rust/fpnum/src/lib.rs
author alfadur
Sat, 06 Jul 2019 22:04:59 +0300
changeset 15239 b2c086629fb8
parent 15235 58a0f2a6527b
child 15240 b71bae455926
permissions -rw-r--r--
optimize 64-bit sqrt some more
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use std::{cmp, ops, ops::Shl};
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const POSITIVE_MASK: u64 = 0x0000_0000_0000_0000;
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const NEGATIVE_MASK: u64 = 0xFFFF_FFFF_FFFF_FFFF;
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#[inline]
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fn bool_mask(is_negative: bool) -> u64 {
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    if is_negative {
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        NEGATIVE_MASK
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    } else {
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        POSITIVE_MASK
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    }
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}
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#[derive(Clone, Debug, Copy)]
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pub struct FPNum {
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    sign_mask: u64,
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    value: u64,
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}
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impl FPNum {
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    #[inline]
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    pub fn new(numerator: i32, denominator: u32) -> Self {
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        FPNum::from(numerator) / denominator
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    }
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    #[inline]
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    pub fn signum(&self) -> i8 {
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        (1u64 ^ self.sign_mask).wrapping_sub(self.sign_mask) as i8
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    }
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    #[inline]
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    pub const fn is_negative(&self) -> bool {
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        self.sign_mask != POSITIVE_MASK
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    }
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    #[inline]
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    pub const fn is_positive(&self) -> bool {
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        self.sign_mask == POSITIVE_MASK
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    }
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    #[inline]
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    pub const fn is_zero(&self) -> bool {
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        self.value == 0
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    }
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    #[inline]
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    pub const fn abs(&self) -> Self {
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        Self {
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            sign_mask: POSITIVE_MASK,
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            value: self.value,
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        }
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    }
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    #[inline]
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    pub fn round(&self) -> i32 {
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        ((self.value >> 32) as i32 ^ self.sign_mask as i32).wrapping_sub(self.sign_mask as i32)
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    }
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    #[inline]
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    pub const 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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    pub fn sqr(&self) -> Self {
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        Self {
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            sign_mask: 0,
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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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    #[inline]
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    pub fn sqrt(&self) -> Self {
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        debug_assert!(self.is_positive());
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        Self {
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            sign_mask: POSITIVE_MASK,
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            value: integral_sqrt(self.value) << 16,
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        }
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    }
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    #[inline]
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    pub fn with_sign(&self, is_negative: bool) -> FPNum {
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        FPNum {
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            sign_mask: bool_mask(is_negative),
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            ..*self
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        }
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    }
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    #[inline]
