From dd7eff57d8491792010b1002b8de6a4b54912e5c Mon Sep 17 00:00:00 2001 From: Ivan Stepanov Date: Sat, 29 Apr 2023 08:34:41 +0300 Subject: [PATCH] llama : new sampling algorithms (#1126) * Sample interface, new samplers. New samplers: - locally typical sampling - tail free sampling - frequency and presence penalty - mirostat Ignore EOS fix: -inf should be used. * mirostat * Added --logit-bias and --no-penalize-nl, removed std::span * Use C++11, clarify llama API documentation, rename Mirostat parameters to --mirostat_lr and --mirostat_ent, add temperature sampling for Mirostat, simplify Mirostat sampling API parameters (removed N and *k) Use C++11, clarify llama API documentation, rename Mirostat parameters to --mirostat_lr and --mirostat_ent, add temperature sampling for Mirostat, simplify Mirostat sampling API parameters (removed N and *k) * Save and load example adjust * Tests * Windows build fix * Windows test fix --- examples/common.cpp | 91 +++- examples/common.h | 21 +- examples/main/main.cpp | 71 ++- examples/save-load-state/save-load-state.cpp | 34 +- llama.cpp | 491 ++++++++++++++----- llama.h | 64 ++- tests/CMakeLists.txt | 1 + tests/test-sampling.cpp | 199 ++++++++ 8 files changed, 812 insertions(+), 160 deletions(-) create mode 100644 tests/test-sampling.cpp diff --git a/examples/common.cpp b/examples/common.cpp index 9f10dc268..6c712c713 100644 --- a/examples/common.cpp +++ b/examples/common.cpp @@ -6,6 +6,8 @@ #include #include #include +#include +#include #if defined (_WIN32) #include @@ -114,6 +116,18 @@ bool gpt_params_parse(int argc, char ** argv, gpt_params & params) { break; } params.temp = std::stof(argv[i]); + } else if (arg == "--tfs") { + if (++i >= argc) { + invalid_param = true; + break; + } + params.tfs_z = std::stof(argv[i]); + } else if (arg == "--typical") { + if (++i >= argc) { + invalid_param = true; + break; + } + params.typical_p = std::stof(argv[i]); } else if (arg == "--repeat_last_n") { if (++i >= argc) { invalid_param = true; @@ -126,6 +140,36 @@ bool gpt_params_parse(int argc, char ** argv, gpt_params & params) { break; } params.repeat_penalty = std::stof(argv[i]); + } else if (arg == "--frequency_penalty") { + if (++i >= argc) { + invalid_param = true; + break; + } + params.frequency_penalty = std::stof(argv[i]); + } else if (arg == "--presence_penalty") { + if (++i >= argc) { + invalid_param = true; + break; + } + params.presence_penalty = std::stof(argv[i]); + } else if (arg == "--mirostat") { + if (++i >= argc) { + invalid_param = true; + break; + } + params.mirostat = std::stoi(argv[i]); + } else if (arg == "--mirostat_lr") { + if (++i >= argc) { + invalid_param = true; + break; + } + params.mirostat_eta = std::stof(argv[i]); + } else if (arg == "--mirostat_ent") { + if (++i >= argc) { + invalid_param = true; + break; + } + params.mirostat_tau = std::stof(argv[i]); } else if (arg == "-b" || arg == "--batch_size") { if (++i >= argc) { invalid_param = true; @@ -185,7 +229,28 @@ bool gpt_params_parse(int argc, char ** argv, gpt_params & params) { } else if (arg == "--perplexity") { params.perplexity = true; } else if (arg == "--ignore-eos") { - params.ignore_eos = true; + params.logit_bias[llama_token_eos()] = -INFINITY; + } else if (arg == "--no-penalize-nl") { + params.penalize_nl = false; + } else if (arg == "-l" || arg == "--logit-bias") { + if (++i >= argc) { + invalid_param = true; + break; + } + std::stringstream ss(argv[i]); + llama_token key; + char sign; + std::string value_str; + try { + if (ss >> key && ss >> sign && std::getline(ss, value_str) && (sign == '+' || sign == '-')) { + params.logit_bias[key] = std::stof(value_str) * ((sign == '-') ? -1.0f : 1.0f); + } else { + throw std::exception(); + } + } catch (const std::exception &e) { + invalid_param = true; + break; + } } else if (arg == "--n_parts") { if (++i >= argc) { invalid_param = true; @@ -240,12 +305,26 @@ void gpt_print_usage(int /*argc*/, char ** argv, const gpt_params & params) { fprintf(stderr, " -f FNAME, --file FNAME\n"); fprintf(stderr, " prompt file to start generation.