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// Copyright © 2018–2023 Trevor Spiteri
// This library is free software: you can redistribute it and/or
// modify it under the terms of either
//
// * the Apache License, Version 2.0 or
// * the MIT License
//
// at your option.
//
// You should have recieved copies of the Apache License and the MIT
// License along with the library. If not, see
// <https://www.apache.org/licenses/LICENSE-2.0> and
// <https://opensource.org/licenses/MIT>.
// the value must be positive for all public functions
pub mod frac_part {
// MAX / 1000 (0) < val <= MAX (255)
// -3 <= log <= -1
#[inline]
pub const fn u8(val: u8) -> i32 {
if val > 25 {
-1
} else if val > 2 {
-2
} else {
debug_assert!(val > 0);
-3
}
}
// MAX / 100_000 (0) < val <= MAX (65_535)
// -5 <= log <= -1
#[inline]
pub const fn u16(val: u16) -> i32 {
if val > 6553 {
-1
} else if val > 655 {
-2
} else if val > 65 {
-3
} else if val > 6 {
-4
} else {
debug_assert!(val > 0);
-5
}
}
// 0 < val <= MAX
// -10 <= log <= -1
pub const fn u32(mut val: u32) -> i32 {
const MAX: u32 = u32::MAX;
if val <= MAX / 100_000_000 {
val *= 100_000_000;
// At this point, we have shifted out 8 digits, and we can only shift out 2 more.
// We can only check up to -2 more because -10 <= log <= -8.
if val > MAX / 10 {
-9
} else {
debug_assert!(val > MAX / 100);
-10
}
} else {
greater_equal_m8_u32(val)
}
}
// 0 < val <= MAX
// -20 <= log <= -1
pub const fn u64(mut val: u64) -> i32 {
const MAX: u64 = u64::MAX;
let mut log = 0;
if val <= MAX / 10_000_000_000_000_000 {
// After this, we can only check up to -4 more because -20 <= log <= -16.
// That is, we can skip the checks against MAX / 100_000_000 and MAX / 10_000.
val *= 10_000_000_000_000_000;
log += -16;
} else {
if val <= MAX / 100_000_000 {
val *= 100_000_000;
log += -8;
}
if val <= MAX / 10_000 {
val *= 10_000;
log += -4;
}
}
log + if val > MAX / 10 {
-1
} else if val > MAX / 100 {
-2
} else if val > MAX / 1000 {
-3
} else {
debug_assert!(val > MAX / 10_000);
-4
}
}
// 0 < val <= MAX
// -39 <= log <= -1
pub const fn u128(mut val: u128) -> i32 {
const MAX: u128 = u128::MAX;
let mut log = 0;
if val <= MAX / 100_000_000_000_000_000_000_000_000_000_000 {
val *= 100_000_000_000_000_000_000_000_000_000_000;
// At this point we have shifted out 32 digits, and we can only shift out 7 more.
// We can
// * use val >> 96 because we have shifted out 32 decimal digits (106 bits)
// * only check up to -8 more because -39 <= log <= -32
return -32 + greater_equal_m8_u32((val >> 96) as u32);
}
if val <= MAX / 10_000_000_000_000_000 {
val *= 10_000_000_000_000_000;
log += -16;
}
if val <= MAX / 100_000_000 {
val *= 100_000_000;
log += -8;
}
if log == -24 {
// At this point we have shifted out 24 digits, and we can only shift out 15 more.
// We can
// * use val >> 64 because we have shifted out 24 decimal digits (79 bits)
// * only check up to -8 more because -32 <= log <= -24
return -24 + greater_equal_m8_u64((val >> 64) as u64);
}
// We have *not* shifted out enough decimal digits, so we must *not* convert to u32 or u64.