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    pub const fn with_sign_as(self, other: FPNum) -> FPNum {
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        FPNum {
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            sign_mask: other.sign_mask,
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            ..self
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        }
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    }
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    #[inline]
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    pub const fn point(self) -> FPPoint {
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        FPPoint::new(self, self)
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    }
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    #[inline]
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    const fn temp_i128(self) -> i128 {
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        ((self.value ^ self.sign_mask) as i128).wrapping_sub(self.sign_mask as i128)
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    }
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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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            sign_mask: bool_mask(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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            sign_mask: POSITIVE_MASK,
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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.sign_mask == other.sign_mask || 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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    #[inline]
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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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        self.temp_i128().cmp(&(rhs.temp_i128()))
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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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        let tmp = self.temp_i128() + rhs.temp_i128();
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        let mask = bool_mask(tmp < 0);
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        Self {
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            sign_mask: mask,
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            value: ((tmp as u64) ^ mask).wrapping_sub(mask),
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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, mut rhs: Self) -> Self {
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        rhs.sign_mask = !rhs.sign_mask;
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        self + rhs
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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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            sign_mask: !self.sign_mask,
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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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            sign_mask: self.sign_mask ^ rhs.sign_mask,
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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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            sign_mask: self.sign_mask ^ bool_mask(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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            sign_mask: self.sign_mask ^ rhs.sign_mask,
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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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            sign_mask: self.sign_mask ^ bool_mask(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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            sign_mask: self.sign_mask,
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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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#[macro_export]
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macro_rules! fp {
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    ($n: literal / $d: tt) => {
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        FPNum::new($n, $d)
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    };
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    ($n: literal) => {
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        FPNum::from($n)
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    };
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}
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const LINEARIZE_TRESHOLD: u64 = 0x1_0000;
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#[derive(Clone, Copy, Debug)]
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pub struct FPPoint {
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    x_sign_mask: u32,
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    y_sign_mask: u32,
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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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    pub const fn new(x: FPNum, y: FPNum) -> Self {
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        Self {
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            x_sign_mask: x.sign_mask as u32,
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            y_sign_mask: y.sign_mask as u32,
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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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    pub fn zero() -> FPPoint {
