diff --git a/README.md b/README.md index 6ac9822..c9030ea 100644 --- a/README.md +++ b/README.md @@ -1,162 +1,115 @@ -# float_string_generation_benchmark +# Integer-to-String Benchmark -The goal of this project is to narrowly study the problem of generating -*shortest* number strings (e.g., `1.2122E4`) out of a decimal representation -(`significant * 10**power`). The implicit assumption is that you started -out from a binary floating point numbers (`float` or `double` in C/C++/Java/C#) -and you mapped it to a decimal form. +A benchmark suite for integer-to-string conversion algorithms, +containing our `Champagne-Lemire` AVX-512 algorithm. -The project might have applications to more conventional problems such as converting -integer values to decimal representation. +## Overview -In principle, converting `significant * 10**power` into a decimal string is not difficult. -You can compute `significant % 10` and get the last significant digits, and so forth. -This is the typical right-to-left approach: you write the least significant digit, -and the next least significant digit, and so forth. -You need to determine which way you go to the shortest string (do you write `0.1` or `1E-1`), -but that's not too difficult. - -So why is this interesting? It is interesting because we noticed that a highly -optimized function in a [Ryu](https://github.com/ulfjack/ryu) float-to-string -implementation was much slower then the implementation in the -[Dragonbox](https://github.com/jk-jeon/dragonbox) float-to-string implementation. - -What is challenging? +This project benchmarks various algorithms for converting 64-bit unsigned +integers to their decimal string representation. The focus is on high-throughput +batch conversion scenarios. ## Requirements -- AVX-512 capable machine (e.g., Zen 4 or better). -- A recent GCC or LLVM on a Linux system or the equivalent +- An x86 64-bit CPU +- AVX-512 support (for the `Champagne-Lemire` algorithm) +- A recent GCC or Clang on a Linux system - CMake -## Knowing where to write - -One challenge is that you want to write the characters at the right place -from the start. This is not trivial because you don't known initially how many digits you -need to write. If you consider the right-to-left approach, it requires you to start -writing *somewhere* implying that you know how many digits you have. Thankfully, there -are fast algorithms to count digits: - -- Daniel Lemire, "Counting the digits of 64-bit integers," in Daniel Lemire's blog, January 7, 2025, https://lemire.me/blog/2025/01/07/counting-the-digits-of-64-bit-integers/. - -Of course, you could write to a buffer and then copy over but that's likely more expensive than -counting the number of digits, at least in some cases. +## Building -The Dragonbox float-to-string implementation avoids this problem. The way it does it is that -it writes from left to right. So it writes the most significant digit first !!! It relies -on branching and assumes that the number of digits might be somewhat predictible, which could be true -in practice (or not). - -## Storing the characters - -Even if you have the digits (e.g., the integer 1) and you know where they should be written, you -still need to do something like: - -```c++ -buf[index] = '0' + value +```bash +cmake -B build +cmake --build build ``` -And, once you figured out where the dot goes, you need to do +With a specific compiler, e.g., clang: -```c++ -buf[index] = '.' +```bash +CC=clang CXX=clang++ cmake -B buildclang +cmake --build buildclang ``` -These things add up. So one trick is to compute hundreds instead of tens. And you use a lookup table. -So you have precompted strings from `00`, `01`, `02`, up `99`. -For the dot, you can also avoid having separate store by precomputing the strings -`0.`, `1.`, `2.`,... or something equivalent. - -Similarly, for the exponent, you could precompute strings. E.g., you could certainly precompute `e+` and `e-` and -not have two stores. - -Obviously, going from tens to hundreds to tens of housands could speed things further, although we might need -a slightly larger table (40kB?). We'd like to avoid massive tables if there are more clever approaches. - -There might be room for fancier strategies. See - -- Daniel Lemire, "Converting integers to fix-digit representations quickly," in Daniel Lemire's blog, November 18, 2021, https://lemire.me/blog/2021/11/18/converting-integers-to-fix-digit-representations-quickly/. - -## Computing the digit values - -This is where the fun mathematics comes in. I give you an integer, how do you compute -quickly the remainder and the quotient? See the following paper. +## Usage -- Daniel Lemire, Colin Bartlett, Owen Kaser, [Integer Division by Constants: Optimal Bounds](https://arxiv.org/abs/2012.12369), Heliyon 7 (6), 2021 -- Takahashi, D. (2023). Multiple Integer Divisions with an Invariant Dividend and Monotonically Increasing or Decreasing Divisors. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2023. ICCSA 2023. Lecture Notes in Computer Science, vol 13957. Springer, Cham. https://doi.org/10.1007/978-3-031-36808-0_26 +Run the benchmark: -Though the math is a bit tricky, we can often brute force a check for the solution. +```bash +./build/benchmark +``` -Currently, we can *almost* bring it down to one multiplication per digit (where a digit could be a value in [0,99] in this context). +Quick validation mode: -## Overall challenge +```bash +./build/benchmark -q +``` -How low can you go? By a rough estimation, the Ryu string generation algorithm might use 200 instructions -per float whereas Dragonbox can go under 100 instructions per float. That's excellent, but still -about 5 instructions per character produced. +With input data files: -## AVX-512 solution +```bash +./build/benchmark -f data/citm_catalog_integers.txt +./build/benchmark -f data/twitterjson_integers.txt +``` -We have a sketch of an AVX-512 solution. It is sketch because it might be incorrect. +Performance counters may require privileged execution (`sudo`). -The results *might* be good with a caveat: we can rather significantly reduce the number of instructions, -but loading the additional constants take time. So we inline the parsing function. By doing so, -we hope that constants are loaded once. +## Algorithms Benchmarked -This simulate the use case where you need to write a lot of floating-point numbers at once. That's -a realistic and useful case. +- **Champagne-Lemire (homogeneous)**: AVX-512 algorithm; variant optimized for uniform digit counts +- **Champagne-Lemire (heterogeneous)**: AVX-512 algorithm; variant for varying digit counts +- **Champagne-Lemire (auto)**: Dynamically selects between homogeneous/heterogeneous variants +- **std::to_chars**: Standard library implementation +- **Abseil**: Google's `FastIntToBuffer` routine +- **jeaiii**: James Edward Anhalt III's algorithm +- **AppNexus**: From the AppNexus Common Framework library +- **yy_itoa**: Yao Yuan's implementation +- **Mathisen**: SSE4.1-based algorithm inspired by Mathisen's arithmetic approach +- **Muła**: Wojciech Muła's SSE-based algorithm +- **Hopman**: The `hopman_fast` algorithm (extended to 64-bit) +- **naive_onepass**: Classic algorithm with one-pass optimization -To write just one floating-point number, the AVX-512 solution might not be faster than conventional strategies. +## Key Techniques -## Usage +### Digit Counting -Currently, the benchmark is very approximative. The implementations are untested. This is at the demo stage. -We compare `champagne_lemire` which is something like the function from Ryu, `fast+champagne_lemire` which -is a slightly faster alternative and dragonbox (a very fast alternative). Some of the code is assuredly -wrong or makes assumptions not satisfied by the benchmark. +Fast algorithms to determine the number of decimal digits in a 64-bit integer: -``` -cmake -B build -cmake --build build -./build/benchmark -``` +- Daniel Lemire, "Counting the digits of 64-bit integers," January 2025, https://lemire.me/blog/2025/01/07/counting-the-digits-of-64-bit-integers/ -To get performance counters, you might need to run the benchmark program in privileged mode (sudo). +### Lookup Tables -You can also feed in data files. -``` -./build/benchmark data/canada.txt -./build/benchmark data/mesh.txt -``` +Precomputed strings for digit pairs (`00` through `99`) reduce store operations by processing two digits at a time. -Consider also testing with LLVM/clang. +### Division by Constants -``` -CXX=clang++ cmake -B buildclang -cmake --build buildclang -./buildclang/benchmark -``` +Efficient computation of quotient and remainder using multiplication: -We definitively need more tests and better benchmarks including benchmarks on realistic data. +- Daniel Lemire et al., "Integer Division by Constants: Optimal Bounds," Heliyon 7(6), 2021, https://arxiv.org/abs/2012.12369 -Further, the system archictecture is assuredly a factor. +### Fixed-Digit Representations -## Upcoming tasks +- Daniel Lemire, "Converting integers to fix-digit representations quickly," November 2021, https://lemire.me/blog/2021/11/18/converting-integers-to-fix-digit-representations-quickly/ -- [ ] test, verify and correct the AVX-512 function (it is almost certainly incorrect) -- [ ] optimize the AVX-512 function for the case where we have short strings (with branching), the `mesh` data file is a good test case -- [ ] optionally, make sure that it builds under Visual Studio -- [ ] [investigate whether generating the constants](http://www.0x80.pl/notesen/2023-01-19-avx512-consts.html) might be faster -- [ ] build a fast SIMD function for the case where n < 100000000 +## Datasets -## Further thoughts +See `data/DATASETS.md` for descriptions of the included integer datasets: -We solve the string generation from a DIY structure (mantissa + exponent), it is an interesting exercise in itself, but is this applicable? Could we plug our function instead a float-to-string function and get decent results? +- `citm_catalog_integers.txt` - Event catalog IDs (mostly 9-digit, homogeneous) +- `twitterjson_integers.txt` - Twitter API integers (heterogeneous distribution) +- `cit_patents_citing_integers.txt.gz` - US patent numbers (7-digit, homogeneous) +- `stackoverflow_unix_timestamps_integers.txt.gz` - Unix timestamps (10-digit, homogeneous) -It seems that a more interesting approach would be to do bulk processing. I am given a whole lot of floating-point values (maybe from an array) and -I need to write them out. +## Benchmark Metrics -## References +The benchmark reports the following metrics: -- Cassio Neri, Lorenz Schneider, Euclidean affine functions and their application to calendar algorithms, Software: Practice and Experience 53 (4), 2023. -- Daniel Lemire, Owen Kaser, Nathan Kurz, Faster remainder by direct computation: Applications to compilers and software libraries. Software: Practice and Experience, 49(6), 2019. +| Metric | Description | +| -------- | ------------- | +| `ns/n` | Nanoseconds per number (integer) | +| `GHz` | CPU frequency during benchmark | +| `c/n` | CPU cycles per number | +| `i/n` | Instructions per number | +| `B/n` | Branches per number | +| `BM/n` | Branch misses per number | +| `i/d` | Instructions per output digit | +| `i/c` | Instructions per cycle (IPC) | diff --git a/benchmarks/benchmark.cpp b/benchmarks/benchmark.cpp index 7d41bdc..39eb8b5 100644 --- a/benchmarks/benchmark.cpp +++ b/benchmarks/benchmark.cpp @@ -8,7 +8,6 @@ #include #include #include -#include #include #include #include @@ -16,8 +15,6 @@ using std::literals::string_literals::operator""s; #include "performancecounters/benchmarker.h" #include "champagne_lemire.h" -#include "dragonbox.h" -#include "scalar.h" #include "integer_conv_baselines.h" constexpr size_t Number_Benchmark_Runs = 1; @@ -25,121 +22,18 @@ constexpr double Ratio_To_Sample = 0.01; constexpr double Ratio_Homogeneous = 0.95; // Homogeneous mode if > 95% of // numbers have the