arXiv subjects

Daniel Lemire

Publications and source records attributed to Daniel Lemire.

At least 19 recordsLinked to original sources

arXiv2026

Converting an Integer to a Decimal String in Under Two Nanoseconds

Converting binary integers to variable-length decimal strings is a fundamental operation in computing. Conventional fast approaches rely on recursive division and small lookup tables. We propose a SIMD-based algorithm that leverages integer multiply-add instructions available on recent AMD and Intel processors. Our method eliminates lookup tables entirely and computes multiple quotients and remainders in parallel. Additionally, we introduce a dual-variant design with dynamic selection that adapts to input characteristics: a branch-heavy variant optimized for homogeneous digit-length distributions and a branch-light variant for heterogeneous datasets. Our single-core algorithm consistently outperforms all competing methods across the full range of integer sizes, running 1.4-2x faster than the closest competitor and 2-4x faster than the C++ standard library function std::to_chars across tested workloads.

cs.DS↗

arXiv2026

Converting Binary Floating-Point Numbers to Shortest Decimal Strings: An Experimental Review

When sharing or logging numerical data, we must convert binary floating-point numbers into their decimal string representations. For example, the number $\pi$ might become 3.1415927. Engineers have perfected many algorithms for producing such accurate, short strings. We present an empirical comparison across diverse hardware architectures and datasets. Cutting-edge techniques like Schubfach and Dragonbox achieve up to a tenfold speedup over Steele and White's Dragon4, executing as few as 210 instructions per conversion compared to Dragon4's 1500-5000 instructions. Often per their specification, none of the implementations we surveyed consistently produced the shortest possible strings-some generate outputs up to 30% longer than optimal. We find that standard library implementations in languages such as C++ and Swift execute significantly more instructions than the fastest methods, with performance gaps varying across CPU architectures and compilers. We suggest some optimization targets for future research.

cs.AR↗

arXiv2026

Fixing ill-formed UTF-16 strings with SIMD instructions

UTF-16 is a widely used Unicode encoding representing characters with one or two 16-bit code units. The format relies on surrogate pairs to encode characters beyond the Basic Multilingual Plane, requiring a high surrogate followed by a low surrogate. Ill-formed UTF-16 strings -- where surrogates are mismatched -- can arise from data corruption or improper encoding, posing security and reliability risks. Consequently, programming languages such as JavaScript include functions to fix ill-formed UTF-16 strings by replacing mismatched surrogates with the Unicode replacement character (U+FFFD). We propose using Single Instruction, Multiple Data (SIMD) instructions to handle multiple code units in parallel, enabling faster and more efficient execution. Our software is part of the Google JavaScript engine (V8) and thus part of several major Web browsers.

cs.OH↗

arXiv2025

Scanning HTML at Tens of Gigabytes per Second on ARM Processors

Modern processors have instructions to process 16 bytes or more at once. These instructions are called SIMD, for single instruction, multiple data. Recent advances have leveraged SIMD instructions to accelerate parsing of common Internet formats such as JSON and base64. During HTML parsing, they quickly identify specific characters with a strategy called vectorized classification. We review their techniques and compare them with a faster alternative. We measure a 20-fold performance improvement in HTML scanning compared to traditional methods on recent ARM processors. Our findings highlight the potential of SIMD-based algorithms for optimizing Web browser performance.

cs.DS↗

arXiv2024

Faster Positional-Population Counts for AVX2, AVX-512, and ASIMD

The positional population count operation pospopcnt() counts for an array of w-bit words how often each of the w bits was set. Various applications in bioinformatics, database engineering, and digital processing exist. Building on earlier work by Klarqvist et al., we show how positional population counts can be rapidly computed using SIMD techniques with good performance from the first byte, approaching memory-bound speeds for input arrays of as little as 4 KiB. Improvements include an improved algorithm structure, better handling of unaligned and very short arrays, as well as faster bit-parallel accumulation of intermediate results. We provide a generic algorithm description as well as implementations for various SIMD instruction set extensions, including Intel AVX2, AVX-512, and ARM ASIMD, and discuss the adaption of our algorithm to other platforms.

