Auto merge of #145 - ollie27:bigint_float, r=cuviper
bigint: fix float conversions The default implementations of to_f32, to_f64, from_32 and from_f64 are limited to numbers fitting in i64 but BigInt can of course be much bigger. The default to_f32 also has double rounding. from_f32 and from_f64 have undefined behaviour if the float is too big to fit in an i64. This fixes these issues and keeps the rounding consistant with other float to int conversions. Also add ToBigUint and ToBigInt implementations for f32 and f64. Currently this returns None if the BigInt is too big for to_f32 and to_f64 but it might make more sense to return Some(INFINITY) but I've decided to match f64::to_f32() for now.
This commit is contained in:
Homu
commit
661e225862
401
src/bigint.rs
401
src/bigint.rs
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@ -68,11 +68,13 @@ use std::ops::{Add, BitAnd, BitOr, BitXor, Div, Mul, Neg, Rem, Shl, Shr, Sub};
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use std::str::{self, FromStr};
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use std::fmt;
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use std::cmp::Ordering::{self, Less, Greater, Equal};
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use std::{f32, f64};
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use std::{u8, i64, u64};
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use rand::Rng;
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use traits::{ToPrimitive, FromPrimitive};
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use traits::Float;
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use {Num, Unsigned, CheckedAdd, CheckedSub, CheckedMul, CheckedDiv, Signed, Zero, One};
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use self::Sign::{Minus, NoSign, Plus};
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@ -1168,6 +1170,67 @@ impl ToPrimitive for BigUint {
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_ => None
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}
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}
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// `DoubleBigDigit` size dependent
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#[inline]
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fn to_f32(&self) -> Option<f32> {
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match self.data.len() {
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0 => Some(f32::zero()),
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1 => Some(self.data[0] as f32),
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len => {
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// this will prevent any overflow of exponent
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if len > (f32::MAX_EXP as usize) / big_digit::BITS {
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None
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} else {
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let exponent = (len - 2) * big_digit::BITS;
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// we need 25 significant digits, 24 to be stored and 1 for rounding
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// this gives at least 33 significant digits
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let mantissa = big_digit::to_doublebigdigit(self.data[len - 1], self.data[len - 2]);
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// this cast handles rounding
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let ret = (mantissa as f32) * 2.0.powi(exponent as i32);
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if ret.is_infinite() {
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None
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} else {
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Some(ret)
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}
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}
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}
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}
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}
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// `DoubleBigDigit` size dependent
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#[inline]
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fn to_f64(&self) -> Option<f64> {
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match self.data.len() {
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0 => Some(f64::zero()),
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1 => Some(self.data[0] as f64),
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2 => Some(big_digit::to_doublebigdigit(self.data[1], self.data[0]) as f64),
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len => {
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// this will prevent any overflow of exponent
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if len > (f64::MAX_EXP as usize) / big_digit::BITS {
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None
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} else {
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let mut exponent = (len - 2) * big_digit::BITS;
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let mut mantissa = big_digit::to_doublebigdigit(self.data[len - 1], self.data[len - 2]);
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// we need at least 54 significant bit digits, 53 to be stored and 1 for rounding
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// so we take enough from the next BigDigit to make it up to 64
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let shift = mantissa.leading_zeros() as usize;
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if shift > 0 {
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mantissa <<= shift;
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mantissa |= self.data[len - 3] as u64 >> (big_digit::BITS - shift);
