ParagonIE_Sodium_Core_Ristretto255::ristretto255_sqrt_ratio_m1( ParagonIE_Sodium_Core_Curve25519_Fe $u, ParagonIE_Sodium_Core_Curve25519_Fe $v ): array{x:

67    public static function ristretto255_sqrt_ratio_m1(68        ParagonIE_Sodium_Core_Curve25519_Fe $u,69        ParagonIE_Sodium_Core_Curve25519_Fe $v70    ) {71        $sqrtm1 = ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(self::$sqrtm1);72 73        $v3 = self::fe_mul(74            self::fe_sq($v),75            $v76        ); /* v3 = v^3 */77        $x = self::fe_mul(78            self::fe_mul(79                self::fe_sq($v3),80                $u81            ),82            $v83        ); /* x = uv^7 */84 85        $x = self::fe_mul(86            self::fe_mul(87                self::fe_pow22523($x), /* x = (uv^7)^((q-5)/8) */88                $v389            ),90            $u91        ); /* x = uv^3(uv^7)^((q-5)/8) */92 93        $vxx = self::fe_mul(94            self::fe_sq($x),95            $v96        ); /* vx^2 */97 98        $m_root_check = self::fe_sub($vxx, $u); /* vx^2-u */99        $p_root_check = self::fe_add($vxx, $u); /* vx^2+u */100        $f_root_check = self::fe_mul($u, $sqrtm1); /* u*sqrt(-1) */101        $f_root_check = self::fe_add($vxx, $f_root_check); /* vx^2+u*sqrt(-1) */102 103        $has_m_root = self::fe_iszero($m_root_check);104        $has_p_root = self::fe_iszero($p_root_check);105        $has_f_root = self::fe_iszero($f_root_check);106 107        $x_sqrtm1 = self::fe_mul($x, $sqrtm1); /* x*sqrt(-1) */108 109        $x = self::fe_abs(110            self::fe_cmov($x, $x_sqrtm1, $has_p_root | $has_f_root)111        );112        return array(113            'x' => $x,114            'nonsquare' => $has_m_root | $has_p_root115        );116    }