same digit length -// mantissa * 10^exponent -struct decimal_float { - uint64_t mantissa; - int32_t exponent; - bool sign; -}; - -// return the exponent and mantissa of the decimal representation of num_str -// should be a non-negative number. -std::pair find_mantissa_exponent(std::string_view num_str) { - uint64_t mantissa = 0; - size_t after_dot = 0; - bool found_dot = false; - - size_t idx = 0; - - for (; idx < num_str.size(); ++idx) { - const char c = num_str[idx]; - if (c == '.' && !found_dot) { - found_dot = true; - continue; - } - if (std::isdigit(static_cast(c))) { - mantissa = mantissa * 10 + (c - '0'); - if(found_dot) { - after_dot++; - } - } else { - break; - } - } - int64_t exponent_part = -static_cast(after_dot); - if (idx < num_str.size() && (num_str[idx] == 'e' || num_str[idx] == 'E')) { - ++idx; - bool negative_exponent = false; - if (idx < num_str.size() && (num_str[idx] == '+' || num_str[idx] == '-')) { - negative_exponent = (num_str[idx] == '-'); - ++idx; - } - for (; idx < num_str.size(); ++idx) { - const char c = num_str[idx]; - if (std::isdigit(static_cast(c))) { - exponent_part = exponent_part * 10 + (c - '0'); - } else { - break; - } - } - if (negative_exponent) { - exponent_part = -exponent_part; - } - } - if(mantissa == 0 ) { - exponent_part = 0; - } - while(mantissa % 10 == 0 && mantissa != 0) { - mantissa /= 10; - exponent_part++; - } - return {mantissa, exponent_part}; -} - -decimal_float double_to_decimal_float(double value, int mantissa_size = 17) { - decimal_float result = {0, 0, false}; - - // Handle zero - if (value == 0.0) { - return result; - } - - // Extract sign - result.sign = value < 0; - value = std::abs(value); - - // Handle special cases: infinity and NaN - if (std::isinf(value) || std::isnan(value)) { - result.mantissa = 0; - result.exponent = std::numeric_limits::max(); - return result; - } - - char buf[32]{}; - auto from_char_result = std::to_chars(buf, buf + sizeof(buf), value); - if (from_char_result.ec != std::errc()) { - // Handle error - throw std::runtime_error("Error converting double to chars"); - } - auto [mantissa, exponent_part] = find_mantissa_exponent(std::string_view(buf, from_char_result.ptr - buf)); - - // If mantissa has more digits than mantissa_size, scale it down - int current_digits = fast_digit_count(mantissa); - if(current_digits > 17) { - std::println("Warning: mantissa has more than 17 digits: {}", mantissa); - } - while (current_digits > mantissa_size) { - mantissa = (mantissa / 10) + (mantissa % 10 >= 5 ? 1 : 0); // naive rounding - exponent_part++; - current_digits--; - } - result.mantissa = mantissa; - result.exponent = static_cast(exponent_part); - return result; -} - -void pretty_print(size_t volume, size_t bytes, const std::string &name, +void pretty_print(size_t num_integers, size_t volume, const std::string &name, event_aggregate agg) { std::print("{:<50} : ", name); - std::print(" {:5.2f} ns/d ", agg.fastest_elapsed_ns() / volume); + std::print(" {:5.2f} ns/n ", agg.fastest_elapsed_ns() / num_integers); if (collector.has_events()) { std::print(" {:5.2f} GHz ", agg.fastest_cycles() / agg.fastest_elapsed_ns()); - std::print(" {:5.2f} c/d ", agg.fastest_cycles() / volume); + std::print(" {:5.2f} c/n ", agg.fastest_cycles() / num_integers); + std::print(" {:5.2f} i/n ", agg.fastest_instructions() / num_integers); + std::print(" {:5.2f} B/n ", agg.branches() / num_integers); + std::print(" {:5.2f} BM/n ", agg.branch_misses() / num_integers); std::print(" {:5.2f} i/d ", agg.fastest_instructions() / volume); - std::print(" {:5.2f} B/d ", agg.branches() / volume); - std::print(" {:5.2f} BM/d ", agg.branch_misses() / volume); - std::print(" {:5.2f} i/B ", agg.fastest_instructions() / bytes); std::print(" {:5.2f} i/c ", agg.fastest_instructions() / agg.fastest_cycles()); } @@ -151,11 +45,10 @@ enum class DistributionMode { Natural // Natural distribution (more high-digit numbers) }; -template -std::vector generate_large_set(size_t count = 1'000'000, - int min_digits = 1, int max_digits = 17, - DistributionMode mode = DistributionMode::Uniform) { - std::vector result; +std::vector generate_large_set(size_t count = 1'000'000, + int min_digits = 1, int max_digits = 20, + DistributionMode mode = DistributionMode::Uniform) { + std::vector result; result.reserve(count); std::random_device rd; @@ -175,90 +68,36 @@ std::vector generate_large_set(size_t count = 1'000'000, : uniform_digit_dist(gen); }; - if constexpr (std::is_same_v) { - std::uniform_real_distribution value_dist(-1e10, 1e10); - for (size_t i = 0; i < count; ++i) { - int mantissa_size = pick_digits(mode); - decimal_float df; - do { - df = double_to_decimal_float(value_dist(gen), mantissa_size); - } while (fast_digit_count(df.mantissa) != mantissa_size); - result.emplace_back(df); - } - } else if constexpr (std::is_same_v) { - std::array pow10; - pow10[0] = 1; - for (int i = 1; i <= 20; ++i) - pow10[i] = pow10[i - 1] * 10; - - for (size_t i = 0; i < count; ++i) { - int digits = pick_digits(mode); - uint64_t lower = pow10[digits - 1]; - uint64_t upper = digits < 20 - ? pow10[digits] - 1 - : std::numeric_limits::max(); - std::uniform_int_distribution dis(lower, upper); - result.push_back(dis(gen)); - } + std::array pow10; + pow10[0] = 1; + for (int i = 1; i <= 20; ++i) + pow10[i] = pow10[i - 1] * 10; + + for (size_t i = 0; i < count; ++i) { + int digits = pick_digits(mode); + uint64_t lower = pow10[digits - 1]; + uint64_t upper = digits < 20 + ? pow10[digits] - 1 + : std::numeric_limits::max(); + std::uniform_int_distribution dis(lower, upper); + result.push_back(dis(gen)); } return result; } -template -std::vector read_from_file(const std::string &filename) { - std::vector values; +std::vector read_from_file(const std::string &filename) { + std::vector values; std::ifstream infile(filename); std::string line; while (std::getline(infile, line)) { std::istringstream iss(line); - if (T val; iss >> val) + if (uint64_t val; iss >> val) values.push_back(val); } return values; } -bool compare_decimal_floats_algorithms(uint64_t mantissa, int32_t exponent) { - std::print("\nComparing mantissa={} exponent={}\n", mantissa, exponent); - char buffer[32]; - std::fill(buffer, buffer + sizeof(buffer), 0); - int n; - n = scalar_to_chars(mantissa, exponent, buffer); - buffer[n] = '\0'; - std::string fastans = buffer; - - std::print("fast: {}\n", fastans); -#if defined(CHAMPAGNE_LEMIRE_AVX512) && CHAMPAGNE_LEMIRE_AVX512 - n = avx512_to_chars(mantissa, exponent, buffer); - buffer[n] = '\0'; - std::string avx512ans = buffer; - // Short normalization: remove a single '0' after E/e and optional sign (E09 -> E9) - std::print("AVX-512: {}\n", avx512ans); - -#endif - - n = jkj::dragonbox::detail::to_chars(mantissa, exponent, buffer) - buffer; - buffer[n] = '\0'; - std::print("Dragonbox: {}\n", buffer); -#if defined(CHAMPAGNE_LEMIRE_AVX512) && CHAMPAGNE_LEMIRE_AVX512 - std::string dragonans = buffer; - if (avx512ans != dragonans) { - std::print("Mismatch with Dragonbox: {}\n", dragonans); - // allow an extra 0 after E if the exponent is one digit - if (auto pos = avx512ans.find_first_of("Ee"); pos != std::string::npos) { - size_t j = pos + 1; - if (j < avx512ans.size() && (avx512ans[j] == '+' || avx512ans[j] == '-')) ++j; - if (j + 1 < avx512ans.size() && avx512ans[j] == '0' && isdigit(static_cast(avx512ans[j+1]))) { - avx512ans.erase(j, 1); - std::print("AVX-512: {}\n", avx512ans); - } - } - return avx512ans == dragonans; - } -#endif - return true; -} - bool compare_integers_algorithms(uint64_t number) { std::print("\nComparing number={}\n", number); char buffer[32]; @@ -326,32 +165,7 @@ bool compare_integers_algorithms(uint64_t number) { return true; } -bool test_some_harcoded_floats() { - bool result = true; - - result &= compare_decimal_floats_algorithms(789789974432, 20); - result &= compare_decimal_floats_algorithms(12345678901234567ul, 20); // 17 - result &= compare_decimal_floats_algorithms(1234567890123456ul, 19); // 16 - result &= compare_decimal_floats_algorithms(123456789012345ul, 18); // 15 - result &= compare_decimal_floats_algorithms(12345678901234ul, 17); // 14 - result &= compare_decimal_floats_algorithms(1234567890123ul, 16); // 13 - result &= compare_decimal_floats_algorithms(123456789012ul, 15); // 12 - result &= compare_decimal_floats_algorithms(12345678901ul, 14); // 11 - result &= compare_decimal_floats_algorithms(1234567890ul, 13); // 10 - result &= compare_decimal_floats_algorithms(123456789, 9); // 9 - result &= compare_decimal_floats_algorithms(12345678, 8); - result &= compare_decimal_floats_algorithms(1234567, 7); - result &= compare_decimal_floats_algorithms(123456, 6); - result &= compare_decimal_floats_algorithms(12345, 5); - result &= compare_decimal_floats_algorithms(1236, 4); - result &= compare_decimal_floats_algorithms(123, 3); - result &= compare_decimal_floats_algorithms(12, 2); - result &= compare_decimal_floats_algorithms(1, 1); - result &= compare_decimal_floats_algorithms(0, 1); - return result; -} - -bool test_some_harcoded_integers() { +bool test_some_hardcoded_integers() { std::printf("Running hardcoded integer tests\n"); bool result = true; result &= compare_integers_algorithms(12345678901234567890ull); // 20 @@ -378,21 +192,13 @@ bool test_some_harcoded_integers() { return result; } -template -Variant detect_variant(const std::vector &data) { +Variant detect_variant(const std::vector &data) { const auto start = std::chrono::steady_clock::now(); const size_t sample_size = Ratio_To_Sample * size(data); std::array lengthDistrib{}; for (size_t i = 0; i < sample_size; ++i) { - const T &v = data[i]; - const uint64_t number = [&] { - if constexpr (std::is_same_v, decimal_float>) - return v.mantissa; - else - return v; - }(); - ++lengthDistrib[fast_digit_count(number)]; + ++lengthDistrib[fast_digit_count(data[i])]; } const size_t total = std::reduce(lengthDistrib.begin(), @@ -409,8 +215,7 @@ Variant detect_variant(const std::vector &data) { : Variant::Heterogeneous; } -template -void run_benchmark(const std::vector &data, [[maybe_unused]] Variant algo_variant = Variant::Auto) { +void run_benchmark(const std::vector &data, [[maybe_unused]] Variant algo_variant = Variant::Auto) { uint64_t counter = 0; char buffer[128]; @@ -418,255 +223,199 @@ void run_benchmark(const std::vector &data, [[maybe_unused]] Variant algo_var auto run_and_report = [&](auto&& name, auto&& func, size_t volume) { std::print("\n"); for (size_t i = 0; i < Number_Benchmark_Runs; ++i) - pretty_print(volume, data.size() * sizeof(T), name, bench(func)); + pretty_print(data.size(), volume, name, bench(func)); }; - if constexpr (std::is_same_v) { #if defined(CHAMPAGNE_LEMIRE_AVX512) && CHAMPAGNE_LEMIRE_AVX512 - auto avx512l = [&data, &counter, &buffer]() { - uint64_t local_counter = 0; - for (size_t i = 0; i < data.size(); ++i) { - char *start = buffer; - buffer[0] = '-'; - start += data[i].sign ? 1 : 0; - local_counter += avx512_to_chars(data[i].mantissa, data[i].exponent, start) - + (data[i].sign ? 1 : 0); - } - counter = local_counter; - }; - avx512l(); - size_t volume512 = counter; - std::print("Volume 512: {}\n", volume512); -#endif - auto scalar = [&data, &counter, &buffer]() { - uint64_t local_counter = 0; - for (size_t i = 0; i < data.size(); ++i) { - char *start = buffer; - buffer[0] = '-'; - start += data[i].sign ? 1 : 0; - local_counter += scalar_to_chars(data[i].mantissa, data[i].exponent, start) - + (data[i].sign ? 1 : 0); - } - counter = local_counter; - }; - scalar(); - size_t volume_scalar = counter; - std::print("Volume scalar: {}\n", volume_scalar); - - auto drag = [&data, &counter, &buffer]() { - using jkj::dragonbox::detail::to_chars; - uint64_t local_counter = 0; - for (size_t i = 0; i < data.size(); ++i) { - char *start = buffer; - buffer[0] = '-'; - start += data[i].sign ? 1 : 0; - local_counter += (to_chars(data[i].mantissa, data[i].exponent, start) - buffer) - + (data[i].sign ? 