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exponent -= shift;
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}
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// this cast handles rounding
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let ret = (mantissa as f64) * 2.0.powi(exponent as i32);
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if ret.is_infinite() {
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None
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} else {
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Some(ret)
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}
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}
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}
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}
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}
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}
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impl FromPrimitive for BigUint {
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@ -1184,6 +1247,36 @@ impl FromPrimitive for BigUint {
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fn from_u64(n: u64) -> Option<BigUint> {
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Some(BigUint::from(n))
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}
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#[inline]
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fn from_f64(mut n: f64) -> Option<BigUint> {
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// handle NAN, INFINITY, NEG_INFINITY
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if !n.is_finite() {
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return None;
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}
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// match the rounding of casting from float to int
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n = n.trunc();
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// handle 0.x, -0.x
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if n.is_zero() {
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return Some(BigUint::zero());
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}
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let (mantissa, exponent, sign) = Float::integer_decode(n);
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if sign == -1 {
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return None;
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}
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let mut ret = BigUint::from(mantissa);
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if exponent > 0 {
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ret = ret << exponent as usize;
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} else if exponent < 0 {
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ret = ret >> (-exponent) as usize;
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}
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Some(ret)
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}
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}
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impl From<u64> for BigUint {
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@ -1261,6 +1354,8 @@ impl_to_biguint!(u8, FromPrimitive::from_u8);
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impl_to_biguint!(u16, FromPrimitive::from_u16);
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impl_to_biguint!(u32, FromPrimitive::from_u32);
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impl_to_biguint!(u64, FromPrimitive::from_u64);
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impl_to_biguint!(f32, FromPrimitive::from_f32);
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impl_to_biguint!(f64, FromPrimitive::from_f64);
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// Extract bitwise digits that evenly divide BigDigit
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fn to_bitwise_digits_le(u: &BigUint, bits: usize) -> Vec<u8> {
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@ -2123,6 +2218,16 @@ impl ToPrimitive for BigInt {
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Minus => None
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}
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}
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#[inline]
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fn to_f32(&self) -> Option<f32> {
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self.data.to_f32().map(|n| if self.sign == Minus { -n } else { n })
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}
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#[inline]
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fn to_f64(&self) -> Option<f64> {
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self.data.to_f64().map(|n| if self.sign == Minus { -n } else { n })
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}
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}
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impl FromPrimitive for BigInt {
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@ -2135,6 +2240,15 @@ impl FromPrimitive for BigInt {
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fn from_u64(n: u64) -> Option<BigInt> {
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Some(BigInt::from(n))
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}
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#[inline]
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fn from_f64(n: f64) -> Option<BigInt> {
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if n >= 0.0 {
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BigUint::from_f64(n).map(|x| BigInt::from_biguint(Plus, x))
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} else {
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BigUint::from_f64(-n).map(|x| BigInt::from_biguint(Minus, x))
