lexical-core

Build Status Latest Version

Low-level, FFI-compatible, lexical conversion routines for use in a no_std context. This crate by default does not use the Rust standard library. And, as of version 0.3, lexical-core uses minimal unsafe features, limiting the chance of memory-unsafe code.

Getting Started

lexical-core is a low-level, partially FFI-compatible API for number-to-string and string-to-number conversions, without requiring a system allocator. If you would like to use a convenient, high-level API, please look at lexical instead.

Add lexical-core to your Cargo.toml:

yaml [dependencies] lexical-core = "0.3"

And an introduction through use:

```rust extern crate lexical_core;

// String to number using Rust slices. // The first argument is the radix, which should be 10 for decimal strings, // and the second argument is the byte string parsed. let f = lexicalcore::atof64slice(b"3.5"); // 3.5 let i = lexicalcore::atoi32slice(b"15"); // 15

// String to number using pointer ranges, for FFI-compatible code. // The first argument is the radix, which should be 10 for decimal strings, // the second argument is a pointer to the start of the parsed byte array, // and the third argument is a pointer to 1-past-the-end. It will process // bytes in the range [first, last). unsafe { let bytes = b"3.5"; let first = bytes.asptr(); let last = first.add(bytes.len()); let f = lexicalcore::atof64_range(first, last); }

// The ato_slice and atorange parsers are not checked, they do not // validate that the input data is entirely correct, and stop parsing // when invalid data is found, returning whatever was parsed up until // that point. The explicit behavior is to wrap on overflow, and // to discard invalid digits. let i = lexicalcore::atoi8slice(b"256"); // 0, wraps from 256 let i = lexicalcore::atoi8_slice(b"1a5"); // 1, discards "a5"

// You should prefer the checked parsers, whenever possible. These detect // numeric overflow, and no invalid trailing digits are present. // The error code for success is 0, all errors are less than 0.

// Ideally, everything works great. let res = lexicalcore::tryatoi8slice(b"15"); asserteq!(res.error.code, lexicalcore::ErrorCode::Success); asserteq!(res.value, 15);

// However, it detects numeric overflow, setting res.error.code // to the appropriate value. let res = lexicalcore::tryatoi8slice(b"256"); asserteq!(res.error.code, lexical_core::ErrorCode::Overflow);

// Errors occurring prematurely terminating the parser due to invalid // digits return the index in the buffer where the invalid digit was // seen. This may useful in contexts like serde, which require numerical // parsers from complex data without having to extract a substring // containing only numeric data ahead of time. If the error is set // to a InvalidDigit, the value is guaranteed to be accurate up until // that point. For example, if the trailing data is whitespace, // the value from an invalid digit may be perfectly valid in some contexts. let res = lexicalcore::tryatoi8slice(b"15 45"); asserteq!(res.error.code, lexicalcore::ErrorCode::InvalidDigit); asserteq!(res.error.index, 2); assert_eq!(res.value, 15);

// Number to string using slices. // The first argument is the value, the second argument is the radix, // and the third argument is the buffer to write to. // The function returns a subslice of the original buffer, and will // always start at the same position (buf.as_ptr() == slc.as_ptr()). let mut buf = [b'0'; lexicalcore::MAXI64SIZE]; let slc = lexicalcore::i64toaslice(15, &mut buf); asserteq!(slc, b"15");

// If an insufficiently long buffer is passed, the serializer will panic. // PANICS let mut buf = [b'0'; 1]; //let slc = lexicalcore::i64toaslice(15, &mut buf);

// In order to guarantee the buffer is long enough, always ensure there // are at least MAX_*_SIZE, where * is the type name in upperase, // IE, for isize, MAX_ISIZE_SIZE. let mut buf = [b'0'; lexicalcore::MAXF64SIZE]; let slc = lexicalcore::f64toaslice(15.1, &mut buf); asserteq!(slc, b"15.1"); ```

Features

Configuration

Lexical-core also includes configuration options that allow you to configure float processing and formatting:

Constants

Lexical-core also includes a few constants to simplify interfacing with number-to-string code. These are named MAX_*_SIZE, and indicate the maximum number of characters a number-to-string function may write. For example, atoi32_range may write up to MAX_I32_SIZE characters. These are provided as Rust constants so they may be used as the size element in arrays. For FFI-code, lexical-core exports unmangled constants named MAX_*_SIZE_FFI, to allow their use in non-Rust code.

FFI Example

First, build lexical-core in release mode from the project home:

bash cargo build --release

Next, add the shared library to the search path, or load it exactly. For example, to use lexical-core from Python, from the project home directory:

```python from ctypes import * import os

This is the path on Unix, on Windows use *.dll and on MacOS X, use *.dylib.

path = os.path.join(os.getcwd(), "target", "release", "liblexical_core.so") lib = CDLL(path)

