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Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
50 lines
1.4 KiB
Plaintext
50 lines
1.4 KiB
Plaintext
;; newton.hs — Newton's method for square root.
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;; Source: classic numerical analysis exercise.
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;;
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;; Exercises Phase 10: `Float`, `abs`, `/`, iteration via `until`.
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(define
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hk-prog-val
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(fn
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(src name)
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(hk-deep-force (get (hk-eval-program (hk-core src)) name))))
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(define
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hk-newton-source
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"improve x guess = (guess + x / guess) / 2\n\ngoodEnough x guess = abs (guess * guess - x) < 0.0001\n\nnewtonSqrt x = newtonHelp x 1.0\n\nnewtonHelp x guess = if goodEnough x guess\n then guess\n else newtonHelp x (improve x guess)\n")
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(hk-test
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"newton.hs — newtonSqrt 4 ≈ 2"
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(hk-prog-val
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(str hk-newton-source "r = abs (newtonSqrt 4.0 - 2.0) < 0.001\n")
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"r")
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(list "True"))
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(hk-test
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"newton.hs — newtonSqrt 9 ≈ 3"
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(hk-prog-val
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(str hk-newton-source "r = abs (newtonSqrt 9.0 - 3.0) < 0.001\n")
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"r")
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(list "True"))
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(hk-test
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"newton.hs — newtonSqrt 2 ≈ 1.41421"
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(hk-prog-val
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(str hk-newton-source "r = abs (newtonSqrt 2.0 - 1.41421) < 0.001\n")
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"r")
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(list "True"))
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(hk-test
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"newton.hs — improve converges (one step)"
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(hk-prog-val (str hk-newton-source "r = improve 4.0 1.0\n") "r")
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2.5)
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(hk-test
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"newton.hs — newtonSqrt 100 ≈ 10"
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(hk-prog-val
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(str hk-newton-source "r = abs (newtonSqrt 100.0 - 10.0) < 0.001\n")
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"r")
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(list "True"))
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{:fails hk-test-fails :pass hk-test-pass :fail hk-test-fail}
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