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13905
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use std::cmp;
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use std::ops;
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#[derive(Clone, Debug, Copy)]
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pub struct FPNum {
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is_negative: bool,
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value: u64,
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}
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impl FPNum {
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13948
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#[inline]
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13949
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pub fn new(numerator: i32, denominator: u32) -> Self {
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13905
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FPNum::from(numerator) / denominator
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}
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13909
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#[inline]
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13949
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pub fn signum(&self) -> i8 {
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13905
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if self.is_negative {
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-1
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} else {
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1
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}
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}
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13909
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#[inline]
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13949
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pub fn is_negative(&self) -> bool {
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13905
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self.is_negative
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}
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13909
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#[inline]
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13949
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pub fn is_positive(&self) -> bool {
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13905
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!self.is_negative
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}
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13909
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#[inline]
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13949
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pub fn is_zero(&self) -> bool {
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13905
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self.value == 0
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}
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13909
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#[inline]
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13949
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pub fn abs(&self) -> Self {
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13905
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Self {
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is_negative: false,
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value: self.value,
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}
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}
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13909
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#[inline]
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13949
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pub fn round(&self) -> i64 {
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13905
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if self.is_negative {
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-((self.value >> 32) as i64)
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} else {
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(self.value >> 32) as i64
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}
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}
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13909
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#[inline]
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14102
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pub fn abs_round(&self) -> u32 {
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(self.value >> 32) as u32
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}
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#[inline]
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13949
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pub fn sqr(&self) -> Self {
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13905
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Self {
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is_negative: false,
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value: ((self.value as u128).pow(2) >> 32) as u64,
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}
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}
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13949
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pub fn sqrt(&self) -> Self {
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13905
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debug_assert!(!self.is_negative);
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let mut t: u64 = 0x4000000000000000;
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let mut r: u64 = 0;
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let mut q = self.value;
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for _ in 0..32 {
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let s = r + t;
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r >>= 1;
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if s <= q {
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q -= s;
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r += t;
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}
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t >>= 2;
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}
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Self {
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is_negative: false,
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value: r << 16,
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}
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}
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13946
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13948
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#[inline]
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13949
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pub fn with_sign(&self, is_negative: bool) -> FPNum {