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        FPPoint::new(fp!(0), fp!(0))
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    }
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    #[inline]
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    pub fn unit_x() -> FPPoint {
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        FPPoint::new(fp!(1), fp!(0))
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    }
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    #[inline]
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    pub fn unit_y() -> FPPoint {
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        FPPoint::new(fp!(0), fp!(1))
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    }
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    #[inline]
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    pub const fn x(&self) -> FPNum {
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        FPNum {
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            sign_mask: self.x_sign_mask as i32 as u64,
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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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    pub const fn y(&self) -> FPNum {
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        FPNum {
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            sign_mask: self.y_sign_mask as i32 as u64,
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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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    pub fn is_zero(&self) -> bool {
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        self.x().is_zero() && self.y().is_zero()
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    }
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    #[inline]
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    pub fn max_norm(&self) -> FPNum {
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        std::cmp::max(self.x().abs(), self.y().abs())
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    }
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    #[inline]
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    pub fn sqr_distance(&self) -> FPNum {
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        self.x().sqr() + self.y().sqr()
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    }
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    #[inline]
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    pub fn distance(&self) -> FPNum {
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        let r = self.x_value | self.y_value;
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        if r < LINEARIZE_TRESHOLD {
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            FPNum::from(r as u32)
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        } else {
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            let sqr: u128 = (self.x_value as u128).pow(2) + (self.y_value as u128).pow(2);
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            FPNum {
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                sign_mask: POSITIVE_MASK,
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                value: integral_sqrt_ext(sqr) as u64,
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   348
            }
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   349
        }
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   350
    }
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   351
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   352
    #[inline]
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5fdc41cd0841 make methods public
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   353
    pub fn is_in_range(&self, radius: FPNum) -> bool {
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   354
        self.max_norm() < radius && self.sqr_distance() < radius.sqr()
13946
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   355
    }
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diff changeset
   356
2ee07e751171 add more fpnum functions
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diff changeset
   357
    #[inline]
13949
5fdc41cd0841 make methods public
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   358
    pub fn dot(&self, other: &FPPoint) -> FPNum {
13946
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diff changeset
   359
        self.x() * other.x() + self.y() * other.y()
2ee07e751171 add more fpnum functions
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diff changeset
   360
    }
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diff changeset
   361
}
2ee07e751171 add more fpnum functions
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diff changeset
   362
2ee07e751171 add more fpnum functions
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parents: 13926
diff changeset
   363
impl PartialEq for FPPoint {
2ee07e751171 add more fpnum functions
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parents: 13926
diff changeset
   364
    #[inline]
2ee07e751171 add more fpnum functions
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diff changeset
   365
    fn eq(&self, other: &Self) -> bool {
2ee07e751171 add more fpnum functions
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diff changeset
   366
        self.x() == other.x() && self.y() == other.y()
2ee07e751171 add more fpnum functions
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diff changeset
   367
    }
2ee07e751171 add more fpnum functions
