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13882
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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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fn new(numerator: i32, denominator: u32) -> Self {
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FPNum::from(numerator) / denominator
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}
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13885
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#[inline]
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13882
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fn signum(&self) -> i8 {
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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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13885
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#[inline]
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13882
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fn is_negative(&self) -> bool {
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self.is_negative
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}
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13885
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#[inline]
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fn is_positive(&self) -> bool {
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!self.is_negative
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}
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13885
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#[inline]
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13882
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fn is_zero(&self) -> bool {
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self.value == 0
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}
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13885
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#[inline]
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fn abs(&self) -> Self {
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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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13885
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#[inline]
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13882
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fn round(&self) -> i64 {
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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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13885
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#[inline]
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fn sqr(&self) -> Self {
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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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fn sqrt(&self) -> Self {
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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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13925
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fn with_sign(&self, is_negative: bool) -> FPNum {
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FPNum{ is_negative, ..*self}
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}
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#[inline]
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fn with_sign_as(self, other: FPNum) -> FPNum {
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self.with_sign(other.is_negative)
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}
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13882
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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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#[inline]
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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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13885
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#[inline]
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13882
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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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13884
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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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13882
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} else {
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13884
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n.value as i128
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13882
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}
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}
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13884
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extend(self).cmp(&(extend(rhs)))
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13882
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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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13891
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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, $d) };
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13905
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(-$n: tt) => { FPNum::from(-$n) };
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13891
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($n: tt) => { FPNum::from($n) };
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}
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13925
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const LINEARIZE_TRESHOLD: u64 = 0x1_0000;
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#[derive(Clone, Copy, Debug)]
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struct FPPoint {
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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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impl FPPoint {
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#[inline]
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fn new(x: FPNum, y: FPNum) -> Self {
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Self {
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x_is_negative: x.is_negative,
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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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fn zero() -> FPPoint { FPPoint::new(fp!(0), fp!(0)) }
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#[inline]
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fn unit_x() -> FPPoint { FPPoint::new(fp!(1), fp!(0)) }
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#[inline]
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fn unit_y() -> FPPoint { FPPoint::new(fp!(0), fp!(1)) }
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#[inline]
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fn x(&self) -> FPNum {
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FPNum {
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is_negative: self.x_is_negative,
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value: self.x_value
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}
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}
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#[inline]
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328 |
fn y(&self) -> FPNum {
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FPNum {
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330 |
is_negative: self.y_is_negative,
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value: self.y_value
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}
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}
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#[inline]
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336 |
fn sqr_distance(&self) -> FPNum {
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self.x().sqr() + self.y().sqr()
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}
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339 |
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#[inline]
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341 |
fn distance(&self) -> FPNum {
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342 |
let r = self.x_value | self.y_value;
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343 |
if r < LINEARIZE_TRESHOLD {
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344 |
FPNum::from(r as u32)
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345 |
} else {
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346 |