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13946
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FPNum{ is_negative, ..*self}
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}
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#[inline]
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13949
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pub fn with_sign_as(self, other: FPNum) -> FPNum {
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13946
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self.with_sign(other.is_negative)
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}
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13948
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#[inline]
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13949
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pub fn point(self) -> FPPoint {
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13948
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FPPoint::new(self, self)
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}
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13905
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}
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impl From<i32> for FPNum {
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#[inline]
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fn from(n: i32) -> Self {
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FPNum {
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is_negative: n < 0,
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value: (n.abs() as u64) << 32,
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}
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}
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}
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impl From<u32> for FPNum {
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#[inline]
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fn from(n: u32) -> Self {
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Self {
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is_negative: false,
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value: (n as u64) << 32,
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}
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}
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}
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impl From<FPNum> for f64 {
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#[inline]
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fn from(n: FPNum) -> Self {
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if n.is_negative {
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n.value as f64 / (-0x10000000 as f64)
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} else {
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n.value as f64 / 0x10000000 as f64
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}
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}
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}
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impl PartialEq for FPNum {
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13909
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#[inline]
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13905
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fn eq(&self, other: &Self) -> bool {
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self.value == other.value && (self.is_negative == other.is_negative || self.value == 0)
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}
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}
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impl Eq for FPNum {}
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impl PartialOrd for FPNum {
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13909
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#[inline]
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13905
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fn partial_cmp(&self, rhs: &Self) -> std::option::Option<std::cmp::Ordering> {
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Some(self.cmp(rhs))
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}
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}
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impl Ord for FPNum {
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#[inline]
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fn cmp(&self, rhs: &Self) -> cmp::Ordering {
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13908
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#[inline]
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fn extend(n: &FPNum) -> i128 {
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if n.is_negative {
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-(n.value as i128)
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13905
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} else {
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13908
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n.value as i128
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13905
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}
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}
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13908
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extend(self).cmp(&(extend(rhs)))
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13905
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}
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}
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impl ops::Add for FPNum {
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type Output = Self;
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#[inline]
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fn add(self, rhs: Self) -> Self {
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if self.is_negative == rhs.is_negative {
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Self {
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is_negative: self.is_negative,
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value: self.value + rhs.value,
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}
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} else if self.value > rhs.value {
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Self {
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is_negative: self.is_negative,
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value: self.value - rhs.value,
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}
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} else {
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Self {
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is_negative: rhs.is_negative,
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value: rhs.value - self.value,
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}
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}
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}
