//! [![github]](https://github.com/dtolnay/zmij) [![crates-io]](https://crates.io/crates/zmij) [![docs-rs]](https://docs.rs/zmij) //! //! [github]: https://img.shields.io/badge/github-8da0cb?style=for-the-badge&labelColor=555555&logo=github //! [crates-io]: https://img.shields.io/badge/crates.io-fc8d62?style=for-the-badge&labelColor=555555&logo=rust //! [docs-rs]: https://img.shields.io/badge/docs.rs-66c2a5?style=for-the-badge&labelColor=555555&logo=docs.rs //! //!
//! //! A double-to-string conversion algorithm based on [Schubfach] and [yy]. //! //! This Rust implementation is a line-by-line port of Victor Zverovich's //! implementation in C++, . //! //! [Schubfach]: https://fmt.dev/papers/Schubfach4.pdf //! [yy]: https://github.com/ibireme/c_numconv_benchmark/blob/master/vendor/yy_double/yy_double.c //! //!
//! //! # Example //! //! ``` //! fn main() { //! let mut buffer = zmij::Buffer::new(); //! let printed = buffer.format(1.234); //! assert_eq!(printed, "1.234"); //! } //! ``` //! //!
//! //! ## Performance //! //! The [dtoa-benchmark] compares this library and other Rust floating point //! formatting implementations across a range of precisions. The vertical axis //! in this chart shows nanoseconds taken by a single execution of //! `zmij::Buffer::new().format_finite(value)` so a lower result indicates a //! faster library. //! //! [dtoa-benchmark]: https://github.com/dtolnay/dtoa-benchmark //! //! ![performance](https://raw.githubusercontent.com/dtolnay/zmij/master/dtoa-benchmark.png) #![no_std] #![doc(html_root_url = "https://docs.rs/zmij/1.0.23")] #![deny(unsafe_op_in_unsafe_fn)] #![allow(non_camel_case_types, non_snake_case)] #![allow( clippy::blocks_in_conditions, clippy::cast_possible_truncation, clippy::cast_possible_wrap, clippy::cast_ptr_alignment, clippy::cast_sign_loss, clippy::doc_markdown, clippy::incompatible_msrv, clippy::items_after_statements, clippy::manual_ilog2, clippy::many_single_char_names, clippy::modulo_one, clippy::must_use_candidate, clippy::needless_doctest_main, clippy::needless_late_init, clippy::never_loop, clippy::redundant_else, clippy::similar_names, clippy::too_many_arguments, clippy::too_many_lines, clippy::unreadable_literal, clippy::used_underscore_items, clippy::while_immutable_condition, clippy::wildcard_imports )] #[cfg(all(target_arch = "x86_64", target_feature = "sse2", not(miri)))] mod stdarch_x86; #[cfg(test)] mod tests; mod traits; #[cfg(all(target_arch = "x86_64", target_feature = "sse2", not(miri)))] use crate::stdarch_x86::{ __m128i, _mm_add_epi64, _mm_cmpgt_epi8, _mm_cvtsi128_si64, _mm_load_si128, _mm_movemask_epi8, _mm_mul_epu32, _mm_mulhi_epu16, _mm_mullo_epi16, _mm_or_si128, _mm_set_epi64x, _mm_setzero_si128, _mm_srli_epi64, }; #[cfg(all( target_arch = "x86_64", target_feature = "sse2", target_feature = "sse4.1", not(miri) ))] use crate::stdarch_x86::{ _mm_insert_epi64, _mm_mullo_epi32, _mm_shuffle_epi8, _mm_srli_epi32, _mm_storeu_si128, }; #[cfg(all( target_arch = "x86_64", target_feature = "sse2", not(target_feature = "sse4.1"), not(miri) ))] use crate::stdarch_x86::{ _mm_shuffle_epi32, _mm_slli_epi16, _mm_slli_epi32, _mm_srli_epi16, _mm_sub_epi16, _MM_SHUFFLE, }; use crate::traits::Float as _; #[cfg(all(target_arch = "aarch64", target_feature = "neon", not(miri)))] use core::arch::aarch64::{ int16x8_t, int32x2_t, int32x4_t, uint16x8_t, uint64x1_t, uint8x16_t, vaddq_u16, vcgtzq_s8, vcombine_s32, vcreate_u64, vdup_n_s32, vdupq_n_s8, vdupq_n_u8, vget_lane_u64, vget_low_u8, vld1q_u8, vmla_n_s32, vmlaq_n_s16, vmlaq_n_s32, vorrq_u8, vqdmulh_n_s32, vqdmulhq_n_s16, vqdmulhq_n_s32, vqtbl1q_u8, vreinterpret_s32_u32, vreinterpret_s32_u64, vreinterpret_u16_s32, vreinterpret_u32_s32, vreinterpret_u64_u8, vreinterpretq_s16_s32, vreinterpretq_s32_u32, vreinterpretq_s8_u8, vreinterpretq_u16_s8, vreinterpretq_u16_u8, vreinterpretq_u64_u8, vreinterpretq_u8_s16, vreinterpretq_u8_u64, vrev64q_u8, vsetq_lane_u64, vshll_n_u16, vshr_n_u32, vshrn_n_u16, vst1q_u8, }; #[cfg(all(any(target_arch = "aarch64", target_arch = "x86_64"), not(miri)))] use core::arch::asm; use core::mem::{self, MaybeUninit}; use core::ops::RangeInclusive; use core::ptr; use core::slice; use core::str; #[cfg(feature = "no-panic")] use no_panic::no_panic; const BUFFER_SIZE: usize = 24; const NAN: &str = "NaN"; const INFINITY: &str = "inf"; const NEG_INFINITY: &str = "-inf"; // Declares struct members that must live in memory on ARM64 but are encoded as // immediates in the x64 assembly. struct AArch64Mem { #[cfg(target_arch = "aarch64")] value: u64, } impl AArch64Mem { const fn new() -> Self { AArch64Mem { #[cfg(target_arch = "aarch64")] value: VALUE, } } #[cfg_attr(not(target_arch = "aarch64"), allow(clippy::unused_self))] const fn get(&self) -> u64 { #[cfg(target_arch = "aarch64")] { self.value } #[cfg(not(target_arch = "aarch64"))] { VALUE } } } #[derive(Copy, Clone)] #[cfg_attr(test, derive(Debug, PartialEq))] struct uint128 { hi: u64, lo: u64, } // Use umul128_hi64 for division. const USE_UMUL128_HI64: bool = cfg!(target_vendor = "apple"); // Computes 128-bit result of multiplication of two 64-bit unsigned integers. const fn umul128(x: u64, y: u64) -> u128 { x as u128 * y as u128 } #[inline] const fn umul128_hi64(x: u64, y: u64) -> u64 { (umul128(x, y) >> 64) as u64 } // Returns (x * y + c) >> 64. #[cfg_attr(feature = "no-panic", no_panic)] fn umul128_add_hi64(x: u64, y: u64, c: u64) -> u64 { ((u128::from(x) * u128::from(y) + u128::from(c)) >> 64) as u64 } #[cfg_attr(feature = "no-panic", no_panic)] fn umul192_hi128(x_hi: u64, x_lo: u64, y: u64) -> uint128 { let p = umul128(x_hi, y); let lo = (p as u64).wrapping_add((umul128(x_lo, y) >> 64) as u64); uint128 { hi: (p >> 64) as u64 + u64::from(lo < p as u64), lo, } } // Returns x / 10 for x <= 2**62. #[cfg_attr(feature = "no-panic", no_panic)] fn div10(x: u64) -> u64 { debug_assert!(x < (1 << 62)); // ceil(2**64 / 10) computed as (1 << 63) / 5 + 1 to avoid int128. const DIV10_SIG64: u64 = (1 << 63) / 5 + 1; umul128_hi64(x, DIV10_SIG64) } // Computes the decimal exponent as floor(log10(2**bin_exp)) if regular or // floor(log10(3/4 * 2**bin_exp)) otherwise, without branching. const fn compute_dec_exp(bin_exp: i32, regular: bool) -> i32 { debug_assert!