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diff changeset
   368
}
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parents: 13926
diff changeset
   369
2ee07e751171 add more fpnum functions
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diff changeset
   370
impl Eq for FPPoint {}
2ee07e751171 add more fpnum functions
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diff changeset
   371
2ee07e751171 add more fpnum functions
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diff changeset
   372
impl ops::Neg for FPPoint {
2ee07e751171 add more fpnum functions
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diff changeset
   373
    type Output = Self;
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diff changeset
   374
2ee07e751171 add more fpnum functions
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diff changeset
   375
    #[inline]
2ee07e751171 add more fpnum functions
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parents: 13926
diff changeset
   376
    fn neg(self) -> Self {
2ee07e751171 add more fpnum functions
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parents: 13926
diff changeset
   377
        Self::new(-self.x(), -self.y())
2ee07e751171 add more fpnum functions
alfadur
parents: 13926
diff changeset
   378
    }
2ee07e751171 add more fpnum functions
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parents: 13926
diff changeset
   379
}
2ee07e751171 add more fpnum functions
alfadur
parents: 13926
diff changeset
   380
2ee07e751171 add more fpnum functions
alfadur
parents: 13926
diff changeset
   381
macro_rules! bin_op_impl {
13948
cf28d7a2b7fe add scalar operations
alfadur
parents: 13947
diff changeset
   382
    ($op: ty, $name: tt) => {
13946
2ee07e751171 add more fpnum functions
alfadur
parents: 13926
diff changeset
   383
        impl $op for FPPoint {
2ee07e751171 add more fpnum functions
alfadur
parents: 13926
diff changeset
   384
            type Output = Self;
2ee07e751171 add more fpnum functions
alfadur
parents: 13926
diff changeset
   385
2ee07e751171 add more fpnum functions
alfadur
parents: 13926
diff changeset
   386
            #[inline]
2ee07e751171 add more fpnum functions
alfadur
parents: 13926
diff changeset
   387
            fn $name(self, rhs: Self) -> Self {
14143
c27461e6a9eb Implement non-overflowing calculations for high values
unc0rr
parents: 14102
diff changeset
   388
                Self::new(self.x().$name(rhs.x()), self.y().$name(rhs.y()))
13946
2ee07e751171 add more fpnum functions
alfadur
parents: 13926
diff changeset
   389
            }
2ee07e751171 add more fpnum functions
alfadur
parents: 13926
diff changeset
   390
        }
14143
c27461e6a9eb Implement non-overflowing calculations for high values
unc0rr
parents: 14102
diff changeset
   391
    };
13946
2ee07e751171 add more fpnum functions
alfadur
parents: 13926
diff changeset
   392
}
2ee07e751171 add more fpnum functions
alfadur
parents: 13926
diff changeset
   393
13953
7bb60596c27e add left scalar operations to fpnum
alfadur
parents: 13950
diff changeset
   394
macro_rules! right_scalar_bin_op_impl {
7bb60596c27e add left scalar operations to fpnum
alfadur
parents: 13950
diff changeset
   395
    ($($op: tt)::+, $name: tt) => {
7bb60596c27e add left scalar operations to fpnum
alfadur
parents: 13950
diff changeset
   396
        impl $($op)::+<FPNum> for FPPoint {
13948
cf28d7a2b7fe add scalar operations
alfadur
parents: 13947
diff changeset
   397
            type Output = Self;
cf28d7a2b7fe add scalar operations
alfadur
parents: 13947
diff changeset
   398
cf28d7a2b7fe add scalar operations
alfadur
parents: 13947
diff changeset
   399
            #[inline]
cf28d7a2b7fe add scalar operations
alfadur
parents: 13947
diff changeset
   400
            fn $name(self, rhs: FPNum) -> Self {
cf28d7a2b7fe add scalar operations
alfadur
parents: 13947
diff changeset
   401
                Self::new(self.x().$name(rhs),
cf28d7a2b7fe add scalar operations
alfadur
parents: 13947
diff changeset
   402
                          self.y().$name(rhs))
cf28d7a2b7fe add scalar operations
alfadur
parents: 13947
diff changeset
   403
            }
cf28d7a2b7fe add scalar operations
alfadur
parents: 13947
diff changeset
   404
        }
14161
3078123e84ea Bezierize land outline
unc0rr
parents: 14160
diff changeset
   405
    };
3078123e84ea Bezierize land outline
unc0rr
parents: 14160
diff changeset
   406
    ($($op: tt)::+<$arg: tt>, $name: tt) => {
3078123e84ea Bezierize land outline
unc0rr
parents: 14160
diff changeset
   407
        impl $($op)::+<$arg> for FPPoint {
3078123e84ea Bezierize land outline
unc0rr
parents: 14160
diff changeset
   408
            type Output = Self;
3078123e84ea Bezierize land outline
unc0rr
parents: 14160
diff changeset
   409
3078123e84ea Bezierize land outline
unc0rr
parents: 14160
diff changeset
   410
            #[inline]
3078123e84ea Bezierize land outline
unc0rr
parents: 14160
diff changeset
   411
            fn $name(self, rhs: $arg) -> Self {
3078123e84ea Bezierize land outline
unc0rr
parents: 14160
diff changeset
   412
                Self::new(self.x().$name(rhs),
3078123e84ea Bezierize land outline
unc0rr
parents: 14160
diff changeset
   413
                          self.y().$name(rhs))
3078123e84ea Bezierize land outline
unc0rr
parents: 14160
diff changeset
   414
            }
3078123e84ea Bezierize land outline
unc0rr
parents: 14160
diff changeset
   415
        }
13948
cf28d7a2b7fe add scalar operations
alfadur
parents: 13947
diff changeset
   416
    }
cf28d7a2b7fe add scalar operations
alfadur
parents: 13947
diff changeset
   417
}
cf28d7a2b7fe add scalar operations
alfadur
parents: 13947
diff changeset
   418
13953