\n"); fprintf(stderr, " -n N, --n_predict N number of tokens to predict (default: %d, -1 = infinity)\n", params.n_predict); - fprintf(stderr, " --top_k N top-k sampling (default: %d)\n", params.top_k); - fprintf(stderr, " --top_p N top-p sampling (default: %.1f)\n", (double)params.top_p); - fprintf(stderr, " --repeat_last_n N last n tokens to consider for penalize (default: %d)\n", params.repeat_last_n); - fprintf(stderr, " --repeat_penalty N penalize repeat sequence of tokens (default: %.1f)\n", (double)params.repeat_penalty); + fprintf(stderr, " --top_k N top-k sampling (default: %d, 0 = disabled)\n", params.top_k); + fprintf(stderr, " --top_p N top-p sampling (default: %.1f, 1.0 = disabled)\n", (double)params.top_p); + fprintf(stderr, " --tfs N tail free sampling, parameter z (default: %.1f, 1.0 = disabled)\n", (double)params.tfs_z); + fprintf(stderr, " --typical N locally typical sampling, parameter p (default: %.1f, 1.0 = disabled)\n", (double)params.typical_p); + fprintf(stderr, " --repeat_last_n N last n tokens to consider for penalize (default: %d, 0 = disabled, -1 = ctx_size)\n", params.repeat_last_n); + fprintf(stderr, " --repeat_penalty N penalize repeat sequence of tokens (default: %.1f, 1.0 = disabled)\n", (double)params.repeat_penalty); + fprintf(stderr, " --presence_penalty N repeat alpha presence penalty (default: %.1f, 0.0 = disabled)\n", (double)params.presence_penalty); + fprintf(stderr, " --frequency_penalty N repeat alpha frequency penalty (default: %.1f, 0.0 = disabled)\n", (double)params.frequency_penalty); + fprintf(stderr, " --mirostat N use Mirostat sampling.\n"); + fprintf(stderr, " Top K, Nucleus, Tail Free and Locally Typical samplers are ignored if used.\n"); + fprintf(stderr, " (default: %d, 0 = disabled, 1 = Mirostat, 2 = Mirostat 2.0)\n", params.mirostat); + fprintf(stderr, " --mirostat_lr N Mirostat learning rate, parameter eta (default: %.1f)\n", (double)params.mirostat_eta); + fprintf(stderr, " --mirostat_ent N Mirostat target entropy, parameter tau (default: %.1f)\n", (double)params.mirostat_tau); + fprintf(stderr, " -l TOKEN_ID(+/-)BIAS, --logit-bias TOKEN_ID(+/-)BIAS\n"); + fprintf(stderr, " modifies the likelihood of token appearing in the completion,\n"); + fprintf(stderr, " i.e. `--logit-bias 15043+1` to increase likelihood of token ' Hello',\n"); + fprintf(stderr, " or `--logit-bias 15043-1` to decrease likelihood of token ' Hello'\n"); fprintf(stderr, " -c N, --ctx_size N size of the prompt context (default: %d)\n", params.n_ctx); - fprintf(stderr, " --ignore-eos ignore end of stream token and continue generating\n"); + fprintf(stderr, " --ignore-eos ignore end of stream token and continue generating (implies --logit-bias 2-inf)\n"); + fprintf(stderr, " --no-penalize-nl do not penalize newline token\n"); fprintf(stderr, " --memory_f32 use f32 instead of f16 for memory key+value\n"); fprintf(stderr, " --temp N temperature (default: %.1f)\n", (double)params.temp); fprintf(stderr, " --n_parts N number of model parts (default: -1 = determine from dimensions)\n"); diff --git a/examples/common.h b/examples/common.h index 9d3697d79..14e6b1ba7 100644 --- a/examples/common.h +++ b/examples/common.h @@ -8,6 +8,7 @@ #include #include #include +#include // // CLI argument parsing @@ -17,17 +18,25 @@ struct gpt_params { int32_t seed = -1; // RNG seed int32_t n_threads = std::min(4, (int32_t) std::thread::hardware_concurrency()); int32_t n_predict = 128; // new tokens to predict - int32_t repeat_last_n = 64; // last n tokens to penalize int32_t n_parts = -1; // amount of model parts (-1 = determine from model dimensions) int32_t n_ctx = 512; // context size int32_t n_batch = 512; // batch size for prompt processing (must be >=32 to use BLAS) int32_t n_keep = 0; // number of tokens to keep from initial prompt // sampling parameters - int32_t top_k = 40; - float top_p = 0.95f; - float temp = 0.80f; - float repeat_penalty = 1.10f; + std::unordered_map logit_bias; // logit bias for specific tokens + int32_t