diff options
author | Justin Bedo <cu@cua0.org> | 2023-02-07 15:27:42 +1100 |
---|---|---|
committer | Justin Bedo <cu@cua0.org> | 2023-02-07 17:08:50 +1100 |
commit | a0b5f58d8d2040306006a8b9deded629692ed8f3 (patch) | |
tree | 9c04ed6efabf67e9bb6b1f8f7ae9029c3b46587a |
init
-rw-r--r-- | .gitignore | 2 | ||||
-rw-r--r-- | LICENSE | 19 | ||||
-rw-r--r-- | default.nix | 8 | ||||
-rw-r--r-- | flake.lock | 42 | ||||
-rw-r--r-- | flake.nix | 16 | ||||
-rw-r--r-- | meson.build | 7 | ||||
-rw-r--r-- | pca.c | 8106 | ||||
-rw-r--r-- | pca.fut | 75 | ||||
-rw-r--r-- | pca.h | 65 |
9 files changed, 8340 insertions, 0 deletions
diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..aaf410d --- /dev/null +++ b/.gitignore @@ -0,0 +1,2 @@ +result +build @@ -0,0 +1,19 @@ +Copyright (c) 2023 Justin Bedo + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. diff --git a/default.nix b/default.nix new file mode 100644 index 0000000..52704ae --- /dev/null +++ b/default.nix @@ -0,0 +1,8 @@ +{ stdenv, meson, ninja }: + +stdenv.mkDerivation { + pname = "codapca"; + version = "0.1"; + src = ./.; + nativeBuildInputs = [meson ninja]; +} diff --git a/flake.lock b/flake.lock new file mode 100644 index 0000000..3b0759d --- /dev/null +++ b/flake.lock @@ -0,0 +1,42 @@ +{ + "nodes": { + "flake-utils": { + "locked": { + "lastModified": 1667395993, + "narHash": "sha256-nuEHfE/LcWyuSWnS8t12N1wc105Qtau+/OdUAjtQ0rA=", + "owner": "numtide", + "repo": "flake-utils", + "rev": "5aed5285a952e0b949eb3ba02c12fa4fcfef535f", + "type": "github" + }, + "original": { + "owner": "numtide", + "repo": "flake-utils", + "type": "github" + } + }, + "nixpkgs": { + "locked": { + "lastModified": 1675745927, + "narHash": "sha256-+iTd4MU5Mj/ZIqmfNUNK5tiRxq6lf35OFyM9sGOcJlo=", + "owner": "nixos", + "repo": "nixpkgs", + "rev": "4ee1a6c3ae9ebf58183e446aa53e5efaac34cbb3", + "type": "github" + }, + "original": { + "owner": "nixos", + "repo": "nixpkgs", + "type": "github" + } + }, + "root": { + "inputs": { + "flake-utils": "flake-utils", + "nixpkgs": "nixpkgs" + } + } + }, + "root": "root", + "version": 7 +} diff --git a/flake.nix b/flake.nix new file mode 100644 index 0000000..38e252b --- /dev/null +++ b/flake.nix @@ -0,0 +1,16 @@ +{ + inputs.nixpkgs.url = "github:nixos/nixpkgs"; + inputs.flake-utils.url = "github:numtide/flake-utils"; + + outputs = { + self, + nixpkgs, + flake-utils, + }: + flake-utils.lib.eachDefaultSystem (system: let + pkgs = import nixpkgs {inherit system;}; + in rec { + packages = {lib = pkgs.callPackage ./. {};}; + defaultPackage = packages.lib; + }); +} diff --git a/meson.build b/meson.build new file mode 100644 index 0000000..0145c5a --- /dev/null +++ b/meson.build @@ -0,0 +1,7 @@ +project('coda-pca', 'c', + version : '0.1', + default_options : ['warning_level=3']) +cc = meson.get_compiler('c') +m_dep = cc.find_library('m', required : false) +install_headers('pca.h') +shared_library('codapca', 'pca.c', dependencies : m_dep, install : true) @@ -0,0 +1,8106 @@ +// Generated by Futhark 0.24.0 (prerelease - include info below when reporting bugs) + +// We need to define _GNU_SOURCE before +// _any_ headers files are imported to get +// the usage statistics of a thread (i.e. have RUSAGE_THREAD) on GNU/Linux +// https://manpages.courier-mta.org/htmlman2/getrusage.2.html +#ifndef _GNU_SOURCE // Avoid possible double-definition warning. +#define _GNU_SOURCE +#endif + +#ifdef __clang__ +#pragma clang diagnostic ignored "-Wunused-function" +#pragma clang diagnostic ignored "-Wunused-variable" +#pragma clang diagnostic ignored "-Wparentheses" +#pragma clang diagnostic ignored "-Wunused-label" +#elif __GNUC__ +#pragma GCC diagnostic ignored "-Wunused-function" +#pragma GCC diagnostic ignored "-Wunused-variable" +#pragma GCC diagnostic ignored "-Wparentheses" +#pragma GCC diagnostic ignored "-Wunused-label" +#pragma GCC diagnostic ignored "-Wunused-but-set-variable" +#endif + +// Headers +#include <stdint.h> +#include <stddef.h> +#include <stdbool.h> +#include <stdio.h> +#include <float.h> + +#ifdef __cplusplus +extern "C" { +#endif + +// Initialisation +struct futhark_context_config; +struct futhark_context_config *futhark_context_config_new(void); +void futhark_context_config_free(struct futhark_context_config *cfg); +int futhark_context_config_set_tuning_param(struct futhark_context_config *cfg, const char *param_name, size_t new_value); +struct futhark_context; +struct futhark_context *futhark_context_new(struct futhark_context_config *cfg); +void futhark_context_free(struct futhark_context *cfg); +void futhark_context_config_set_debugging(struct futhark_context_config *cfg, int flag); +void futhark_context_config_set_profiling(struct futhark_context_config *cfg, int flag); +void futhark_context_config_set_logging(struct futhark_context_config *cfg, int flag); +int futhark_get_tuning_param_count(void); +const char *futhark_get_tuning_param_name(int); +const char *futhark_get_tuning_param_class(int); + +// Arrays +struct futhark_f64_2d; +struct futhark_f64_2d *futhark_new_f64_2d(struct futhark_context *ctx, const double *data, int64_t dim0, int64_t dim1); +struct futhark_f64_2d *futhark_new_raw_f64_2d(struct futhark_context *ctx, const unsigned char *data, int64_t offset, int64_t dim0, int64_t dim1); +int futhark_free_f64_2d(struct futhark_context *ctx, struct futhark_f64_2d *arr); +int futhark_values_f64_2d(struct futhark_context *ctx, struct futhark_f64_2d *arr, double *data); +unsigned char *futhark_values_raw_f64_2d(struct futhark_context *ctx, struct futhark_f64_2d *arr); +const int64_t *futhark_shape_f64_2d(struct futhark_context *ctx, struct futhark_f64_2d *arr); + +// Opaque values + + + +// Entry points +int futhark_entry_dloss(struct futhark_context *ctx, struct futhark_f64_2d **out0, struct futhark_f64_2d **out1, const struct futhark_f64_2d *in0, const struct futhark_f64_2d *in1, const struct futhark_f64_2d *in2); +int futhark_entry_loss(struct futhark_context *ctx, double *out0, const struct futhark_f64_2d *in0, const struct futhark_f64_2d *in1, const struct futhark_f64_2d *in2); +int futhark_entry_pcaWithQuantile(struct futhark_context *ctx, struct futhark_f64_2d **out0, struct futhark_f64_2d **out1, struct futhark_f64_2d **out2, double *out3, const double in0, const int64_t in1, const struct futhark_f64_2d *in2); + +// Miscellaneous +int futhark_context_sync(struct futhark_context *ctx); +void futhark_context_config_set_cache_file(struct futhark_context_config *cfg, const char *f); +char *futhark_context_report(struct futhark_context *ctx); +char *futhark_context_get_error(struct futhark_context *ctx); +void futhark_context_set_logging_file(struct futhark_context *ctx, FILE *f); +void futhark_context_pause_profiling(struct futhark_context *ctx); +void futhark_context_unpause_profiling(struct futhark_context *ctx); +int futhark_context_clear_caches(struct futhark_context *ctx); +#define FUTHARK_BACKEND_c +#define FUTHARK_SUCCESS 0 +#define FUTHARK_PROGRAM_ERROR 2 +#define FUTHARK_OUT_OF_MEMORY 3 + +#ifdef __cplusplus +} +#endif + +#include <stdio.h> +#include <stdlib.h> +#include <stdbool.h> +#include <math.h> +#include <stdint.h> +// If NDEBUG is set, the assert() macro will do nothing. Since Futhark +// (unfortunately) makes use of assert() for error detection (and even some +// side effects), we want to avoid that. +#undef NDEBUG +#include <assert.h> +#include <stdarg.h> +// Start of util.h. +// +// Various helper functions that are useful in all generated C code. + +#include <errno.h> +#include <string.h> + +static const char *fut_progname = "(embedded Futhark)"; + +static void futhark_panic(int eval, const char *fmt, ...) __attribute__((noreturn)); +static char* msgprintf(const char *s, ...); +static void* slurp_file(const char *filename, size_t *size); +static int dump_file(const char *file, const void *buf, size_t n); +struct str_builder; +static void str_builder_init(struct str_builder *b); +static void str_builder(struct str_builder *b, const char *s, ...); +static char *strclone(const char *str); + +static void futhark_panic(int eval, const char *fmt, ...) { + va_list ap; + va_start(ap, fmt); + fprintf(stderr, "%s: ", fut_progname); + vfprintf(stderr, fmt, ap); + va_end(ap); + exit(eval); +} + +// For generating arbitrary-sized error messages. It is the callers +// responsibility to free the buffer at some point. +static char* msgprintf(const char *s, ...) { + va_list vl; + va_start(vl, s); + size_t needed = 1 + (size_t)vsnprintf(NULL, 0, s, vl); + char *buffer = (char*) malloc(needed); + va_start(vl, s); // Must re-init. + vsnprintf(buffer, needed, s, vl); + return buffer; +} + +static inline void check_err(int errval, int sets_errno, const char *fun, int line, + const char *msg, ...) { + if (errval) { + char errnum[10]; + + va_list vl; + va_start(vl, msg); + + fprintf(stderr, "ERROR: "); + vfprintf(stderr, msg, vl); + fprintf(stderr, " in %s() at line %d with error code %s\n", + fun, line, + sets_errno ? strerror(errno) : errnum); + exit(errval); + } +} + +#define CHECK_ERR(err, ...) check_err(err, 0, __func__, __LINE__, __VA_ARGS__) +#define CHECK_ERRNO(err, ...) check_err(err, 1, __func__, __LINE__, __VA_ARGS__) + +// Read the rest of an open file into a NUL-terminated string; returns +// NULL on error. +static void* fslurp_file(FILE *f, size_t *size) { + long start = ftell(f); + fseek(f, 0, SEEK_END); + long src_size = ftell(f)-start; + fseek(f, start, SEEK_SET); + unsigned char *s = (unsigned char*) malloc((size_t)src_size + 1); + if (fread(s, 1, (size_t)src_size, f) != (size_t)src_size) { + free(s); + s = NULL; + } else { + s[src_size] = '\0'; + } + + if (size) { + *size = (size_t)src_size; + } + + return s; +} + +// Read a file into a NUL-terminated string; returns NULL on error. +static void* slurp_file(const char *filename, size_t *size) { + FILE *f = fopen(filename, "rb"); // To avoid Windows messing with linebreaks. + if (f == NULL) return NULL; + unsigned char *s = fslurp_file(f, size); + fclose(f); + return s; +} + +// Dump 'n' bytes from 'buf' into the file at the designated location. +// Returns 0 on success. +static int dump_file(const char *file, const void *buf, size_t n) { + FILE *f = fopen(file, "w"); + + if (f == NULL) { + return 1; + } + + if (fwrite(buf, sizeof(char), n, f) != n) { + return 1; + } + + if (fclose(f) != 0) { + return 1; + } + + return 0; +} + +struct str_builder { + char *str; + size_t capacity; // Size of buffer. + size_t used; // Bytes used, *not* including final zero. +}; + +static void str_builder_init(struct str_builder *b) { + b->capacity = 10; + b->used = 0; + b->str = malloc(b->capacity); + b->str[0] = 0; +} + +static void str_builder(struct str_builder *b, const char *s, ...) { + va_list vl; + va_start(vl, s); + size_t needed = (size_t)vsnprintf(NULL, 0, s, vl); + + while (b->capacity < b->used + needed + 1) { + b->capacity *= 2; + b->str = realloc(b->str, b->capacity); + } + + va_start(vl, s); // Must re-init. + vsnprintf(b->str+b->used, b->capacity-b->used, s, vl); + b->used += needed; +} + + +static char *strclone(const char *str) { + size_t size = strlen(str) + 1; + char *copy = (char*) malloc(size); + if (copy == NULL) { + return NULL; + } + + memcpy(copy, str, size); + return copy; +} + +// End of util.h. +// Start of cache.h + +#define CACHE_HASH_SIZE 8 // In 32-bit words. + +struct cache_hash { + uint32_t hash[CACHE_HASH_SIZE]; +}; + +// Initialise a blank cache. +static void cache_hash_init(struct cache_hash *c); + +// Hash some bytes and add them to the accumulated hash. +static void cache_hash(struct cache_hash *out, const char *in, size_t n); + +// Try to restore cache contents from a file with the given name. +// Assumes the cache is invalid if it contains the given hash. +// Allocates memory and reads the cache conents, which is returned in +// *buf with size *buflen. If the cache is successfully loaded, this +// function returns 0. Otherwise it returns nonzero. Errno is set if +// the failure to load the cache is due to anything except invalid +// cache conents. Note that failing to restore the cache is not +// necessarily a problem: it might just be invalid or not created yet. +static int cache_restore(const char *fname, const struct cache_hash *hash, + unsigned char **buf, size_t *buflen); + +// Store cache contents in the given file, with the given hash. +static int cache_store(const char *fname, const struct cache_hash *hash, + const unsigned char *buf, size_t buflen); + +// Now for the implementation. + +static void cache_hash_init(struct cache_hash *c) { + memset(c->hash, 0, CACHE_HASH_SIZE * sizeof(uint32_t)); +} + +static void cache_hash(struct cache_hash *out, const char *in, size_t n) { + // Adaptation of djb2 for larger output size by storing intermediate + // states. + uint32_t hash = 5381; + for (size_t i = 0; i < n; i++) { + hash = ((hash << 5) + hash) + in[i]; + out->hash[i % CACHE_HASH_SIZE] ^= hash; + } +} + +#define CACHE_HEADER_SIZE 8 +static const char cache_header[CACHE_HEADER_SIZE] = "FUTHARK\0"; + +static int cache_restore(const char *fname, const struct cache_hash *hash, + unsigned char **buf, size_t *buflen) { + FILE *f = fopen(fname, "rb"); + + if (f == NULL) { + return 1; + } + + char f_header[CACHE_HEADER_SIZE]; + + if (fread(f_header, sizeof(char), CACHE_HEADER_SIZE, f) != CACHE_HEADER_SIZE) { + goto error; + } + + if (memcmp(f_header, cache_header, CACHE_HEADER_SIZE) != 0) { + goto error; + } + + if (fseek(f, 0, SEEK_END) != 0) { + goto error; + } + int64_t f_size = (int64_t)ftell(f); + if (fseek(f, CACHE_HEADER_SIZE, SEEK_SET) != 0) { + goto error; + } + + int64_t expected_size; + + if (fread(&expected_size, sizeof(int64_t), 1, f) != 1) { + goto error; + } + + if (f_size != expected_size) { + errno = 0; + goto