To access global variables, use $type.in_dll($lib, "$variable")

i8size = csizet.indll(lib, "MAXI8SIZEFFI") print(i8size) # c_ulong(4)

exponentchar = cchar.indll(lib, "EXPONENTDEFAULTCHAR") print(exponentchar) # c_char(b'e')

Define our result types for the error-checked parsers.

class error(Structure): fields = [("code", cint), ("index", csize_t)]

class resultf32(Structure): _fields = [("value", c_float), ("error", error)]

Need to set the appropriate restypes for our functions, Python assumes

they're all c_int.

lib.atof32range.restype = cfloat lib.tryatof32range.restype = resultf32 lib.f32toarange.restype = POINTER(c_char)

Call string-to-number parsers. This isn't elegant, because we want

a valid range of values, but it works.

def toaddress(ptr): '''Get address from pointer.''' return cast(ptr, cvoidp).value

def tocharp(address): '''Get char* pointer from address or another pointer.''' return cast(address, POINTER(cchar))

def distance(first, last): '''Calculate the distance between two ranges''' return toaddress(last) - toaddress(first)

data = b"1.2345" first = tocharp(data) last = tocharp(toaddress(first) + len(data)) result = lib.atof32range(first, last) print(result) # 1.2345000505447388

result = lib.tryatof32range(first, last) print(result.value) # 1.2345000505447388 print(result.error.code) # 0

Call the number-to-string serializers.

First, create a buffer type of sufficient length.

f32size = csizet.indll(lib, "MAXF32SIZEFFI") F32BufferType = cchar * f32_size.value buf = F32BufferType()

Next, initialize our arguments for the call.

value = cfloat(1.2345) first = tocharp(buf) last = tocharp(toaddress(first) + len(buf))

Call the serializer and create a Python string from our result.

ptr = lib.f32toarange(value, first, last) length = distance(first, ptr) result = stringat(buf, 6) print(result) # "1.2345" ```

Documentation

Lexical-core's documentation can be found on docs.rs.

Validation

Float parsing is difficult to do correctly, and major bugs have been found in implementations from libstdc++'s strtod to Python. In order to validate the accuracy of the lexical, we employ the following external tests:

  1. Hrvoje Abraham's strtod test cases.
  2. Rust's test-float-parse unittests.
  3. Testbase's stress tests for converting from decimal to binary.
  4. Various difficult cases reported on blogs.

Although lexical may contain bugs leading to rounding error, it is tested against a comprehensive suite of random-data and near-halfway representations, and should be fast and correct for the vast majority of use-cases.

Implementation Details

Float to String

For more information on the Grisu2 and Grisu3 algorithms, see Printing Floating-Point Numbers Quickly and Accurately with Integers.

For more information on the Ryu algorithm, see Ryū: fast float-to-string conversion.

String to Float

In order to implement an efficient parser in Rust, lexical uses the following steps:

  1. We ignore the sign until the end, and merely toggle the sign bit after creating a correct representation of the positive float.
  2. We handle special floats, such as "NaN", "inf", "Infinity". If we do not have a special float, we continue to the next step.
  3. We parse up to 64-bits from the string for the mantissa, ignoring any trailing digits, and parse the exponent (if present) as a signed 32-bit integer. If the exponent overflows or underflows, we set the value to i32::maxvalue() or i32::minvalue(), respectively.
  4. Fast Path We then try to create an exact representation of a native binary float from parsed mantissa and exponent. If both can be exactly represented, we multiply the two to create an exact representation, since IEEE754 floats mandate the use of guard digits to minimizing rounding error. If either component cannot be exactly represented as the native float, we continue to the next step.
  5. Moderate Path We create an approximate, extended, 80-bit float type (64-bits for the mantissa, 16-bits for the exponent) from both components, and multiplies them together. This minimizes the rounding error, through guard digits. We then estimate the error from the parsing and multiplication steps, and if the float +/- the error differs significantly from b+h, we return the correct representation (b or b+u). If we cannot unambiguously determine the correct floating-point representation, we continue to the next step.
  6. Fallback Moderate Path Next, we create a 128-bit representation of the numerator and denominator for b+h, to disambiguate b from b+u by comparing the actual digits in the input to theoretical digits generated from b+h. This is accurate for ~36 significant digits from a 128-bit approximation with decimal float strings. If the input is less than or equal to 36 digits, we return the value from this step. Otherwise, we continue to the next step.
  7. Slow Path We use arbitrary-precision arithmetic to disambiguate the correct representation without any rounding error. We create an exact representation of the input digits as a big integer, to determine how to round the top 53 bits for the mantissa. If there is a fraction or a negative exponent, we create a representation of the significant digits for b+h and scale the input digits by the binary exponent in b+h, and scale the significant digits in b+h by the decimal exponent, and compare the two to determine if we need to round up or down.

