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xo-ratio: ++ default ctor, .is_zero() .is_unit() methods

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Roland Conybeare 2024-04-23 15:53:42 -04:00
commit 30cc8586ba
1 changed files with 46 additions and 38 deletions
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84
include/xo/ratio/ratio.hpp
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@ -42,6 +42,8 @@ namespace xo {
public:
/** @defgroup ratio-ctor **/
///@{
/** @brief construct ratio 0/1 **/
constexpr ratio() = default;
/** @brief construct ratio with numerator @p n and denominator @p d.
*
* Ratio need not be normalized
@ -132,41 +134,6 @@ namespace xo {
return multiply(x, y.reciprocal());
}
/** @brief compute integer exponent @p p of this ratio
*
* @note time complexity is O(log p)
**/
constexpr ratio power(int p) const {
constexpr ratio retval = ratio(1, 1);
if (p == 0)
return ratio(1, 1);
if (p < 0)
return this->reciprocal().power(-p);
/* inv: x^p = aj.xj^pj */
ratio aj = ratio(1, 1);
ratio xj = *this;
int pj = p;
while (pj > 0) {
if (pj % 2 == 0) {
/* a.x^(2q) = a.(x^2)^q */
xj = xj * xj;
pj = pj / 2;
} else {
/* a.x^(2q+1) = (a.x).x^(2q) */
aj = aj * xj;
pj = (pj - 1);
}
}
/* pj = 0, so: x^p = aj.xj^pj = aj.xj^0 = aj */
return aj;
}
/** @brief 3-way compare two ratios **/
static constexpr auto compare(ratio x, ratio y) {
/* ensure minus signs in numerators only */
@ -186,6 +153,12 @@ namespace xo {
/** @brief fetch ratio's denominator **/
constexpr Int den() const noexcept { return den_; }
/** @brief true if and only if ratio is equal to zero **/
constexpr bool is_zero() const noexcept { return (num_ == 0) && (den_ != 0); }
/** @brief true if and only if ratio is equal to one **/
constexpr bool is_unity() const noexcept { return (num_ != 0) && (num_ == den_); }
/** @brief true if and only if ratio represents an integer
*
* (denominator is +/- 1)
@ -233,7 +206,42 @@ namespace xo {
* @pre @c Int type must be totally ordered
**/
constexpr ratio frac() const requires std::totally_ordered<Int> {
return ratio::subtract(*this, this->floor());
return ratio::subtract(*this, ratio(this->floor(), 1));
}
/** @brief compute integer exponent @p p of this ratio
*
* @note time complexity is O(log p)
**/
constexpr ratio power(int p) const {
constexpr ratio retval = ratio(1, 1);
if (p == 0)
return ratio(1, 1);
if (p < 0)
return this->reciprocal().power(-p);
/* inv: x^p = aj.xj^pj */
ratio aj = ratio(1, 1);
ratio xj = *this;
int pj = p;
while (pj > 0) {
if (pj % 2 == 0) {
/* a.x^(2q) = a.(x^2)^q */
xj = xj * xj;
pj = pj / 2;
} else {
/* a.x^(2q+1) = (a.x).x^(2q) */
aj = aj * xj;
pj = (pj - 1);
}
}
/* pj = 0, so: x^p = aj.xj^pj = aj.xj^0 = aj */
return aj;
}
/** @brief negate operator **/
@ -315,9 +323,9 @@ namespace xo {
/** @defgroup ratio-instance-variables **/
///@{
/** @brief numerator **/
Int num_;
Int num_ = 0;
/** @brief denominator **/
Int den_;
Int den_ = 1;
///@}
};