error; + } + + int32_t f_hash[CACHE_HASH_SIZE]; + + if (fread(f_hash, sizeof(int32_t), CACHE_HASH_SIZE, f) != CACHE_HASH_SIZE) { + goto error; + } + + if (memcmp(f_hash, hash->hash, CACHE_HASH_SIZE) != 0) { + errno = 0; + goto error; + } + + *buflen = f_size - CACHE_HEADER_SIZE - sizeof(int64_t) - CACHE_HASH_SIZE*sizeof(int32_t); + *buf = malloc(*buflen); + if (fread(*buf, sizeof(char), *buflen, f) != *buflen) { + free(*buf); + goto error; + } + + fclose(f); + + return 0; + + error: + fclose(f); + return 1; +} + +static int cache_store(const char *fname, const struct cache_hash *hash, + const unsigned char *buf, size_t buflen) { + FILE *f = fopen(fname, "wb"); + + if (f == NULL) { + return 1; + } + + if (fwrite(cache_header, CACHE_HEADER_SIZE, 1, f) != 1) { + goto error; + } + + int64_t size = CACHE_HEADER_SIZE + sizeof(int64_t) + CACHE_HASH_SIZE*sizeof(int32_t) + buflen; + + if (fwrite(&size, sizeof(size), 1, f) != 1) { + goto error; + } + + if (fwrite(hash->hash, sizeof(int32_t), CACHE_HASH_SIZE, f) != CACHE_HASH_SIZE) { + goto error; + } + + if (fwrite(buf, sizeof(unsigned char), buflen, f) != buflen) { + goto error; + } + + fclose(f); + + return 0; + + error: + fclose(f); + return 1; +} + +// End of cache.h +// Start of half.h. + +// Conversion functions are from http://half.sourceforge.net/, but +// translated to C. +// +// Copyright (c) 2012-2021 Christian Rau +// +// Permission is hereby granted, free of charge, to any person obtaining a copy +// of this software and associated documentation files (the "Software"), to deal +// in the Software without restriction, including without limitation the rights +// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +// copies of the Software, and to permit persons to whom the Software is +// furnished to do so, subject to the following conditions: +// +// The above copyright notice and this permission notice shall be included in +// all copies or substantial portions of the Software. +// +// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +// THE SOFTWARE. + +#ifndef __OPENCL_VERSION__ +#define __constant +#endif + +__constant static const uint16_t base_table[512] = { + 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, + 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, + 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, + 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, + 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, + 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, + 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0001, 0x0002, 0x0004, 0x0008, 0x0010, 0x0020, 0x0040, 0x0080, 0x0100, + 0x0200, 0x0400, 0x0800, 0x0C00, 0x1000, 0x1400, 0x1800, 0x1C00, 0x2000, 0x2400, 0x2800, 0x2C00, 0x3000, 0x3400, 0x3800, 0x3C00, + 0x4000, 0x4400, 0x4800, 0x4C00, 0x5000, 0x5400, 0x5800, 0x5C00, 0x6000, 0x6400, 0x6800, 0x6C00, 0x7000, 0x7400, 0x7800, 0x7C00, + 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, + 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, + 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, + 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, + 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, + 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, + 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, + 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, + 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, + 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, + 