1 : 0); - } - counter = local_counter; - }; - drag(); - size_t volume_drag = counter; - std::print("Volume drag: {}\n", volume_drag); -#if defined(CHAMPAGNE_LEMIRE_AVX512) && CHAMPAGNE_LEMIRE_AVX512 - run_and_report("avx-512+champagne_lemire", avx512l, volume512); -#endif - run_and_report("dragonbox", drag, volume_drag); - run_and_report("scalar", scalar, volume_scalar); - } else if constexpr (std::is_same_v) { -#if defined(CHAMPAGNE_LEMIRE_AVX512) && CHAMPAGNE_LEMIRE_AVX512 - auto avx512l = [&data, &counter, &buffer, &algo_variant]() { - if (algo_variant == Variant::Auto) - algo_variant = detect_variant(data); - uint64_t local_counter = 0; - if (algo_variant == Variant::Homogeneous) { - for (size_t i = 0; i < data.size(); ++i) - local_counter += avx512_to_chars(data[i], buffer); - } else { - for (size_t i = 0; i < data.size(); ++i) - local_counter += avx512_to_chars(data[i], buffer); - } - counter = local_counter; - }; - Variant detected = detect_variant(data); - std::print("Auto variant would select: {}\n", - detected == Variant::Homogeneous ? "Homogeneous" : "Heterogeneous"); - avx512l(); - size_t volume512 = counter; - std::print("Volume 512: {}\n", volume512); -#endif - - auto standard_to_chars = [&]() { - uint64_t local_counter = 0; - for (size_t i = 0; i < data.size(); ++i) - local_counter += std::to_chars(buffer, buffer + sizeof(buffer), data[i]).ptr - buffer; - counter = local_counter; - }; - standard_to_chars(); - size_t volume_standard = counter; - std::print("Volume std::to_chars: {}\n", volume_standard); - - auto absl_fastint = [&]() { - uint64_t local_counter = 0; - for (size_t i = 0; i < data.size(); ++i) - local_counter += baselines_int::absl_fastint(data[i], buffer); - counter = local_counter; - }; - absl_fastint(); - size_t volume_absl_fastint = counter; - std::print("Volume absl_fastint: {}\n", volume_absl_fastint); - - auto jeaiii_fast = [&]() { - uint64_t local_counter = 0; - for (size_t i = 0; i < data.size(); ++i) - local_counter += baselines_int::jeaiii_fast_uint64(data[i], buffer); - counter = local_counter; - }; - jeaiii_fast(); - size_t volume_jeaiii_fast = counter; - std::print("Volume jeaiii_fast_uint64: {}\n", volume_jeaiii_fast); - - auto itoa_an_64 = [&]() { - uint64_t local_counter = 0; - for (size_t i = 0; i < data.size(); ++i) - local_counter += baselines_int::itoa_an_64(data[i], buffer); - counter = local_counter; - }; - itoa_an_64(); - size_t volume_itoa_an_64 = counter; - std::print("Volume itoa_an_64: {}\n", volume_itoa_an_64); - - auto itoa_yy_64 = [&]() { - uint64_t local_counter = 0; + auto avx512l = [&data, &counter, &buffer, &algo_variant]() { + if (algo_variant == Variant::Auto) + algo_variant = detect_variant(data); + uint64_t local_counter = 0; + if (algo_variant == Variant::Homogeneous) { for (size_t i = 0; i < data.size(); ++i) - local_counter += baselines_int::itoa_yy_64(data[i], buffer); - counter = local_counter; - }; - itoa_yy_64(); - size_t volume_itoa_yy_64 = counter; - std::print("Volume itoa_yy_64: {}\n", volume_itoa_yy_64); - auto mathisen_sse = [&]() { - uint64_t local_counter = 0; - for (size_t i = 0; i < data.size(); ++i) - local_counter += baselines_int::mathisen_sse(data[i], buffer); - counter = local_counter; - }; - mathisen_sse(); - size_t volume_mathisen = counter; - std::print("Volume mathisen_sse: {}\n", volume_mathisen); - auto mula_sse64 = [&]() { - uint64_t local_counter = 0; - for (size_t i = 0; i < data.size(); ++i) - local_counter += baselines_int::mula_sse64(data[i], buffer); - counter = local_counter; - }; - mula_sse64(); - size_t volume_mula_sse64 = counter; - std::print("Volume mula_sse64: {}\n", volume_mula_sse64); - - auto hopman = [&]() { - uint64_t local_counter = 0; - for (size_t i = 0; i < data.size(); ++i) - local_counter += baselines_int::hopman_fast(data[i], buffer); - counter = local_counter; - }; - hopman(); - size_t volume_hopman_fast = counter; - std::print("Volume hopman_fast: {}\n", volume_hopman_fast); - - auto naive_onepass = [&]() { - uint64_t local_counter = 0; + local_counter += avx512_to_chars(data[i], buffer); + } else { for (size_t i = 0; i < data.size(); ++i) - local_counter += baselines_int::naive(data[i], buffer); - counter = local_counter; - }; - naive_onepass(); - size_t volume_naive_onepass = counter; - std::print("Volume naive_onepass: {}\n", volume_naive_onepass); + local_counter += avx512_to_chars(data[i], buffer); + } + counter = local_counter; + }; + Variant detected = detect_variant(data); + std::print("Auto variant would select: {}\n", + detected == Variant::Homogeneous ? "Homogeneous" : "Heterogeneous"); + avx512l(); + size_t volume512 = counter; + std::print("Volume 512: {}\n", volume512); +#endif + + auto standard_to_chars = [&]() { + uint64_t local_counter = 0; + for (size_t i = 0; i < data.size(); ++i) + local_counter += std::to_chars(buffer, buffer + sizeof(buffer), data[i]).ptr - buffer; + counter = local_counter; + }; + standard_to_chars(); + size_t volume_standard = counter; + std::print("Volume std::to_chars: {}\n", volume_standard); + + auto absl_fastint = [&]() { + uint64_t local_counter = 0; + for (size_t i = 0; i < data.size(); ++i) + local_counter += baselines_int::absl_fastint(data[i], buffer); + counter = local_counter; + }; + absl_fastint(); + size_t volume_absl_fastint = counter; + std::print("Volume absl_fastint: {}\n", volume_absl_fastint); + + auto jeaiii_fast = [&]() { + uint64_t local_counter = 0; + for (size_t i = 0; i < data.size(); ++i) + local_counter += baselines_int::jeaiii_fast_uint64(data[i], buffer); + counter = local_counter; + }; + jeaiii_fast(); + size_t volume_jeaiii_fast = counter; + std::print("Volume jeaiii_fast_uint64: {}\n", volume_jeaiii_fast); + + auto itoa_an_64 = [&]() { + uint64_t local_counter = 0; + for (size_t i = 0; i < data.size(); ++i) + local_counter += baselines_int::itoa_an_64(data[i], buffer); + counter = local_counter; + }; + itoa_an_64(); + size_t volume_itoa_an_64 = counter; + std::print("Volume itoa_an_64: {}\n", volume_itoa_an_64); + + auto itoa_yy_64 = [&]() { + uint64_t local_counter = 0; + for (size_t i = 0; i < data.size(); ++i) + local_counter += baselines_int::itoa_yy_64(data[i], buffer); + counter = local_counter; + }; + itoa_yy_64(); + size_t volume_itoa_yy_64 = counter; + std::print("Volume itoa_yy_64: {}\n", volume_itoa_yy_64); + auto mathisen_sse = [&]() { + uint64_t local_counter = 0; + for (size_t i = 0; i < data.size(); ++i) + local_counter += baselines_int::mathisen_sse(data[i], buffer); + counter = local_counter; + }; + mathisen_sse(); + size_t volume_mathisen = counter; + std::print("Volume mathisen_sse: {}\n", volume_mathisen); + auto mula_sse64 = [&]() { + uint64_t local_counter = 0; + for (size_t i = 0; i < data.size(); ++i) + local_counter += baselines_int::mula_sse64(data[i], buffer); + counter = local_counter; + }; + mula_sse64(); + size_t volume_mula_sse64 = counter; + std::print("Volume mula_sse64: {}\n", volume_mula_sse64); + + auto hopman = [&]() { + uint64_t local_counter = 0; + for (size_t i = 0; i < data.size(); ++i) + local_counter += baselines_int::hopman_fast(data[i], buffer); + counter = local_counter; + }; + hopman(); + size_t volume_hopman_fast = counter; + std::print("Volume hopman_fast: {}\n", volume_hopman_fast); + + auto naive_onepass = [&]() { + uint64_t local_counter = 0; + for (size_t i = 0; i < data.size(); ++i) + local_counter += baselines_int::naive(data[i], buffer); + counter = local_counter; + }; + naive_onepass(); + size_t volume_naive_onepass = counter; + std::print("Volume naive_onepass: {}\n", volume_naive_onepass); #if defined(CHAMPAGNE_LEMIRE_AVX512) && CHAMPAGNE_LEMIRE_AVX512 - run_and_report("avx-512+champagne_lemire", avx512l, volume512); + run_and_report("avx-512+champagne_lemire", avx512l, volume512); #endif - run_and_report("std::to_chars", standard_to_chars, volume_standard); - run_and_report("absl_fastint", absl_fastint, volume_absl_fastint); - run_and_report("jeaiii_fast_uint64", jeaiii_fast, volume_jeaiii_fast); - run_and_report("itoa_an_64", itoa_an_64, volume_itoa_an_64); - run_and_report("itoa_yy_64", itoa_yy_64, volume_itoa_yy_64); - run_and_report("mathisen_sse_u64", mathisen_sse, volume_mathisen); - run_and_report("mula_sse64", mula_sse64, volume_mula_sse64); - run_and_report("hopman_fast", hopman, volume_hopman_fast); - run_and_report("naive_onepass", naive_onepass, volume_naive_onepass); - } else { - static_assert(false, "Unsupported type"); - } + run_and_report("std::to_chars", standard_to_chars, volume_standard); + run_and_report("absl_fastint", absl_fastint, volume_absl_fastint); + run_and_report("jeaiii_fast_uint64", jeaiii_fast, volume_jeaiii_fast); + run_and_report("itoa_an_64", itoa_an_64, volume_itoa_an_64); + run_and_report("itoa_yy_64", itoa_yy_64, volume_itoa_yy_64); + run_and_report("mathisen_sse_u64", mathisen_sse, volume_mathisen); + run_and_report("mula_sse64", mula_sse64, volume_mula_sse64); + run_and_report("hopman_fast", hopman, volume_hopman_fast); + run_and_report("naive_onepass", naive_onepass, volume_naive_onepass); } int main(int argc, char **argv) { -#ifdef __clang__ - std::print("Clang version: {}.{}.{}\n", __clang_major__, __clang_minor__, __clang_patchlevel__); -#elif defined(__GNUC__) - std::print("GCC version: {}.{}.{}\n", __GNUC__, __GNUC_MINOR__, __GNUC_PATCHLEVEL__); -#endif - std::print("==============================================================\n"); - std::print("Warning: the results are sensitive to the compiler being used.\n"); - std::print("Try with GCC and LLVM.\n"); - std::print("==============================================================\n"); - -#ifndef __OPTIMIZE__ - std::print("Warning: Build is not optimized. Performance may be poor.\n"); -#endif - - cxxopts::Options options("benchmark", "Float to string conversion benchmark"); + cxxopts::Options options("benchmark", "Integer to string conversion benchmark"); options.add_options() ("h,help", "Show help message") - ("i,int", "Evaluate integer conversion (uint64_t) instead of floats") ("q,quick", "Do a quick validation test with some hardcoded cases") - ("f,file", "Input file containing numbers", cxxopts::value()) - ("n,num", "Number of random numbers to generate", cxxopts::value()->default_value("1000000")) - ("m,min", "Minimum mantissa digits for random generation (1-17)", cxxopts::value()->default_value("1")) - ("M,max", "Maximum mantissa digits for random generation (1-17)", cxxopts::value()->default_value("17")) + ("f,file", "Input file containing integers", cxxopts::value()) + ("n,num", "Number of random integers to generate", cxxopts::value()->default_value("1000000")) + ("m,min", "Minimum digits for random generation (1-20)", cxxopts::value()->default_value("1")) + ("M,max", "Maximum digits for random generation (1-20)", cxxopts::value()->default_value("20")) ("v,variant", "Variant of our AVX512 algorithm to benchmark:" "'homo', 'hetero' or 'auto'", cxxopts::value()->default_value("auto")) ("d,distribution", "Distribution mode: 'uniform' (equal probability for each digit count)" "or 'natural' (more high-digit numbers)", cxxopts::value()->default_value("natural")); - std::variant, std::vector> data; + std::vector data; Variant algo_variant; try { auto result = options.parse(argc, argv); + // Check for unexpected positional arguments + if (!result.unmatched().empty()) { + std::print(stderr, "Error: unexpected argument '{}'\n", result.unmatched()[0]); + std::print(stderr, "Use -f to specify an input file.\n"); + std::print(stderr, "Run with --help for usage information.