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}
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}
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}
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impl From<i64> for BigInt {
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@ -2248,6 +2362,8 @@ impl_to_bigint!(u8, FromPrimitive::from_u8);
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impl_to_bigint!(u16, FromPrimitive::from_u16);
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impl_to_bigint!(u32, FromPrimitive::from_u32);
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impl_to_bigint!(u64, FromPrimitive::from_u64);
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impl_to_bigint!(f32, FromPrimitive::from_f32);
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impl_to_bigint!(f64, FromPrimitive::from_f64);
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pub trait RandBigInt {
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/// Generate a random `BigUint` of the given bit size.
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@ -2544,6 +2660,7 @@ mod biguint_tests {
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use super::Sign::Plus;
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use std::cmp::Ordering::{Less, Equal, Greater};
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use std::{f32, f64};
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use std::i64;
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use std::iter::repeat;
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use std::str::FromStr;
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@ -2552,6 +2669,7 @@ mod biguint_tests {
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use rand::thread_rng;
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use {Num, Zero, One, CheckedAdd, CheckedSub, CheckedMul, CheckedDiv};
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use {ToPrimitive, FromPrimitive};
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use Float;
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/// Assert that an op works for all val/ref combinations
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macro_rules! assert_op {
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@ -3031,6 +3149,137 @@ mod biguint_tests {
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assert_eq!(BigUint::new(vec!(N1, N1, N1)).to_u64(), None);
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}
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#[test]
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fn test_convert_f32() {
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fn check(b1: &BigUint, f: f32) {
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let b2 = BigUint::from_f32(f).unwrap();
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assert_eq!(b1, &b2);
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assert_eq!(b1.to_f32().unwrap(), f);
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}
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check(&BigUint::zero(), 0.0);
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check(&BigUint::one(), 1.0);
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check(&BigUint::from(u16::MAX), 2.0.powi(16) - 1.0);
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check(&BigUint::from(1u64 << 32), 2.0.powi(32));
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check(&BigUint::from_slice(&[0, 0, 1]), 2.0.powi(64));
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check(&((BigUint::one() << 100) + (BigUint::one() << 123)), 2.0.powi(100) + 2.0.powi(123));
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check(&(BigUint::one() << 127), 2.0.powi(127));
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check(&(BigUint::from((1u64 << 24) - 1) << (128 - 24)), f32::MAX);
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// keeping all 24 digits with the bits at different offsets to the BigDigits
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let x: u32 = 0b00000000101111011111011011011101;
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let mut f = x as f32;
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let mut b = BigUint::from(x);
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for _ in 0..64 {
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check(&b, f);
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f *= 2.0;
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b = b << 1;
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}
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// this number when rounded to f64 then f32 isn't the same as when rounded straight to f32
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let n: u64 = 0b0000000000111111111111111111111111011111111111111111111111111111;
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assert!((n as f64) as f32 != n as f32);
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assert_eq!(BigUint::from(n).to_f32(), Some(n as f32));
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// test rounding up with the bits at different offsets to the BigDigits
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let mut f = ((1u64 << 25) - 1) as f32;
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let mut b = BigUint::from(1u64 << 25);
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for _ in 0..64 {
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assert_eq!(b.to_f32(), Some(f));
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f *= 2.0;
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b = b << 1;
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}
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// rounding
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assert_eq!(BigUint::from_f32(-1.0), None);
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assert_eq!(BigUint::from_f32(-0.99999), Some(BigUint::zero()));