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, + 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, + 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, + 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8001, 0x8002, 0x8004, 0x8008, 0x8010, 0x8020, 0x8040, 0x8080, 0x8100, + 0x8200, 0x8400, 0x8800, 0x8C00, 0x9000, 0x9400, 0x9800, 0x9C00, 0xA000, 0xA400, 0xA800, 0xAC00, 0xB000, 0xB400, 0xB800, 0xBC00, + 0xC000, 0xC400, 0xC800, 0xCC00, 0xD000, 0xD400, 0xD800, 0xDC00, 0xE000, 0xE400, 0xE800, 0xEC00, 0xF000, 0xF400, 0xF800, 0xFC00, + 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, + 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, + 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, + 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, + 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, + 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, + 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00 }; + +__constant static const unsigned char shift_table[512] = { + 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, + 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, + 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, + 24, 24, 24, 24, 24, 24, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, + 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, + 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, + 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, + 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 13, + 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, + 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, + 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, + 24, 24, 24, 24, 24, 24, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, + 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, + 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, + 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, + 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 13 }; + +__constant static const uint32_t mantissa_table[2048] = { + 0x00000000, 0x33800000, 0x34000000, 0x34400000, 0x34800000, 0x34A00000, 0x34C00000, 0x34E00000, 0x35000000, 0x35100000, 0x35200000, 0x35300000, 0x35400000, 0x35500000, 0x35600000, 0x35700000, + 0x35800000, 0x35880000, 0x35900000, 0x35980000, 0x35A00000, 0x35A80000, 0x35B00000, 0x35B80000, 0x35C00000, 0x35C80000, 0x35D00000, 0x35D80000, 0x35E00000, 0x35E80000, 0x35F00000, 0x35F80000, + 0x36000000, 0x36040000, 0x36080000, 0x360C0000, 0x36100000, 0x36140000, 0x36180000, 0x361C0000, 0x36200000, 0x36240000, 0x36280000, 0x362C0000, 0x36300000, 0x36340000, 0x36380000, 0x363C0000, + 0x36400000, 0x36440000, 0x36480000, 0x364C0000, 0x36500000, 0x36540000, 0x36580000, 0x365C0000, 0x36600000, 0x36640000, 0x36680000, 0x366C0000, 0x36700000, 0x36740000, 0x36780000, 0x367C0000, + 0x36800000, 0x36820000, 0x36840000, 0x36860000, 0x36880000, 0x368A0000, 0x368C0000, 0x368E0000, 0x36900000, 0x36920000, 0x36940000, 0x36960000, 0x36980000, 0x369A0000, 0x369C0000, 0x369E0000, + 0x36A00000, 0x36A20000, 0x36A40000, 0x36A60000, 0x36A80000, 0x36AA0000, 0x36AC0000, 0x36AE0000, 0x36B00000, 0x36B20000, 0x36B40000, 0x36B60000, 0x36B80000, 0x36BA0000, 0x36BC0000, 0x36BE0000, + 0x36C00000, 0x36C20000, 0x36C40000, 0x36C60000, 0x36C80000, 0x36CA0000, 0x36CC0000, 0x36CE0000, 0x36D00000, 0x36D20000, 0x36D40000, 0x36D60000, 0x36D80000, 0x36DA0000, 0x36DC0000, 0x36DE0000, + 0x36E00000, 