(bin_exp >= -1334 && bin_exp <= 2620); // log10_3_over_4_sig = -log10(3/4) * 2**log10_2_exp rounded to a power of 2 const LOG10_3_OVER_4_SIG: i32 = 131_072; // log10_2_sig = round(log10(2) * 2**log10_2_exp) const LOG10_2_SIG: i32 = 315_653; const LOG10_2_EXP: i32 = 20; (bin_exp * LOG10_2_SIG - !regular as i32 * LOG10_3_OVER_4_SIG) >> LOG10_2_EXP } trait FloatTraits: traits::Float { // Note: Rust port uses wider fixed-notation ranges than upstream. const FIXED_DEC_EXP: RangeInclusive; const NUM_BITS: i32; const NUM_SIG_BITS: i32 = Self::MANTISSA_DIGITS as i32 - 1; const NUM_EXP_BITS: i32 = Self::NUM_BITS - Self::NUM_SIG_BITS - 1; const EXP_MASK: i32 = (1 << Self::NUM_EXP_BITS) - 1; const EXP_BIAS: i32 = (1 << (Self::NUM_EXP_BITS - 1)) - 1; const EXP_OFFSET: i32 = Self::EXP_BIAS + Self::NUM_SIG_BITS; type SigType: traits::UInt; const IMPLICIT_BIT: Self::SigType; type DecDigitsType: Copy; #[cfg(any( all(target_arch = "aarch64", target_feature = "neon", not(miri)), all(target_arch = "x86_64", target_feature = "sse4.1", not(miri)), ))] type DecUnshuffledType; fn to_bits(self) -> Self::SigType; fn is_negative(bits: Self::SigType) -> bool { (bits >> (Self::NUM_BITS - 1)) != Self::SigType::from(0) } fn get_sig(bits: Self::SigType) -> Self::SigType { bits & (Self::IMPLICIT_BIT - Self::SigType::from(1)) } fn get_exp(bits: Self::SigType) -> i64 { (bits << 1u8 >> (Self::NUM_SIG_BITS + 1)).into() as i64 } // Converts a significand to a string, removing trailing zeros. value has up // to 17 decimal digits (16-17 for normals) for f64 and up to 9 digits (8-9 // for normals) for f32. fn to_digits(value: u64, d: &Data) -> DecDigits; unsafe fn write_exp_float_simd( buffer: *mut u8, dig: &DecDigits, last_digit: i32, has_last_digit: bool, has_extra_digit: bool, exp_data: u64, d: &Data, ) -> *mut u8; } impl FloatTraits for f32 { // Upstream uses -4..=6. const FIXED_DEC_EXP: RangeInclusive = -6..=12; const NUM_BITS: i32 = 32; const IMPLICIT_BIT: u32 = 1 << Self::NUM_SIG_BITS; type SigType = u32; type DecDigitsType = u64; #[cfg(all(target_arch = "aarch64", target_feature = "neon", not(miri)))] type DecUnshuffledType = uint8x16_t; #[cfg(all(target_arch = "x86_64", target_feature = "sse4.1", not(miri)))] type DecUnshuffledType = __m128i; #[inline] fn to_bits(self) -> Self::SigType { self.to_bits() } #[inline] fn to_digits(value: u64, d: &Data) -> DecDigits { to_digits_32(value, d) } #[inline] unsafe fn write_exp_float_simd( buffer: *mut u8, dig: &DecDigits, last_digit: i32, has_last_digit: bool, has_extra_digit: bool, exp_data: u64, d: &Data, ) -> *mut u8 { unsafe { write_exp_float_simd_32( buffer, dig, last_digit, has_last_digit, has_extra_digit, exp_data, d, ) } } } impl FloatTraits for f64 { // Upstream uses -4..=15. const FIXED_DEC_EXP: RangeInclusive = -5..=15; const NUM_BITS: i32 = 64; const IMPLICIT_BIT: u64 = 1 << Self::NUM_SIG_BITS; type SigType = u64; #[cfg(all(target_arch = "aarch64", target_feature = "neon", not(miri)))] type DecDigitsType = uint16x8_t; #[cfg(all(target_arch = "x86_64", target_feature = "sse2", not(miri)))] type DecDigitsType = __m128i; #[cfg(not(any( all(target_arch = "aarch64", target_feature = "neon", not(miri)), all(target_arch = "x86_64", target_feature = "sse2", not(miri)), )))] type DecDigitsType = [u64; 2]; #[cfg(any( all(target_arch = "aarch64", target_feature = "neon", not(miri)), all(target_arch = "x86_64", target_feature = "sse4.1", not(miri)), ))] type DecUnshuffledType = (); #[inline] fn to_bits(self) -> Self::SigType { self.to_bits() } #[inline] fn to_digits(value: u64, d: &Data) -> DecDigits { to_digits_64(value, d) } #[inline] unsafe fn write_exp_float_simd( _buffer: *mut u8, _dig: &DecDigits, _last_digit: i32, _has_last_digit: bool, _has_extra_digit: bool, _exp_data: u64, _d: &Data, ) -> *mut u8 { ptr::null_mut() } } #[rustfmt::skip] const POW10_MINOR: [u64; 28] = [ 0x8000000000000000, 0xa000000000000000, 0xc800000000000000, 0xfa00000000000000, 0x9c40000000000000, 0xc350000000000000, 0xf424000000000000, 0x9896800000000000, 0xbebc200000000000, 0xee6b280000000000, 0x9502f90000000000, 0xba43b74000000000, 0xe8d4a51000000000, 0x9184e72a00000000, 0xb5e620f480000000, 0xe35fa931a0000000, 0x8e1bc9bf04000000, 0xb1a2bc2ec5000000, 0xde0b6b3a76400000, 0x8ac7230489e80000, 0xad78ebc5ac620000, 0xd8d726b7177a8000, 0x878678326eac9000, 0xa968163f0a57b400, 0xd3c21bcecceda100, 0x84595161401484a0, 0xa56fa5b99019a5c8, 0xcecb8f27f4200f3a, ]; #[rustfmt::skip] const POW10_MAJOR: [uint128; 23] = [ uint128 { hi: 0xaf8e5410288e1b6f, lo: 0x07ecf0ae5ee44dda }, // -303 uint128 { hi: 0xb1442798f49ffb4a, lo: 0x99cd11cfdf41779d }, // -275 uint128 { hi: 0xb2fe3f0b8599ef07, lo: 0x861fa7e6dcb4aa15 }, // -247 uint128 { hi: 0xb4bca50b065abe63, lo: 0x0fed077a756b53aa }, // -219 uint128 { hi: 0xb67f6455292cbf08, lo: 0x1a3bc84c17b1d543 }, // -191 uint128 { hi: 0xb84687c269ef3bfb, lo: 0x3d5d514f40eea742 }, // -163 uint128 { hi: 0xba121a4650e4ddeb, lo: 0x92f34d62616ce413 }, // -135 uint128 { hi: 0xbbe226efb628afea, lo: 0x890489f70a55368c }, // -107 uint128 { hi: 0xbdb6b8e905cb600f, lo: 0x5400e987bbc1c921 }, // -79 uint128 { hi: 0xbf8fdb78849a5f96, lo: 0xde98520472bdd034 }, // -51 uint128 { hi: 0xc16d9a0095928a27, lo: 0x75b7053c0f178294 }, // -23 uint128 { hi: 0xc350000000000000, lo: 0x0000000000000000 }, // 5 uint128 { hi: 0xc5371912364ce305, lo: 0x6c28000000000000 }, // 33 uint128 { hi: 0xc722f0ef9d80aad6, lo: 0x424d3ad2b7b97ef6 }, // 61 uint128 { hi: 0xc913936dd571c84c, lo: 0x03bc3a19cd1e38ea }, // 89 uint128 { hi: 0xcb090c8001ab551c, lo: 0x5cadf5bfd3072cc6 }, // 117 uint128 { hi: 0xcd036837130890a1, lo: 0x36dba887c37a8c10 }, // 145 uint128 { hi: 0xcf02b2c21207ef2e, lo: 0x94f967e45e03f4bc }, // 173 uint128 { hi: 0xd106f86e69d785c7, lo: 0xe13336d701beba52 }, // 201 uint128 { hi: 0xd31045a8341ca07c, lo: 0x1ede48111209a051 }, // 229 uint128 { hi: 0xd51ea6fa85785631, lo: 0x552a74227f3ea566 }, // 257 uint128 { hi: 0xd732290fbacaf133, lo: 0xa97c177947ad4096 }, // 285 uint128 { hi: 0xd94ad8b1c7380874, lo: 0x18375281ae7822bc }, // 313 ]; #[rustfmt::skip] const POW10_FIXUPS: [u32; 20] = [ 0x0a4e363f, 0x00001840, 0x00006400, 0x24200040, 0x00000000, 0x0c000000, 0x82c81380, 0x5e4ce01f, 0xd730f60f, 0x0000001b, 0x00000000, 0xcdf7fffc, 0x6e8201d8, 0x40cd3fd1, 0xdb642501, 0x00000d0d, 0x14042400, 0x53713840, 0x11781db4, 0x00000000, ]; // 128-bit significands of powers of 10 rounded down. #[repr(C, align(64))] struct Pow10SignificandTable { data: [u64; if Self::COMPRESS { 0 } else { Self::NUM_POW10S * 2 }], } impl Pow10SignificandTable { const COMPRESS: bool = cfg!(opt_level = "s"); const SPLIT_TABLES: bool = !Self::COMPRESS && cfg!