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assert_eq!(BigUint::from_f32(-0.5), Some(BigUint::zero()));
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assert_eq!(BigUint::from_f32(-0.0), Some(BigUint::zero()));
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assert_eq!(BigUint::from_f32(f32::MIN_POSITIVE / 2.0), Some(BigUint::zero()));
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assert_eq!(BigUint::from_f32(f32::MIN_POSITIVE), Some(BigUint::zero()));
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assert_eq!(BigUint::from_f32(0.5), Some(BigUint::zero()));
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assert_eq!(BigUint::from_f32(0.99999), Some(BigUint::zero()));
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assert_eq!(BigUint::from_f32(f32::consts::E), Some(BigUint::from(2u32)));
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assert_eq!(BigUint::from_f32(f32::consts::PI), Some(BigUint::from(3u32)));
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// special float values
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assert_eq!(BigUint::from_f32(f32::NAN), None);
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assert_eq!(BigUint::from_f32(f32::INFINITY), None);
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assert_eq!(BigUint::from_f32(f32::NEG_INFINITY), None);
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assert_eq!(BigUint::from_f32(f32::MIN), None);
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// largest BigUint that will round to a finite f32 value
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let big_num = (BigUint::one() << 128) - BigUint::one() - (BigUint::one() << (128 - 25));
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assert_eq!(big_num.to_f32(), Some(f32::MAX));
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assert_eq!((big_num + BigUint::one()).to_f32(), None);
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assert_eq!(((BigUint::one() << 128) - BigUint::one()).to_f32(), None);
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assert_eq!((BigUint::one() << 128).to_f32(), None);
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}
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#[test]
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fn test_convert_f64() {
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fn check(b1: &BigUint, f: f64) {
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let b2 = BigUint::from_f64(f).unwrap();
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assert_eq!(b1, &b2);
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assert_eq!(b1.to_f64().unwrap(), f);
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}
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check(&BigUint::zero(), 0.0);
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check(&BigUint::one(), 1.0);
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check(&BigUint::from(u32::MAX), 2.0.powi(32) - 1.0);
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check(&BigUint::from(1u64 << 32), 2.0.powi(32));
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check(&BigUint::from_slice(&[0, 0, 1]), 2.0.powi(64));
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check(&((BigUint::one() << 100) + (BigUint::one() << 152)), 2.0.powi(100) + 2.0.powi(152));
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check(&(BigUint::one() << 1023), 2.0.powi(1023));
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check(&(BigUint::from((1u64 << 53) - 1) << (1024 - 53)), f64::MAX);
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// keeping all 53 digits with the bits at different offsets to the BigDigits
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let x: u64 = 0b0000000000011110111110110111111101110111101111011111011011011101;
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let mut f = x as f64;
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let mut b = BigUint::from(x);
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for _ in 0..128 {
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check(&b, f);
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f *= 2.0;
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b = b << 1;
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}
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// test rounding up with the bits at different offsets to the BigDigits
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let mut f = ((1u64 << 54) - 1) as f64;
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let mut b = BigUint::from(1u64 << 54);
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for _ in 0..128 {
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assert_eq!(b.to_f64(), Some(f));
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f *= 2.0;
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b = b << 1;
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}
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// rounding
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assert_eq!(BigUint::from_f64(-1.0), None);
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assert_eq!(BigUint::from_f64(-0.99999), Some(BigUint::zero()));
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assert_eq!(BigUint::from_f64(-0.5), Some(BigUint::zero()));
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assert_eq!(BigUint::from_f64(-0.0), Some(BigUint::zero()));
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assert_eq!(BigUint::from_f64(f64::MIN_POSITIVE / 2.0), Some(BigUint::zero()));
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assert_eq!(BigUint::from_f64(f64::MIN_POSITIVE), Some(BigUint::zero()));
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assert_eq!(BigUint::from_f64(0.5), Some(BigUint::zero()));
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assert_eq!(BigUint::from_f64(0.99999), Some(BigUint::zero()));