7bb60596c27e add left scalar operations to fpnum
alfadur
parents: 13950
diff changeset
   419
macro_rules! left_scalar_bin_op_impl {
7bb60596c27e add left scalar operations to fpnum
alfadur
parents: 13950
diff changeset
   420
    ($($op: tt)::+, $name: tt) => {
7bb60596c27e add left scalar operations to fpnum
alfadur
parents: 13950
diff changeset
   421
        impl $($op)::+<FPPoint> for FPNum {
7bb60596c27e add left scalar operations to fpnum
alfadur
parents: 13950
diff changeset
   422
            type Output = FPPoint;
7bb60596c27e add left scalar operations to fpnum
alfadur
parents: 13950
diff changeset
   423
7bb60596c27e add left scalar operations to fpnum
alfadur
parents: 13950
diff changeset
   424
            #[inline]
7bb60596c27e add left scalar operations to fpnum
alfadur
parents: 13950
diff changeset
   425
            fn $name(self, rhs: FPPoint) -> Self::Output {
7bb60596c27e add left scalar operations to fpnum
alfadur
parents: 13950
diff changeset
   426
                Self::Output::new(self.$name(rhs.x()),
7bb60596c27e add left scalar operations to fpnum
alfadur
parents: 13950
diff changeset
   427
                                  self.$name(rhs.y()))
7bb60596c27e add left scalar operations to fpnum
alfadur
parents: 13950
diff changeset
   428
            }
7bb60596c27e add left scalar operations to fpnum
alfadur
parents: 13950
diff changeset
   429
        }
7bb60596c27e add left scalar operations to fpnum
alfadur
parents: 13950
diff changeset
   430
    }
7bb60596c27e add left scalar operations to fpnum
alfadur
parents: 13950
diff changeset
   431
}
7bb60596c27e add left scalar operations to fpnum
alfadur
parents: 13950
diff changeset
   432
13946
2ee07e751171 add more fpnum functions
alfadur
parents: 13926
diff changeset
   433
bin_op_impl!(ops::Add, add);
2ee07e751171 add more fpnum functions
alfadur
parents: 13926
diff changeset
   434
bin_op_impl!(ops::Sub, sub);
2ee07e751171 add more fpnum functions
alfadur
parents: 13926
diff changeset
   435
bin_op_impl!(ops::Mul, mul);
13950
ff77c9920007 add opassign implementations
alfadur
parents: 13949
diff changeset
   436
bin_op_impl!(ops::Div, div);
13953
7bb60596c27e add left scalar operations to fpnum
alfadur
parents: 13950
diff changeset
   437
right_scalar_bin_op_impl!(ops::Add, add);
7bb60596c27e add left scalar operations to fpnum
alfadur
parents: 13950
diff changeset
   438
right_scalar_bin_op_impl!(ops::Mul, mul);
7bb60596c27e add left scalar operations to fpnum
alfadur
parents: 13950
diff changeset
   439
right_scalar_bin_op_impl!(ops::Sub, sub);
7bb60596c27e add left scalar operations to fpnum
alfadur
parents: 13950
diff changeset
   440
right_scalar_bin_op_impl!(ops::Div, div);
14161
3078123e84ea Bezierize land outline
unc0rr
parents: 14160
diff changeset
   441
right_scalar_bin_op_impl!(ops::Div<u32>, div);
13953
7bb60596c27e add left scalar operations to fpnum
alfadur
parents: 13950
diff changeset
   442
left_scalar_bin_op_impl!(ops::Mul, mul);
13946
2ee07e751171 add more fpnum functions
alfadur
parents: 13926
diff changeset
   443
13950
ff77c9920007 add opassign implementations
alfadur
parents: 13949
diff changeset
   444
macro_rules! bin_assign_op_impl {
ff77c9920007 add opassign implementations
alfadur
parents: 13949
diff changeset
   445
    ($typ: tt, $($op: tt)::+, $name: tt, $delegate: tt) => {
ff77c9920007 add opassign implementations
alfadur
parents: 13949
diff changeset
   446
        bin_assign_op_impl!($typ, $($op)::+<$typ>, $name, $delegate);
ff77c9920007 add opassign implementations
alfadur
parents: 13949
diff changeset
   447
    };
ff77c9920007 add opassign implementations
alfadur
parents: 13949
diff changeset
   448
    ($typ: tt, $($op: tt)::+<$arg: tt>, $name: tt, $delegate: tt) => {
ff77c9920007 add opassign implementations
alfadur
parents: 13949
diff changeset
   449
        impl $($op)::+<$arg> for $typ {
ff77c9920007 add opassign implementations
alfadur
parents: 13949
diff changeset
   450
            #[inline]
ff77c9920007 add opassign implementations
alfadur
parents: 13949
diff changeset
   451
            fn $name(&mut self, rhs: $arg) {
ff77c9920007 add opassign implementations
alfadur
parents: 13949
diff changeset
   452
                *self = *self $delegate rhs;
ff77c9920007 add opassign implementations
alfadur
parents: 13949
diff changeset
   453
            }
ff77c9920007 add opassign implementations
alfadur
parents: 13949
diff changeset
   454
        }
ff77c9920007 add opassign implementations
alfadur
parents: 13949
diff changeset
   455
    }
ff77c9920007 add opassign implementations
alfadur
parents: 13949
diff changeset
   456
}
ff77c9920007 add opassign implementations
alfadur
parents: 13949
diff changeset
   457
ff77c9920007 add opassign implementations
alfadur
parents: 13949
diff changeset
   458
bin_assign_op_impl!(FPNum, ops::AddAssign, add_assign, +);
ff77c9920007 add opassign implementations
alfadur
parents: 13949
diff changeset
   459
bin_assign_op_impl!(FPNum, ops::SubAssign, sub_assign, -);
ff77c9920007 add opassign implementations
alfadur
parents: 13949
diff changeset
   460
bin_assign_op_impl!(FPNum, ops::MulAssign, mul_assign, *);
ff77c9920007 add opassign implementations
alfadur
parents: 13949
diff changeset
   461
bin_assign_op_impl!(FPNum, ops::DivAssign, div_assign, /);
ff77c9920007 add opassign implementations
alfadur
parents: 13949
diff changeset
   462
bin_assign_op_impl!(FPNum, ops::MulAssign<i32>, mul_assign, *);
ff77c9920007 add opassign implementations
alfadur
parents: 13949
diff changeset
   463
bin_assign_op_impl!(FPNum, ops::DivAssign<i32>, div_assign, /);
ff77c9920007 add opassign implementations
alfadur
parents: 13949
diff changeset
   464
bin_assign_op_impl!(FPNum, ops::DivAssign<u32>, div_assign, /);
