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tompng/sqrt_with_mult.rb

Created August 24, 2025 13:53
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sqrt_with_mult.rb
def sqrt(x, prec)
y = BigDecimal(Math.sqrt(x.to_f))
yinv = BigDecimal(1 / y.to_f)
(0..prec.bit_length).reverse_each do |i|
p = [[(prec >> i) + 2, BigDecimal.double_fig].max, prec].min
yinv = yinv.mult(BigDecimal(2).sub(y * yinv, p / 2), p / 2)
yinv = yinv.mult(BigDecimal(2).sub(y * yinv, p), p)
y = (y + x * yinv).div(2, p)
end
y
end
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