Number_types: fix Lazy_exact_nt operator<< to write exact() value

[RajdeepKushwaha5]

Description

Summary of Changes

operator<< for Lazy_exact_nt<ET> was using to_double(a), which loses precision and breaks round-trip save/load of exact kernel coordinates. For example, writing Lazy_exact_nt<Gmpq>(1/3) would output 0.333333 instead of 1/3, and reading it back would produce a different exact value.

This PR changes operator<< to output a.exact() instead, so that operator>> (which already uses read_float_or_quotient() and handles both floating-point and rational n/d formats) can reconstruct the same exact number.

Changes

• Number_types/include/CGAL/Lazy_exact_nt.h: Changed operator<< from os << CGAL_NTS to_double(a) to os << a.exact()
• Number_types/doc/Number_types/CGAL/Lazy_exact_nt.h: Updated documentation to reflect the new exact output format
• Number_types/test/Number_types/Lazy_exact_nt_io.cpp: Added round-trip I/O regression test covering rationals (1/3), integers (42), negatives (-5/7), computed sums (10/21), large values (99999999999999999999/100000000000000000007), and zero
• Number_types/test/Number_types/CMakeLists.txt: Registered the new test

Release Management

• Affected package(s): Number_types
• Issue(s) solved (if any): fix operator<< (std::ostream & os, const Lazy_exact_nt<ET> & a) should insert a.exact() in the stream #135
• Feature/Small Feature (if any):
• License and copyright ownership: already covered by existing headers

[Copilot]

Pull request overview

Fixes Lazy_exact_nt<ET> stream output so that saving/loading exact values round-trips without precision loss, addressing issue #135 in the Number_types package.

Changes:

• Update operator<< for Lazy_exact_nt<ET> to write a.exact() instead of to_double(a).
• Update documentation to describe the new exact output behavior.
• Add and register a regression test that exercises round-trip I/O for several rational/integer cases.

Reviewed changes

Copilot reviewed 4 out of 4 changed files in this pull request and generated 7 comments.

File	Description
Number_types/include/CGAL/Lazy_exact_nt.h	Changes streaming output to use the exact value (exact()), enabling lossless round-trip with existing operator>>.
Number_types/doc/Number_types/CGAL/Lazy_exact_nt.h	Updates docs to match the new exact-output semantics and round-trip intent.
Number_types/test/Number_types/Lazy_exact_nt_io.cpp	Adds regression coverage for round-trip I/O of exact rationals/integers (including large values).
Number_types/test/Number_types/CMakeLists.txt	Registers the new single-source test program.

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[Copilot]

Same issue as above: the test should assert the stream extraction succeeded after iss >> b to avoid false positives if parsing fails.

[Copilot]

Same issue as above: please assert the stream is still good after iss >> b so the test can’t pass if parsing fails.

[Copilot]

Same issue as above: add a stream-state assertion after iss >> d to ensure the read succeeded before comparing c == d.

Suggested change

	iss >> d;
	iss >> d;
	assert(iss);

[Copilot]

Same issue as above: assert successful extraction after iss >> b so the test can’t pass if parsing fails.

[Copilot]

Same issue as above: because the expected value is 0 here, a failed parse could leave b at the default value and make the assertion pass. Add an assert(iss) / assert(!iss.fail()) after iss >> b.

Suggested change

	iss >> b;
	iss >> b;
	assert(iss);

[Copilot]

The test doesn’t verify that extraction succeeded (stream state) before comparing values. If parsing fails, b can remain at its default value (which is 0 for Lazy_exact_nt), potentially making the test pass spuriously (notably in the zero case). Add an assertion like assert(iss) / assert(!iss.fail()) after iss >> b (and similarly in the other test blocks).