fn sqrt_ratio_behavior()

in src/field.rs [369:405]

• 27 lines of code
• 1 McCabe index (conditional complexity)

    fn sqrt_ratio_behavior() {
        let zero = FieldElement::zero();
        let one = FieldElement::one();
        let i = constants::SQRT_M1;
        let two = &one + &one; // 2 is nonsquare mod p.
        let four = &two + &two; // 4 is square mod p.

        // 0/0 should return (1, 0) since u is 0
        let (choice, sqrt) = FieldElement::sqrt_ratio_i(&zero, &zero);
        assert_eq!(choice.unwrap_u8(), 1);
        assert_eq!(sqrt, zero);
        assert_eq!(sqrt.is_negative().unwrap_u8(), 0);

        // 1/0 should return (0, 0) since v is 0, u is nonzero
        let (choice, sqrt) = FieldElement::sqrt_ratio_i(&one, &zero);
        assert_eq!(choice.unwrap_u8(), 0);
        assert_eq!(sqrt, zero);
        assert_eq!(sqrt.is_negative().unwrap_u8(), 0);

        // 2/1 is nonsquare, so we expect (0, sqrt(i*2))
        let (choice, sqrt) = FieldElement::sqrt_ratio_i(&two, &one);
        assert_eq!(choice.unwrap_u8(), 0);
        assert_eq!(sqrt.square(), &two * &i);
        assert_eq!(sqrt.is_negative().unwrap_u8(), 0);

        // 4/1 is square, so we expect (1, sqrt(4))
        let (choice, sqrt) = FieldElement::sqrt_ratio_i(&four, &one);
        assert_eq!(choice.unwrap_u8(), 1);
        assert_eq!(sqrt.square(), four);
        assert_eq!(sqrt.is_negative().unwrap_u8(), 0);

        // 1/4 is square, so we expect (1, 1/sqrt(4))
        let (choice, sqrt) = FieldElement::sqrt_ratio_i(&one, &four);
        assert_eq!(choice.unwrap_u8(), 1);
        assert_eq!(&sqrt.square() * &four, one);
        assert_eq!(sqrt.is_negative().unwrap_u8(), 0);
    }