LESSON 34 OF 52 · CHAPTER 04
Float Refinement
Newton-style square-root refinement, bounded steps, typed contracts
10-float-refinement.srp
// Newton refinement uses float values and an integer iteration count.
pure funcra root(value: float, steps: integer = 6) -> float
needs value > 0.0;
needs steps >= 0;
ensures result > 0.0;
{
var estimate = 1.0;
repeat steps as iteration {
estimate = (estimate + value / estimate) / 2.0;
}
return estimate;
}
bind sqrt2 = root(2.0);
print("sqrt2 checked", sqrt2 > 1.414 and sqrt2 < 1.415);
print("sqrt9", root(9.0));
stdout
sqrt2 checked true
sqrt9 3.0
Write what you expect this program to print. Check prediction for a line-level hint without revealing the answer, or reveal the verified output when ready. This checks displayed text only; it does not run Scarp or save your input.
UNDERSTAND THE CODE
Explanation & practice
What this example teaches
Newton-style square-root refinement, bounded steps, typed contracts
Expected behavior
sqrt2 checked true, then sqrt9 3.0
Practice: Read the source before looking at the output. Predict the values and their order, then use the pinned compiler to execute this lesson and compare the exact fixture. Identify which operation produces the result.
दशमलव में न्यूटन विधि
pure funcra root किसी सकारात्मक मान का वर्गमूल अनुमानित करता है। repeat के साथ निर्धारित संख्या में सुधार होता है; needs मान और चरणों की पूर्वशर्तें देता है, ensures परिणाम सकारात्मक होने की शर्त रखता है। √2 को एक दायरे में जाँचा जाता है, पूर्णतः बराबर नहीं माना जाता।
आउटपुट: sqrt2 checked true और sqrt9 3.0।
अभ्यास: सकारात्मक इनपुट की पूर्वशर्त क्यों आवश्यक है? डिफ़ॉल्ट steps कितना है?
Explanations are sourced from the project's English chapter guide and हिन्दी अध्याय. The Scarp program and output are unchanged.
LEARNING PROGRESS
Keep your place
Mark this lesson complete when you are ready.
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TRY IT LOCALLY
Verify, then execute
Use the pinned compiler from the course root. Keep any imported _support files next to the source.
scarp verify examples/04-collections/10-float-refinement.srp
scarp exec examples/04-collections/10-float-refinement.srpThe website does not run code. Read the CLI guide ↗
Pinned compiler: Scarp v0.0.6-alpha.3
· ceff07d9014f. No simulated output.