Calculators - CORDIC MethodDate: 05/16/99 at 03:15:37 From: Warren Subject: How can a computer or calculator calculate? How can a computer or calculator calculate square roots, cube roots, Xth root, x^y, logarithm, sine, cosine, ...? Date: 05/16/99 at 06:44:01 From: Doctor Jerry Subject: Re: How can a computer or calculator calculate? Hi Warren, Calculators use what is called the CORDIC method. TI and HP use several stored constants and calculate the values of several sequences of numbers, using only addition and multiplication. They continue the calculation until sufficient accuracy is obtained. The algorithm looks like this: I'll use x_k to mean x sub k, and x_{k+1} to mean x sub k+1, and so on. Let x_{k+1} = x_k - d_k*y_k*2^(-k) y_{k+1} = y_k + d_k*x_k*2^(-k) z_{k+1} = z_k - d_k*s_k The numbers d_k are equal to the sign of z_k (if z_k >= 0, d_k = 1; if z_k < 0, then d_k = -1). Also, s_k = arctan(2^(-k)). The numbers s_k are permanently stored in the calculator, maybe up to k = 50 or so. Starting values for the calculation are calculated. If z_0 = t is given, where t is a given angle (in radians), then y_0 = 0 and x_0 = cos(s_0)*cos(s_1)*...*cos(s_{47}). As k increases, x_k approaches cos(t) and y_k approaches sin(t). Similar calculations give other trig functions. - Doctor Jerry, The Math Forum http://mathforum.org/dr.math/ |
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