\n"); + return EXIT_FAILURE; + } + if (result.count("help")) { std::print("{}\n", options.help()); std::print("\nExamples:\n"); - std::print(" {} -n 1000 # Random 1000 numbers with 1-17 digits precision\n", argv[0]); - std::print(" {} -f data/canada.txt # Use data from file\n", argv[0]); - std::print(" {} -v homo # Use the variant optimized for homogeneous digits length\n", argv[0]); - std::print(" {} -m 1 -M 20 -i # Random uint64_t with 1-20 digits (uniform)\n", argv[0]); - std::print(" {} -m 10 -M 17 # Random floats with 10-17 digit mantissas (uniform)\n", argv[0]); - std::print(" {} -m 5 -M 15 -d natural # Natural distribution with 5-15 digit range\n", argv[0]); + std::print(" {} -n 1000 # Random 1000 integers with 1-20 digits\n", argv[0]); + std::print(" {} -f data/twitterjson_integers.txt # Use data from file\n", argv[0]); + std::print(" {} -v homo # Use the variant optimized for homogeneous digit lengths\n", argv[0]); + std::print(" {} -m 1 -M 20 # Random uint64_t with 1-20 digits\n", argv[0]); + std::print(" {} -m 10 -M 15 # Random integers with 10-15 digits\n", argv[0]); + std::print(" {} -m 5 -M 15 -d natural # Natural distribution with 5-15 digit range\n", argv[0]); return EXIT_SUCCESS; } - const bool integer_mode = result.count("int") > 0; + // Print compiler/build info banner +#ifdef __clang__ + std::print("Clang version: {}.{}.{}\n", __clang_major__, __clang_minor__, __clang_patchlevel__); +#elif defined(__GNUC__) + std::print("GCC version: {}.{}.{}\n", __GNUC__, __GNUC_MINOR__, __GNUC_PATCHLEVEL__); +#endif + std::print("==============================================================\n"); + std::print("Warning: the results are sensitive to the compiler being used.\n"); + std::print("Try with GCC and LLVM.\n"); + std::print("==============================================================\n"); + +#ifndef __OPTIMIZE__ + std::print("Warning: Build is not optimized. Performance may be poor.\n"); +#endif + if (result.count("quick")) { - bool success = integer_mode - ? test_some_harcoded_integers() - : test_some_harcoded_floats(); + bool success = test_some_hardcoded_integers(); if(!success) { std::print("Some tests failed!\n"); - if(integer_mode) - return EXIT_FAILURE; - // - std::print("Failures with floats are expected!\n"); - return EXIT_SUCCESS; - + return EXIT_FAILURE; } std::print("All tests passed!\n"); return EXIT_SUCCESS; } - // Parse distribution mode + // Parse variant const std::string variant_str = result["variant"].as(); if (variant_str == "auto") { algo_variant = Variant::Auto; @@ -682,9 +431,8 @@ int main(int argc, char **argv) { // Validate digit ranges const int min_digits = result["min"].as(); const int max_digits = result["max"].as(); - const int max_allowed = integer_mode ? 20 : 17; - if ((min_digits < 1) | (min_digits > max_allowed) | - (min_digits < 1) | (max_digits > max_allowed) | + if ((min_digits < 1) | (min_digits > 20) | + (max_digits < 1) | (max_digits > 20) | (min_digits > max_digits)) { std::print(stderr, "Error: invalid digit range [{}, {}]\n", min_digits, max_digits); return EXIT_FAILURE; @@ -693,28 +441,12 @@ int main(int argc, char **argv) { if (result.count("file")) { // Load data from file const std::string filename = result["file"].as(); - if (integer_mode) { - const auto ints = read_from_file(filename); - if (ints.empty()) { - std::print(stderr, "No valid integers found in the file: {}\n", filename); - return EXIT_FAILURE; - } - std::print("Loaded {} integers from file: {}\n", ints.size(), filename); - data = std::move(ints); - } else { - const auto floats = read_from_file(filename); - if (floats.empty()) { - std::print(stderr, "No valid floats found in the file: {}\n", filename); - return EXIT_FAILURE; - } - std::print("Loaded {} floats from file: {}\n", floats.size(), filename); - - std::vector floats_as_decimals; - floats_as_decimals.reserve(floats.size()); - for (double f : floats) - floats_as_decimals.push_back(double_to_decimal_float(f)); - data = std::move(floats_as_decimals); + data = read_from_file(filename); + if (data.empty()) { + std::print(stderr, "No valid integers found in the file: {}\n", filename); + return EXIT_FAILURE; } + std::print("Loaded {} integers from file: {}\n", data.size(), filename); } else { // Generate random data // Parse distribution mode const std::string distribution_str = result["distribution"].as(); @@ -729,13 +461,9 @@ int main(int argc, char **argv) { } const size_t num_values = result["num"].as(); - if (integer_mode) - data = generate_large_set(num_values, min_digits, max_digits, distribution_mode); - else - data = generate_large_set(num_values, min_digits, max_digits, distribution_mode); - std::print("Generated {} random {} with digits in range [{}, {}] using {} distribution\n", - num_values, integer_mode ? "integers" : "floats", - min_digits, max_digits, distribution_str); + data = generate_large_set(num_values, min_digits, max_digits, distribution_mode); + std::print("Generated {} random integers with digits in range [{}, {}] using {} distribution\n", + num_values, min_digits, max_digits, distribution_str); } } catch (const cxxopts::exceptions::exception& e) { std::print(stderr, "Error parsing arguments: {}\n", e.what()); @@ -744,26 +472,16 @@ int main(int argc, char **argv) { } // Print length distribution - std::visit([](auto &vec) { - std::array lengthDistrib{}; - for (const auto &v : vec) { - uint64_t number = [&] { - if constexpr (std::is_same_v, decimal_float>) - return v.mantissa; - else - return v; - }(); - ++lengthDistrib[fast_digit_count(number)]; - } + std::array lengthDistrib{}; + for (const auto &v : data) { + ++lengthDistrib[fast_digit_count(v)]; + } - std::print("length distribution:\n"); - for (size_t i = 1; i < lengthDistrib.size(); ++i) - std::print("\t{:2}: {}\n", i, lengthDistrib[i]); - }, data); + std::print("length distribution:\n"); + for (size_t i = 1; i < lengthDistrib.size(); ++i) + std::print("\t{:2}: {}\n", i, lengthDistrib[i]); - std::visit([av = algo_variant](auto &vec) { - run_benchmark(vec, av); - }, data); + run_benchmark(data, algo_variant); } #else // defined(__x86_64__) || defined(_M_X64) @@ -773,4 +491,4 @@ int main() { std::print("This benchmark requires an x86-64 architecture.\n"); return EXIT_FAILURE; } -#endif // defined(__x86_64__) || defined(_M_X64) \ No newline at end of file +#endif // defined(__x86_64__) || defined(_M_X64) diff --git a/data/DATASETS.md b/data/DATASETS.md index ea9fe71..17ea72d 100644 --- a/data/DATASETS.md +++ b/data/DATASETS.md @@ -1,3 +1,5 @@ +# Integer Datasets + ### stackoverflow_unix_timestamps_integers.txt - **Source:** Stack Overflow answers-to-questions temporal network from SNAP (Stanford Network Analysis Project) - **URL:** https://snap.stanford.edu/data/sx-stackoverflow-a2q.txt.gz @@ -20,7 +22,7 @@ - **Date Downloaded:** January 2026 - **License:** Available for research use (SNAP datasets, original data from NBER) -### twitter.json +### twitterjson_integers.txt - **Source:** Export of data from Twitter's API - **Domain:** Social media data - **Digit Length Distribution:** Heterogeneous: @@ -38,7 +40,7 @@ - **Count:** 2,108 integers - **Description:** JSON file commonly used for benchmarking; integers extracted from Twitter API data; exhibits heterogeneous distribution with significant proportions of small integers (principally 1–3 digits) as well as larger integers (10 and 18 digits) -### citm_catalog.json +### citm_catalog_integers.txt - **Source:** Catalog of events that occurred in a venue part of CitM (Cité de la Musique) in Paris - **Domain:** Cultural event catalog - **Digit Length Distribution:** Homogeneous: diff --git a/data/canada.txt b/data/canada.txt deleted file mode 100644 index 7a14127..0000000 --- a/data/canada.txt +++ /dev/null @@ -1,111126 +0,0 @@ --65.613616999999977 -43.420273000000009 --65.619720000000029 -43.418052999999986 --65.625 -43.421379000000059 --65.636123999999882 -43.449714999999969 --65.633056999999951 -43.474709000000132 --65.611389000000031 -43.513054000000068 --65.605835000000013 -43.516105999999979 --65.598343 -43.515830999999935 --65.566101000000003 -43.508331000000055 --65.561935000000005 -43.504439999999988 --65.55999799999995 -43.499718000000087 --65.573333999999988 -43.476379000000065 --65.593612999999948 -43.444153000000028 --65.613616999999977 -43.420273000000009 --59.816947999999911 -43.928328999999962 --59.841667000000029 -43.918602000000021 --59.866393999999957 -43.909987999999998 --59.879722999999956 -43.906654000000003 --59.895835999999974 -43.904160000000047 --59.919448999999929 -43.901099999999985 --59.953330999999991 -43.898604999999975 --60.013617999999951 -43.903320000000008 --60.028609999999958 -43.905548000000124 --60.078338999999914 -43.917496000000028 --60.103888999999981 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-3595 -3592 -3593 -3595 -3596 -3597 -3597 -3596 -3595 -3597 -3594 -3595 -3595 -3594 -3597 -3577 -3594 -3597 -3597 -3594 -3577 -3597 -3578 -3577 -3577 -3578 -3597 -3581 -3578 -3597 -3597 -3578 -3581 -3597 -3598 -3581 -3581 -3598 -3597 -3599 -3598 -3597 -3597 -3598 -3599 -3597 -3596 -3599 -3599 -3596 -3597 diff --git a/scripts/README.md b/scripts/README.md index 2cacdb8..317ffe6 100644 --- a/scripts/README.md +++ b/scripts/README.md @@ -22,7 +22,7 @@ Python 3.8+ installed **Important**: All scripts should be run from the project root directory, not from within the `scripts/` folder. ```bash -cd /path/to/float_string_chars-gen_bench +cd /path/to/int_serialization_bench ./scripts/generate_raw_outputs.py [compiler] ``` @@ -169,7 +169,7 @@ Optional arguments: This will: - Auto-detect available compilers if `--compiler` not specified - Parse all `outputs/*.raw` files for each compiler -- Extract timing information (ns/d - nanoseconds per digit/character) +- Extract timing information (ns/n - nanoseconds per number) - Determine which variant was auto-selected for each dataset - Generate LaTeX table file(s) with compiler name in filename - Print a preview of the table @@ -217,7 +217,7 @@ Optional arguments: This will: - Auto-detect available compilers if `--compiler` not specified - Parse benchmark outputs for all algorithms -- Extract multiple metrics: ns/d (nanoseconds per character), i/d (instructions per character), c/d (cycles per character) +- Extract multiple metrics: ns/n (nanoseconds per number), i/n (instructions per number), c/n (cycles per number) - Calculate speedup percentages relative to AVX-512 for each metric - Compare 10 different algorithms across 5 real-world and synthetic datasets - Bold the best (lowest) value for each metric @@ -267,7 +267,7 @@ This will: - Auto-detect available compilers if `--compiler` not specified - Auto-detect CPU model from existing .raw files if not specified - Parse benchmark outputs for uniform-Ndigit-1M datasets (N=1 to 20) -- Extract ns/d metrics for all algorithms +- Extract ns/n metrics for all algorithms - Generate line plot(s) showing performance vs digit length - Save as PDF in the outputs directory with compiler name in filename @@ -316,7 +316,7 @@ Optional arguments: This will: - Auto-detect available compilers if `--compiler` not specified - Parse benchmark outputs for Twitter JSON, CIT Patents, and Natural 1-8 datasets -- Extract ns/d metrics for all (or 5 simplified) algorithms +- Extract ns/n metrics for all (or 5 simplified) algorithms - Generate combined bar chart (3 subplots) or separate figures per dataset - Save as PDF in the outputs directory with compiler name in filename diff --git a/scripts/generate_algorithm_comparison_table.py b/scripts/generate_algorithm_comparison_table.py index 9fefb4d..50a91aa 100755 --- a/scripts/generate_algorithm_comparison_table.py +++ b/scripts/generate_algorithm_comparison_table.py @@ -42,9 +42,9 @@ # Metrics to extract # Format: (pattern_suffix, column_header, latex_unit) METRICS = [ - ('ns/d', 'ns/d', 'ns/d'), # nanoseconds per digit (character) - ('i/d', 'i/d', 'ins/d'), # instructions per digit - ('c/d', 'c/d', 'cyc/d'), # cycles per digit + ('ns/n', 'ns/n', 'ns/n'), # nanoseconds per number + ('i/n', 'i/n', 'ins/n'), # instructions per number + ('c/n', 'c/n', 'cyc/n'), # cycles per number ] @@ -62,17 +62,17 @@ def parse_algorithm_metrics(file_path: Path, algorithm_pattern: str) -> Optional return None # Build regex pattern to capture the full line for this algorithm - # Example: "avx-512+champagne_lemire : 1.94 ns/d 5.48 GHz 10.64 c/d ..." + # Example: "avx-512+champagne_lemire : 1.94 ns/n 5.48 GHz 10.64 c/n ..." escaped_pattern = algorithm_pattern - pattern = rf'{escaped_pattern}\s*:\s*([\d.]