self.sqr_distance().sqrt()
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}
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348 |
}
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349 |
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350 |
#[inline]
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351 |
fn is_in_range(&self, radius: FPNum) -> bool {
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352 |
std::cmp::max(self.x(), self.y()) < radius
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&& self.sqr_distance() < radius.sqr()
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354 |
}
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355 |
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356 |
#[inline]
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357 |
fn dot(&self, other: &FPPoint) -> FPNum {
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358 |
self.x() * other.x() + self.y() * other.y()
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359 |
}
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360 |
}
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361 |
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362 |
impl PartialEq for FPPoint {
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363 |
#[inline]
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364 |
fn eq(&self, other: &Self) -> bool {
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365 |
self.x() == other.x() && self.y() == other.y()
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366 |
}
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367 |
}
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368 |
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369 |
impl Eq for FPPoint {}
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370 |
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371 |
impl ops::Neg for FPPoint {
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372 |
type Output = Self;
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373 |
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374 |
#[inline]
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375 |
fn neg(self) -> Self {
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376 |
Self::new(-self.x(), -self.y())
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377 |
}
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378 |
}
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379 |
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380 |
macro_rules! bin_op_impl {
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381 |
($op: path, $name: tt) => {
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382 |
impl $op for FPPoint {
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383 |
type Output = Self;
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384 |
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385 |
#[inline]
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386 |
fn $name(self, rhs: Self) -> Self {
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387 |
Self::new(self.x().$name(rhs.x()),
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388 |
self.y().$name(rhs.y()))
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389 |
}
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390 |
}
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391 |
}
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392 |
}
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393 |
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394 |
bin_op_impl!(ops::Add, add);
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395 |
bin_op_impl!(ops::Sub, sub);
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396 |
bin_op_impl!(ops::Mul, mul);
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397 |
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|
398 |
#[inline]
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|
399 |
fn distance<T>(x: T, y: T) -> FPNum
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|
400 |
where T: ops::Add + ops::Mul + Copy +
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|
401 |
From<<T as ops::Add>::Output> +
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|
402 |
From<<T as ops::Mul>::Output> +
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|
403 |
Into<FPNum>
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|
404 |
{
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|
405 |
let sqr: FPNum = T::from(T::from(x * x) + T::from(y * y)).into();
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|
406 |
sqr.sqrt()
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|
407 |
}
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|
408 |
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13882
|
409 |
/* TODO:
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|
410 |
AngleSin
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|
411 |
AngleCos
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|
412 |
*/
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413 |
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|
414 |
#[cfg(test)]
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|
415 |
#[test]
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|
416 |
fn basics() {
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13891
|
417 |
let n = fp!(15/2);
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13882
|
418 |
assert!(n.is_positive());
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|
419 |
assert!(!n.is_negative());
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|
420 |
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|
421 |
assert!(!(-n).is_positive());
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|
422 |
assert!((-n).is_negative());
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|
423 |
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|
424 |
assert_eq!(-(-n), n);
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|
425 |
assert_eq!((-n).abs(), n);
|
|
13891
|
426 |
assert_eq!(-n, fp!(-15/2));
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|
13882
|
427 |
|
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|
428 |
assert_eq!(n.round(), 7);
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|
429 |
assert_eq!((-n).round(), -7);
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|
430 |
}
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|
431 |
|
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|
432 |
#[test]
|
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|
433 |
fn zero() {
|
|
13891
|
434 |
let z = fp!(0);
|
|
|
435 |
let n = fp!(15/2);
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|
13882
|
436 |
|
|
|
437 |
assert!(z.is_zero());
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|
438 |
assert!(z.is_positive());
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|
|
439 |
assert!((-z).is_negative);
|
|
13883
|
440 |
assert_eq!(n - n, z);
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|
|
441 |
assert_eq!(-n + n, z);
|
|
13925
|
442 |
assert_eq!(z.with_sign_as(-n), -z);
|
|
13882
|
443 |
}
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|
|
444 |
|
|
|
445 |
#[test]
|
|
13884
|
446 |
fn ord() {
|
|
13891
|
447 |
let z = fp!(0);
|
|
|
448 |
let n1_5 = fp!(3/2);
|
|
|
449 |
let n2_25 = fp!(9/4);
|
|
13884
|
450 |
|
|
|
451 |
assert!(!(z > z));
|
|
|
452 |
assert!(!(z < z));
|
|
|
453 |
assert!(n2_25 > n1_5);
|
|
|
454 |
assert!(-n2_25 < n1_5);
|
|
|
455 |
assert!(-n2_25 < -n1_5);
|
|
|
456 |
}
|
|
|
457 |
|
|
|
458 |
#[test]
|
|
13882
|
459 |
fn arith() {
|
|
13891
|
460 |
let n1_5 = fp!(3/2);
|
|
|
461 |
let n2_25 = fp!(9/4);
|
|
|
462 |
let n_0_15 = fp!(-15/100);
|
|
13882
|
463 |
|
|
13891
|
464 |
assert_eq!(n1_5 + n1_5, fp!(3));
|
|
|
465 |
assert_eq!(-n1_5 - n1_5, fp!(-3));
|
|
13882
|
466 |
|
|
|
467 |
assert_eq!(n1_5 * n1_5, n2_25);
|
|
|
468 |
assert_eq!(-n1_5 * -n1_5, n2_25);
|
|
|
469 |
assert_eq!(n1_5 * -n1_5, -n2_25);
|
|
|
470 |
assert_eq!(-n1_5 * n1_5, -n2_25);
|
|
|
471 |
|
|
13883
|
472 |
assert_eq!(-n2_25 / -n1_5, n1_5);
|
|
|
473 |
assert_eq!(n1_5 / -10, n_0_15);
|
|
|
474 |
|
|
13882
|
475 |
assert_eq!(n1_5.sqr(), n2_25);
|
|
|
476 |
assert_eq!((-n1_5).sqr(), n2_25);
|
|
|
477 |
|
|
|
478 |
assert_eq!(n2_25.sqrt(), n1_5);
|
|
|
479 |
|
|
|
480 |
assert_eq!((n1_5 * n1_5 * n1_5.sqr()).sqrt(), n2_25);
|
|
|
481 |
}
|
|
13925
|
482 |
|
|
|
483 |
#[test]
|
|
|
484 |
fn point() {
|
|
|
485 |
let z = FPPoint::zero();
|
|
|
486 |
let p = FPPoint::new(fp!(1), fp!(-2));
|
|
|
487 |
|
|
|
488 |
assert_eq!(p.sqr_distance(), fp!(5));
|
|
|
489 |
assert_eq!(p + -p, FPPoint::zero());
|
|
|
490 |
assert_eq!(p * z, z);
|
|
|
491 |
assert_eq!(p.dot(&z), fp!(0));
|
|
|
492 |
assert_eq!(distance(4, 3), fp!(5));
|
|
|
493 |
} |