0x36E20000, 0x36E40000, 0x36E60000, 0x36E80000, 0x36EA0000, 0x36EC0000, 0x36EE0000, 0x36F00000, 0x36F20000, 0x36F40000, 0x36F60000, 0x36F80000, 0x36FA0000, 0x36FC0000, 0x36FE0000, + 0x37000000, 0x37010000, 0x37020000, 0x37030000, 0x37040000, 0x37050000, 0x37060000, 0x37070000, 0x37080000, 0x37090000, 0x370A0000, 0x370B0000, 0x370C0000, 0x370D0000, 0x370E0000, 0x370F0000, + 0x37100000, 0x37110000, 0x37120000, 0x37130000, 0x37140000, 0x37150000, 0x37160000, 0x37170000, 0x37180000, 0x37190000, 0x371A0000, 0x371B0000, 0x371C0000, 0x371D0000, 0x371E0000, 0x371F0000, + 0x37200000, 0x37210000, 0x37220000, 0x37230000, 0x37240000, 0x37250000, 0x37260000, 0x37270000, 0x37280000, 0x37290000, 0x372A0000, 0x372B0000, 0x372C0000, 0x372D0000, 0x372E0000, 0x372F0000, + 0x37300000, 0x37310000, 0x37320000, 0x37330000, 0x37340000, 0x37350000, 0x37360000, 0x37370000, 0x37380000, 0x37390000, 0x373A0000, 0x373B0000, 0x373C0000, 0x373D0000, 0x373E0000, 0x373F0000, + 0x37400000, 0x37410000, 0x37420000, 0x37430000, 0x37440000, 0x37450000, 0x37460000, 0x37470000, 0x37480000, 0x37490000, 0x374A0000, 0x374B0000, 0x374C0000, 0x374D0000, 0x374E0000, 0x374F0000, + 0x37500000, 0x37510000, 0x37520000, 0x37530000, 0x37540000, 0x37550000, 0x37560000, 0x37570000, 0x37580000, 0x37590000, 0x375A0000, 0x375B0000, 0x375C0000, 0x375D0000, 0x375E0000, 0x375F0000, + 0x37600000, 0x37610000, 0x37620000, 0x37630000, 0x37640000, 0x37650000, 0x37660000, 0x37670000, 0x37680000, 0x37690000, 0x376A0000, 0x376B0000, 0x376C0000, 0x376D0000, 0x376E0000, 0x376F0000, + 0x37700000, 0x37710000, 0x37720000, 0x37730000, 0x37740000, 0x37750000, 0x37760000, 0x37770000, 0x37780000, 0x37790000, 0x377A0000, 0x377B0000, 0x377C0000, 0x377D0000, 0x377E0000, 0x377F0000, + 0x37800000, 0x37808000, 0x37810000, 0x37818000, 0x37820000, 0x37828000, 0x37830000, 0x37838000, 0x37840000, 0x37848000, 0x37850000, 0x37858000, 0x37860000, 0x37868000, 0x37870000, 0x37878000, + 0x37880000, 0x37888000, 0x37890000, 0x37898000, 0x378A0000, 0x378A8000, 0x378B0000, 0x378B8000, 0x378C0000, 0x378C8000, 0x378D0000, 0x378D8000, 0x378E0000, 0x378E8000, 0x378F0000, 0x378F8000, + 0x37900000, 0x37908000, 0x37910000, 0x37918000, 0x37920000, 0x37928000, 0x37930000, 0x37938000, 0x37940000, 0x37948000, 0x37950000, 0x37958000, 0x37960000, 0x37968000, 0x37970000, 0x37978000, + 0x37980000, 0x37988000, 0x37990000, 0x37998000, 0x379A0000, 0x379A8000, 0x379B0000, 0x379B8000, 0x379C0000, 0x379C8000, 0x379D0000, 0x379D8000, 0x379E0000, 0x379E8000, 0x379F0000, 0x379F8000, + 0x37A00000, 0x37A08000, 0x37A10000, 0x37A18000, 0x37A20000, 0x37A28000, 0x37A30000, 0x37A38000, 0x37A40000, 0x37A48000, 0x37A50000, 0x37A58000, 0x37A60000, 0x37A68000, 0x37A70000, 0x37A78000, + 0x37A80000, 0x37A88000, 0x37A90000, 0x37A98000, 0x37AA0000, 0x37AA8000, 0x37AB0000, 0x37AB8000, 0x37AC0000, 0x37AC8000, 0x37AD0000, 0x37AD8000, 0x37AE0000, 0x37AE8000, 0x37AF0000, 0x37AF8000, + 0x37B00000, 0x37B08000, 0x37B10000, 0x37B18000, 0x37B20000, 0x37B28000, 0x37B30000, 0x37B38000, 0x37B40000, 0x37B48000, 0x37B50000, 0x37B58000, 0x37B60000, 0x37B68000, 0x37B70000, 0x37B78000, + 0x37B80000, 0x37B88000, 0x37B90000, 0x37B98000, 0x37BA0000, 0x37BA8000, 0x37BB0000, 0x37BB8000, 0x37BC0000, 0x37BC8000, 0x37BD0000, 0x37BD8000, 0x37BE0000, 0x37BE8000, 0x37BF0000, 0x37BF8000, + 0x37C00000, 0x37C08000, 0x37C10000, 0x37C18000, 0x37C20000, 0x37C28000, 0x37C30000, 0x37C38000, 0x37C40000, 0x37C48000, 0x37C50000, 0x37C58000, 