ff77c9920007 add opassign implementations
alfadur
parents: 13949
diff changeset
   465
ff77c9920007 add opassign implementations
alfadur
parents: 13949
diff changeset
   466
bin_assign_op_impl!(FPPoint, ops::AddAssign, add_assign, +);
ff77c9920007 add opassign implementations
alfadur
parents: 13949
diff changeset
   467
bin_assign_op_impl!(FPPoint, ops::SubAssign, sub_assign, -);
ff77c9920007 add opassign implementations
alfadur
parents: 13949
diff changeset
   468
bin_assign_op_impl!(FPPoint, ops::MulAssign, mul_assign, *);
ff77c9920007 add opassign implementations
alfadur
parents: 13949
diff changeset
   469
bin_assign_op_impl!(FPPoint, ops::DivAssign, div_assign, /);
ff77c9920007 add opassign implementations
alfadur
parents: 13949
diff changeset
   470
bin_assign_op_impl!(FPPoint, ops::AddAssign<FPNum>, add_assign, +);
ff77c9920007 add opassign implementations
alfadur
parents: 13949
diff changeset
   471
bin_assign_op_impl!(FPPoint, ops::SubAssign<FPNum>, sub_assign, -);
ff77c9920007 add opassign implementations
alfadur
parents: 13949
diff changeset
   472
bin_assign_op_impl!(FPPoint, ops::MulAssign<FPNum>, mul_assign, *);
ff77c9920007 add opassign implementations
alfadur
parents: 13949
diff changeset
   473
bin_assign_op_impl!(FPPoint, ops::DivAssign<FPNum>, div_assign, /);
ff77c9920007 add opassign implementations
alfadur
parents: 13949
diff changeset
   474
15239
b2c086629fb8 optimize 64-bit sqrt some more
alfadur
parents: 15235
diff changeset
   475
pub fn integral_sqrt(value: u64) -> u64 {
b2c086629fb8 optimize 64-bit sqrt some more
alfadur
parents: 15235
diff changeset
   476
    let mut digits = (64u32 - 1).saturating_sub(value.leading_zeros()) & 0xFFFF_FFFE;
b2c086629fb8 optimize 64-bit sqrt some more
alfadur
parents: 15235
diff changeset
   477
    let mut result = if value == 0 { 0u64 } else { 1u64 };
15235
58a0f2a6527b optimize sqrts
alfadur
parents: 15234
diff changeset
   478
15239
b2c086629fb8 optimize 64-bit sqrt some more
alfadur
parents: 15235
diff changeset
   479
    while digits != 0 {
b2c086629fb8 optimize 64-bit sqrt some more
alfadur
parents: 15235
diff changeset
   480
        result <<= 1;
b2c086629fb8 optimize 64-bit sqrt some more
alfadur
parents: 15235
diff changeset
   481
        if (result + 1).pow(2) <= value >> (digits - 2) {
b2c086629fb8 optimize 64-bit sqrt some more
alfadur
parents: 15235
diff changeset
   482
            result += 1;
b2c086629fb8 optimize 64-bit sqrt some more
alfadur
parents: 15235
diff changeset
   483
        }
b2c086629fb8 optimize 64-bit sqrt some more
alfadur
parents: 15235
diff changeset
   484
        digits -= 2;
b2c086629fb8 optimize 64-bit sqrt some more
alfadur
parents: 15235
diff changeset
   485
    }
15235
58a0f2a6527b optimize sqrts
alfadur
parents: 15234
diff changeset
   486
58a0f2a6527b optimize sqrts
alfadur
parents: 15234
diff changeset
   487
    result
58a0f2a6527b optimize sqrts
alfadur
parents: 15234
diff changeset
   488
}
58a0f2a6527b optimize sqrts
alfadur
parents: 15234
diff changeset
   489
58a0f2a6527b optimize sqrts
alfadur
parents: 15234
diff changeset
   490
pub fn integral_sqrt_ext(mut value: u128) -> u128 {
58a0f2a6527b optimize sqrts
alfadur
parents: 15234
diff changeset
   491
    let mut digit_sqr =
58a0f2a6527b optimize sqrts
alfadur
parents: 15234
diff changeset
   492
        0x40000000_00000000_00000000_00000000u128.wrapping_shr(value.leading_zeros() & 0xFFFF_FFFE);
58a0f2a6527b optimize sqrts
alfadur
parents: 15234
diff changeset
   493
    let mut result = 0u128;
58a0f2a6527b optimize sqrts
alfadur
parents: 15234
diff changeset
   494
58a0f2a6527b optimize sqrts
alfadur
parents: 15234
diff changeset
   495
    while digit_sqr != 0 {
58a0f2a6527b optimize sqrts
alfadur
parents: 15234
diff changeset
   496
        let approx = result + digit_sqr;
58a0f2a6527b optimize sqrts
alfadur
parents: 15234
diff changeset
   497
        result >>= 1;
58a0f2a6527b optimize sqrts
alfadur
parents: 15234
diff changeset
   498
58a0f2a6527b optimize sqrts
alfadur
parents: 15234
diff changeset
   499
        if approx <= value {
58a0f2a6527b optimize sqrts
alfadur
parents: 15234
diff changeset
   500
            value -= approx;
58a0f2a6527b optimize sqrts
alfadur
parents: 15234
diff changeset
   501
            result += digit_sqr;
58a0f2a6527b optimize sqrts
alfadur
parents: 15234
diff changeset
   502
        }
58a0f2a6527b optimize sqrts
alfadur
parents: 15234
diff changeset
   503
        digit_sqr >>= 2;
58a0f2a6527b optimize sqrts
alfadur
parents: 15234
diff changeset
   504
    }
58a0f2a6527b optimize sqrts
alfadur
parents: 15234
diff changeset
   505
    result
58a0f2a6527b optimize sqrts
alfadur
parents: 15234
diff changeset
   506
}
58a0f2a6527b optimize sqrts
alfadur
parents: 15234
diff changeset
   507
15239
b2c086629fb8 optimize 64-bit sqrt some more
alfadur
parents: 15235
diff changeset
   508
#[inline]
13949
5fdc41cd0841 make methods public
alfadur
parents: 13948
diff changeset
   509
pub fn distance<T>(x: T, y: T) -> FPNum
14143
c27461e6a9eb Implement non-overflowing calculations for high values
unc0rr
parents: 14102
diff changeset
   510
where
c27461e6a9eb Implement non-overflowing calculations for high values
unc0rr
parents: 14102
diff changeset
   511
    T: Into<i64> + std::fmt::Debug,
13946
2ee07e751171 add more fpnum functions
alfadur
parents: 13926
diff changeset
   512
{
15235
58a0f2a6527b optimize sqrts
alfadur
parents: 15234
diff changeset
   513
    let sqr: u128 = (x.into().pow(2) as u128).shl(64) + (y.into().pow(2) as u128).shl(64);
14143
c27461e6a9eb Implement non-overflowing calculations for high values
unc0rr
parents: 14102
diff changeset
   514
c27461e6a9eb Implement non-overflowing calculations for high values