cs.DS↗

arXiv2024

Parsing Millions of DNS Records per Second

The Domain Name System (DNS) plays a critical role in the functioning of the Internet. It provides a hierarchical name space for locating resources. Data is typically stored in plain text files, possibly spanning gigabytes. Frequent parsing of these files to refresh the data is computationally expensive: processing a zone file can take minutes. We propose a novel approach called simdzone to enhance DNS parsing throughput. We use data parallelism, specifically the Single Instruction Multiple Data (SIMD) instructions available on commodity processors. We show that we can multiply the parsing speed compared to state-of-the-art parsers found in Knot DNS and the NLnet Labs Name Server Daemon (NSD). The resulting software library replaced the parser in NSD.

cs.DS↗

arXiv2024

Batched Ranged Random Integer Generation

Pseudorandom values are often generated as 64-bit binary words. These random words need to be converted into ranged values without statistical bias. We present an efficient algorithm to generate multiple independent uniformly-random bounded integers from a single uniformly-random binary word, without any bias. In the common case, our method uses one multiplication and no division operations per value produced. In practice, our algorithm can more than double the speed of unbiased random shuffling for small to moderately large arrays.

cs.DS↗

arXiv2023

On-Demand JSON: A Better Way to Parse Documents?

JSON is a popular standard for data interchange on the Internet. Ingesting JSON documents can be a performance bottleneck. A popular parsing strategy consists in converting the input text into a tree-based data structure -- sometimes called a Document Object Model or DOM. We designed and implemented a novel JSON parsing interface -- called On-Demand -- that appears to the programmer like a conventional DOM-based approach. However, the underlying implementation is a pointer iterating through the content, only materializing the results (objects, arrays, strings, numbers) lazily.On recent commodity processors, an implementation of our approach provides superior performance in multiple benchmarks. To ensure reproducibility, our work is freely available as open source software. Several systems use On-Demand: e.g., Apache Doris, the Node.js JavaScript runtime, Milvus, and Velox.

cs.DB↗

arXiv2023

Parsing Millions of URLs per Second

URLs are fundamental elements of web applications. By applying vector algorithms, we built a fast standard-compliant C++ implementation. Our parser uses three times fewer instructions than competing parsers following the WHATWG standard (e.g., Servo's rust-url) and up to eight times fewer instructions than the popular curl parser. The Node.js environment adopted our C++ library. In our tests on realistic data, a recent Node.js version (20.0) with our parser is four to five times faster than the last version with the legacy URL parser.

cs.PL↗

arXiv2023

Unicode at Gigabytes per Second

We often represent text using Unicode formats (UTF-8 and UTF-16). The UTF-8 format is increasingly popular, especially on the web (XML, HTML, JSON, Rust, Go, Swift, Ruby). The UTF-16 format is most common in Java, .NET, and inside operating systems such as Windows. Software systems frequently have to convert text from one Unicode format to the other. While recent disks have bandwidths of 5 GiB/s or more, conventional approaches transcode non-ASCII text at a fraction of a gigabyte per second. We show that we can validate and transcode Unicode text at gigabytes per second on current systems (x64 and ARM) without sacrificing safety. Our open-source library can be ten times faster than the popular ICU library on non-ASCII strings and even faster on ASCII strings.

cs.PL↗

arXiv2023

Exact Short Products From Truncated Multipliers

We sometimes need to compute the most significant digits of the product of small integers with a multiplier requiring much storage: e.g., a large integer (e.g., $5^{100}$) or an irrational number ($\pi$). We only need to access the most significant digits of the multiplier-as long as the integers are sufficiently small. We provide an efficient algorithm to compute the range of integers given a truncated multiplier and a desired number of digits.

cs.DS↗

arXiv2023

Fast Number Parsing Without Fallback

In recent work, Lemire (2021) presented a fast algorithm to convert number strings into binary floating-point numbers. The algorithm has been adopted by several important systems: e.g., it is part of the runtime libraries of GCC 12, Rust 1.55, and Go 1.16. The algorithm parses any number string with a significand containing no more than 19 digits into an IEEE floating-point number. However, there is a check leading to a fallback function to ensure correctness. This fallback function is never called in practice. We prove that the fallback is unnecessary. Thus we can slightly simplify the algorithm and its implementation.