Since arbitrary-precision arithmetic is slow and scales poorly for decimal strings with many digits or exponents of high magnitude, lexical also supports a lossy algorithm, which returns the result from the moderate path. The result from the lossy parser should be accurate to within 1 ULP.

Arbitrary-Precision Arithmetic

Lexical uses arbitrary-precision arithmetic to exactly represent strings between two floating-point representations, and is highly optimized for performance. The following section is a comparison of different algorithms to determine the correct float representation. The arbitrary-precision arithmetic logic is not dependent on memory allocation: it only uses the heap when the radix feature is enabled.

Algorithm Background and Comparison

For close-to-halfway representations of a decimal string s, where s is close between two representations, b and the next float b+u, arbitrary-precision arithmetic is used to determine the correct representation. This means s is close to b+h, where h is the halfway point between b and b+u.

For the following example, we will use the following values for our test case:

Algorithm M

Algorithm M represents the significant digits of a float as a fraction of arbitrary-precision integers (a more in-depth description can be found here). For example, 1.23 would be 123/100, while 314.159 would be 314159/1000. We then scale the numerator and denominator by powers of 2 until the quotient is in the range [2^52, 2^53), generating the correct significant digits of the mantissa.

A naive implementation, in Python, is as follows:

```python def algorithm_m(num, b): # Ensure numerator >= 2**52 bits = int(math.ceil(math.log2(num))) if bits <= 53: num <<= 53 b -= 53

# Track number of steps required (optional).
steps = 0
while True:
    steps += 1
    c = num//b
    if c < 2**52:
        b //= 2
    elif c >= 2**53:
        b *= 2
    else:
        break

return (num, b, steps-1)

```

bigcomp

Bigcomp is the canonical string-to-float parser, which creates an exact representation of b+h as a big integer, and compares the theoretical digits from b+h scaled into the range [1, 10) by a power of 10 to the actual digits in the input string (a more in-depth description can be found here). A maximum of 768 digits need to be compared to determine the correct representation, and the size of the big integers in the ratio does not depend on the number of digits in the input string.

Bigcomp is used as a fallback algorithm for lexical-core when the radix feature is enabled, since the radix-representation of a binary float may never terminate if the radix is not divisible by 2. Since bigcomp uses constant memory, it is used as the default algorithm if more than 2^15 digits are passed and the representation is potentially non-terminating.

bhcomp

Bhcomp is a simple, performant algorithm that compared the significant digits to the theoretical significant digits for b+h. Simply, the significant digits from the string are parsed, creating a ratio. A ratio is generated for b+h, and these two ratios are scaled using the binary and radix exponents.

For example, "2.470328e-324" produces a ratio of 2470328/10^329, while b+h produces a binary ratio of 1/2^1075. We're looking to compare these ratios, so we need to scale them using common factors. Here, we convert this to (2470328*5^329*2^1075)/10^329 and (1*5^329*2^1075)/2^1075, which converts to 2470328*2^746 and 1*5^329.

Our significant digits (realdigits) and b+h (bhdigits) therefore start like: real_digits = 91438982... bh_digits = 91438991...

Since our real digits are below the theoretical halfway point, we know we need to round-down, meaning our literal value is b, or 0.0. This approach allows us to calculate whether we need to round-up or down with a single comparison step, without any native divisions required. This is the default algorithm lexical-core uses.

Other Optimizations

  1. We remove powers of 2 during exponentiation in bhcomp.
  2. We limit the number of parsed digits to the theoretical max number of digits produced by b+h (768 for decimal strings), and merely compare any trailing digits to '0'. This provides an upper-bound on the computation cost.
  3. We use fast exponentiation and multiplication algorithms to scale the significant digits for comparison.
  4. For the fallback bigcomp algorithm, we use a division algorithm optimized for the generation of a single digit from a given radix, by setting the leading bit in the denominator 4 below the most-significant bit (in decimal strings). This requires only 1 native division per digit generated.
  5. The individual "limbs" of the big integers are optimized to the architecture we compile on, for example, u32 on x86 and u64 on x86-64, minimizing the number of native operations required. Currently, 64-bit limbs are used on target architectures aarch64, powerpc64, mips64, and x86_64.

License

Lexical-core is dual licensed under the Apache 2.0 license as well as the MIT license. See the LICENCE-MIT and the LICENCE-APACHE files for the licenses.

Lexical-core also ports some code from V8, libgo and fpconv, and therefore might be subject to the terms of a 3-clause BSD license or BSD-like license.

Contributing

Unless you explicitly state otherwise, any contribution intentionally submitted for inclusion in lexical by you, as defined in the Apache-2.0 license, shall be dual licensed as above, without any additional terms or conditions.