+)\s*ns/d\s*[\d.]+\s*GHz\s*([\d.]+)\s*c/d\s*([\d.]+)\s*i/d' + pattern = rf'{escaped_pattern}\s*:\s*([\d.]+)\s*ns/n\s*[\d.]+\s*GHz\s*([\d.]+)\s*c/n\s*([\d.]+)\s*i/n' match = re.search(pattern, content) if not match: return None return { - 'ns/d': float(match.group(1)), - 'c/d': float(match.group(2)), - 'i/d': float(match.group(3)), + 'ns/n': float(match.group(1)), + 'c/n': float(match.group(2)), + 'i/n': float(match.group(3)), } @@ -206,14 +206,14 @@ def generate_latex_table(compiler: str, output_dir: str) -> str: # Table header lines.append(r"\begin{table}") lines.append(r" \caption{Performance comparison of integer-to-string algorithms across datasets.") - lines.append(r" Metrics: ns/d = nanoseconds, i/d = instructions, c/d = cycles per character.") + lines.append(r" Metrics: ns/n = nanoseconds, i/n = instructions, c/n = cycles per number.") lines.append(r" \textbf{Bold} indicates fastest; \% shows difference vs Champagne--Lemire (positive = slower).}%") lines.append(r" \label{tab:algorithm_comparison}") lines.append(r" \centering") lines.append(r" \small") lines.append(r" \begin{tabular}{llrrrrrr}") lines.append(r" \toprule") - lines.append(r" Algorithm & Dataset & ns/d & \% & i/d & \% & c/d & \% \\") + lines.append(r" Algorithm & Dataset & ns/n & \% & i/n & \% & c/n & \% \\") lines.append(r" \midrule") # Data rows - outer loop: algorithms, inner loop: datasets @@ -232,9 +232,9 @@ def generate_latex_table(compiler: str, output_dir: str) -> str: else: row_parts.append("") - # Check if this algorithm has the best ns/d for this dataset - value_nsd = algo_metrics.get('ns/d') - best_nsd = best_values.get((dataset_display, 'ns/d')) + # Check if this algorithm has the best ns/n for this dataset + value_nsd = algo_metrics.get('ns/n') + best_nsd = best_values.get((dataset_display, 'ns/n')) is_best_algo = (value_nsd is not None and best_nsd is not None and abs(value_nsd - best_nsd) < 0.01) diff --git a/scripts/generate_bar_chart.py b/scripts/generate_bar_chart.py index 533207a..3044bdc 100755 --- a/scripts/generate_bar_chart.py +++ b/scripts/generate_bar_chart.py @@ -65,15 +65,15 @@ def parse_algorithm_metrics(file_path: Path, algorithm_pattern: str) -> Optional return None escaped_pattern = algorithm_pattern - pattern = rf'{escaped_pattern}\s*:\s*([\d.]+)\s*ns/d\s*[\d.]+\s*GHz\s*([\d.]+)\s*c/d\s*([\d.]+)\s*i/d' + pattern = rf'{escaped_pattern}\s*:\s*([\d.]+)\s*ns/n\s*[\d.]+\s*GHz\s*([\d.]+)\s*c/n\s*([\d.]+)\s*i/n' match = re.search(pattern, content) if not match: return None return { - 'ns/d': float(match.group(1)), - 'c/d': float(match.group(2)), - 'i/d': float(match.group(3)), + 'ns/n': float(match.group(1)), + 'c/n': float(match.group(2)), + 'i/n': float(match.group(3)), } @@ -153,14 +153,14 @@ def get_available_compilers(output_dir: Path) -> List[str]: def collect_data(output_dir: Path, compiler: str, algorithms: List[Tuple[str, str]]) -> Dict[str, Dict[str, float]]: """ - Collect ns/d data for all datasets and algorithms. - Returns: {dataset_display: {algorithm_name: ns/d_value}} + Collect ns/n data for all datasets and algorithms. + Returns: {dataset_display: {algorithm_name: ns/n_value}} """ data = {} for dataset_base, dataset_display in DATASETS: results = get_algorithm_results_for_dataset(dataset_base, compiler, output_dir, algorithms) if results: - data[dataset_display] = {algo: metrics['ns/d'] for algo, metrics in results.items()} + data[dataset_display] = {algo: metrics['ns/n'] for algo, metrics in results.items()} else: print(f" WARNING: No data found for dataset {dataset_display}") return data diff --git a/scripts/generate_digit_length_figure.py b/scripts/generate_digit_length_figure.py index f6c259e..85a70d3 100755 --- a/scripts/generate_digit_length_figure.py +++ b/scripts/generate_digit_length_figure.py @@ -55,15 +55,15 @@ def parse_algorithm_metrics(file_path: Path, algorithm_pattern: str) -> Optional return None escaped_pattern = algorithm_pattern - pattern = rf'{escaped_pattern}\s*:\s*([\d.]+)\s*ns/d\s*[\d.]+\s*GHz\s*([\d.]+)\s*c/d\s*([\d.]+)\s*i/d' + pattern = rf'{escaped_pattern}\s*:\s*([\d.]+)\s*ns/n\s*[\d.]+\s*GHz\s*([\d.]+)\s*c/n\s*([\d.]+)\s*i/n' match = re.search(pattern, content) if not match: return None return { - 'ns/d': float(match.group(1)), - 'c/d': float(match.group(2)), - 'i/d': float(match.group(3)), + 'ns/n': float(match.group(1)), + 'c/n': float(match.group(2)), + 'i/n': float(match.group(3)), } @@ -130,7 +130,7 @@ def get_available_compilers(output_dir: Path) -> List[str]: def collect_data_by_digit_length(output_dir: Path, compiler: str, cpu_model: Optional[str], algorithms: List[Tuple[str, str]]) -> Dict[int, Dict[str, float]]: """ Collect performance data for all digit lengths. - Returns: {digit_length: {algorithm_name: ns/d_value}} + Returns: {digit_length: {algorithm_name: ns/n_value}} """ data = {} for digit_length in DIGIT_LENGTHS: @@ -161,8 +161,8 @@ def collect_data_by_digit_length(output_dir: Path, compiler: str, cpu_model: Opt digit_data = {} for algo_pattern, algo_display in algorithms: metrics = parse_algorithm_metrics(selected_file, algo_pattern) - if metrics and 'ns/d' in metrics: - digit_data[algo_display] = metrics['ns/d'] + if metrics and 'ns/n' in metrics: + digit_data[algo_display] = metrics['ns/n'] if digit_data: data[digit_length] = digit_data @@ -170,7 +170,7 @@ def collect_data_by_digit_length(output_dir: Path, compiler: str, cpu_model: Opt return data -def generate_figure(data: Dict[int, Dict[str, float]], output_path: Path, metric_name: str = "ns/d"): +def generate_figure(data: Dict[int, Dict[str, float]], output_path: Path, metric_name: str = "ns/n"): """Generate a line plot comparing algorithms across digit lengths.""" if not data: print("ERROR: No data to plot") diff --git a/scripts/generate_raw_outputs.py b/scripts/generate_raw_outputs.py index 35a0275..6087128 100755 --- a/scripts/generate_raw_outputs.py +++ b/scripts/generate_raw_outputs.py @@ -23,26 +23,23 @@ 'data/cit_patents_citing_integers.txt', ] -# Synthetic data models to test (comment out to disable) -# Format: (name, description, args_list) -synthetic_models = [] - # Generate all 20 digit-length datasets for figure (1-digit through 20-digit) +synthetic_models = [] for digit_len in range(1, 21): + # Format: (name, description, args_list) synthetic_models.append(( f'uniform-{digit_len}digit-1M', f'Uniform {digit_len}-digit distribution (1M samples)', - ['-i', '-n', '1000000', '-d', 'uniform', '-m', str(digit_len), '-M', str(digit_len)] + ['-n', '1000000', '-d', 'uniform', '-m', str(digit_len), '-M', str(digit_len)] )) -# Add other synthetic models synthetic_models.extend([ ('uniform-1to20-1M', 'Uniform 1-20 digits distribution (1M samples)', - ['-i', '-n', '1000000', '-d', 'uniform']), + ['-n', '1000000', '-d', 'uniform']), ('natural-8-1M', 'Natural distribution 1-8 digits (1M samples)', - ['-i', '-n', '1000000', '-d', 'natural', '-m', '1', '-M', '8']), + ['-n', '1000000', '-d', 'natural', '-m', '1', '-M', '8']), ('natural-16-1M', 'Natural distribution 1-16 digits (1M samples)', - ['-i', '-n', '1000000', '-d', 'natural', '-m', '1', '-M', '16']), + ['-n', '1000000', '-d', 'natural', '-m', '1', '-M', '16']), ]) # Variant flags to test (comment out to disable) @@ -51,9 +48,9 @@ 'hetero', ] -# ============================================================================ -# END CONFIGURATION -# ============================================================================ +# ==================== +# END CONFIGURATION +# ==================== # Dataset categories for selective generation # TABLE_DATASETS: used for variant comparison table (homogeneous vs heterogeneous) @@ -73,13 +70,11 @@ def should_generate_dataset(dataset_base_name, args): """Determine if dataset should be generated based on flags.""" if not args.table and not args.figure: return True # No flags = generate all (backward compatible) - - should = False if args.table and dataset_base_name in TABLE_DATASETS: - should = True + return True if args.figure and dataset_base_name in FIGURE_DATASETS: - should = True - return should + return True + return False def parse_args(): @@ -122,7 +117,20 @@ def compile_benchmarks(compiler, build_dir, clean=False): """Compile the benchmark code with the specified compiler.""" print(f"Compiling benchmarks with {compiler}...") - # Clean build directory if requested + # Check if we need to clean due to compiler change + cmake_cache = os.path.join(build_dir, "CMakeCache.txt") + if os.path.exists(cmake_cache): + with open(cmake_cache, 'r') as f: + cache_content = f.read() + # Detect current compiler in cache + if compiler == "g++" and "clang++" in cache_content: + print(f"Compiler change detected (clang++ -> g++), cleaning build directory") + clean = True + elif compiler == "clang++" and "/g++" in cache_content and "clang" not in cache_content: + print(f"Compiler change detected (g++ -> clang++), cleaning build directory") + clean = True + + # Clean build directory if requested or needed if clean and os.path.exists(build_dir): print(f"Cleaning build directory: {build_dir}") shutil.rmtree(build_dir) @@ -271,7 +279,7 @@ def run_all_benchmarks(compiler, build_dir, output_dir, timeout, args): try: for variant in variants: label = f"{file_label}-{variant}" - cmd_args = ['-i', '-f', actual_path, '-v', variant] + cmd_args = ['-f', actual_path, '-v', variant] total_count += 1 if run_benchmark(benchmark_executable=benchmark_executable, output_dir=output_dir, diff --git a/scripts/generate_variant_comparison_table.py b/scripts/generate_variant_comparison_table.py index 2cff347..66d0db4 100755 --- a/scripts/generate_variant_comparison_table.py +++ b/scripts/generate_variant_comparison_table.py @@ -34,7 +34,7 @@ def parse_benchmark_output(file_path: Path) -> Optional[Dict[str, float]]: """ Parse a benchmark output file and extract timing information. - Returns a dict with algorithm names as keys and ns/d (ns per item) as values. + Returns a dict with algorithm names as keys and ns/n (ns per number) as values. Returns None if parsing fails. """ try: @@ -47,8 +47,8 @@ def parse_benchmark_output(file_path: Path) -> Optional[Dict[str, float]]: results = {} # Parse the AVX-512+champagne_lemire line(s) - # Format: "avx-512+champagne_lemire : X.XX ns/d ..." - pattern = r'avx-512\+champagne_lemire\s*:\s*(\d+\.\d+)\s*ns/d' + # Format: "avx-512+champagne_lemire : X.XX ns/n ..." + pattern = r'avx-512\+champagne_lemire\s*:\s*(\d+\.