cs.DS↗

arXiv2022

Transcoding Unicode Characters with AVX-512 Instructions

Intel includes in its recent processors a powerful set of instructions capable of processing 512-bit registers with a single instruction (AVX-512). Some of these instructions have no equivalent in earlier instruction sets. We leverage these instructions to efficiently transcode strings between the most common formats: UTF-8 and UTF-16. With our novel algorithms, we are often twice as fast as the previous best solutions. For example, we transcode Chinese text from UTF-8 to UTF-16 at more than 5 GiB/s using fewer than 2 CPU instructions per character. To ensure reproducibility, we make our software freely available as an open source library. Our library is part of the popular Node.js JavaScript runtime.

cs.DS↗

arXiv2022

Transcoding Billions of Unicode Characters per Second with SIMD Instructions

In software, text is often represented using Unicode formats (UTF-8 and UTF-16). We frequently have to convert text from one format to the other, a process called transcoding. Popular transcoding functions are slower than state-of-the-art disks and networks. These transcoding functions make little use of the single-instruction-multiple-data (SIMD) instructions available on commodity processors. By designing transcoding algorithms for SIMD instructions, we multiply the speed of transcoding on current systems (x64 and ARM). To ensure reproducibility, we make our software freely available as an open source library.

cs.DC↗

arXiv2022

Number Parsing at a Gigabyte per Second

With disks and networks providing gigabytes per second, parsing decimal numbers from strings becomes a bottleneck. We consider the problem of parsing decimal numbers to the nearest binary floating-point value. The general problem requires variable-precision arithmetic. However, we need at most 17 digits to represent 64-bit standard floating-point numbers (IEEE 754). Thus we can represent the decimal significand with a single 64-bit word. By combining the significand and precomputed tables, we can compute the nearest floating-point number using as few as one or two 64-bit multiplications. Our implementation can be several times faster than conventional functions present in standard C libraries on modern 64-bit systems (Intel, AMD, ARM and POWER9). Our work is available as open source software used by major systems such as Apache Arrow and Yandex ClickHouse. The Go standard library has adopted a version of our approach.

cs.DS↗

arXiv2022

Roaring Bitmaps: Implementation of an Optimized Software Library

Compressed bitmap indexes are used in systems such as Git or Oracle to accelerate queries. They represent sets and often support operations such as unions, intersections, differences, and symmetric differences. Several important systems such as Elasticsearch, Apache Spark, Netflix's Atlas, LinkedIn's Pinot, Metamarkets' Druid, Pilosa, Apache Hive, Apache Tez, Microsoft Visual Studio Team Services and Apache Kylin rely on a specific type of compressed bitmap index called Roaring. We present an optimized software library written in C implementing Roaring bitmaps: CRoaring. It benefits from several algorithms designed for the single-instruction-multiple-data (SIMD) instructions available on commodity processors. In particular, we present vectorized algorithms to compute the intersection, union, difference and symmetric difference between arrays. We benchmark the library against a wide range of competitive alternatives, identifying weaknesses and strengths in our software. Our work is available under a liberal open-source license.

cs.DB↗

arXiv2022

Binary Fuse Filters: Fast and Smaller Than Xor Filters

Bloom and cuckoo filters provide fast approximate set membership while using little memory. Engineers use them to avoid expensive disk and network accesses. The recently introduced xor filters can be faster and smaller than Bloom and cuckoo filters. The xor filters are within 23% of the theoretical lower bound in storage as opposed to 44% for Bloom filters. Inspired by Dietzfelbinger and Walzer, we build probabilistic filters -- called binary fuse filters -- that are within 13% of the storage lower bound -- without sacrificing query speed. As an additional benefit, the construction of the new binary fuse filters can be more than twice as fast as the construction of xor filters. By slightly sacrificing query speed, we further reduce storage to within 8% of the lower bound. We compare the performance against a wide range of competitive alternatives such as Bloom filters, blocked Bloom filters, vector quotient filters, cuckoo filters, and the recent ribbon filters. Our experiments suggest that binary fuse filters are superior to xor filters.

cs.DS↗

arXiv2021

Integer Division by Constants: Optimal Bounds

The integer division of a numerator n by a divisor d gives a quotient q and a remainder r. Optimizing compilers accelerate software by replacing the division of n by d with the division of c * n (or c * n + c) by m for convenient integers c and m chosen so that they approximate the reciprocal: c/m ~= 1/d. Such techniques are especially advantageous when m is chosen to be a power of two and when d is a constant so that c and m can be precomputed. The literature contains many bounds on the distance between c/m and the divisor d. Some of these bounds are optimally tight, while others are not. We present optimally tight bounds for quotient and remainder computations.

cs.DS↗