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Algorithms for trig. on scientific calculators ?
12-06-2024, 07:01 PM (This post was last modified: 12-06-2024 07:02 PM by SlideRule.)
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RE: Algorithms for trig. on scientific calculators ?
a small contribution:
   
pg 195 CORDIC, 58, 120, 121, 122, 123, 124

pg58 Another example of IQ format application can be
using it to express numbers during performing CORDIC algorithm suited for
estimation of nonlinear functions. The ST Microelectronics company prepared
STM32G4-CORDIC co-processor. It provides hardware acceleration
of some mathematical functions, notably trigonometric, commonly used in
motor control, metering, signal processing and many other applications. It
speeds up the calculation of these functions compared to a software implementation,
freeing up processor cycles in order to perform other tasks. In this
case, the q1.31 or q1.5 formats are available. For processors without hardware
support as FPU or CORDIC units this mathematical capability can be
realized by software CORDIC library or math library.

pgs 117 - 124: 3.3 NONLINEAR FUNCTIONS

pg120 What about the other functions except square root, e.g.
trigonometric or logarithms? Do we really have to look for individual
methods of approximation or is there any universal technique for precise
and quick function evaluation? Luckily there is a way to do that. It is
named CORDIC proposed many years ago by Jack Volder [Volder 1959]
and commonly applied nowadays. The CORDIC abbreviation is from
‘coordinate rotation digital computer’.

pg121 The CORDIC algorithm can also be
used for calculating hyperbolic functions by replacing the successive circular
rotations by steps along a hyperbola. Thanks to this idea computers
can calculate the following functions: cosine (cos(x)), sine (sin(x)),
atan2(y,x), modulus i.e. sqrt(x2+y2), arctangent (tan−1(x)), hyperbolic sin
(sinh(x)), hyperbolic cosine (cosh(x)) and hyperbolic arctangent (atanh(x)).
If needed, the other functions can be evaluated from known identities …
From the algorithmic point of view, the CORDIC can be seen as a sequence
of micro rotations, where the vector XY is rotated by an angle θ expressed
in radians.

pg122 The CORDIC algorithm can work in circular of hyperbolic modes …
The CORDIC algorithm can also be used for calculating hyperbolic functions
(sinh, cosh, atanh) by replacing the circular rotations by hyperbolic angles

pg123 Figure 3.1 Functions evaluated by CORDIC algorithm vs. perfect
sin/cos function shapes.

pg124 Figure 3.2 Maximal error of sinus evaluation by CORDIC algorithm.


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RE: Algorithms for trig. on scientific calculators ? - SlideRule - 12-06-2024 07:01 PM



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