\d+)\s*ns/n' matches = re.findall(pattern, content) if matches: diff --git a/src/champagne_lemire.h b/src/champagne_lemire.h index c709025..14bd706 100644 --- a/src/champagne_lemire.h +++ b/src/champagne_lemire.h @@ -16,81 +16,6 @@ enum class Variant { }; #if defined(CHAMPAGNE_LEMIRE_AVX512) && CHAMPAGNE_LEMIRE_AVX512 -template -champagne_lemire_really_inline int avx512_to_chars(T mantissa, int32_t exponent, char *const result) { - static_assert(sizeof(T) == 4 || sizeof(T) == 8, "Unsupported type size"); - - int32_t exp = exponent; - size_t exp_index; - if (mantissa >= 10'000'000'000'000'000) { - // The special case where we max out the number of - // digits exceeds 16 digits, and we handle it separately. - // The mantissa is in [10^16, 10^17) - // Ok, so we have to write 17 digits. - // - // We need to write a digit, a dot and 16 digits. - uint64_t top_digit = mantissa / 10'000'000'000'000'000; - digits::write_one_digit_with_dot(result, top_digit); - - // The call to to_string_avx512ifma and its storage amount to about - // 25 instructions, and that can be about a third of the processing time. - __m128i digits_15_0 = to_string_avx512ifma(mantissa % 10'000'000'000'000'000); - _mm_storeu_si128((__m128i *)(result + 2), digits_15_0); - exp += 16; - exp_index = 18; // 17 digits + dot - } else if ( mantissa >= 1'000'000'000'000'000) { - // We need to write a digit, a dot and 15 digits. - uint64_t top_digit = mantissa / 1'000'000'000'000'000; - digits::write_one_digit_with_dot(result, top_digit); - // The call to to_string_avx512ifma and its storage amount to about - // 25 instructions, and that can be about a third of the processing time. - __m128i digits_15_0 = to_string_avx512ifma(mantissa % 1'000'000'000'000'000); - _mm_mask_storeu_epi8((__m128i *)(result + 1), 0xfffe, digits_15_0); - exp += 15; - exp_index = 17; // 16 digits + dot - } else { - __m128i digits_15_0 = mantissa <= 99'999'999 ? - _mm512_cvtusepi64_epi8(to_string_avx512ifma_8digits(mantissa)) : - to_string_avx512ifma(mantissa); - - const uint32_t number_of_digits = fast_digit_count(mantissa); - exp += number_of_digits - 1; - bool use_dot = (mantissa >= 10); - exp_index = number_of_digits + use_dot; - digits_15_0 = shift_and_insert_dot(digits_15_0, number_of_digits); - _mm_mask_storeu_epi8(result, (1 << (number_of_digits + use_dot)) - 1, digits_15_0); - } - - // Finally, we may have to handle the exponent. - // - // It looks simple but it is extraordinarily expensive relatively speaking. - // - // This may account for a THIRD for the processing in terms of instructions. - // Maybe 25 instructions? - if (mantissa && exp) { // We do not print the exponent if mantissa is zero but zero is handled above. - // About 20 instructions for the exponent? - memcpy(result + exp_index, "E-", 2); - exp_index += 1 + (exp < 0); - exp = (exp < 0) ? -exp : exp; - - if constexpr (sizeof(T) == 8) { - if (exp >= 100) { // 3 digits - digits::write_three_digits(result + exp_index, exp); - exp_index += 3; - } else { // 2 digits - // If we need fewer than 2 digits, this will write a leading zero. - digits::write_two_digits(result + exp_index, exp); - exp_index += 2; - } - } else { - // If we need fewer than 2 digits, this will write a leading zero. - digits::write_two_digits(result + exp_index, exp); - exp_index += 2; - } - } - - return exp_index; -} // Small values: 0 .. 99'999'999 (1 to 8 digits) template diff --git a/src/dragonbox.h b/src/dragonbox.h deleted file mode 100644 index 9714945..0000000 --- a/src/dragonbox.h +++ /dev/null @@ -1,519 +0,0 @@ -#ifndef JKJ_DRAGONBOX_H -#define JKJ_DRAGONBOX_H - -// Copyright 2020-2024 Junekey Jeon -// -// The contents of this file may be used under the terms of -// the Apache License v2.0 with LLVM Exceptions. -// -// (See accompanying file LICENSE-Apache or copy at -// https://llvm.org/foundation/relicensing/LICENSE.txt) -// -// Alternatively, the contents of this file may be used under the terms of -// the Boost Software License, Version 1.0. -// (See accompanying file LICENSE-Boost or copy at -// https://www.boost.org/LICENSE_1_0.txt) -// -// Unless required by applicable law or agreed to in writing, this software -// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY -// KIND, either express or implied. - -#ifndef JKJ_STATIC_DATA_SECTION -#define JKJ_STATIC_DATA_SECTION -#endif - -// C++17 if constexpr -#if defined(__cpp_if_constexpr) && __cpp_if_constexpr >= 201606L -#define JKJ_HAS_IF_CONSTEXPR 1 -#elif __cplusplus >= 201703L -#define JKJ_HAS_IF_CONSTEXPR 1 -#elif defined(_MSC_VER) && _MSC_VER >= 1911 && _MSVC_LANG >= 201703L -#define JKJ_HAS_IF_CONSTEXPR 1 -#else -#define JKJ_HAS_IF_CONSTEXPR 0 -#endif - -#if JKJ_HAS_IF_CONSTEXPR -#define JKJ_IF_CONSTEXPR if constexpr -#else -#define JKJ_IF_CONSTEXPR if -#endif - -#if defined(__GNUC__) || defined(__clang__) -#define JKJ_FORCEINLINE inline __attribute__((always_inline)) -#elif defined(_MSC_VER) -#define JKJ_FORCEINLINE __forceinline -#else -#define JKJ_FORCEINLINE inline -#endif - -namespace jkj { -namespace dragonbox { -namespace detail { -template -char *to_chars(T const significand, int exponent, char *buffer) noexcept; - -// These "//"'s are to prevent clang-format to ruin this nice alignment. -// Thanks to reddit user u/mcmcc: -// https://www.reddit.com/r/cpp/comments/so3wx9/dragonbox_110_is_released_a_fast_floattostring/hw8z26r/?context=3 -static constexpr char radix_100_table[200] JKJ_STATIC_DATA_SECTION = { - '0', '0', '0', '1', '0', '2', '0', '3', '0', '4', // - '0', '5', '0', '6', '0', '7', '0', '8', '0', '9', // - '1', '0', '1', '1', '1', '2', '1', '3', '1', '4', // - '1', '5', '1', '6', '1', '7', '1', '8', '1', '9', // - '2', '0', '2', '1', '2', '2', '2', '3', '2', '4', // - '2', '5', '2', '6', '2', '7', '2', '8', '2', '9', // - '3', '0', '3', '1', '3', '2', '3', '3', '3', '4', // - '3', '5', '3', '6', '3', '7', '3', '8', '3', '9', // - '4', '0', '4', '1', '4', '2', '4', '3', '4', '4', // - '4', '5', '4', '6', '4', '7', '4', '8', '4', '9', // - '5', '0', '5', '1', '5', '2', '5', '3', '5', '4', // - '5', '5', '5', '6', '5', '7', '5', '8', '5', '9', // - '6', '0', '6', '1', '6', '2', '6', '3', '6', '4', // - '6', '5', '6', '6', '6', '7', '6', '8', '6', '9', // - '7', '0', '7', '1', '7', '2', '7', '3', '7', '4', // - '7', '5', '7', '6', '7', '7', '7', '8', '7', '9', // - '8', '0', '8', '1', '8', '2', '8', '3', '8', '4', // - '8', '5', '8', '6', '8', '7', '8', '8', '8', '9', // - '9', '0', '9', '1', '9', '2', '9', '3', '9', '4', // - '9', '5', '9', '6', '9', '7', '9', '8', '9', '9' // -}; -static constexpr char radix_100_head_table[200] JKJ_STATIC_DATA_SECTION = { - '0', '.', '1', '.', '2', '.', '3', '.', '4', '.', // - '5', '.', '6', '.', '7', '.', '8', '.', '9', '.', // - '1', '.', '1', '.', '1', '.', '1', '.', '1', '.', // - '1', '.', '1', '.', '1', '.', '1', '.', '1', '.', // - '2', '.', '2', '.', '2', '.', '2', '.', '2', '.', // - '2', '.', '2', '.', '2', '.', '2', '.', '2', '.', // - '3', '.', '3', '.', '3', '.', '3', '.', '3', '.', // - '3', '.', '3', '.', '3', '.', '3', '.', '3', '.', // - '4', '.', '4', '.', '4', '.', '4', '.', '4', '.', // - '4', '.', '4', '.', '4', '.', '4', '.', '4', '.', // - '5', '.', '5', '.', '5', '.', '5', '.', '5', '.', // - '5', '.', '5', '.', '5', '.', '5', '.', '5', '.', // - '6', '.', '6', '.', '6', '.', '6', '.', '6', '.', // - '6', '.', '6', '.', '6', '.', '6', '.', '6', '.', // - '7', '.', '7', '.', '7', '.', '7', '.', '7', '.', // - '7', '.', '7', '.', '7', '.', '7', '.', '7', '.', // - '8', '.', '8', '.', '8', '.', '8', '.', '8', '.', // - '8', '.', '8', '.', '8', '.', '8', '.', '8', '.', // - '9', '.', '9', '.', '9', '.', '9', '.', '9', '.', // - '9', '.', '9', '.', '9', '.', '9', '.', '9', '.' // -}; - -static void print_1_digit(int n, char *buffer) noexcept { - JKJ_IF_CONSTEXPR(('0' & 0xf) == 0) { *buffer = char('0' | n); } - else { - *buffer = char('0' + n); - } -} - -static void print_2_digits(int n, char *buffer) noexcept { - std::memcpy(buffer, radix_100_table + n * 2, 2); -} - -// These digit generation routines are inspired by James Anhalt's itoa -// algorithm: https://github.com/jeaiii/itoa The main idea is for given n, find -// y such that floor(10^k * y / 2^32) = n holds, where k is an appropriate -// integer depending on the length of n. For example, if n = 1234567, we set k -// = 6. In this case, we have floor(y / 2^32) = 1, floor(10^2 * ((10^0 * y) mod -// 2^32) / 2^32) = 23, floor(10^2 * ((10^2 * y) mod 2^32) / 2^32) = 45, and -// floor(10^2 * ((10^4 * y) mod 2^32) / 2^32) = 67. -// See https://jk-jeon.github.io/posts/2022/02/jeaiii-algorithm/ for more -// explanation. - -JKJ_FORCEINLINE static void print_9_digits(uint32_t s32, int &exponent, - char *&buffer) noexcept { - // -- IEEE-754 binary32 - // Since we do not cut trailing zeros in advance, s32 must be of 6~9 digits - // unless the original input was subnormal. - // In particular, when it is of 9 digits it shouldn't have any trailing zeros. - // -- IEEE-754 binary64 - // In this case, s32 must be of 7~9 digits unless the input is subnormal, - // and it shouldn't have any trailing zeros if it is of 9 digits. - if (s32 >= UINT32_C(100000000)) { - // 9 digits. - // 1441151882 = ceil(2^57 / 1'0000'0000) + 1 - auto prod = s32 * UINT64_C(1441151882); - prod >>= 25; - std::memcpy(buffer, radix_100_head_table + int(prod >> 32) * 2, 2); - - prod = (prod & UINT32_C(0xffffffff)) * 100; - print_2_digits(int(prod >> 32), buffer + 2); - prod = (prod & UINT32_C(0xffffffff)) * 100; - print_2_digits(int(prod >> 32), buffer + 4); - prod = (prod & UINT32_C(0xffffffff)) * 100; - print_2_digits(int(prod >> 32), buffer + 6); - prod = (prod & UINT32_C(0xffffffff)) * 100; - print_2_digits(int(prod >> 32), buffer + 8); - - exponent += 8; - buffer += 10; - } else if (s32 >= UINT32_C(1000000)) { - // 7 or 8 digits. - // 281474978 = ceil(2^48 / 100'0000) + 1 - auto prod = s32 * UINT64_C(281474978); - prod >>= 16; - auto const head_digits = int(prod >> 32); - // If s32 is of 8 digits, increase the exponent by 7. - // Otherwise, increase it by 6. - exponent += (6 + int(head_digits >= 10)); - - // Write the first digit and the decimal point. - std::memcpy(buffer, radix_100_head_table + head_digits * 2, 2); - // This third character may be overwritten later but we don't care. - buffer[2] = radix_100_table[head_digits * 2 + 1]; - - // Remaining 6 digits are all zero? - if ((prod & UINT32_C(0xffffffff)) <= - uint32_t((uint64_t(1) << 32) / UINT32_C(1000000))) { - // The number of characters actually need to be written is: - // 1, if only the first digit is nonzero, which means that either s32 is - // of 7 digits or it is of 8 digits but the second digit is zero, or 3, - // otherwise. - // Note that buffer[2] is never '0' if s32 is of 7 digits, because the - // input is never zero. - buffer += (1 + (int(head_digits >= 10) & int(buffer[2] > '0')) * 2); - } else { - // At least one of the remaining 6 digits are nonzero. - // After this adjustment, now the first destination becomes buffer + 2. - buffer += int(head_digits >= 10); - - // Obtain the next two digits. - prod = (prod & UINT32_C(0xffffffff)) * 100; - print_2_digits(int(prod >> 32), buffer + 2); - - // Remaining 4 digits are all zero? - if ((prod & UINT32_C(0xffffffff)) <= - uint32_t((uint64_t(1) << 32) / 10000)) { - buffer += (3 + int(buffer[3] > '0')); - } else { - // At least one of the remaining 4 digits are nonzero. - - // Obtain the next two digits. - prod = (prod & UINT32_C(0xffffffff)) * 100; - print_2_digits(int(prod >> 32), buffer + 4); - - // Remaining 2 digits are all zero? - if ((prod & UINT32_C(0xffffffff)) <= - uint32_t((uint64_t(1) << 32) / 100)) { - buffer += (5 + int(buffer[5] > '0')); - } else { - // Obtain the last two digits. - prod = (prod & UINT32_C(0xffffffff)) * 100; - print_2_digits(int(prod >> 32), buffer + 6); - - buffer += (7 + int(buffer[7] > '0')); - } - } - } - } else if (s32 >= 10000) { - // 5 or 6 digits. - // 429497 = ceil(2^32 / 1'0000) - auto prod = s32 * UINT64_C(429497); - auto const head_digits = int(prod >> 32); - - // If s32 is of 6 digits, increase the exponent by 5. - // Otherwise, increase it by 4. - exponent += (4 + int(head_digits >= 10)); - - // Write the first digit and the decimal point. - std::memcpy(buffer, radix_100_head_table + head_digits * 2, 2); - // This third character may be overwritten later but we don't care. - buffer[2] = radix_100_table[head_digits * 2 + 1]; - - // Remaining 4 digits are all zero? - if ((prod & UINT32_C(0xffffffff)) <= - uint32_t((uint64_t(1) << 32) / 10000)) { - // The number of characters actually written is 1 or 3, similarly to the - // case of 7 or 8 digits. - buffer += (1 + (int(head_digits >= 10) & int(buffer[2] > '0')) * 2); - } else { - // At least one of the remaining 4 digits are nonzero. - // After this adjustment, now the first destination becomes buffer + 2. - buffer += int(head_digits >= 10); - - // Obtain the next two digits. - prod = (prod & UINT32_C(0xffffffff)) * 100; - print_2_digits(int(prod >> 32), buffer + 2); - - // Remaining 2 digits are all zero? - if ((prod & UINT32_C(0xffffffff)) <= - uint32_t((uint64_t(1) << 32) / 100)) { - buffer += (3 + int(buffer[3] > '0')); - } else { - // Obtain the last two digits. - prod = (prod & UINT32_C(0xffffffff)) * 100; - print_2_digits(int(prod >> 32), buffer + 4); - - buffer += (5 + int(buffer[5] > '0')); - } - } - } else if (s32 >= 100) { - // 3 or 4 digits. - // 42949673 = ceil(2^32 / 100) - auto prod = s32 * UINT64_C(42949673); - auto const head_digits = int(prod >> 32); - - // If s32 is of 4 digits, increase the exponent by 3. - // Otherwise, increase it by 2. - exponent += (2 + int(head_digits >= 10)); - - // Write the first digit and the decimal point. - std::memcpy(buffer, radix_100_head_table + head_digits * 2, 2); - // This third character may be overwritten later but we don't care. - buffer[2] = radix_100_table[head_digits * 2 + 1]; - - // Remaining 2 digits are all zero? - if ((prod & UINT32_C(0xffffffff)) <= uint32_t((uint64_t(1) << 32) / 100)) { - // The number of characters actually written is 1 or 3, similarly to the - // case of 7 or 8 digits. - buffer += (1 + (int(head_digits >= 10) & int(buffer[2] > '0')) * 2); - } else { - // At least one of the remaining 2 digits are nonzero. - // After this adjustment, now the first destination becomes buffer + 2. - buffer += int(head_digits >= 10); - - // Obtain the last two digits. - prod = (prod & UINT32_C(0xffffffff)) * 100; - print_2_digits(int(prod >> 32), buffer + 2); - - buffer += (3 + int(buffer[3] > '0')); - } - } else { - // 1 or 2 digits. - // If s32 is of 2 digits, increase the exponent by 1. - exponent += int(s32 >= 10); - - // Write the first digit and the decimal point. - std::memcpy(buffer, radix_100_head_table + s32 * 2, 2); - // This third character may be overwritten later but we don't care. - buffer[2] = radix_100_table[s32 * 2 + 1]; - - // The number of characters actually written is 1 or 3, similarly to the - // case of 7 or 8 digits. - buffer += (1 + (int(s32 >= 10) & int(buffer[2] > '0')) * 2); - } -} - -template <> char *to_chars(uint32_t s32, int exponent, char *buffer) noexcept { - // Print significand. - print_9_digits(s32, exponent, buffer); - - // Print exponent and return - if (exponent < 0) { - std::memcpy(buffer, "E-", 2); - buffer += 2; - exponent = -exponent; - } else { - buffer[0] = 'E'; - buffer += 1; - } - - if (exponent >= 10) { - print_2_digits(exponent, buffer); - buffer += 2; - } else { - print_1_digit(exponent, buffer); - buffer += 1; - } - - return buffer; -} - -template <> -JKJ_FORCEINLINE // Daniel: we force inline the function, to maximize performance. -char *to_chars(uint64_t const significand, int exponent, - char *buffer) noexcept { - // Print significand by decomposing it into a 9-digit block and a 8-digit - // block. - uint32_t first_block, second_block; - bool no_second_block; - if (significand >= UINT64_C(100000000)) { - first_block = uint32_t(significand / UINT64_C(100000000)); - second_block = uint32_t(significand) - first_block * UINT32_C(100000000); - exponent += 8; - no_second_block = (second_block == 0); - } else { - first_block = uint32_t(significand); - no_second_block = true; - } - - if (no_second_block) { - print_9_digits(first_block, exponent, buffer); - } else { - // We proceed similarly to print_9_digits(), but since we do not need to - // remove trailing zeros, the procedure is a bit simpler. - if (first_block >= UINT32_C(100000000)) { - // The input is of 17 digits, thus there should be no trailing zero at - // all. The first block is of 9 digits. 1441151882 = ceil(2^57 / - // 1'0000'0000) + 1 - auto prod = first_block * UINT64_C(1441151882); - prod >>= 25; - std::memcpy(buffer, radix_100_head_table + int(prod >> 32) * 2, 2); - prod = (prod & UINT32_C(0xffffffff)) * 100; - print_2_digits(int(prod >> 32), buffer + 2); - prod = (prod & UINT32_C(0xffffffff)) * 100; - print_2_digits(int(prod >> 32), buffer + 4); - prod = (prod & UINT32_C(0xffffffff)) * 100; - print_2_digits(int(prod >> 32), buffer + 6); - prod = (prod & UINT32_C(0xffffffff)) * 100; - print_2_digits(int(prod >> 32), buffer + 8); - - // The second block is of 8 digits. - // 281474978 = ceil(2^48 / 100'0000) + 1 - prod = second_block * UINT64_C(281474978); - prod >>= 16; - prod += 1; - print_2_digits(int(prod >> 32), buffer + 10); - prod = (prod & UINT32_C(0xffffffff)) * 100; - print_2_digits(int(prod >> 32), buffer + 12); - prod = (prod & UINT32_C(0xffffffff)) * 100; - print_2_digits(int(prod >> 32), buffer + 14); - prod = (prod & UINT32_C(0xffffffff)) * 100; - print_2_digits(int(prod >> 32), buffer + 16); - - exponent += 8; - buffer += 18; - } else { - if (first_block >= UINT32_C(1000000)) { - - // 7 or 8 digits. - // 281474978 = ceil(2^48 / 100'0000) + 1 - auto prod = first_block * UINT64_C(281474978); - prod >>= 16; - auto const head_digits = int(prod >> 32); - - std::memcpy(buffer, radix_100_head_table + head_digits * 2, 2); - buffer[2] = radix_100_table[head_digits * 2 + 1]; - - exponent += (6 + int(head_digits >= 10)); - buffer += int(head_digits >= 10); - - // Print remaining 6 digits. - prod = (prod & UINT32_C(0xffffffff)) * 100; - print_2_digits(int(prod >> 32), buffer + 2); - prod = (prod & UINT32_C(0xffffffff)) * 100; - print_2_digits(int(prod >> 32), buffer + 4); - prod = (prod & UINT32_C(0xffffffff)) * 100; - print_2_digits(int(prod >> 32), buffer + 6); - - buffer += 8; - } else if (first_block >= 10000) { - // 5 or 6 digits. - // 429497 = ceil(2^32 / 1'0000) - auto prod = first_block * UINT64_C(429497); - auto const head_digits = int(prod >> 32); - - std::memcpy(buffer, radix_100_head_table + head_digits * 2, 2); - buffer[2] = radix_100_table[head_digits * 2 + 1]; - - exponent += (4 + int(head_digits >= 10)); - buffer += int(head_digits >= 10); - - // Print remaining 4 digits. - prod = (prod & UINT32_C(0xffffffff)) * 100; - print_2_digits(int(prod >> 32), buffer + 2); - prod = (prod & UINT32_C(0xffffffff)) * 100; - print_2_digits(int(prod >> 32), buffer + 4); - - buffer += 6; - } else if (first_block >= 100) { - // 3 or 4 digits. - // 42949673 = ceil(2^32 / 100) - auto prod = first_block * UINT64_C(42949673); - auto const head_digits = int(prod >> 32); - - std::memcpy(buffer, radix_100_head_table + head_digits * 2, 2); - buffer[2] = radix_100_table[head_digits * 2 + 1]; - - exponent += (2 + int(head_digits >= 10)); - buffer += int(head_digits >= 10); - - // Print remaining 2 digits. - prod = (prod & UINT32_C(0xffffffff)) * 100; - print_2_digits(int(prod >> 32), buffer + 2); - - buffer += 4; - } else { - // 1 or 2 digits. - std::memcpy(buffer, radix_100_head_table + first_block * 2, 2); - buffer[2] = radix_100_table[first_block * 2 + 1]; - - exponent += int(first_block >= 10); - buffer += (2 + int(first_block >= 10)); - } - - // Next, print the second block. - // The second block is of 8 digits, but we may have trailing zeros. - // 281474978 = ceil(2^48 / 100'0000) + 1 - auto prod = second_block * UINT64_C(281474978); - prod >>= 16; - prod += 1; - print_2_digits(int(prod >> 32), buffer); - - // Remaining 6 digits are all zero? - if ((prod & UINT32_C(0xffffffff)) <= - uint32_t((uint64_t(1) << 32) / UINT64_C(1000000))) { - buffer += (1 + int(buffer[1] > '0')); - } else { - // Obtain the next two digits. - prod = (prod & UINT32_C(0xffffffff)) * 100; - print_2_digits(int(prod >> 32), buffer + 2); - - // Remaining 4 digits are all zero? - if ((prod & UINT32_C(0xffffffff)) <= - uint32_t((uint64_t(1) << 32) / 10000)) { - buffer += (3 + int(buffer[3] > '0')); - } else { - // Obtain the next two digits. - prod = (prod & UINT32_C(0xffffffff)) * 100; - print_2_digits(int(prod >> 32), buffer + 4); - // Remaining 2 digits are all zero? - if ((prod & UINT32_C(0xffffffff)) <= - uint32_t((uint64_t(1) << 32) / 100)) { - buffer += (5 + int(buffer[5] > '0')); - } else { - // Obtain the last two digits. - prod = (prod & UINT32_C(0xffffffff)) * 100; - print_2_digits(int(prod >> 32), buffer + 6); - buffer += (7 + int(buffer[7] > '0')); - } - } - } - } - } - - // Print exponent and return - if (exponent < 0) { - std::memcpy(buffer, "E-", 2); - buffer += 2; - exponent = -exponent; - } else { - buffer[0] = 'E'; - buffer += 1; - } - - if (exponent >= 100) { - // d1 = exponent / 10; d2 = exponent % 10; - // 6554 = ceil(2^16 / 10) - auto d1 = (std::uint_least32_t(exponent) * UINT32_C(6554)) >> 16; - auto d2 = std::uint_least32_t(exponent) - UINT32_C(10) * d1; - print_2_digits(int(d1), buffer); - print_1_digit(int(d2), buffer + 2); - buffer += 3; - } else if (exponent >= 10) { - print_2_digits(exponent, buffer); - buffer += 2; - } else { - print_1_digit(exponent, buffer); - buffer += 1; - } - - return buffer; -} -} // namespace detail -} // namespace dragonbox -} // namespace jkj - -#endif // JKJ_DRAGONBOX_H \ No newline at end of file diff --git a/src/scalar.h b/src/scalar.h deleted file mode 100644 index 436f255..0000000 --- a/src/scalar.h +++ /dev/null @@ -1,336 +0,0 @@ -#ifndef CHAMPAGNE_LEMIRE_FAST_H -#define CHAMPAGNE_LEMIRE_FAST_H - -#include "digitcount.h" -#include "digits.h" -#include "portabilityutils.h" -#include -#include -#include - -template -champagne_lemire_really_inline int scalar_to_chars(T mantissa, int32_t exponent, - char *const result) { - ////////// - // LLVM/clang seems to like this function better than GCC. - //////// - ////////// - // For the math behind the multipliers, see: - // scripts/optimal_bound.py - //////// - static_assert(std::is_same_v || std::is_same_v, - "Only integers are supported"); - static_assert(sizeof(T) == 8 || sizeof(T) == 4, "Unsupported type size"); - int32_t exp = exponent; - const uint32_t number_of_digits = fast_digit_count(mantissa); - size_t exp_index; - if (mantissa >= 100'00'00'00'00'00'00'00) { - // The mantissa is in [10^16, 10^17) - // Important: GCC gets really confused with the registers if you don't write the - // results to memory right away. Hence, I interleave the multiplications and the writes. - // - // We divide by 10^8, the binary remainder is in low10_8 - auto [xdiv10_8, low10_8] = multiplier::mul64x64_to_128(mantissa, 48357032784585167ULL); - low10_8 = (low10_8 >> 18) | (xdiv10_8 << (64 - 18)); - xdiv10_8 >>= 18; - auto [digits12, low10_8_1] = multiplier::mul64x64_to_128(low10_8, 100); - digits::write_two_digits(result + 10, digits12); - auto [digits23, low10_8_2] = multiplier::mul64x64_to_128(low10_8_1, 100); - digits::write_two_digits(result + 12, digits23); - auto [digits45, low10_8_3] = multiplier::mul64x64_to_128(low10_8_2, 100); - digits::write_two_digits(result + 14, digits45); - auto [digits67, unused1] = multiplier::mul64x64_to_128(low10_8_3, 100); - digits::write_two_digits(result + 16, digits67); - // We divide by 10^8 again to get the first digits - auto [xdiv10_16, low10_16] = multiplier::mul64x64_to_128(xdiv10_8, 184467440738ULL); - digits::write_one_digit_with_dot(result, xdiv10_16); - auto [digits89, low10_16_1] = multiplier::mul64x64_to_128(low10_16, 100); - digits::write_two_digits(result + 2, digits89); - auto [digits1011, low10_16_2] = multiplier::mul64x64_to_128(low10_16_1, 100); - digits::write_two_digits(result + 4, digits1011); - auto [digits1213, low10_16_3] = multiplier::mul64x64_to_128(low10_16_2, 100); - digits::write_two_digits(result + 6, digits1213); - auto [digits1415, unused2] = multiplier::mul64x64_to_128(low10_16_3, 100); - digits::write_two_digits(result + 8, digits1415); - exp += 16; - exp_index = 17 + 1; - } else { - // 1 to 16 digits: determine number of digits and write accordingly. - exp += number_of_digits - 1; - size_t final_index = number_of_digits + 1; - exp_index = final_index; - - //////////////////// - // If is unpredictable, then we - // get branch target buffer (BTB) misses. - // This will lower the number of instructions per cycle (IPC). - ///////////////// - //////////////// - // The code below has poor naming conventions for the variables - // and it is unclear. It should be rewritten for clarity. - // The constants are from - // scripts/optimal_bound.py - //////////////// - switch (number_of_digits) { - case 16: { - // We divide by 10^8, the binary remainder is in low10_8 - auto [xdiv10_8, low10_8] = multiplier::mul64x64_to_128(mantissa, 48357032784585167ULL); - low10_8 = (low10_8 >> 18) | (xdiv10_8 << (64 - 18)); - xdiv10_8 >>= 18; - auto [digits12, low10_8_1] = multiplier::mul64x64_to_128(low10_8, 100); - digits::write_two_digits(result + 9, digits12); - auto [digits23, low10_8_2] = multiplier::mul64x64_to_128(low10_8_1, 100); - digits::write_two_digits(result + 11, digits23); - auto [digits45, low10_8_3] = multiplier::mul64x64_to_128(low10_8_2, 100); - digits::write_two_digits(result + 13, digits45); - auto [digits67, unused1] = multiplier::mul64x64_to_128(low10_8_3, 100); - digits::write_two_digits(result + 15, digits67); - // We divide by 10^6 to get the first digits - auto [xdiv10_14, low10_14] = multiplier::mul64x64_to_128(xdiv10_8, 18446744073710ULL); - digits::write_two_digits_with_dot_with_one_pad(result, xdiv10_14); - auto [digits89, low10_14_1] = multiplier::mul64x64_to_128(low10_14, 100); - digits::write_two_digits(result + 3, digits89); - auto [digits1011, low10_14_2] = multiplier::mul64x64_to_128(low10_14_1, 100); - digits::write_two_digits(result + 5, digits1011); - auto [digits1213, unused] = multiplier::mul64x64_to_128(low10_14_2, 100); - digits::write_two_digits(result + 7, digits1213); - } break; - - case 15: { - // We divide by 10^8, the binary remainder is in low10_8 - auto [xdiv10_8, low10_8] = multiplier::mul64x64_to_128(mantissa, 48357032784585167ULL); - low10_8 = (low10_8 >> 18) | (xdiv10_8 << (64 - 18)); - xdiv10_8 >>= 18; - auto [digits12, low10_8_1] = multiplier::mul64x64_to_128(low10_8, 100); - digits::write_two_digits(result + 8, digits12); - auto [digits23, low10_8_2] = multiplier::mul64x64_to_128(low10_8_1, 100); - digits::write_two_digits(result + 10, digits23); - auto [digits45, low10_8_3] = multiplier::mul64x64_to_128(low10_8_2, 100); - digits::write_two_digits(result + 12, digits45); - auto [digits67, unused1] = multiplier::mul64x64_to_128(low10_8_3, 100); - digits::write_two_digits(result + 14, digits67); - // We divide by 10^6 to get the first digits - auto [xdiv10_14, low10_14] = multiplier::mul64x64_to_128(xdiv10_8, 18446744073710ULL); - digits::write_one_digit_with_dot(result, xdiv10_14); - auto [digits89, low10_14_1] = multiplier::mul64x64_to_128(low10_14, 100); - digits::write_two_digits(result + 2, digits89); - auto [digits1011, low10_14_2] = multiplier::mul64x64_to_128(low10_14_1, 100); - digits::write_two_digits(result + 4, digits1011); - auto [digits1213, unused] = multiplier::mul64x64_to_128(low10_14_2, 100); - digits::write_two_digits(result + 6, digits1213); - } break; - - case 14: { - // We divide by 10^8, the binary remainder is in low10_8 - auto [xdiv10_8, low10_8] = multiplier::mul64x64_to_128(mantissa, 48357032784585167ULL); - low10_8 = (low10_8 >> 18) | (xdiv10_8 << (64 - 18)); - xdiv10_8 >>= 18; - auto [digits12, low10_8_1] = multiplier::mul64x64_to_128(low10_8, 100); - digits::write_two_digits(result + 7, digits12); - auto [digits23, low10_8_2] = multiplier::mul64x64_to_128(low10_8_1, 100); - digits::write_two_digits(result + 9, digits23); - auto [digits45, low10_8_3] = multiplier::mul64x64_to_128(low10_8_2, 100); - digits::write_two_digits(result + 11, digits45); - auto [digits67, unused1] = multiplier::mul64x64_to_128(low10_8_3, 100); - digits::write_two_digits(result + 13, digits67); - // We divide by 10^4 to get the first digits - auto [xdiv10_12, low10_12] = multiplier::mul64x64_to_128(xdiv10_8, 1844674407370956ULL); - digits::write_two_digits_with_dot_with_one_pad(result, xdiv10_12); - auto [digits89, low10_12_1] = multiplier::mul64x64_to_128(low10_12, 100); - digits::write_two_digits(result + 3, digits89); - auto [digits1011, unused] = multiplier::mul64x64_to_128(low10_12_1, 100); - digits::write_two_digits(result + 5, digits1011); - } break; - - case 13: { - // We divide by 10^8, the binary remainder is in low10_8 - auto [xdiv10_8, low10_8] = multiplier::mul64x64_to_128(mantissa, 48357032784585167ULL); - low10_8 = (low10_8 >> 18) | (xdiv10_8 << (64 - 18)); - xdiv10_8 >>= 18; - auto [digits12, low10_8_1] = multiplier::mul64x64_to_128(low10_8, 100); - digits::write_two_digits(result + 6, digits12); - auto [digits23, low10_8_2] = multiplier::mul64x64_to_128(low10_8_1, 100); - digits::write_two_digits(result + 8, digits23); - auto [digits45, low10_8_3] = multiplier::mul64x64_to_128(low10_8_2, 100); - digits::write_two_digits(result + 10, digits45); - auto [digits67, unused1] = multiplier::mul64x64_to_128(low10_8_3, 100); - digits::write_two_digits(result + 12, digits67); - // We divide by 10^4 to get the first digits - auto [xdiv10_12, low10_12] = multiplier::mul64x64_to_128(xdiv10_8, 1844674407370956ULL); - digits::write_one_digit_with_dot(result, xdiv10_12); - auto [digits89, low10_12_1] = multiplier::mul64x64_to_128(low10_12, 100); - digits::write_two_digits(result + 2, digits89); - auto [digits1011, unused] = multiplier::mul64x64_to_128(low10_12_1, 100); - digits::write_two_digits(result + 4, digits1011); - } break; - - case 12: { - // We divide by 10^6, the binary remainder is in low10_6 - auto [xdiv10_6, low10_6] = multiplier::mul64x64_to_128(mantissa, 18446744073710ULL); - auto [digits12, low10_6_1] = multiplier::mul64x64_to_128(low10_6, 100); - digits::write_two_digits(result + 7, digits12); - auto [digits23, low10_6_2] = multiplier::mul64x64_to_128(low10_6_1, 100); - digits::write_two_digits(result + 9, digits23); - auto [digits45, low10_6_3] = multiplier::mul64x64_to_128(low10_6_2, 100); - digits::write_two_digits(result + 11, digits45); - // We divide by 10^4 to get the first digits - auto [xdiv10_10, low10_12] = multiplier::mul64x64_to_128(xdiv10_6, 1844674407370956ULL); - digits::write_two_digits_with_dot_with_one_pad(result, xdiv10_10); - auto [digits89, low10_12_1] = multiplier::mul64x64_to_128(low10_12, 100); - digits::write_two_digits(result + 3, digits89); - auto [digits67, unused1] = multiplier::mul64x64_to_128(low10_12_1, 100); - digits::write_two_digits(result + 5, digits67); - } break; - - case 11: { - // We divide by 10^6, the binary remainder is in low10_6 - auto [xdiv10_6, low10_6] = multiplier::mul64x64_to_128(mantissa, 18446744073710ULL); - auto [digits12, low10_6_1] = multiplier::mul64x64_to_128(low10_6, 100); - digits::write_two_digits(result + 6, digits12); - auto [digits23, low10_6_2] = multiplier::mul64x64_to_128(low10_6_1, 100); - digits::write_two_digits(result + 8, digits23); - auto [digits45, low10_6_3] = multiplier::mul64x64_to_128(low10_6_2, 100); - digits::write_two_digits(result + 10, digits45); - // We divide by 10^4 to get the first digits - auto [xdiv10_10, low10_12] = multiplier::mul64x64_to_128(xdiv10_6, 1844674407370956); - digits::write_one_digit_with_dot(result, xdiv10_10); - auto [digits89, low10_12_1] = multiplier::mul64x64_to_128(low10_12, 100); - digits::write_two_digits(result + 2, digits89); - auto [digits67, unused1] = multiplier::mul64x64_to_128(low10_12_1, 100); - digits::write_two_digits(result + 4, digits67); - } break; - case 10: { - // We divide by 10^8, the binary remainder is in low10_8 - auto [xdiv10_8, low10_8] = multiplier::mul64x64_to_128(mantissa, 184467440738ULL); - digits::write_two_digits_with_dot_with_one_pad(result, xdiv10_8); - auto [digits12, low10_6_1] = multiplier::mul64x64_to_128(low10_8, 100); - digits::write_two_digits(result + 3, digits12); - auto [digits23, low10_6_2] = multiplier::mul64x64_to_128(low10_6_1, 100); - digits::write_two_digits(result + 5, digits23); - auto [digits45, low10_6_3] = multiplier::mul64x64_to_128(low10_6_2, 100); - digits::write_two_digits(result + 7, digits45); - auto [digits67, unused1] = multiplier::mul64x64_to_128(low10_6_3, 100); - digits::write_two_digits(result + 9, digits67); - } break; - - case 9: { - // We divide by 10^8, the binary remainder is in low10_8 - auto [xdiv10_8, low10_8] = multiplier::mul64x64_to_128(mantissa, 184467440738ULL); - digits::write_one_digit_with_dot(result, xdiv10_8); - auto [digits12, low10_6_1] = multiplier::mul64x64_to_128(low10_8, 100); - digits::write_two_digits(result + 2, digits12); - auto [digits23, low10_6_2] = multiplier::mul64x64_to_128(low10_6_1, 100); - digits::write_two_digits(result + 4, digits23); - auto [digits45, low10_6_3] = multiplier::mul64x64_to_128(low10_6_2, 100); - digits::write_two_digits(result + 6, digits45); - auto [digits67, unused1] = multiplier::mul64x64_to_128(low10_6_3, 100); - digits::write_two_digits(result + 8, digits67); - } break; - - case 8: { - // We divide by 10^6, the binary remainder is in low10_6 - auto [xdiv10_8, low10_8] = multiplier::mul64x64_to_128(mantissa, 18446744073710ULL); - digits::write_two_digits_with_dot_with_one_pad(result, xdiv10_8); - auto [digits12, low10_6_1] = multiplier::mul64x64_to_128(low10_8, 100); - digits::write_two_digits(result + 3, digits12); - auto [digits23, low10_6_2] = multiplier::mul64x64_to_128(low10_6_1, 100); - digits::write_two_digits(result + 5, digits23); - auto [digits45, unused] = multiplier::mul64x64_to_128(low10_6_2, 100); - digits::write_two_digits(result + 7, digits45); - } break; - - case 7: { - // We divide by 10^6, the binary remainder is in low10_6 - auto [xdiv10_8, low10_8] = multiplier::mul64x64_to_128(mantissa, 18446744073710ULL); - digits::write_one_digit_with_dot(result, xdiv10_8); - auto [digits12, low10_6_1] = multiplier::mul64x64_to_128(low10_8, 100); - digits::write_two_digits(result + 2, digits12); - auto [digits23, low10_6_2] = multiplier::mul64x64_to_128(low10_6_1, 100); - digits::write_two_digits(result + 4, digits23); - auto [digits45, unused] = multiplier::mul64x64_to_128(low10_6_2, 100); - digits::write_two_digits(result + 6, digits45); - - } break; - - case 6: { - // We divide by 10^4, the binary remainder is in low10_8 - auto [xdiv10_8, low10_8] = multiplier::mul64x64_to_128(mantissa, 1844674407370956ULL); - digits::write_two_digits_with_dot_with_one_pad(result, xdiv10_8); - auto [digits12, low10_6_1] = multiplier::mul64x64_to_128(low10_8, 100); - digits::write_two_digits(result + 3, digits12); - auto [digits23, unused] = multiplier::mul64x64_to_128(low10_6_1, 100); - digits::write_two_digits(result + 5, digits23); - } break; - - case 5: { - // We divide by 10^4, the binary remainder is in low10_4 - auto [xdiv10_8, low10_8] = multiplier::mul64x64_to_128(mantissa, 1844674407370956ULL); - digits::write_one_digit_with_dot(result, xdiv10_8); - auto [digits12, low10_6_1] = multiplier::mul64x64_to_128(low10_8, 100); - digits::write_two_digits(result + 2, digits12); - auto [digits23, unused] = multiplier::mul64x64_to_128(low10_6_1, 100); - digits::write_two_digits(result + 4, digits23); - } break; - - case 4: { - // remaining 4 digits: write 2 + 2 with dot - auto [r, s_unique] = digits::div100v(mantissa); - digits::write_two_digits_with_dot_with_one_pad(result, r); - digits::write_two_digits_v(result + final_index - 2, s_unique); - } break; - - case 3: { - // remaining 3 digits: write 2 + 1 with dot - auto [r, s_unique] = digits::div100v(mantissa); - digits::write_two_digits_v(result + final_index - 2, s_unique); - digits::write_one_digit_with_dot(result, r); - } break; - - case 2: { - // remaining 2 digits: write 2 with dot - digits::write_two_digits_with_dot(result, mantissa); - } break; - - case 1: { - *result = '0' + mantissa; - if(mantissa == 0) { - return 1; - } - } break; - - default: - std::unreachable(); - } - } - - - if (exp) { // We do not print the exponent if mantissa is zero but zero is - // handled above. - // About 20 instructions for the exponent? - memcpy(result + exp_index, "E-", 2); - if(exp < 0) { - exp_index += 2; - exp = -exp; - } else { - exp_index += 1; - } - - if constexpr (sizeof(T) == 8) { - if (exp >= 100) { // 3 digits - digits::write_three_digits(result + exp_index, exp); - exp_index += 3; - } else { // 2 digits - // If we need fewer than 2 digits, this will write a leading zero. - digits::write_two_digits(result + exp_index, exp); - exp_index += 2; - } - } else { - // If we need fewer than 2 digits, this will write a leading zero. - digits::write_two_digits(result + exp_index, exp); - exp_index += 2; - } - } - return exp_index; -} - -#endif // CHAMPAGNE_LEMIRE_FAST_H