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44 lines
1.1 KiB
Plaintext
44 lines
1.1 KiB
Plaintext
/*
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* Copyright (c) 1995 David I. Bell
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* Permission is granted to use, distribute, or modify this source,
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* provided that this copyright notice remains intact.
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*
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* Solve the equation f(x) = 0 to within the desired error value for x.
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* The function 'f' must be defined outside of this routine, and the low
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* and high values are guesses which must produce values with opposite signs.
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*/
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define solve(low, high, epsilon)
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{
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local flow, fhigh, fmid, mid, places;
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if (isnull(epsilon))
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epsilon = epsilon();
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if (epsilon <= 0)
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quit "Non-positive epsilon value";
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places = highbit(1 + int(1/epsilon)) + 1;
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flow = f(low);
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if (abs(flow) < epsilon)
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return low;
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fhigh = f(high);
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if (abs(flow) < epsilon)
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return high;
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if (sgn(flow) == sgn(fhigh))
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quit "Non-opposite signs";
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while (1) {
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mid = bround(high - fhigh * (high - low) / (fhigh - flow), places);
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if ((mid == low) || (mid == high))
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places++;
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fmid = f(mid);
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if (abs(fmid) < epsilon)
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return mid;
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if (sgn(fmid) == sgn(flow)) {
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low = mid;
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flow = fmid;
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} else {
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high = mid;
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fhigh = fmid;
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}
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}
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}
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