if val <= MAX / 10_000 {
val *= 10_000;
log += -4;
}
log + if val > MAX / 10 {
-1
} else if val > MAX / 100 {
-2
} else if val > MAX / 1000 {
-3
} else {
debug_assert!(val > MAX / 10_000);
-4
}
}
// MAX / 100_000_000 < val <= MAX
// -8 <= log <= -1
const fn greater_equal_m8_u32(mut val: u32) -> i32 {
const MAX: u32 = u32::MAX;
debug_assert!(val > MAX / 100_000_000);
let mut log = 0;
if val <= MAX / 10_000 {
val *= 10_000;
log += -4;
}
log + if val > MAX / 10 {
-1
} else if val > MAX / 100 {
-2
} else if val > MAX / 1000 {
-3
} else {
debug_assert!(val > MAX / 10_000);
-4
}
}
// MAX / 100_000_000 < val <= MAX
// -8 <= log <= 1
const fn greater_equal_m8_u64(mut val: u64) -> i32 {
const MAX: u64 = u64::MAX;
debug_assert!(val > MAX / 100_000_000);
let mut log = 0;
if val <= MAX / 10_000 {
val *= 10_000;
log += -4;
}
log + if val > MAX / 10 {
-1
} else if val > MAX / 100 {
-2
} else if val > MAX / 1000 {
-3
} else {
debug_assert!(val > MAX / 10_000);
-4
}
}
}
// check log10() and log(10) in tandem
#[cfg(test)]
mod tests {
use crate::{log, log10};
macro_rules! check_loop {
($T:ident) => {
for i in 0..=$T::MAX.ilog10() as i32 {
let p = (10 as $T).pow(i as u32);
if i > 0 {
assert_eq!((p - 1).ilog10() as i32, i - 1);
assert_eq!(log::int_part::$T(p - 1, 10), i - 1);
}
assert_eq!(p.ilog10() as i32, i);
assert_eq!(log::int_part::$T(p, 10), i);
assert_eq!((p + 1).ilog10() as i32, i);
assert_eq!(log::int_part::$T(p + 1, 10), i);
}
for i in 0..-log10::frac_part::$T(1) {
let p = <$T>::MAX / (10 as $T).pow(i as u32);
if p > 1 {
assert_eq!(log10::frac_part::$T(p - 1), -1 - i);
assert_eq!(log::frac_part::$T(p - 1, 10), -1 - i);
}
assert_eq!(log10::frac_part::$T(p), -1 - i);
assert_eq!(log::frac_part::$T(p, 10), -1 - i);
if i > 0 {
assert_eq!(log10::frac_part::$T(p + 1), -i);
assert_eq!(log::frac_part::$T(p + 1, 10), -i);
}
}
};
}
#[test]
fn log10_u8() {
assert_eq!(1u8.ilog10(), 0);
assert_eq!(log::int_part::u8(1, 10), 0);
assert_eq!(u8::MAX.ilog10(), 2);
assert_eq!(log::int_part::u8(u8::MAX, 10), 2);
assert_eq!(log10::frac_part::u8(1), -3);
assert_eq!(log::frac_part::u8(1, 10), -3);
assert_eq!(log10::frac_part::u8(u8::MAX), -1);
assert_eq!(log::frac_part::u8(u8::MAX, 10), -1);
check_loop! { u8 }
}
#[test]
fn log10_u16() {
assert_eq!(1u16.ilog10(), 0);
assert_eq!(log::int_part::u16(1, 10), 0);
assert_eq!(u16::MAX.ilog10(), 4);
assert_eq!(log::int_part::u16(u16::MAX, 10), 4);
assert_eq!(log10::frac_part::u16(1), -5);
assert_eq!(log::frac_part::u16(1, 10), -5);
assert_eq!(log10::frac_part::u16(u16::MAX), -1);
assert_eq!(log::frac_part::u16(u16::MAX, 10), -1);
check_loop! { u16 }
}
#[test]
fn log10_u32() {
assert_eq!(1u32.ilog10(), 0);
assert_eq!(log::int_part::u32(1, 10), 0);
assert_eq!(u32::MAX.ilog10(), 9);
assert_eq!(log::int_part::u32(u32::MAX, 10), 9);
assert_eq!(log10::frac_part::u32(1), -10);
assert_eq!(log::frac_part::u32(1, 10), -10);
assert_eq!(log10::frac_part::u32(u32::MAX), -1);
assert_eq!(log::frac_part::u32(u32::MAX, 10), -1);
check_loop! { u32 }
}
#[test]
fn log10_u64() {
assert_eq!(1u64.ilog10(), 0);
assert_eq!(log::int_part::u64(1, 10), 0);
assert_eq!(u64::MAX.ilog10(), 19);
assert_eq!(log::int_part::u64(u64::MAX, 10), 19);
assert_eq!(log10::frac_part::u64(1), -20);
assert_eq!(log::frac_part::u64(1, 10), -20);
assert_eq!(log10::frac_part::u64(u64::MAX), -1);
assert_eq!(log::frac_part::u64(u64::MAX, 10), -1);
check_loop! { u64 }
}
#[test]
fn log10_u128() {
assert_eq!(1u128.ilog10(), 0);
assert_eq!(log::int_part::u128(1, 10), 0);
assert_eq!(u128::MAX.ilog10(), 38);
assert_eq!(log::int_part::u128(u128::MAX, 10), 38);
assert_eq!(log10::frac_part::u128(1), -39);
assert_eq!(log::frac_part::u128(1, 10), -39);
assert_eq!(log10::frac_part::u128(u128::MAX), -1);
assert_eq!(log::frac_part::u128(u128::MAX, 10), -1);
check_loop! { u128 }
}
}