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assert_eq!(BigUint::from_f64(f64::consts::E), Some(BigUint::from(2u32)));
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assert_eq!(BigUint::from_f64(f64::consts::PI), Some(BigUint::from(3u32)));
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// special float values
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assert_eq!(BigUint::from_f64(f64::NAN), None);
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assert_eq!(BigUint::from_f64(f64::INFINITY), None);
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assert_eq!(BigUint::from_f64(f64::NEG_INFINITY), None);
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assert_eq!(BigUint::from_f64(f64::MIN), None);
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// largest BigUint that will round to a finite f64 value
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let big_num = (BigUint::one() << 1024) - BigUint::one() - (BigUint::one() << (1024 - 54));
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assert_eq!(big_num.to_f64(), Some(f64::MAX));
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assert_eq!((big_num + BigUint::one()).to_f64(), None);
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assert_eq!(((BigInt::one() << 1024) - BigInt::one()).to_f64(), None);
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assert_eq!((BigUint::one() << 1024).to_f64(), None);
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}
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#[test]
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fn test_convert_to_bigint() {
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fn check(n: BigUint, ans: BigInt) {
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@ -3585,6 +3834,7 @@ mod bigint_tests {
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use super::Sign::{Minus, NoSign, Plus};
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use std::cmp::Ordering::{Less, Equal, Greater};
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use std::{f32, f64};
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use std::{i8, i16, i32, i64, isize};
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use std::iter::repeat;
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use std::{u8, u16, u32, u64, usize};
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@ -3593,6 +3843,7 @@ mod bigint_tests {
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use rand::thread_rng;
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use {Zero, One, Signed, ToPrimitive, FromPrimitive, Num};
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use Float;
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/// Assert that an op works for all val/ref combinations
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macro_rules! assert_op {
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@ -3793,6 +4044,156 @@ mod bigint_tests {
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assert_eq!(BigInt::from_biguint(Minus, BigUint::new(vec!(1, 2, 3, 4, 5))).to_u64(), None);
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}
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#[test]
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fn test_convert_f32() {
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fn check(b1: &BigInt, f: f32) {
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let b2 = BigInt::from_f32(f).unwrap();
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assert_eq!(b1, &b2);
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assert_eq!(b1.to_f32().unwrap(), f);
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let neg_b1 = -b1;
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let neg_b2 = BigInt::from_f32(-f).unwrap();
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assert_eq!(neg_b1, neg_b2);
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assert_eq!(neg_b1.to_f32().unwrap(), -f);
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}
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check(&BigInt::zero(), 0.0);
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check(&BigInt::one(), 1.0);
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check(&BigInt::from(u16::MAX), 2.0.powi(16) - 1.0);
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check(&BigInt::from(1u64 << 32), 2.0.powi(32));
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check(&BigInt::from_slice(Plus, &[0, 0, 1]), 2.0.powi(64));
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check(&((BigInt::one() << 100) + (BigInt::one() << 123)), 2.0.powi(100) + 2.0.powi(123));
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check(&(BigInt::one() << 127), 2.0.powi(127));
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check(&(BigInt::from((1u64 << 24) - 1) << (128 - 24)), f32::MAX);
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// keeping all 24 digits with the bits at different offsets to the BigDigits
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let x: u32 = 0b00000000101111011111011011011101;
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let mut f = x as f32;
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let mut b = BigInt::from(x);
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for _ in 0..64 {
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check(&b, f);
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f *= 2.0;
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b = b << 1;
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}
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// this number when rounded to f64 then f32 isn't the same as when rounded straight to f32
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let mut n: i64 = 0b0000000000111111111111111111111111011111111111111111111111111111;
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assert!((n as f64) as f32 != n as f32);