(target_arch = "aarch64"); const NUM_POW10S: usize = 618; // Computes the 128-bit significand of 10**i using method by Dougall Johnson. #[inline] const fn compute(i: u32) -> uint128 { const STRIDE: u32 = POW10_MINOR.len() as u32; let m = unsafe { *POW10_MINOR.as_ptr().add(((i + 10) % STRIDE) as usize) }; let h = unsafe { *POW10_MAJOR.as_ptr().add(((i + 10) / STRIDE) as usize) }; let h1 = umul128_hi64(h.lo, m); let c0 = h.lo.wrapping_mul(m); let c1 = h1.wrapping_add(h.hi.wrapping_mul(m)); let c2 = (c1 < h1) as u64 + umul128_hi64(h.hi, m); let mut result = if (c2 >> 63) != 0 { uint128 { hi: c2, lo: c1 } } else { uint128 { hi: (c2 << 1) | (c1 >> 63), lo: (c1 << 1) | (c0 >> 63), } }; result.lo -= ((unsafe { *POW10_FIXUPS.as_ptr().add((i >> 5) as usize) } >> (i & 31)) & 1) as u64; result } const fn new() -> Self { let mut data = [0; if Self::COMPRESS { 0 } else { Self::NUM_POW10S * 2 }]; let mut i = 0; while i < Self::NUM_POW10S && !Self::COMPRESS { let result = Self::compute(i as u32); if Self::SPLIT_TABLES { data[Self::NUM_POW10S - i - 1] = result.hi; data[Self::NUM_POW10S * 2 - i - 1] = result.lo; } else { data[i * 2] = result.hi; data[i * 2 + 1] = result.lo; } i += 1; } Pow10SignificandTable { data } } #[inline] unsafe fn get_unchecked(&self, dec_exp: i32) -> uint128 { const DEC_EXP_MIN: i32 = -293; let i = dec_exp - DEC_EXP_MIN; if Self::COMPRESS { return Self::compute(i as u32); } if !Self::SPLIT_TABLES { let p = unsafe { self.data.as_ptr().add((i * 2) as usize) }; return uint128 { hi: unsafe { *p }, lo: unsafe { *p.add(1) }, }; } unsafe { // The caller passes -e - 1 as dec_exp, so ~dec_exp recovers e. // Picking the base so that e itself is the index lets both loads // share sxtw addressing. #[cfg_attr( not(all(any(target_arch = "x86_64", target_arch = "aarch64"), not(miri))), allow(unused_mut) )] let mut p = self .data .as_ptr() .offset(Self::NUM_POW10S as isize + DEC_EXP_MIN as isize); #[cfg(all(any(target_arch = "x86_64", target_arch = "aarch64"), not(miri)))] asm!("/*{0}*/", inout(reg) p); uint128 { hi: *p.offset(!(dec_exp as isize)), lo: *p.offset(!(dec_exp as isize) + Self::NUM_POW10S as isize), } } } #[cfg(test)] fn get(&self, dec_exp: i32) -> uint128 { const DEC_EXP_MIN: i32 = -292; assert!((DEC_EXP_MIN..DEC_EXP_MIN + Self::NUM_POW10S as i32).contains(&dec_exp)); unsafe { self.get_unchecked(dec_exp) } } } // Computes a shift so that, after scaling by a power of 10, the intermediate // result always has a fixed 128-bit fractional part (for double). // // Different binary exponents can map to the same decimal exponent, but place // the decimal point at different bit positions. The shift compensates for this. // // For example, both 3 * 2**59 and 3 * 2**60 have dec_exp = 2, but dividing by // 10^dec_exp puts the decimal point in different bit positions: // 3 * 2**59 / 100 = 1.72...e+16 (needs shift = 1 + 1) // 3 * 2**60 / 100 = 3.45...e+16 (needs shift = 2 + 1) #[inline] const fn compute_exp_shift(bin_exp: i32, dec_exp: i32) -> u8 { debug_assert!(dec_exp >= -350 && dec_exp <= 350); // log2_pow10_sig = round(log2(10) * 2**log2_pow10_exp) + 1 const LOG2_POW10_SIG: i32 = 217_707; const LOG2_POW10_EXP: i32 = 16; // pow10_bin_exp = floor(log2(10**-dec_exp)) let pow10_bin_exp = (-dec_exp * LOG2_POW10_SIG) >> LOG2_POW10_EXP; // pow10 = ((pow10_hi << 64) | pow10_lo) * 2**(pow10_bin_exp - 127) (bin_exp + pow10_bin_exp + 1) as u8 } struct ExpShiftTable { data: [u8; if Self::ENABLE { f64::EXP_MASK as usize + 1 } else { 0 }], } impl ExpShiftTable { const ENABLE: bool = cfg!(not(opt_level = "s")); // extra_shift must be >= 3 to keep shift non-negative and <= 11 to fit the // significand into 64 bits after the shift. const EXTRA_SHIFT: usize = 6; const fn new() -> Self { let mut data = [0u8; if Self::ENABLE { f64::EXP_MASK as usize + 1 } else { 0 }]; let mut raw_exp = 0; while raw_exp < data.len() && Self::ENABLE { let mut bin_exp = raw_exp as i32 - f64::EXP_OFFSET; if raw_exp == 0 { bin_exp += 1; } let dec_exp = compute_dec_exp(bin_exp, true); data[raw_exp] = compute_exp_shift(bin_exp, dec_exp + 1).wrapping_add(Self::EXTRA_SHIFT as u8); raw_exp += 1; } ExpShiftTable { data } } } // An optional table of precomputed exponent strings for exponential notation. // Each entry packs "e+dd" or "e+ddd" into a u64 with the length in byte 7. struct ExpStringTable { data: [u64; if Self::ENABLE { (f64::MAX_10_EXP - Self::MIN_DEC_EXP + 1) as usize } else { 0 }], } impl ExpStringTable { const ENABLE: bool = cfg!(not(opt_level = "s")); const MIN_DEC_EXP: i32 = f64::MIN_10_EXP - f64::MAX_DIGITS10 as i32; const OFFSET: i32 = -Self::MIN_DEC_EXP; const fn new() -> Self { let mut data = [0u64; if Self::ENABLE { (f64::MAX_10_EXP - Self::MIN_DEC_EXP + 1) as usize } else { 0 }]; let mut e = Self::MIN_DEC_EXP; while e <= f64::MAX_10_EXP && Self::ENABLE { let abs_e = e.unsigned_abs() as u64; let mut val = abs_e % 10 + b'0' as u64; if abs_e >= 10 { val = (val << 8) | (abs_e / 10 % 10 + b'0' as u64); } if abs_e >= 100 { val = (val << 8) | (abs_e / 100 + b'0' as u64); } let len = 3 + (abs_e >= 10) as u64 + (abs_e >= 100) as u64; data[(e + Self::OFFSET) as usize] = (len << 48) | (val << 16) | (if e >= 0 { b'+' as u64 } else { b'-' as u64 } << 8) | b'e' as u64; e += 1; } ExpStringTable { data } } } // Shuffle vectors to build strings for exponential notation. // // Byte positions in the source register assembled by write_exp_float_simd: // bytes [0, exp_pos): BCD ASCII digits (reversed) // bytes [exp_pos, exp_pos + 4): exponent string "e±NN" // byte last_digit_pos: rounded last digit // byte point_pos: '.' // // The shuffle length (max 14) is stored in byte 15; the corresponding output // byte is past the string and ignored by the caller. #[repr(C, align(16))] struct ExpFloatShuffleTable { data: [u8; if Self::ENABLE { 32 * 16 } else { 0 }], } struct ExpFloatShuffleTableEntry { #[cfg_attr( not(any( all(target_arch = "x86_64", target_feature = "sse4.1", not(miri)), all(target_arch = "aarch64", target_feature = "neon", not(miri)), )), allow(dead_code) )] shuffle: *const u8, length: u8, } impl ExpFloatShuffleTable { const ENABLE: bool = cfg!(any( all(target_arch = "x86_64", target_feature = "sse4.1", not(miri)), all(target_arch = "aarch64", target_feature = "neon", not(miri)), )) && ExpStringTable::ENABLE; const EXP_POS: u8 = 8; const LAST_DIGIT_POS: u8 = 12; const POINT_POS: u8 = 13; unsafe fn get_entry( &self, num_digits: i32, has_last_digit: bool, has_extra_digit: bool, ) -> ExpFloatShuffleTableEntry { let idx = (num_digits - 1) * 4 + i32::from(has_last_digit) * 2 + i32::from(has_extra_digit); ExpFloatShuffleTableEntry { shuffle: unsafe { self.data.as_ptr().add(idx as usize * 16) }, length: *unsafe { self.data.get_unchecked(idx as usize * 16 + 15) }, } } const fn new() -> Self { let mut data = [0u8; if Self::ENABLE { 32 * 16 } else { 0 }]; let mut idx = 0; while idx < 32 && Self::ENABLE { let num_digits = (idx >> 2) + 1; let has_last_digit = ((idx >> 1) & 1) != 0; let has_extra_digit = (idx & 1) != 0; let out = idx * 16; let mut i = 0; while i < 16 { data[out + i] = 0x80; // shuffle high bit: output 0 i += 1; } let leading_digit_pos = if has_extra_digit { 7 } else { 6 }; let mut length = 0; if has_last_digit { // Always 8 BCD chars in the significand plus a last-digit char; // for !has_extra_digit the leading '0' of the 8-digit padded // BCD is shown. data[out + length] = leading_digit_pos; length += 1; data[out + length] = Self::POINT_POS; length += 1; let mut i = leading_digit_pos - 1; loop { data[out + length] = i; length += 1; if i == 0 { break; } i -= 1; } data[out + length] = Self::LAST_DIGIT_POS; length += 1; } else { length = num_digits + has_extra_digit as usize; // Drop the '.' for single-digit output: "5e+02", not "5.0e+02". if length == 2 { length = 1; } data[out] = leading_digit_pos; data[out + 1] = Self::POINT_POS; let mut i = 2; while i < length { data[out + i] = leading_digit_pos + 1 - i as u8; i += 1; } } let mut i = 0; while i < 4 { data[out + length] = Self::EXP_POS + i; length += 1; i += 1; } data[out + 15] = length as u8; idx += 1; } ExpFloatShuffleTable { data } } } #[cfg(any( not(any( all(target_arch = "aarch64", target_feature = "neon", not(miri)), all(target_arch = "x86_64", target_feature = "sse4.1", not(miri)), )), all(test, target_endian = "little"), ))] #[cfg_attr(feature = "no-panic", no_panic)] fn count_trailing_nonzeros(x: u64) -> usize { // We count the number of bytes until there are only zeros left. // The code is equivalent to // 8 - x.leading_zeros() / 8 // but if the BSR instruction is emitted (as gcc on x64 does with default // settings), subtracting the constant before dividing allows the compiler // to combine it with the subtraction which it inserts due to BSR counting // in the opposite direction. // // Additionally, the BSR instruction requires a zero check. Since the high // bit is unused we can avoid the zero check by shifting the datum left by // one and inserting a sentinel bit at the end. This can be faster than the // automatically inserted range check. (70 - ((x.to_le() << 1) | 1).leading_zeros() as usize) / 8 } // Align data since unaligned access may be slower when crossing a // hardware-specific boundary. #[repr(C, align(2))] struct Digits2([u8; 200]); static DIGITS2: Digits2 = Digits2( *b"0001020304050607080910111213141516171819\ 2021222324252627282930313233343536373839\ 4041424344454647484950515253545556575859\ 6061626364656667686970717273747576777879\ 8081828384858687888990919293949596979899", ); // Converts value in the range [0, 100) to a string. GCC generates a bit better // code when value is pointer-size (https://www.godbolt.org/z/5fEPMT1cc). #[cfg_attr(feature = "no-panic", no_panic)] unsafe fn digits2(value: usize) -> &'static u16 { debug_assert!(value < 100); #[allow(clippy::cast_ptr_alignment)] unsafe { &*DIGITS2.0.as_ptr().cast::().add(value) } } const DIV10K_EXP: i32 = 40; const DIV10K_SIG: u32 = ((1u64 << DIV10K_EXP) / 10000 + 1) as u32; const NEG10K: u32 = ((1u64 << 32) - 10000) as u32; const DIV100_EXP: i32 = 19; const DIV100_SIG: u32 = (1 << DIV100_EXP) / 100 + 1; #[cfg(not(all( target_arch = "x86_64", target_feature = "sse2", not(target_feature = "sse4.1"), not(miri) )))] const NEG100: u32 = (1 << 16) - 100; #[cfg(not(any( all(target_arch = "x86_64", target_feature = "sse2", not(miri)), all(target_arch = "aarch64", target_feature = "neon", not(miri)), )))] const DIV10_EXP: i32 = 10; #[cfg(not(any( all(target_arch = "x86_64", target_feature = "sse2", not(miri)), all(target_arch = "aarch64", target_feature = "neon", not(miri)), )))] const DIV10_SIG: u32 = (1 << DIV10_EXP) / 10 + 1; #[cfg(not(all(target_arch = "x86_64", target_feature = "sse2", not(miri))))] const NEG10: u32 = (1 << 8) - 10; const ZEROS: u64 = 0x0101010101010101 * b'0' as u64; #[repr(C, align(64))] struct Data { threshold: AArch64Mem<1_000_000_000_000_000>, // +6 is needed for boundary cases found by verify.py. biased_half: AArch64Mem<{ (1 << 63) + 6 }>, #[cfg(all(target_arch = "aarch64", target_feature = "neon", not(miri)))] mul_const: u64, #[cfg(all(target_arch = "aarch64", target_feature = "neon", not(miri)))] hundred_million: u64, #[cfg(all(target_arch = "aarch64", target_feature = "neon", not(miri)))] multipliers32: int32x4_t, #[cfg(all(target_arch = "aarch64", target_feature = "neon", not(miri)))] multipliers16: int16x8_t, // Ordered so that the values used to format floats fit in a single cache // line. #[cfg(all(target_arch = "x86_64", target_feature = "sse2", not(miri)))] div100: u128, #[cfg(all(target_arch = "x86_64", target_feature = "sse2", not(miri)))] div10: u128, #[cfg(all(target_arch = "x86_64", target_feature = "sse4.1", not(miri)))] neg100: u128, #[cfg(all(target_arch = "x86_64", target_feature = "sse4.1", not(miri)))] neg10: u128, #[cfg(all(target_arch = "x86_64", target_feature = "sse4.1", not(miri)))] bswap: u128, #[cfg(all( target_arch = "x86_64", target_feature = "sse2", not(target_feature = "sse4.1"), not(miri) ))] hundred: u128, #[cfg(all( target_arch = "x86_64", target_feature = "sse2", not(target_feature = "sse4.1"), not(miri) ))] moddiv10: u128, #[cfg(all(target_arch = "x86_64", target_feature = "sse2", not(miri)))] div10k: u128, #[cfg(all(target_arch = "x86_64", target_feature = "sse2", not(miri)))] neg10k: u128, #[cfg(all(target_arch = "x86_64", target_feature = "sse2", not(miri)))] zeros: u128, exp_shifts: ExpShiftTable, exp_strings: ExpStringTable, pow10_significands: Pow10SignificandTable, exp_float_shuffles: ExpFloatShuffleTable, } impl Data { #[cfg(all(target_arch = "x86_64", target_feature = "sse2", not(miri)))] const fn splat64(x: u64) -> u128 { ((x as u128) << 64) | x as u128 } #[cfg(all(target_arch = "x86_64", target_feature = "sse2", not(miri)))] const fn splat32(x: u32) -> u128 { Self::splat64(((x as u64) << 32) | x as u64) } #[cfg(all(target_arch = "x86_64", target_feature = "sse2", not(miri)))] const fn splat16(x: u16) -> u128 { Self::splat32(((x as u32) << 16) | x as u32) } #[cfg(all(target_arch = "x86_64", target_feature = "sse4.1", not(miri)))] const fn pack8(a: u8, b: u8, c: u8, d: u8, e: u8, f: u8, g: u8, h: u8) -> u64 { ((h as u64) << 56) | ((g as u64) << 48) | ((f as u64) << 40) | ((e as u64) << 32) | ((d as u64) << 24) | ((c as u64) << 16) | ((b as u64) << 8) | a as u64 } #[cfg(all(target_arch = "aarch64", target_feature = "neon", not(miri)))] const NEG10K: i32 = 0x10000 - 10000; } static STATIC_DATA: Data = Data { threshold: AArch64Mem::new(), biased_half: AArch64Mem::new(), #[cfg(all(target_arch = "aarch64", target_feature = "neon", not(miri)))] mul_const: 0xabcc77118461cefd, #[cfg(all(target_arch = "aarch64", target_feature = "neon", not(miri)))] hundred_million: 100000000, #[cfg(all(target_arch = "aarch64", target_feature = "neon", not(miri)))] multipliers32: unsafe { mem::transmute::<[i32; 4], int32x4_t>([ DIV10K_SIG as i32, Data::NEG10K, (DIV100_SIG << 12) as i32, NEG100 as i32, ]) }, #[cfg(all(target_arch = "aarch64", target_feature = "neon", not(miri)))] multipliers16: unsafe { mem::transmute::<[i16; 8], int16x8_t>([0xce0, NEG10 as i16, 0, 0, 0, 0, 0, 0]) }, #[cfg(all(target_arch = "x86_64", target_feature = "sse2", not(miri)))] div100: Data::splat32(DIV100_SIG), #[cfg(all(target_arch = "x86_64", target_feature = "sse2", not(miri)))] div10: Data::splat16(((1u32 << 16) / 10 + 1) as u16), #[cfg(all(target_arch = "x86_64", target_feature = "sse4.1", not(miri)))] neg100: Data::splat32(NEG100), #[cfg(all(target_arch = "x86_64", target_feature = "sse4.1", not(miri)))] neg10: Data::splat16((1 << 8) - 10), #[cfg(all(target_arch = "x86_64", target_feature = "sse4.1", not(miri)))] bswap: Data::pack8(15, 14, 13, 12, 11, 10, 9, 8) as u128 | (Data::pack8(7, 6, 5, 4, 3, 2, 1, 0) as u128) << 64, #[cfg(all( target_arch = "x86_64", target_feature = "sse2", not(target_feature = "sse4.1"), not(miri) ))] hundred: Data::splat32(100), #[cfg(all( target_arch = "x86_64", target_feature = "sse2", not(target_feature = "sse4.1"), not(miri) ))] moddiv10: Data::splat16(10 * (1 << 8) - 1), #[cfg(all(target_arch = "x86_64", target_feature = "sse2", not(miri)))] div10k: Data::splat64(DIV10K_SIG as u64), #[cfg(all(target_arch = "x86_64", target_feature = "sse2", not(miri)))] neg10k: Data::splat64(NEG10K as u64), #[cfg(all(target_arch = "x86_64", target_feature = "sse2", not(miri)))] zeros: Data::splat64(ZEROS), exp_shifts: ExpShiftTable::new(), exp_strings: ExpStringTable::new(), pow10_significands: Pow10SignificandTable::new(), exp_float_shuffles: ExpFloatShuffleTable::new(), }; // Converts four numbers < 10000, one in each 32-bit lane, to BCD digits. #[cfg(all(target_arch = "aarch64", target_feature = "neon", not(miri)))] #[cfg_attr(feature = "no-panic", no_panic)] fn to_bcd_4x4(mut efgh_abcd_mnop_ijkl: int32x4_t, d: &Data) -> uint8x16_t { unsafe { // Compiler barrier, or clang breaks the subsequent MLA into UADDW + // MUL. asm!("/*{:v}*/", inout(vreg) efgh_abcd_mnop_ijkl); let ef_ab_mn_ij: int32x4_t = vqdmulhq_n_s32( efgh_abcd_mnop_ijkl, mem::transmute::(d.multipliers32)[2], ); let gh_ef_cd_ab_op_mn_kl_ij: int16x8_t = vreinterpretq_s16_s32(vmlaq_n_s32( efgh_abcd_mnop_ijkl, ef_ab_mn_ij, mem::transmute::(d.multipliers32)[3], )); let high_10s: int16x8_t = vqdmulhq_n_s16( gh_ef_cd_ab_op_mn_kl_ij, mem::transmute::(d.multipliers16)[0], ); vreinterpretq_u8_s16(vmlaq_n_s16( gh_ef_cd_ab_op_mn_kl_ij, high_10s, mem::transmute::(d.multipliers16)[1], )) } } // An optimized version for NEON by Dougall Johnson. #[cfg(all(target_arch = "aarch64", target_feature = "neon", not(miri)))] #[cfg_attr(feature = "no-panic", no_panic)] #[inline] fn to_unshuffled_digits(value: u64, d: &Data) -> uint8x16_t { let mut hundred_million = d.hundred_million; // Compiler barrier, or clang narrows the load to 32-bit and unpairs it. unsafe { asm!("/*{0}*/", inout(reg) hundred_million); } // abcdefgh = value / 100000000, ijklmnop = value % 100000000. let abcdefgh = (umul128(value, d.mul_const) >> 90) as u64; let ijklmnop = value - abcdefgh * hundred_million; unsafe { let ijklmnop_abcdefgh_64: uint64x1_t = mem::transmute::((ijklmnop << 32) | abcdefgh); let abcdefgh_ijklmnop: int32x2_t = vreinterpret_s32_u64(ijklmnop_abcdefgh_64); let abcd_ijkl: int32x2_t = vreinterpret_s32_u32(vshr_n_u32( vreinterpret_u32_s32(vqdmulh_n_s32( abcdefgh_ijklmnop, mem::transmute::(d.multipliers32)[0], )), 9, )); let efgh_abcd_mnop_ijkl_32: int32x2_t = vmla_n_s32( abcdefgh_ijklmnop, abcd_ijkl, mem::transmute::(d.multipliers32)[1], ); let efgh_abcd_mnop_ijkl: int32x4_t = vreinterpretq_s32_u32(vshll_n_u16(vreinterpret_u16_s32(efgh_abcd_mnop_ijkl_32), 0)); to_bcd_4x4(efgh_abcd_mnop_ijkl, d) } } // Converts four numbers < 10000, one in each 32-bit lane, to BCD digits. // Digits in each 32-bit lane will be in order for SSE2, reversed for SSE4.1. #[cfg(all(target_arch = "x86_64", target_feature = "sse2", not(miri)))] #[cfg_attr(feature = "no-panic", no_panic)] fn to_bcd_4x4(y: __m128i, d: &Data) -> __m128i { unsafe { let div100 = _mm_load_si128(ptr::addr_of!(d.div100).cast::<__m128i>()); let div10 = _mm_load_si128(ptr::addr_of!(d.div10).cast::<__m128i>()); #[cfg(target_feature = "sse4.1")] { let neg100 = _mm_load_si128(ptr::addr_of!(d.neg100).cast::<__m128i>()); let neg10 = _mm_load_si128(ptr::addr_of!(d.neg10).cast::<__m128i>()); // _mm_mullo_epi32 is SSE 4.1 let z: __m128i = _mm_add_epi64( y, _mm_mullo_epi32(neg100, _mm_srli_epi32(_mm_mulhi_epu16(y, div100), 3)), ); _mm_add_epi64(z, _mm_mullo_epi16(neg10, _mm_mulhi_epu16(z, div10))) } #[cfg(not(target_feature = "sse4.1"))] { let hundred = _mm_load_si128(ptr::addr_of!(d.hundred).cast::<__m128i>()); let moddiv10 = _mm_load_si128(ptr::addr_of!(d.moddiv10).cast::<__m128i>()); let y_div_100: __m128i = _mm_srli_epi16(_mm_mulhi_epu16(y, div100), 3); let y_mod_100: __m128i = _mm_sub_epi16(y, _mm_mullo_epi16(y_div_100, hundred)); let z: __m128i = _mm_or_si128(_mm_slli_epi32(y_mod_100, 16), y_div_100); _mm_sub_epi16( _mm_slli_epi16(z, 8), _mm_mullo_epi16(moddiv10, _mm_mulhi_epu16(z, div10)), ) } } } #[cfg(not(any( all(target_arch = "x86_64", target_feature = "sse4.1", not(miri)), all(target_arch = "aarch64", target_feature = "neon", not(miri)), )))] struct BcdResult { bcd: u64, len: usize, } #[cfg(not(any( all(target_arch = "x86_64", target_feature = "sse4.1", not(miri)), all(target_arch = "aarch64", target_feature = "neon", not(miri)), )))] #[cfg_attr(feature = "no-panic", no_panic)] fn to_bcd8(abcdefgh: u64) -> BcdResult { #[cfg(not(all(target_arch = "x86_64", target_feature = "sse2", not(miri))))] let bcd = { // An optimization from Xiang JunBo. // Three steps BCD. Base 10000 -> base 100 -> base 10. // div and mod are evaluated simultaneously as, e.g. // (abcdefgh / 10000) << 32 + (abcdefgh % 10000) // == abcdefgh + (2**32 - 10000) * (abcdefgh / 10000))) // where the division on the RHS is implemented by the usual multiply + shift // trick and the fractional bits are masked away. let abcd_efgh = abcdefgh + u64::from(NEG10K) * ((abcdefgh * u64::from(DIV10K_SIG)) >> DIV10K_EXP); let ab_cd_ef_gh = abcd_efgh + u64::from(NEG100) * (((abcd_efgh * u64::from(DIV100_SIG)) >> DIV100_EXP) & 0x7f0000007f); let a_b_c_d_e_f_g_h = ab_cd_ef_gh + u64::from(NEG10) * (((ab_cd_ef_gh * u64::from(DIV10_SIG)) >> DIV10_EXP) & 0xf000f000f000f); a_b_c_d_e_f_g_h.to_be() }; #[cfg(all(target_arch = "x86_64", target_feature = "sse2", not(miri)))] let bcd = { // Load constants from memory. let mut d = ptr::addr_of!(STATIC_DATA); let d = unsafe { asm!