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}
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impl ops::Sub for FPNum {
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type Output = Self;
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#[inline]
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fn sub(self, rhs: Self) -> Self {
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if self.is_negative == rhs.is_negative {
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if self.value > rhs.value {
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Self {
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is_negative: self.is_negative,
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value: self.value - rhs.value,
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}
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} else {
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Self {
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is_negative: !rhs.is_negative,
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value: rhs.value - self.value,
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}
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}
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} else {
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Self {
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is_negative: self.is_negative,
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value: self.value + rhs.value,
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}
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}
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}
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}
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impl ops::Neg for FPNum {
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type Output = Self;
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#[inline]
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fn neg(self) -> Self {
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Self {
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is_negative: !self.is_negative,
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value: self.value,
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}
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}
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}
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impl ops::Mul for FPNum {
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type Output = Self;
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#[inline]
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fn mul(self, rhs: Self) -> Self {
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Self {
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is_negative: self.is_negative ^ rhs.is_negative,
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value: ((self.value as u128 * rhs.value as u128) >> 32) as u64,
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}
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}
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}
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impl ops::Mul<i32> for FPNum {
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type Output = Self;
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#[inline]
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fn mul(self, rhs: i32) -> Self {
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Self {
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is_negative: self.is_negative ^ (rhs < 0),
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value: self.value * rhs.abs() as u64,
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}
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}
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}
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impl ops::Div for FPNum {
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type Output = Self;
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#[inline]
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fn div(self, rhs: Self) -> Self {
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Self {
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is_negative: self.is_negative ^ rhs.is_negative,
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value: (((self.value as u128) << 32) / rhs.value as u128) as u64,
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}
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}
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}
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impl ops::Div<i32> for FPNum {
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type Output = Self;
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#[inline]
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fn div(self, rhs: i32) -> Self {
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Self {
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is_negative: self.is_negative ^ (rhs < 0),
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value: self.value / rhs.abs() as u64,
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}
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}
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}
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impl ops::Div<u32> for FPNum {
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type Output = Self;
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#[inline]
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fn div(self, rhs: u32) -> Self {
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Self {
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is_negative: self.is_negative,
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value: self.value / rhs as u64,
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}
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}
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}
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13949
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#[macro_export]
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13911
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macro_rules! fp {
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(-$n: tt / $d: tt) => { FPNum::new(-$n, $d) };
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($n: tt / $d: tt) => { FPNum::new($n, $d) };
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13926
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(-$n: tt) => { FPNum::from(-$n) };
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13911
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($n: tt) => { FPNum::from($n) };
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}
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13946
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const LINEARIZE_TRESHOLD: u64 = 0x1_0000;
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#[derive(Clone, Copy, Debug)]
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13949
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305 |
