimization has been done by varying the
FLC-Based DTC Scheme to Improve the Dynamic Performance of an IM Drive
This paper presents a fuzzy logic hysteresis comparator-based direct torque control (DTC) scheme of an induction motor (IM) under varying dynamic conditions. The fuzzy logic controller (FLC) is used
FLC-Based DTC Scheme to Improve the Dynamic Performance of an IM Drive
  • M. Uddin, M. Hafeez
  • Engineering, Computer Science
    IEEE Transactions on Industry Applications
  • 2012
A simpler algorithm than the conventional trigonometric function-based algorithm to evaluate the sector number (required for DTC scheme) of the stator flux-linkage space vector is proposed, which reduces the computational burden on the microprocessor.
All-optical decrementing of a packet's time-to-live (TTL) field and subsequent dropping of a zero-TTL packet
An optical time-to-live (TTL) decrementing module for optical packet-switched networks that acts on a standard NRZ-modulated binary TTL field within a 10 Gb/s packet and decrements it by one if the TTL is nonzero.
Optical performance monitoring in optical packet-switched networks
Para poder satisfacer la demanda de mayores anchos de banda y los requisitos de los nuevos servicios, se espera que se produzca una evolucion de las redes opticas hacia arquitecturas reconfigurables


Hardware evaluation of mathematical functions
The paper presents a family of algorithms for evaluating the elementary mathematical functions including division, sine, cosine, tangent, arctangent, logarithm, exponential and square root. The
The CORDIC Trigonometric Computing Technique
  • Jack E. Volder
  • Mathematics, Computer Science
    IRE Trans. Electron. Comput.
  • 1959
The trigonometric algorithms used in this computer and the instrumentation of these algorithms are discussed in this paper.
Digital Hardware for Sine-Cosine Function
The design of a high-speed digital processor for the sine and cosine functions is discussed. The hardware provides a significant speed advantage over software calculations of these functions. The
A unified algorithm for elementary functions
  • J. S. Walther
  • Mathematics, Computer Science
    AFIPS '71 (Spring)
  • 1971
This paper describes a single unified algorithm for the calculation of elementary functions including multiplication, division, sin, cos, tan, arctan, sinh, cosh, tanh, arctanh, In, exp and
Survey of Square Rooting Algorithms
The paper reviews the algorithms for the computation of square roots for binary machines by considering their specific peculiarities and properties and makes some comments regarding their ideal and effective implementation in hardware, software or microcode.
Pseudo Division and Pseudo Multiplication Processes
Some digit-by-digit methods for the evaluation of the elementary functions are described. The methods involve processes that resemble repeated-addition multiplication and repeated-subtraction
A Cordic Processor for Laser Trimming
A coordinate rotation algorithm can be used to correct the position of a microcircuit on a laser trimming platform, but a software implementation was too slow and special-purpose hardware solved the problem.
The Cordic Magnification Function
This analysis shows that the Cordic scaling constant need not be evaluated for each word length. On the contrary, a single ¿master¿ constant can be used for all cases.
however (for it was the literal soul of the life of the Redeemer, John xv. io), is the peculiar token of fellowship with the Redeemer. That love to God (what is meant here is not God’s love to men)
Minimal hardware algorithms for trigonometric functions
  • WESCON '91 Con$ Rec
  • 1991