("/*{0}*/", inout(reg) d); &*d }; // Evaluate the 4-digit limbs and arrange them such that we get a // result which is in the correct order. let abcd_efgh = (abcdefgh << 32) - ((10000u64 << 32) - 1) * ((abcdefgh * u64::from(DIV10K_SIG)) >> DIV10K_EXP); let v: __m128i = to_bcd_4x4(_mm_set_epi64x(0, abcd_efgh as i64), d); (unsafe { _mm_cvtsi128_si64(v) }) as u64 }; BcdResult { bcd, len: count_trailing_nonzeros(bcd), } } struct DecDigits { digits: Float::DecDigitsType, // `unshuffled` is the byte-reversed BCD vector used by write_exp_float_simd. #[cfg(any( all(target_arch = "aarch64", target_feature = "neon", not(miri)), all(target_arch = "x86_64", target_feature = "sse4.1", not(miri)), ))] unshuffled: Float::DecUnshuffledType, num_digits: usize, } #[cfg_attr(feature = "no-panic", no_panic)] #[inline] fn to_digits_64(value: u64, #[allow(unused_variables)] d: &Data) -> DecDigits { #[cfg(not(any( all(target_arch = "aarch64", target_feature = "neon", not(miri)), all(target_arch = "x86_64", target_feature = "sse2", not(miri)), )))] { let hi = (value / 100_000_000) as u32; let lo = (value % 100_000_000) as u32; let hi_bcd = to_bcd8(hi as u64); if lo == 0 { return DecDigits { digits: [hi_bcd.bcd + ZEROS, ZEROS], num_digits: hi_bcd.len, }; } let lo_bcd = to_bcd8(lo as u64); DecDigits { digits: [hi_bcd.bcd + ZEROS, lo_bcd.bcd + ZEROS], num_digits: 8 + lo_bcd.len, } } #[cfg(all(target_arch = "aarch64", target_feature = "neon", not(miri)))] { unsafe { let unshuffled_digits = to_unshuffled_digits(value, d); let digits: uint8x16_t = vrev64q_u8(unshuffled_digits); let str: uint16x8_t = vaddq_u16( vreinterpretq_u16_u8(digits), vreinterpretq_u16_s8(vdupq_n_s8(b'0' as i8)), ); let is_not_zero: uint16x8_t = vreinterpretq_u16_u8(vcgtzq_s8(vreinterpretq_s8_u8(digits))); let nonzero_mask: u64 = vget_lane_u64(vreinterpret_u64_u8(vshrn_n_u16(is_not_zero, 4)), 0); DecDigits { digits: str, unshuffled: (), num_digits: 16 - (nonzero_mask.leading_zeros() as usize >> 2), } } } #[cfg(all(target_arch = "x86_64", target_feature = "sse2", not(miri)))] { let hi = (value / 100_000_000) as u32; let lo = (value % 100_000_000) as u32; unsafe { let div10k = _mm_load_si128(ptr::addr_of!(d.div10k).cast::<__m128i>()); let neg10k = _mm_load_si128(ptr::addr_of!(d.neg10k).cast::<__m128i>()); let x: __m128i = _mm_set_epi64x(i64::from(hi), i64::from(lo)); #[cfg_attr(target_feature = "sse4.1", allow(unused_mut))] let mut y: __m128i = _mm_add_epi64( x, _mm_mul_epu32(neg10k, _mm_srli_epi64(_mm_mul_epu32(x, div10k), DIV10K_EXP)), ); // Shuffle to ensure correctly ordered result from SSE2 path. #[cfg(not(target_feature = "sse4.1"))] { y = _mm_shuffle_epi32(y, _MM_SHUFFLE(0, 1, 2, 3)); } #[cfg_attr(not(target_feature = "sse4.1"), allow(unused_mut))] let mut bcd: __m128i = to_bcd_4x4(y, d); let zeros = _mm_load_si128(ptr::addr_of!(d.zeros).cast::<__m128i>()); // Computed against current bcd (rather than the post-bswap bcd) so // the mask is derived in parallel with the shuffle on the SSE4.1 // path. let mask = _mm_movemask_epi8(_mm_cmpgt_epi8(bcd, _mm_setzero_si128())) as u64; // Trailing zeros are in the low bits for SSE4.1, the high bits for // SSE2. let len = if cfg!(target_feature = "sse4.1") { 16 - mask.trailing_zeros() } else { 64 - mask.leading_zeros() }; #[cfg(target_feature = "sse4.1")] { bcd = _mm_shuffle_epi8( bcd, _mm_load_si128(ptr::addr_of!(d.bswap).cast::<__m128i>()), ); // SSSE3 } DecDigits { digits: _mm_or_si128(bcd, zeros), #[cfg(target_feature = "sse4.1")] unshuffled: (), num_digits: len as usize, } } } } #[cfg_attr(feature = "no-panic", no_panic)] #[inline] fn to_digits_32(value: u64, #[allow(unused_variables)] d: &Data) -> DecDigits { #[cfg(all(target_arch = "x86_64", target_feature = "sse4.1", not(miri)))] { // Inline to_bcd8's SSE4.1 body so we can return the unshuffled xmm too; // the exponential-notation path uses it to skip the bswap-via-gpr. let abcd_efgh = value + u64::from(NEG10K) * ((value * u64::from(DIV10K_SIG)) >> DIV10K_EXP); let bcd_xmm = to_bcd_4x4(_mm_set_epi64x(0, abcd_efgh as i64), d); let unshuffled_bcd = unsafe { _mm_cvtsi128_si64(bcd_xmm) } as u64; let len = if unshuffled_bcd != 0 { 8 - unshuffled_bcd.trailing_zeros() / 8 } else { 0 }; DecDigits { digits: unshuffled_bcd.swap_bytes() + ZEROS, unshuffled: bcd_xmm, num_digits: len as usize, } } #[cfg(all(target_arch = "aarch64", target_feature = "neon", not(miri)))] { // Inline to_bcd8's NEON body so we can return the unshuffled vector // too; the exponential-notation path uses it to skip the // simd->gpr->bswap->simd roundtrip needed to materialize `digits`. let abcd_efgh = value + u64::from(NEG10K) * ((value * u64::from(DIV10K_SIG)) >> DIV10K_EXP); let unshuffled: uint8x16_t = unsafe { let input: int32x4_t = vcombine_s32(vreinterpret_s32_u64(vcreate_u64(abcd_efgh)), vdup_n_s32(0)); to_bcd_4x4(input, d) }; let unshuffled_bcd = unsafe { vget_lane_u64(vreinterpret_u64_u8(vget_low_u8(unshuffled)), 0) }; let len = if unshuffled_bcd != 0 { 8 - unshuffled_bcd.trailing_zeros() / 8 } else { 0 }; DecDigits { digits: unshuffled_bcd.swap_bytes() + ZEROS, unshuffled, num_digits: len as usize, } } #[cfg(not(any( all(target_arch = "x86_64", target_feature = "sse4.1", not(miri)), all(target_arch = "aarch64", target_feature = "neon", not(miri)), )))] { let result = to_bcd8(value); DecDigits { digits: result.bcd + ZEROS, num_digits: result.len, } } } #[cfg_attr(feature = "no-panic", no_panic)] unsafe fn write_exp_float_simd_32( buffer: *mut u8, dig: &DecDigits, last_digit: i32, has_last_digit: bool, has_extra_digit: bool, exp_data: u64, d: &Data, ) -> *mut u8 { // Packed for insertion into lane 1: byte 0 of `tail` lands at register byte // exp_pos (8), so the exp string fills exp_pos..exp_pos+3; the prefix // shifts place '0'+last_digit at last_digit_pos (12) and '.' at point_pos // (13). let prefix = (u32::from(b'.') << 8) + u32::from(b'0') + last_digit as u32; #[cfg_attr( not(any( all(target_arch = "x86_64", target_feature = "sse4.1", not(miri)), all(target_arch = "aarch64", target_feature = "neon", not(miri)), )), allow(unused_variables) )] let tail = exp_data | (u64::from(prefix) << 32); let entry = unsafe { d.exp_float_shuffles .get_entry(dig.num_digits as i32, has_last_digit, has_extra_digit) }; #[cfg(all(target_arch = "x86_64", target_feature = "sse4.1", not(miri)))] unsafe { let ascii: __m128i = _mm_or_si128( dig.unshuffled, _mm_load_si128(ptr::addr_of!