pub struct FPPoint {
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13946
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306 |
x_is_negative: bool,
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y_is_negative: bool,
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x_value: u64,
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y_value: u64,
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}
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311 |
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impl FPPoint {
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#[inline]
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13949
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pub fn new(x: FPNum, y: FPNum) -> Self {
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13946
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Self {
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316 |
x_is_negative: x.is_negative,
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317 |
y_is_negative: y.is_negative,
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x_value: x.value,
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y_value: y.value
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}
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}
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#[inline]
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13949
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324 |
pub fn zero() -> FPPoint { FPPoint::new(fp!(0), fp!(0)) }
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13946
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325 |
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326 |
#[inline]
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13949
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pub fn unit_x() -> FPPoint { FPPoint::new(fp!(1), fp!(0)) }
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13946
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328 |
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329 |
#[inline]
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13949
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330 |
pub fn unit_y() -> FPPoint { FPPoint::new(fp!(0), fp!(1)) }
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13946
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331 |
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332 |
#[inline]
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13949
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333 |
pub fn x(&self) -> FPNum {
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13946
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334 |
FPNum {
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335 |
is_negative: self.x_is_negative,
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336 |
value: self.x_value
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337 |
}
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338 |
}
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339 |
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340 |
#[inline]
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13949
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341 |
pub fn y(&self) -> FPNum {
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13946
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342 |
FPNum {
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343 |
is_negative: self.y_is_negative,
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344 |
value: self.y_value
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345 |
}
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}
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347 |
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348 |
#[inline]
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13949
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349 |
pub fn max_norm(&self) -> FPNum {
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13960
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350 |
std::cmp::max(self.x().abs(), self.y().abs())
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13949
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351 |
}
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352 |
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353 |
#[inline]
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354 |
pub fn sqr_distance(&self) -> FPNum {
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13946
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355 |
self.x().sqr() + self.y().sqr()
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356 |
}
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357 |
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358 |
#[inline]
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13949
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359 |
pub fn distance(&self) -> FPNum {
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13946
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360 |
let r = self.x_value | self.y_value;
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361 |
if r < LINEARIZE_TRESHOLD {
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362 |
FPNum::from(r as u32)
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363 |
} else {
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364 |
self.sqr_distance().sqrt()
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365 |
}
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366 |
}
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367 |
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368 |
#[inline]
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13949
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369 |
pub fn is_in_range(&self, radius: FPNum) -> bool {
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370 |
self.max_norm() < radius && self.sqr_distance() < radius.sqr()
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13946
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371 |
}
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372 |
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373 |
#[inline]
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13949
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374 |
pub fn dot(&self, other: &FPPoint) -> FPNum {
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13946
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375 |
self.x() * other.x() + self.y() * other.y()
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376 |
}
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377 |
}
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378 |
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379 |
impl PartialEq for FPPoint {
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380 |
#[inline]
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381 |
fn eq(&self, other: &Self) -> bool {
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382 |
self.x() == other.x() && self.y() == other.y()
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383 |
}
