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#!/usr/bin/bc -ql
/*
Challenge 011
Challenge #1
Write a script that computes the equal point in the Fahrenheit and Celsius
scales, knowing that the freezing point of water is 32 �F and 0 �C, and that
the boiling point of water is 212 �F and 100 �C. This challenge was proposed
by Laurent Rosenfeld.
*/
scale = 10
/*
F = (C * 9/5) + 32
F = C = x
=> f(x) = (x * 9/5) + 32 - x = 0
<=> f(x) = (9/5 - 1) * x + 32
f'(x) = 9/5 - 1
*/
define f(x) { return (9/5 - 1) * x + 32 }
define df(x) { return 9/5 - 1 }
define newton(x0) {
auto x1, tmp
x1 = x0+1
while (x0 != x1) {
x1 = x0 - f(x0)/df(x0)
tmp = x1; x1 = x0; x0 = tmp
}
return x0
}
t = newton(0)
scale = 1
t/1
quit
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