(d.zeros).cast::<__m128i>()), ); let src: __m128i = _mm_insert_epi64(ascii, tail as i64, 1); let shuffle: __m128i = _mm_load_si128(entry.shuffle.cast::<__m128i>()); let out: __m128i = _mm_shuffle_epi8(src, shuffle); _mm_storeu_si128(buffer.cast::<__m128i>(), out); } #[cfg(all(target_arch = "aarch64", target_feature = "neon", not(miri)))] unsafe { let ascii: uint8x16_t = vorrq_u8(dig.unshuffled, vdupq_n_u8(b'0')); let src: uint8x16_t = vreinterpretq_u8_u64(vsetq_lane_u64(tail, vreinterpretq_u64_u8(ascii), 1)); let shuffle: uint8x16_t = vld1q_u8(entry.shuffle); let out: uint8x16_t = vqtbl1q_u8(src, shuffle); vst1q_u8(buffer, out); } let length = entry.length as usize - usize::from((exp_data & 0xff000000) == 0); unsafe { buffer.add(length) } } struct ToDecimalResult { sig: i64, exp: i32, last_digit: u8, has_last_digit: bool, } // Here be 🐉s. // Converts a binary FP number bin_sig * 2**bin_exp to the shortest decimal // representation, where bin_exp = raw_exp - exp_offset. #[cfg_attr(feature = "no-panic", no_panic)] #[inline] fn to_decimal(bin_sig: UInt, raw_exp: i64, regular: bool, d: &Data) -> ToDecimalResult where Float: FloatTraits, UInt: traits::UInt, { let bin_exp = raw_exp - i64::from(Float::EXP_OFFSET); let num_bits = mem::size_of::() as i32 * 8; const EXTRA_SHIFT: usize = ExpShiftTable::EXTRA_SHIFT; if !regular { let dec_exp = compute_dec_exp(bin_exp as i32, false); let shift = compute_exp_shift(bin_exp as i32, dec_exp + 1).wrapping_add(EXTRA_SHIFT as u8); let pow10 = unsafe { d.pow10_significands.get_unchecked(-dec_exp - 1) }; let p = umul192_hi128(pow10.hi, pow10.lo, (bin_sig << shift).into()); let mut integral = p.hi >> EXTRA_SHIFT; let fractional = (p.hi << (64 - EXTRA_SHIFT)) | (p.lo >> EXTRA_SHIFT); let half_ulp = pow10.hi >> (EXTRA_SHIFT + 1 - shift as usize); let round_up = half_ulp > u64::MAX - fractional; let round_down = (half_ulp >> 1) > fractional; integral += u64::from(round_up); let mut digit = umul128_add_hi64(fractional, 10, (1 << 63) - 1) as i32; let lo = umul128_add_hi64(fractional.wrapping_sub(half_ulp >> 1), 10, !0) as i32; if digit < lo { digit = lo; } return ToDecimalResult { sig: integral as i64, exp: dec_exp, last_digit: digit as u8, has_last_digit: !(round_up || round_down), }; } const LOG10_2_SIG: u64 = 78_913; const LOG10_2_EXP: i32 = 18; #[allow(unused_mut)] let mut dec_exp = if USE_UMUL128_HI64 { umul128_hi64(bin_exp as u64, LOG10_2_SIG << (64 - LOG10_2_EXP)) as i32 } else { compute_dec_exp(bin_exp as i32, true) }; #[cfg(not(miri))] #[allow(unused_unsafe)] unsafe { // Force 32-bit reg for sxtw addressing. #[cfg(target_arch = "x86_64")] asm!("/*{0:e}*/", inout(reg) dec_exp); #[cfg(target_arch = "aarch64")] asm!("/*{0:w}*/", inout(reg) dec_exp); } let mut shift = if ExpShiftTable::ENABLE { *unsafe { d.exp_shifts .data .get_unchecked((bin_exp + i64::from(f64::EXP_OFFSET)) as usize) } } else { compute_exp_shift(bin_exp as i32, dec_exp + 1).wrapping_add(EXTRA_SHIFT as u8) }; let even = UInt::from(1) - (bin_sig & UInt::from(1)); if num_bits == 32 { const EXTRA_SHIFT: usize = 34; shift += (EXTRA_SHIFT - ExpShiftTable::EXTRA_SHIFT) as u8; let pow10_hi = unsafe { d.pow10_significands.get_unchecked(-dec_exp - 1) }.hi; let p = umul128_hi64(pow10_hi + 1, bin_sig.into() << shift); let mut integral = p >> EXTRA_SHIFT; let fractional = p & ((1u64 << EXTRA_SHIFT) - 1); let half_ulp = (pow10_hi >> (65 - shift as usize)) + even.into(); let round_up = ((fractional + half_ulp) >> EXTRA_SHIFT) != 0; let round_down = half_ulp > fractional; integral += u64::from(round_up); let mut digit = ((fractional * 10 + (1u64 << (EXTRA_SHIFT - 1))) >> EXTRA_SHIFT) as i32; if fractional == (1u64 << (EXTRA_SHIFT - 2)) { digit = 2; // Round 2.5 to 2. } return ToDecimalResult { sig: integral as i64, exp: dec_exp, last_digit: digit as u8, has_last_digit: !(round_up || round_down), }; } // An optimization by Xiang JunBo: // Scale by 10**(-dec_exp-1) to directly produce the shorter candidate // (15-16 digits), deriving the extra digit from the fractional part. // This eliminates div10 from the critical path. // // value = 5.0507837461e-27 // next = 5.0507837461000010e-27 // // c = integral.fractional' = 5050783746100000.3153987... (value) // 5050783746100001.0328635... (next) // half_ulp = 0.3587324... // // fractional = fractional' * 2**64 = 5818079786399166407 // // 5050783746100000.0 c upper 5050783746100001.0 // s l| L | S // ──┬────┬────┼────┬────┬────┼*───┼────┬────┬───*┬────┬────┬────┼─*──┬─── // .8 .9 .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 .0 | .1 // └─────────────────┼─────────────────┘ next // 1ulp // // s - shorter underestimate, S - shorter overestimate // l - longer underestimate, L - longer overestimate let pow10 = unsafe { d.pow10_significands.get_unchecked(-dec_exp - 1) }; let p = umul192_hi128(pow10.hi, pow10.lo, (bin_sig << shift).into()); let mut integral = p.hi >> EXTRA_SHIFT; let fractional = (p.hi << (64 - EXTRA_SHIFT)) | (p.lo >> EXTRA_SHIFT); let half_ulp = (pow10.hi >> (EXTRA_SHIFT + 1 - shift as usize)) + even.into(); let round_up = fractional.wrapping_add(half_ulp) < fractional; let round_down = half_ulp > fractional; integral += u64::from(round_up); // Compute integral before digit. // Derive the extra digit from the fractional part (parallel with rounding). let mut digit = umul128_add_hi64(fractional, 10, d.biased_half.get()) as i32; if fractional == (1u64 << 62) { digit = 2; // Round 2.5 to 2. } ToDecimalResult { sig: integral as i64, exp: dec_exp, last_digit: digit as u8, has_last_digit: !(round_up || round_down), } } /// Writes the shortest correctly rounded decimal representation of `value` to /// `buffer`. `buffer` should point to a buffer of size `buffer_size` or larger. #[cfg_attr(feature = "no-panic", no_panic)] unsafe fn write(value: Float, mut buffer: *mut u8) -> *mut u8 where Float: FloatTraits, { let bits = value.to_bits(); // It is beneficial to extract exponent and significand early. let bin_exp = Float::get_exp(bits); // binary exponent let bin_sig = Float::get_sig(bits); // binary significand unsafe { *buffer = b'-'; } buffer = unsafe { buffer.add(usize::from(Float::is_negative(bits))) }; #[allow(unused_mut)] let mut d = ptr::addr_of!(STATIC_DATA); let d = unsafe { // Load constants from memory. #[cfg(all(any(target_arch = "aarch64", target_arch = "x86_64"), not(miri)))] asm!("/*{0}*/", inout(reg) d); &*d }; let threshold = if Float::NUM_BITS == 64 { d.threshold.get() } else { 10_000_000 }; let mut dec; if bin_exp == 0 { if bin_sig == Float::SigType::from(0) { return unsafe { *buffer = b'0'; *buffer.add(1) = b'.'; *buffer.add(2) = b'0'; buffer.add(3) }; } dec = to_decimal::(bin_sig, 1, true, d); let mut dec_sig = dec.sig * 10 + (-i64::from(dec.has_last_digit) & i64::from(dec.last_digit)); let mut dec_exp = dec.exp; while dec_sig < threshold as i64 { dec_sig *= 10; dec_exp -= 1; } let d = div10(dec_sig as u64); let last_digit = dec_sig - d as i64 * 10; dec = ToDecimalResult { sig: d as i64, exp: dec_exp, last_digit: last_digit as u8, has_last_digit: last_digit != 0, }; } else { dec = to_decimal::( bin_sig | Float::IMPLICIT_BIT, bin_exp, bin_sig != Float::SigType::from(0), d, ); } let mut has_last_digit = dec.has_last_digit; let has_extra_digit = dec.sig >= threshold as i64; let mut dec_exp = dec.exp + Float::MAX_DIGITS10 as i32 - 2 + i32::from(has_extra_digit); if Float::NUM_BITS == 32 && dec.sig < 1_000_000 { dec.sig = 10 * dec.sig + (-i64::from(has_last_digit) & i64::from(dec.last_digit)); has_last_digit = false; dec_exp -= 1; } // Write significand. let dig = Float::to_digits(dec.sig as u64, d); if Float::NUM_BITS == 32 && ExpFloatShuffleTable::ENABLE && !Float::FIXED_DEC_EXP.contains(&dec_exp) { unsafe { let exp_data = *d .exp_strings .data .get_unchecked((dec_exp + ExpStringTable::OFFSET) as usize); return Float::write_exp_float_simd( buffer, &dig, i32::from(dec.last_digit), has_last_digit, has_extra_digit, exp_data, d, ); } } let bcd_size = if Float::NUM_BITS == 64 { 16 } else { 8 }; unsafe { buffer .add(usize::from(has_extra_digit)) .cast::() .write_unaligned(dig.digits); buffer .add(usize::from(has_extra_digit) + bcd_size) .write(b'0' + dec.last_digit); } let length = usize::from(has_extra_digit) + if has_last_digit { bcd_size + 1 } else { dig.num_digits } - 1; if Float::FIXED_DEC_EXP.contains(&dec_exp) { if length as i32 - 1 <= dec_exp { // 1234e7 -> 12340000000.0 return unsafe { ptr::copy(buffer.add(1), buffer, length); ptr::write_bytes(buffer.add(length), b'0', dec_exp as usize + 3 - length); *buffer.add(dec_exp as usize + 1) = b'.'; buffer.add(dec_exp as usize + 3) }; } else if 0 <= dec_exp { // 1234e-2 -> 12.34 return unsafe { ptr::copy(buffer.add(1), buffer, dec_exp as usize + 1); *buffer.add(dec_exp as usize + 1) = b'.'; buffer.add(length + 1) }; } else { // 1234e-6 -> 0.001234 return unsafe { ptr::copy(buffer.add(1), buffer.add((1 - dec_exp) as usize), length); ptr::write_bytes(buffer, b'0', (1 - dec_exp) as usize); *buffer.add(1) = b'.'; buffer.add((1 - dec_exp) as usize + length) }; } } unsafe { // 1234e30 -> 1.234e33 *buffer = *buffer.add(1); *buffer.add(1) = b'.'; } buffer = unsafe { buffer.add(length + usize::from(length > 1)) }; // Write exponent. if ExpStringTable::ENABLE { let mut exp_data = unsafe { *d.exp_strings .data .get_unchecked((dec_exp + ExpStringTable::OFFSET) as usize) }; let len = (exp_data >> 48) as usize; exp_data = exp_data.to_le(); unsafe { ptr::copy_nonoverlapping( ptr::addr_of!(exp_data).cast::(), buffer, if Float::MAX_10_EXP >= 100 { 5 } else { 4 }, ); return buffer.add(len); } } let sign_ptr = buffer; let e_sign = if dec_exp >= 0 { (u16::from(b'+') << 8) | u16::from(b'e') } else { (u16::from(b'-') << 8) | u16::from(b'e') }; buffer = unsafe { buffer.add(1) }; dec_exp = if dec_exp >= 0 { dec_exp } else { -dec_exp }; buffer = unsafe { buffer.add(usize::from(dec_exp >= 10)) }; if Float::MAX_10_EXP >= 100 { // digit = dec_exp / 100 let digit = if USE_UMUL128_HI64 { umul128_hi64(dec_exp as u64, 0x290000000000000) as u32 } else { (dec_exp as u32 * DIV100_SIG) >> DIV100_EXP }; unsafe { *buffer = b'0' + digit as u8; } buffer = unsafe { buffer.add(usize::from(dec_exp >= 100)) }; dec_exp -= (digit * 100) as i32; } unsafe { buffer .cast::() .write_unaligned(*digits2(dec_exp as usize)); sign_ptr.cast::().write_unaligned(e_sign.to_le()); buffer.add(2) } } /// Safe API for formatting floating point numbers to text. /// /// ## Example /// /// ``` /// let mut buffer = zmij::Buffer::new(); /// let printed = buffer.format_finite(1.234); /// assert_eq!(printed, "1.234"); /// ``` pub struct Buffer { bytes: [MaybeUninit; BUFFER_SIZE], } impl Buffer { /// This is a cheap operation; you don't need to worry about reusing buffers /// for efficiency. #[inline] #[cfg_attr(feature = "no-panic", no_panic)] pub fn new() -> Self { let bytes = [MaybeUninit::::uninit(); BUFFER_SIZE]; Buffer { bytes } } /// Print a floating point number into this buffer and return a reference to /// its string representation within the buffer. /// /// # Special cases /// /// This function formats NaN as the string "NaN", positive infinity as /// "inf", and negative infinity as "-inf" to match std::fmt. /// /// If your input is known to be finite, you may get better performance by /// calling the `format_finite` method instead of `format` to avoid the /// checks for special cases. #[cfg_attr(feature = "no-panic", no_panic)] pub fn format(&mut self, f: F) -> &str { if f.is_nonfinite() { f.format_nonfinite() } else { self.format_finite(f) } } /// Print a floating point number into this buffer and return a reference to /// its string representation within the buffer. /// /// # Special cases /// /// This function **does not** check for NaN or infinity. If the input /// number is not a finite float, the printed representation will be some /// correctly formatted but unspecified numerical value. /// /// Please check [`is_finite`] yourself before calling this function, or /// check [`is_nan`] and [`is_infinite`] and handle those cases yourself. /// /// [`is_finite`]: f64::is_finite /// [`is_nan`]: f64::is_nan /// [`is_infinite`]: f64::is_infinite #[cfg_attr(feature = "no-panic", no_panic)] pub fn format_finite(&mut self, f: F) -> &str { unsafe { let end = f.write_to_zmij_buffer(self.bytes.as_mut_ptr().cast::()); let len = end.offset_from(self.bytes.as_ptr().cast::()) as usize; let slice = slice::from_raw_parts(self.bytes.as_ptr().cast::(), len); str::from_utf8_unchecked(slice) } } } /// A floating point number, f32 or f64, that can be written into a /// [`zmij::Buffer`][Buffer]. /// /// This trait is sealed and cannot be implemented for types outside of the /// `zmij` crate. #[allow(unknown_lints)] // rustc older than 1.74 #[allow(private_bounds)] pub trait Float: private::Sealed {} impl Float for f32 {} impl Float for f64 {} mod private { pub trait Sealed: crate::traits::Float { fn is_nonfinite(self) -> bool; fn format_nonfinite(self) -> &'static str; unsafe fn write_to_zmij_buffer(self, buffer: *mut u8) -> *mut u8; } impl Sealed for f32 { #[inline] fn is_nonfinite(self) -> bool { const EXP_MASK: u32 = 0x7f800000; let bits = self.to_bits(); bits & EXP_MASK == EXP_MASK } #[cold] #[cfg_attr(feature = "no-panic", inline)] fn format_nonfinite(self) -> &'static str { const MANTISSA_MASK: u32 = 0x007fffff; const SIGN_MASK: u32 = 0x80000000; let bits = self.to_bits(); if bits & MANTISSA_MASK != 0 { crate::NAN } else if bits & SIGN_MASK != 0 { crate::NEG_INFINITY } else { crate::INFINITY } } #[cfg_attr(feature = "no-panic", inline)] unsafe fn write_to_zmij_buffer(self, buffer: *mut u8) -> *mut u8 { unsafe { crate::write(self, buffer) } } } impl Sealed for f64 { #[inline] fn is_nonfinite(self) -> bool { const EXP_MASK: u64 = 0x7ff0000000000000; let bits = self.to_bits(); bits & EXP_MASK == EXP_MASK } #[cold] #[cfg_attr(feature = "no-panic", inline)] fn format_nonfinite(self) -> &'static str { const MANTISSA_MASK: u64 = 0x000fffffffffffff; const SIGN_MASK: u64 = 0x8000000000000000; let bits = self.to_bits(); if bits & MANTISSA_MASK != 0 { crate::NAN } else if bits & SIGN_MASK != 0 { crate::NEG_INFINITY } else { crate::INFINITY } } #[cfg_attr(feature = "no-panic", inline)] unsafe fn write_to_zmij_buffer(self, buffer: *mut u8) -> *mut u8 { unsafe { crate::write(self, buffer) } } } } impl Default for Buffer { #[inline] #[cfg_attr(feature = "no-panic", no_panic)] fn default() -> Self { Buffer::new() } }