Implement num_traits::FloatConst for Df64

[sakuraba07]

Closes #18

Summary

This PR implements the num_traits::FloatConst trait for Df64, providing standard mathematical constants in double-double precision.

Changes

New constants in consts.rs

• SQRT_2 - Square root of 2
• FRAC_1_SQRT_2 - Reciprocal of square root of 2 (1/√2)
• LOG10_2 - Logarithm base-10 of 2
• LOG2_10 - Logarithm base-2 of 10

FloatConst implementation in traits.rs

• All 16 required methods: E, PI, FRAC_1_PI, FRAC_2_PI, FRAC_PI_2, FRAC_PI_3, FRAC_PI_4, FRAC_PI_6, FRAC_PI_8, FRAC_1_SQRT_2, FRAC_2_SQRT_PI, LN_2, LN_10, LOG2_E, LOG10_E, SQRT_2
• All 3 provided methods with optimized implementations: TAU, LOG10_2, LOG2_10

Tests

• Added accuracy tests for new constants in consts.rs

[shinaoka]

Review Comments

1. Recommend testing SQRT_2 / FRAC_1_SQRT_2 against computed values

The existing tests validate other constants against their computing functions (e.g., exp::exp(ONE) == EULER_E, circular::sin(PI_HALF) == ONE). For consistency and stronger validation, consider adding:

assert_ulps_eq!(SQRT_2, roots::sqrt(Df64::from(2.0)));
assert_ulps_eq!(FRAC_1_SQRT_2, roots::inv_sqrt(Df64::from(2.0)));

The current algebraic identity test (SQRT_2 * SQRT_2 == 2) alone may not catch a transcription error in hi/lo that degrades precision.

2. Recommend independent verification tests for LOG10_2 / LOG2_10

Currently only the product LOG10_2 * LOG2_10 == 1 is tested. Testing each constant independently would be more robust, since the product test cannot detect errors if both constants are off in the same direction:

assert_ulps_eq!(LOG10_2, LOG10_E * LN_2);  // log10(2) = log10(e) * ln(2)
assert_ulps_eq!(LOG2_10, LOG2_E * LN_10);  // log2(10) = log2(e) * ln(10)

3. (Nice-to-have) Test FloatConst trait methods directly

The tests only validate the raw constants in consts.rs. A brief sanity check through the trait interface would confirm the mapping is correct:

use num_traits::FloatConst;
assert_eq!(Df64::PI(), consts::PI);
assert_eq!(Df64::SQRT_2(), consts::SQRT_2);

[sakuraba07]

Thank you for the review. I have updated the tests to address your suggestions:

• Robust validation for SQRT_2 and FRAC_1_SQRT_2: These are now validated against computed values from arith::sqrt_q and roots::inv_sqrt.
• Independent verification for LOG10_2 and LOG2_10: Replaced the product test with independent identity checks (log10(2) = log10(e) * ln(2) and log2(10) = log2(e) * ln(10)).
• Direct FloatConst trait testing: Added a new test test_float_const in src/traits.rs to verify that all trait methods are correctly implemented.

All tests passed.