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384 |
}
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385 |
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386 |
impl Eq for FPPoint {}
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|
387 |
|
|
|
388 |
impl ops::Neg for FPPoint {
|
|
|
389 |
type Output = Self;
|
|
|
390 |
|
|
|
391 |
#[inline]
|
|
|
392 |
fn neg(self) -> Self {
|
|
|
393 |
Self::new(-self.x(), -self.y())
|
|
|
394 |
}
|
|
|
395 |
}
|
|
|
396 |
|
|
|
397 |
macro_rules! bin_op_impl {
|
|
13948
|
398 |
($op: ty, $name: tt) => {
|
|
13946
|
399 |
impl $op for FPPoint {
|
|
|
400 |
type Output = Self;
|
|
|
401 |
|
|
|
402 |
#[inline]
|
|
|
403 |
fn $name(self, rhs: Self) -> Self {
|
|
|
404 |
Self::new(self.x().$name(rhs.x()),
|
|
|
405 |
self.y().$name(rhs.y()))
|
|
|
406 |
}
|
|
|
407 |
}
|
|
|
408 |
}
|
|
|
409 |
}
|
|
|
410 |
|
|
13953
|
411 |
macro_rules! right_scalar_bin_op_impl {
|
|
|
412 |
($($op: tt)::+, $name: tt) => {
|
|
|
413 |
impl $($op)::+<FPNum> for FPPoint {
|
|
13948
|
414 |
type Output = Self;
|
|
|
415 |
|
|
|
416 |
#[inline]
|
|
|
417 |
fn $name(self, rhs: FPNum) -> Self {
|
|
|
418 |
Self::new(self.x().$name(rhs),
|
|
|
419 |
self.y().$name(rhs))
|
|
|
420 |
}
|
|
|
421 |
}
|
|
|
422 |
}
|
|
|
423 |
}
|
|
|
424 |
|
|
13953
|
425 |
macro_rules! left_scalar_bin_op_impl {
|
|
|
426 |
($($op: tt)::+, $name: tt) => {
|
|
|
427 |
impl $($op)::+<FPPoint> for FPNum {
|
|
|
428 |
type Output = FPPoint;
|
|
|
429 |
|
|
|
430 |
#[inline]
|
|
|
431 |
fn $name(self, rhs: FPPoint) -> Self::Output {
|
|
|
432 |
Self::Output::new(self.$name(rhs.x()),
|
|
|
433 |
self.$name(rhs.y()))
|
|
|
434 |
}
|
|
|
435 |
}
|
|
|
436 |
}
|
|
|
437 |
}
|
|
|
438 |
|
|
13946
|
439 |
bin_op_impl!(ops::Add, add);
|
|
|
440 |
bin_op_impl!(ops::Sub, sub);
|
|
|
441 |
bin_op_impl!(ops::Mul, mul);
|
|
13950
|
442 |
bin_op_impl!(ops::Div, div);
|
|
13953
|
443 |
right_scalar_bin_op_impl!(ops::Add, add);
|
|
|
444 |
right_scalar_bin_op_impl!(ops::Mul, mul);
|
|
|
445 |
right_scalar_bin_op_impl!(ops::Sub, sub);
|
|
|
446 |
right_scalar_bin_op_impl!(ops::Div, div);
|
|
|
447 |
left_scalar_bin_op_impl!(ops::Mul, mul);
|
|
13946
|
448 |
|
|
13950
|
449 |
macro_rules! bin_assign_op_impl {
|
|
|
450 |
($typ: tt, $($op: tt)::+, $name: tt, $delegate: tt) => {
|
|
|
451 |
bin_assign_op_impl!($typ, $($op)::+<$typ>, $name, $delegate);
|
|
|
452 |
};
|
|
|
453 |
($typ: tt, $($op: tt)::+<$arg: tt>, $name: tt, $delegate: tt) => {
|
|
|
454 |
impl $($op)::+<$arg> for $typ {
|
|
|
455 |
#[inline]
|
|
|
456 |
fn $name(&mut self, rhs: $arg) {
|
|
|
457 |
*self = *self $delegate rhs;
|
|
|
458 |
}
|
|
|
459 |
}
|
|
|
460 |
}
|
|
|
461 |
}
|
|
|
462 |
|
|
|
463 |
bin_assign_op_impl!(FPNum, ops::AddAssign, add_assign, +);
|
|
|
464 |
bin_assign_op_impl!(FPNum, ops::SubAssign, sub_assign, -);
|
|
|
465 |
bin_assign_op_impl!(FPNum, ops::MulAssign, mul_assign, *);
|
|
|
466 |
bin_assign_op_impl!(FPNum, ops::DivAssign, div_assign, /);
|
|
|
467 |
bin_assign_op_impl!(FPNum, ops::MulAssign<i32>, mul_assign, *);
|
|
|
468 |
bin_assign_op_impl!(FPNum, ops::DivAssign<i32>, div_assign, /);
|
|
|
469 |
bin_assign_op_impl!(FPNum, ops::DivAssign<u32>, div_assign, /);
|
|
|
470 |
|
|
|
471 |
bin_assign_op_impl!(FPPoint, ops::AddAssign, add_assign, +);
|
|
|
472 |
bin_assign_op_impl!(FPPoint, ops::SubAssign, sub_assign, -);
|
|
|
473 |
bin_assign_op_impl!(FPPoint, ops::MulAssign, mul_assign, *);
|
|
|
474 |
bin_assign_op_impl!(FPPoint, ops::DivAssign, div_assign, /);
|
|
|
475 |
bin_assign_op_impl!(FPPoint, ops::AddAssign<FPNum>, add_assign, +);
|
|
|
476 |
bin_assign_op_impl!(FPPoint, ops::SubAssign<FPNum>, sub_assign, -);
|
|
|
477 |
bin_assign_op_impl!(FPPoint, ops::MulAssign<FPNum>, mul_assign, *);
|
|
|
478 |
bin_assign_op_impl!(FPPoint, ops::DivAssign<FPNum>, div_assign, /);
|
|
|
479 |
|
|
13946
|
480 |
#[inline]
|
|
13949
|
481 |
pub fn distance<T>(x: T, y: T) -> FPNum
|
|
13946
|
482 |
where T: ops::Add + ops::Mul + Copy +
|
|
|
483 |
From<<T as ops::Add>::Output> +
|
|
|
484 |
From<<T as ops::Mul>::Output> +
|
|
|
485 |
Into<FPNum>
|
|
|
486 |
{
|
|
|
487 |
let sqr: FPNum = T::from(T::from(x * x) + T::from(y * y)).into();
|
|
|
488 |
sqr.sqrt()
|
|
|
489 |
}
|
|
|
490 |
|
|
13905
|
491 |
/* TODO:
|
|
|
492 |
AngleSin
|
|
|
493 |
AngleCos
|
|
|
494 |
*/
|
|
|
495 |
|
|
|
496 |
#[cfg(test)]
|
|
|
497 |
#[test]
|
|
|
498 |
fn basics() {
|
|
13911
|
499 |
let n = fp!(15/2);
|
|
13905
|
500 |
assert!(n.is_positive());
|
|
|
501 |
assert!(!n.is_negative());
|
|
|
502 |
|
|
|
503 |
assert!(!(-n).is_positive());
|
|
|
504 |
assert!((-n).is_negative());
|
|
|
505 |
|
|
|
506 |
assert_eq!(-(-n), n);
|
|
|
507 |
assert_eq!((-n).abs(), n);
|
|
13911
|
508 |
assert_eq!(-n, fp!(-15/2));
|
|
13905
|
509 |
|
|
|
510 |
assert_eq!(n.round(), 7);
|
|
|
511 |
assert_eq!((-n).round(), -7);
|
|
|
512 |
}
|
|
|
513 |
|
|
|
514 |
#[test]
|
|
|
515 |
fn zero() {
|
|
13911
|
516 |
let z = fp!(0);
|
|
|
517 |
let n = fp!(15/2);
|
|
13905
|
518 |
|
|
|
519 |
assert!(z.is_zero());
|
|
|
520 |
assert!(z.is_positive());
|
|
|
521 |
assert!((-z).is_negative);
|
|
13907
|
522 |
assert_eq!(n - n, z);
|
|
|
523 |
assert_eq!(-n + n, z);
|
|
13947
|
524 |
assert_eq!(n.with_sign_as(-n), -n);
|
|
13905
|
525 |
}
|
|
|
526 |
|
|
|
527 |
#[test]
|
|
13908
|
528 |
fn ord() {
|
|
13911
|
529 |
let z = fp!(0);
|
|
|
530 |
let n1_5 = fp!(3/2);
|
|
|
531 |
let n2_25 = fp!(9/4);
|
|
13908
|
532 |
|
|
|
533 |
assert!(!(z > z));
|
|
|
534 |
assert!(!(z < z));
|
|
|
535 |
assert!(n2_25 > n1_5);
|
|
|
536 |
assert!(-n2_25 < n1_5);
|
|
|
537 |
assert!(-n2_25 < -n1_5);
|
|
|
538 |
}
|
|
|
539 |
|
|
|
540 |
#[test]
|
|
13905
|
541 |
fn arith() {
|
|
13911
|
542 |
let n1_5 = fp!(3/2);
|
|
|
543 |
let n2_25 = fp!(9/4);
|
|
|
544 |
let n_0_15 = fp!(-15/100);
|
|
13905
|
545 |
|
|
13911
|
546 |
assert_eq!(n1_5 + n1_5, fp!(3));
|
|
|
547 |
assert_eq!(-n1_5 - n1_5, fp!(-3));
|
|
13905
|
548 |
|
|
|
549 |
assert_eq!(n1_5 * n1_5, n2_25);
|
|
|
550 |
assert_eq!(-n1_5 * -n1_5, n2_25);
|
|
|
551 |
assert_eq!(n1_5 * -n1_5, -n2_25);
|
|
|
552 |
assert_eq!(-n1_5 * n1_5, -n2_25);
|
|
|
553 |
|
|
13907
|
554 |
assert_eq!(-n2_25 / -n1_5, n1_5);
|
|
|
555 |
assert_eq!(n1_5 / -10, n_0_15);
|
|
|
556 |
|
|
13905
|
557 |
assert_eq!(n1_5.sqr(), n2_25);
|
|
|
558 |
assert_eq!((-n1_5).sqr(), n2_25);
|
|
|
559 |
|
|
|
560 |
assert_eq!(n2_25.sqrt(), n1_5);
|
|
|
561 |
|
|
|
562 |
assert_eq!((n1_5 * n1_5 * n1_5.sqr()).sqrt(), n2_25);
|
|
13950
|
563 |
|
|
|
564 |
let mut m = fp!(1);
|
|
|
565 |
m += n1_5;
|
|
|
566 |
assert_eq!(m, fp!(5/2));
|
|
13905
|
567 |
}
|
|
13946
|
568 |
|
|
|
569 |
#[test]
|
|
|
570 |
fn point() {
|
|
|
571 |
let z = FPPoint::zero();
|
|
13953
|
572 |
let n = fp!(16/9);
|
|
13946
|
573 |
let p = FPPoint::new(fp!(1), fp!(-2));
|
|
|
574 |
|
|
|
575 |
assert_eq!(p.sqr_distance(), fp!(5));
|
|
|
576 |
assert_eq!(p + -p, FPPoint::zero());
|
|
|
577 |
assert_eq!(p * z, z);
|
|
|
578 |
assert_eq!(p.dot(&z), fp!(0));
|
|
13953
|
579 |
assert_eq!(n * p, p * n);
|
|
13946
|
580 |
assert_eq!(distance(4, 3), fp!(5));
|
|
13948
|
581 |
assert_eq!(p * fp!(-3), FPPoint::new(fp!(-3), fp!(6)));
|
|
13960
|
582 |
assert_eq!(p.max_norm(), fp!(2));
|
|
13946
|
583 |
} |