0x37C60000, 0x37C68000, 0x37C70000, 0x37C78000, + 0x37C80000, 0x37C88000, 0x37C90000, 0x37C98000, 0x37CA0000, 0x37CA8000, 0x37CB0000, 0x37CB8000, 0x37CC0000, 0x37CC8000, 0x37CD0000, 0x37CD8000, 0x37CE0000, 0x37CE8000, 0x37CF0000, 0x37CF8000, + 0x37D00000, 0x37D08000, 0x37D10000, 0x37D18000, 0x37D20000, 0x37D28000, 0x37D30000, 0x37D38000, 0x37D40000, 0x37D48000, 0x37D50000, 0x37D58000, 0x37D60000, 0x37D68000, 0x37D70000, 0x37D78000, + 0x37D80000, 0x37D88000, 0x37D90000, 0x37D98000, 0x37DA0000, 0x37DA8000, 0x37DB0000, 0x37DB8000, 0x37DC0000, 0x37DC8000, 0x37DD0000, 0x37DD8000, 0x37DE0000, 0x37DE8000, 0x37DF0000, 0x37DF8000, + 0x37E00000, 0x37E08000, 0x37E10000, 0x37E18000, 0x37E20000, 0x37E28000, 0x37E30000, 0x37E38000, 0x37E40000, 0x37E48000, 0x37E50000, 0x37E58000, 0x37E60000, 0x37E68000, 0x37E70000, 0x37E78000, + 0x37E80000, 0x37E88000, 0x37E90000, 0x37E98000, 0x37EA0000, 0x37EA8000, 0x37EB0000, 0x37EB8000, 0x37EC0000, 0x37EC8000, 0x37ED0000, 0x37ED8000, 0x37EE0000, 0x37EE8000, 0x37EF0000, 0x37EF8000, + 0x37F00000, 0x37F08000, 0x37F10000, 0x37F18000, 0x37F20000, 0x37F28000, 0x37F30000, 0x37F38000, 0x37F40000, 0x37F48000, 0x37F50000, 0x37F58000, 0x37F60000, 0x37F68000, 0x37F70000, 0x37F78000, + 0x37F80000, 0x37F88000, 0x37F90000, 0x37F98000, 0x37FA0000, 0x37FA8000, 0x37FB0000, 0x37FB8000, 0x37FC0000, 0x37FC8000, 0x37FD0000, 0x37FD8000, 0x37FE0000, 0x37FE8000, 0x37FF0000, 0x37FF8000, + 0x38000000, 0x38004000, 0x38008000, 0x3800C000, 0x38010000, 0x38014000, 0x38018000, 0x3801C000, 0x38020000, 0x38024000, 0x38028000, 0x3802C000, 0x38030000, 0x38034000, 0x38038000, 0x3803C000, + 0x38040000, 0x38044000, 0x38048000, 0x3804C000, 0x38050000, 0x38054000, 0x38058000, 0x3805C000, 0x38060000, 0x38064000, 0x38068000, 0x3806C000, 0x38070000, 0x38074000, 0x38078000, 0x3807C000, + 0x38080000, 0x38084000, 0x38088000, 0x3808C000, 0x38090000, 0x38094000, 0x38098000, 0x3809C000, 0x380A0000, 0x380A4000, 0x380A8000, 0x380AC000, 0x380B0000, 0x380B4000, 0x380B8000, 0x380BC000, + 0x380C0000, 0x380C4000, 0x380C8000, 0x380CC000, 0x380D0000, 0x380D4000, 0x380D8000, 0x380DC000, 0x380E0000, 0x380E4000, 0x380E8000, 0x380EC000, 0x380F0000, 0x380F4000, 0x380F8000, 0x380FC000, + 0x38100000, 0x38104000, 0x38108000, 0x3810C000, 0x38110000, 0x38114000, 0x38118000, 0x3811C000, 0x38120000, 0x38124000, 0x38128000, 0x3812C000, 0x38130000, 0x38134000, 0x38138000, 0x3813C000, + 0x38140000, 0x38144000, 0x38148000, 0x3814C000, 0x38150000, 0x38154000, 0x38158000, 0x3815C000, 0x38160000, 0x38164000, 0x38168000, 0x3816C000, 0x38170000, 0x38174000, 0x38178000, 0x3817C000, + 0x38180000, 0x38184000, 0x38188000, 0x3818C000, 0x38190000, 0x38194000, 0x38198000, 0x3819C000, 0x381A0000, 0x381A4000, 0x381A8000, 0x381AC000, 0x381B0000, 0x381B4000, 0x381B8000, 0x381BC000, + 0x381C0000, 0x381C4000, 0x381C8000, 0x381CC000, 0x381D0000, 0x381D4000, 0x381D8000, 0x381DC000, 0x381E0000, 0x381E4000, 0x381E8000, 0x381EC000, 0x381F0000, 0x381F4000, 0x381F8000, 0x381FC000, + 0x38200000, 0x38204000, 0x38208000, 0x3820C000, 0x38210000, 0x38214000, 0x38218000, 0x3821C000, 0x38220000, 0x38224000, 0x38228000, 0x3822C000, 0x38230000, 0x38234000, 0x38238000, 0x3823C000, + 0x38240000, 0x38244000, 0x38248000, 0x3824C000, 0x38250000, 0x38254000, 0x38258000, 0x3825C000, 0x38260000, 0x38264000, 0x38268000, 0x3826C000, 0x38270000, 0x38274000, 0x38278000, 0x3827C000, + 0x38280000, 0x38284000, 0x38288000, 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