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assert_eq!(BigInt::from(n).to_f32(), Some(n as f32));
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n = -n;
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assert!((n as f64) as f32 != n as f32);
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assert_eq!(BigInt::from(n).to_f32(), Some(n as f32));
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// test rounding up with the bits at different offsets to the BigDigits
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let mut f = ((1u64 << 25) - 1) as f32;
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let mut b = BigInt::from(1u64 << 25);
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for _ in 0..64 {
|
||||
assert_eq!(b.to_f32(), Some(f));
|
||||
f *= 2.0;
|
||||
b = b << 1;
|
||||
}
|
||||
|
||||
// rounding
|
||||
assert_eq!(BigInt::from_f32(-f32::consts::PI), Some(BigInt::from(-3i32)));
|
||||
assert_eq!(BigInt::from_f32(-f32::consts::E), Some(BigInt::from(-2i32)));
|
||||
assert_eq!(BigInt::from_f32(-0.99999), Some(BigInt::zero()));
|
||||
assert_eq!(BigInt::from_f32(-0.5), Some(BigInt::zero()));
|
||||
assert_eq!(BigInt::from_f32(-0.0), Some(BigInt::zero()));
|
||||
assert_eq!(BigInt::from_f32(f32::MIN_POSITIVE / 2.0), Some(BigInt::zero()));
|
||||
assert_eq!(BigInt::from_f32(f32::MIN_POSITIVE), Some(BigInt::zero()));
|
||||
assert_eq!(BigInt::from_f32(0.5), Some(BigInt::zero()));
|
||||
assert_eq!(BigInt::from_f32(0.99999), Some(BigInt::zero()));
|
||||
assert_eq!(BigInt::from_f32(f32::consts::E), Some(BigInt::from(2u32)));
|
||||
assert_eq!(BigInt::from_f32(f32::consts::PI), Some(BigInt::from(3u32)));
|
||||
|
||||
// special float values
|
||||
assert_eq!(BigInt::from_f32(f32::NAN), None);
|
||||
assert_eq!(BigInt::from_f32(f32::INFINITY), None);
|
||||
assert_eq!(BigInt::from_f32(f32::NEG_INFINITY), None);
|
||||
|
||||
// largest BigInt that will round to a finite f32 value
|
||||
let big_num = (BigInt::one() << 128) - BigInt::one() - (BigInt::one() << (128 - 25));
|
||||
assert_eq!(big_num.to_f32(), Some(f32::MAX));
|
||||
assert_eq!((&big_num + BigInt::one()).to_f32(), None);
|
||||
assert_eq!((-&big_num).to_f32(), Some(f32::MIN));
|
||||
assert_eq!(((-&big_num) - BigInt::one()).to_f32(), None);
|
||||
|
||||
assert_eq!(((BigInt::one() << 128) - BigInt::one()).to_f32(), None);
|
||||
assert_eq!((BigInt::one() << 128).to_f32(), None);
|
||||
assert_eq!((-((BigInt::one() << 128) - BigInt::one())).to_f32(), None);
|
||||
assert_eq!((-(BigInt::one() << 128)).to_f32(), None);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_convert_f64() {
|
||||
fn check(b1: &BigInt, f: f64) {
|
||||
let b2 = BigInt::from_f64(f).unwrap();
|
||||
assert_eq!(b1, &b2);
|
||||
assert_eq!(b1.to_f64().unwrap(), f);
|
||||
let neg_b1 = -b1;
|
||||
let neg_b2 = BigInt::from_f64(-f).unwrap();
|
||||
assert_eq!(neg_b1, neg_b2);
|
||||
assert_eq!(neg_b1.to_f64().unwrap(), -f);
|
||||
}
|
||||
|
||||
check(&BigInt::zero(), 0.0);
|
||||
check(&BigInt::one(), 1.0);
|
||||
check(&BigInt::from(u32::MAX), 2.0.powi(32) - 1.0);
|
||||
check(&BigInt::from(1u64 << 32), 2.0.powi(32));
|
||||
check(&BigInt::from_slice(Plus, &[0, 0, 1]), 2.0.powi(64));
|
||||
check(&((BigInt::one() << 100) + (BigInt::one() << 152)), 2.0.powi(100) + 2.0.powi(152));
|
||||
check(&(BigInt::one() << 1023), 2.0.powi(1023));
|
||||
check(&(BigInt::from((1u64 << 53) - 1) << (1024 - 53)), f64::MAX);
|
||||
|
||||
// keeping all 53 digits with the bits at different offsets to the BigDigits
|
||||
let x: u64 = 0b0000000000011110111110110111111101110111101111011111011011011101;
|
||||
let mut f = x as f64;
|
||||
let mut b = BigInt::from(x);
|
||||
for _ in 0..128 {
|
||||
check(&b, f);
|
||||
f *= 2.0;
|
||||
b = b << 1;
|
||||
}
|
||||
|
||||
// test rounding up with the bits at different offsets to the BigDigits
|
||||
let mut f = ((1u64 << 54) - 1) as f64;
|
||||
let mut b = BigInt::from(1u64 << 54);
|
||||
for _ in 0..128 {
|
||||
assert_eq!(b.to_f64(), Some(f));
|
||||
f *= 2.0;
|
||||
b = b << 1;
|
||||
}
|
||||
|
||||
// rounding
|
||||
assert_eq!(BigInt::from_f64(-f64::consts::PI), Some(BigInt::from(-3i32)));
|
||||
assert_eq!(BigInt::from_f64(-f64::consts::E), Some(BigInt::from(-2i32)));
|
||||
assert_eq!(BigInt::from_f64(-0.99999), Some(BigInt::zero()));
|
||||
assert_eq!(BigInt::from_f64(-0.5), Some(BigInt::zero()));
|
||||
assert_eq!(BigInt::from_f64(-0.0), Some(BigInt::zero()));
|
||||
assert_eq!(BigInt::from_f64(f64::MIN_POSITIVE / 2.0), Some(BigInt::zero()));
|
||||
assert_eq!(BigInt::from_f64(f64::MIN_POSITIVE), Some(BigInt::zero()));
|
||||
assert_eq!(BigInt::from_f64(0.5), Some(BigInt::zero()));
|
||||
assert_eq!(BigInt::from_f64(0.99999), Some(BigInt::zero()));
|
||||
assert_eq!(BigInt::from_f64(f64::consts::E), Some(BigInt::from(2u32)));
|
||||
assert_eq!(BigInt::from_f64(f64::consts::PI), Some(BigInt::from(3u32)));
|
||||
|
||||
// special float values
|
||||
assert_eq!(BigInt::from_f64(f64::NAN), None);
|
||||
assert_eq!(BigInt::from_f64(f64::INFINITY), None);
|
||||
assert_eq!(BigInt::from_f64(f64::NEG_INFINITY), None);
|
||||
|
||||
// largest BigInt that will round to a finite f64 value
|
||||
let big_num = (BigInt::one() << 1024) - BigInt::one() - (BigInt::one() << (1024 - 54));
|
||||
assert_eq!(big_num.to_f64(), Some(f64::MAX));
|
||||
assert_eq!((&big_num + BigInt::one()).to_f64(), None);
|
||||
assert_eq!((-&big_num).to_f64(), Some(f64::MIN));
|
||||
assert_eq!(((-&big_num) - BigInt::one()).to_f64(), None);
|
||||
|
||||
assert_eq!(((BigInt::one() << 1024) - BigInt::one()).to_f64(), None);
|
||||
assert_eq!((BigInt::one() << 1024).to_f64(), None);
|
||||
assert_eq!((-((BigInt::one() << 1024) - BigInt::one())).to_f64(), None);
|
||||
assert_eq!((-(BigInt::one() << 1024)).to_f64(), None);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_convert_to_biguint() {
|
||||
fn check(n: BigInt, ans_1: BigUint) {
|
||||
|
|
|
|||
Loading…
Reference in New Issue