unc0rr
parents: 14102
diff changeset
   515
    FPNum {
15232
924f7e38815e optimize fpnum operations
alfadur
parents: 14722
diff changeset
   516
        sign_mask: POSITIVE_MASK,
15235
58a0f2a6527b optimize sqrts
alfadur
parents: 15234
diff changeset
   517
        value: integral_sqrt_ext(sqr) as u64,
14143
c27461e6a9eb Implement non-overflowing calculations for high values
unc0rr
parents: 14102
diff changeset
   518
    }
13946
2ee07e751171 add more fpnum functions
alfadur
parents: 13926
diff changeset
   519
}
2ee07e751171 add more fpnum functions
alfadur
parents: 13926
diff changeset
   520
13905
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   521
/* TODO:
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   522
 AngleSin
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   523
 AngleCos
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   524
*/
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   525
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   526
#[cfg(test)]
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   527
#[test]
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   528
fn basics() {
14143
c27461e6a9eb Implement non-overflowing calculations for high values
unc0rr
parents: 14102
diff changeset
   529
    let n = fp!(15 / 2);
13905
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   530
    assert!(n.is_positive());
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   531
    assert!(!n.is_negative());
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   532
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   533
    assert!(!(-n).is_positive());
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   534
    assert!((-n).is_negative());
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   535
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   536
    assert_eq!(-(-n), n);
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   537
    assert_eq!((-n).abs(), n);
14143
c27461e6a9eb Implement non-overflowing calculations for high values
unc0rr
parents: 14102
diff changeset
   538
    assert_eq!(-n, fp!(-15 / 2));
13905
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   539
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   540
    assert_eq!(n.round(), 7);
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   541
    assert_eq!((-n).round(), -7);
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   542
}
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   543
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   544
#[test]
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   545
fn zero() {
13911
9ae1184886db add fpnum literal macro
alfadur
parents: 13909
diff changeset
   546
    let z = fp!(0);
14143
c27461e6a9eb Implement non-overflowing calculations for high values
unc0rr
parents: 14102
diff changeset
   547
    let n = fp!(15 / 2);
13905
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   548
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   549
    assert!(z.is_zero());
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   550
    assert!(z.is_positive());
15232
924f7e38815e optimize fpnum operations
alfadur
parents: 14722
diff changeset
   551
    assert!((-z).is_negative());
13907
2bfd7472ef1d Add some more tests
unc0rr
parents: 13905
diff changeset
   552
    assert_eq!(n - n, z);
2bfd7472ef1d Add some more tests
unc0rr
parents: 13905
diff changeset
   553
    assert_eq!(-n + n, z);
13947
2717a5289d88 fix test
alfadur
parents: 13946
diff changeset
   554
    assert_eq!(n.with_sign_as(-n), -n);
13905
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   555
}
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   556
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   557
#[test]
13908
fbbb4fcd6a75 delegate cmp to rustlib
alfadur
parents: 13907
diff changeset
   558
fn ord() {
13911
9ae1184886db add fpnum literal macro
alfadur
parents: 13909
diff changeset
   559
    let z = fp!(0);
14143
c27461e6a9eb Implement non-overflowing calculations for high values
unc0rr
parents: 14102
diff changeset
   560
    let n1_5 = fp!(3 / 2);
c27461e6a9eb Implement non-overflowing calculations for high values
unc0rr
parents: 14102
diff changeset
   561
    let n2_25 = fp!(9 / 4);
13908
fbbb4fcd6a75 delegate cmp to rustlib
alfadur
parents: 13907
diff changeset
   562
fbbb4fcd6a75 delegate cmp to rustlib
alfadur
parents: 13907
diff changeset
   563
    assert!(!(z > z));
fbbb4fcd6a75 delegate cmp to rustlib
alfadur
parents: 13907
diff changeset
   564
    assert!(!(z < z));
fbbb4fcd6a75 delegate cmp to rustlib
alfadur
parents: 13907
diff changeset
   565
    assert!(n2_25 > n1_5);
fbbb4fcd6a75 delegate cmp to rustlib
alfadur
parents: 13907
diff changeset
   566
    assert!(-n2_25 < n1_5);
fbbb4fcd6a75 delegate cmp to rustlib
alfadur
parents: 13907
diff changeset
   567
    assert!(-n2_25 < -n1_5);
15232
924f7e38815e optimize fpnum operations
alfadur
parents: 14722
diff changeset
   568
924f7e38815e optimize fpnum operations
alfadur
parents: 14722
diff changeset
   569
    assert_eq!(n1_5.signum(), 1);
924f7e38815e optimize fpnum operations
alfadur
parents: 14722
diff changeset
   570
    assert_eq!((-n1_5).signum(), -1);
13908
fbbb4fcd6a75 delegate cmp to rustlib
alfadur
parents: 13907
diff changeset
   571
}
fbbb4fcd6a75 delegate cmp to rustlib
alfadur
parents: 13907
diff changeset
   572
fbbb4fcd6a75 delegate cmp to rustlib
alfadur
parents: 13907
diff changeset
   573
#[test]
13905
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   574
fn arith() {
14143
c27461e6a9eb Implement non-overflowing calculations for high values
unc0rr
parents: 14102
diff changeset
   575
    let n1_5 = fp!(3 / 2);
c27461e6a9eb Implement non-overflowing calculations for high values
unc0rr
parents: 14102
diff changeset
   576
    let n2_25 = fp!(9 / 4);
c27461e6a9eb Implement non-overflowing calculations for high values
unc0rr
parents: 14102
diff changeset
   577
    let n_0_15 = fp!(-15 / 100);
13905
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   578
13911
9ae1184886db add fpnum literal macro
alfadur
parents: 13909
diff changeset
   579
    assert_eq!(n1_5 + n1_5, fp!(3));
9ae1184886db add fpnum literal macro
alfadur
parents: 13909
diff changeset
   580
    assert_eq!(-n1_5 - n1_5, fp!(-3));
15232
924f7e38815e optimize fpnum operations
alfadur
parents: 14722
diff changeset
   581
    assert_eq!(n1_5 - n1_5, fp!(0));
13905
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   582
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   583
    assert_eq!(n1_5 * n1_5, n2_25);
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   584
    assert_eq!(-n1_5 * -n1_5, n2_25);
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   585
    assert_eq!(n1_5 * -n1_5, -n2_25);
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   586
    assert_eq!(-n1_5 * n1_5, -n2_25);
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   587
13907
2bfd7472ef1d Add some more tests
unc0rr
parents: 13905
diff changeset
   588
    assert_eq!(-n2_25 / -n1_5, n1_5);
2bfd7472ef1d Add some more tests
unc0rr
parents: 13905
diff changeset
   589
    assert_eq!(n1_5 / -10, n_0_15);
2bfd7472ef1d Add some more tests
unc0rr
parents: 13905
diff changeset
   590
13905
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   591
    assert_eq!(n1_5.sqr(), n2_25);
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   592
    assert_eq!((-n1_5).sqr(), n2_25);
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   593
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   594
    assert_eq!(n2_25.sqrt(), n1_5);
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   595
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   596
    assert_eq!((n1_5 * n1_5 * n1_5.sqr()).sqrt(), n2_25);
13950
ff77c9920007 add opassign implementations
alfadur
parents: 13949
diff changeset
   597
ff77c9920007 add opassign implementations
alfadur
parents: 13949
diff changeset
   598
    let mut m = fp!(1);
ff77c9920007 add opassign implementations
alfadur
parents: 13949
diff changeset
   599
    m += n1_5;
14143
c27461e6a9eb Implement non-overflowing calculations for high values
unc0rr
parents: 14102
diff changeset
   600
    assert_eq!(m, fp!(5 / 2));
c27461e6a9eb Implement non-overflowing calculations for high values
unc0rr
parents: 14102
diff changeset
   601
}
c27461e6a9eb Implement non-overflowing calculations for high values
unc0rr
parents: 14102
diff changeset
   602
c27461e6a9eb Implement non-overflowing calculations for high values
unc0rr
parents: 14102
diff changeset
   603
#[test]
c27461e6a9eb Implement non-overflowing calculations for high values
unc0rr
parents: 14102
diff changeset
   604
fn test_distance_high_values() {
c27461e6a9eb Implement non-overflowing calculations for high values
unc0rr
parents: 14102
diff changeset
   605
    assert_eq!(distance(1_000_000i32, 0), fp!(1_000_000));
c27461e6a9eb Implement non-overflowing calculations for high values
unc0rr
parents: 14102
diff changeset
   606
    assert_eq!(
c27461e6a9eb Implement non-overflowing calculations for high values
unc0rr
parents: 14102
diff changeset
   607
        FPPoint::new(fp!(1_000_000), fp!(0)).distance(),
c27461e6a9eb Implement non-overflowing calculations for high values
unc0rr
parents: 14102
diff changeset
   608
        fp!(1_000_000)
c27461e6a9eb Implement non-overflowing calculations for high values
unc0rr
parents: 14102
diff changeset
   609
    );
13905
b172a5d40eee Reimplement hwFloat library in rust for future use
unc0rr
parents:
diff changeset
   610
}
13946
2ee07e751171 add more fpnum functions
alfadur
parents: 13926
diff changeset
   611
2ee07e751171 add more fpnum functions
alfadur
parents: 13926
diff changeset
   612
#[test]
2ee07e751171 add more fpnum functions
alfadur
parents: 13926
diff changeset
   613
fn point() {
2ee07e751171 add more fpnum functions
alfadur
parents: 13926
diff changeset
   614
    let z = FPPoint::zero();
14143
c27461e6a9eb Implement non-overflowing calculations for high values
unc0rr
parents: 14102
diff changeset
   615
    let n = fp!(16 / 9);
13946
2ee07e751171 add more fpnum functions
alfadur
parents: 13926
diff changeset
   616
    let p = FPPoint::new(fp!(1), fp!(-2));
2ee07e751171 add more fpnum functions
alfadur
parents: 13926
diff changeset
   617
2ee07e751171 add more fpnum functions
alfadur
parents: 13926
diff changeset
   618
    assert_eq!(p.sqr_distance(), fp!(5));
2ee07e751171 add more fpnum functions
alfadur
parents: 13926
diff changeset
   619
    assert_eq!(p + -p, FPPoint::zero());
2ee07e751171 add more fpnum functions
alfadur
parents: 13926
diff changeset
   620
    assert_eq!(p * z, z);
2ee07e751171 add more fpnum functions
alfadur
parents: 13926
diff changeset
   621
    assert_eq!(p.dot(&z), fp!(0));
13953
7bb60596c27e add left scalar operations to fpnum
alfadur
parents: 13950
diff changeset
   622
    assert_eq!(n * p, p * n);
13946
2ee07e751171 add more fpnum functions
alfadur
parents: 13926
diff changeset
   623
    assert_eq!(distance(4, 3), fp!(5));
13948
cf28d7a2b7fe add scalar operations
alfadur
parents: 13947
diff changeset
   624
    assert_eq!(p * fp!(-3), FPPoint::new(fp!(-3), fp!(6)));
13960
665b4c6612ee fix fppoint.max_norm
alfadur
parents: 13953
diff changeset
   625
    assert_eq!(p.max_norm(), fp!(2));
14143
c27461e6a9eb Implement non-overflowing calculations for high values
unc0rr
parents: 14102
diff changeset
   626
}