top_k = 0; // <= 0 to use vocab size + float top_p = 1.0f; // 1.0 = disabled + float tfs_z = 1.0f; // 1.0 = disabled + float typical_p = 1.0f; // 1.0 = disabled + float temp = 1.0f; // 1.0 = disabled + float repeat_penalty = 1.0f; // 1.0 = disabled + int32_t repeat_last_n = -1; // last n tokens to penalize (0 = disable penalty, -1 = context size) + float frequency_penalty = 0.0f; // 0.0 = disabled + float presence_penalty = 0.0f; // 0.0 = disabled + int mirostat = 0; // 0 = disabled, 1 = mirostat, 2 = mirostat 2.0 + float mirostat_tau = 5.0f; // target entropy + float mirostat_eta = 0.1f; // learning rate std::string model = "models/lamma-7B/ggml-model.bin"; // model path std::string prompt = ""; @@ -47,7 +56,7 @@ struct gpt_params { bool interactive_first = false; // wait for user input immediately bool instruct = false; // instruction mode (used for Alpaca models) - bool ignore_eos = false; // do not stop generating after eos + bool penalize_nl = true; // consider newlines as a repeatable token bool perplexity = false; // compute perplexity over the prompt bool use_mmap = true; // use mmap for faster loads bool use_mlock = false; // use mlock to keep model in memory diff --git a/examples/main/main.cpp b/examples/main/main.cpp index fda65574f..674920b8a 100644 --- a/examples/main/main.cpp +++ b/examples/main/main.cpp @@ -276,8 +276,8 @@ int main(int argc, char ** argv) { fprintf(stderr, "Input prefix: '%s'\n", params.input_prefix.c_str()); } } - fprintf(stderr, "sampling: temp = %f, top_k = %d, top_p = %f, repeat_last_n = %i, repeat_penalty = %f\n", - params.temp, params.top_k, params.top_p, params.repeat_last_n, params.repeat_penalty); + fprintf(stderr, "sampling: repeat_last_n = %d, repeat_penalty = %f, presence_penalty = %f, frequency_penalty = %f, top_k = %d, tfs_z = %f, top_p = %f, typical_p = %f, temp = %f, mirostat = %d, mirostat_lr = %f, mirostat_ent = %f\n", + params.repeat_last_n, params.repeat_penalty, params.presence_penalty, params.frequency_penalty, params.top_k, params.tfs_z, params.top_p, params.typical_p, params.temp, params.mirostat, params.mirostat_eta, params.mirostat_tau); fprintf(stderr, "generate: n_ctx = %d, n_batch = %d, n_predict = %d, n_keep = %d\n", n_ctx, params.n_batch, params.n_predict, params.n_keep); fprintf(stderr, "\n\n"); @@ -387,10 +387,19 @@ int main(int argc, char ** argv) { if ((int) embd_inp.size() <= n_consumed && !is_interacting) { // out of user input, sample next token - const int32_t top_k = params.top_k; - const float top_p = params.top_p; const float temp = params.temp; + const int32_t top_k = params.top_k <= 0 ? llama_n_vocab(ctx) : params.top_k; + const float top_p = params.top_p; + const float tfs_z = params.tfs_z; + const float typical_p = params.typical_p; + const int32_t repeat_last_n = params.repeat_last_n < 0 ? n_ctx : params.repeat_last_n; const float repeat_penalty = params.repeat_penalty; + const float alpha_presence = params.presence_penalty; + const float alpha_frequency = params.frequency_penalty; + const int mirostat = params.mirostat; + const float mirostat_tau = params.mirostat_tau; + const float mirostat_eta = params.mirostat_eta; + const bool penalize_nl = params.penalize_nl; // optionally save the session on first sample (for faster prompt loading next time) if (!path_session.empty() && need_to_save_session) { @@ -402,14 +411,58 @@ int main(int argc, char ** argv) { { auto logits = llama_get_logits(ctx); + auto n_vocab = llama_n_vocab(ctx); - if (params.ignore_eos) { - logits[llama_token_eos()] = 0; + // Apply params.logit_bias map + for (auto it = params.logit_bias.begin(); it != params.logit_bias.end(); it++) { + logits[it->first] += it->second; } - id = llama_sample_top_p_top_k(ctx, - last_n_tokens.data() + n_ctx - params.repeat_last_n, - params.repeat_last_n, top_k, top_p, temp, repeat_penalty); + std::vector candidates; + candidates.reserve(n_vocab); + for (llama_token token_id = 0; token_id < n_vocab; token_id++) { + candidates.emplace_back(llama_token_data{token_id, logits[token_id], 0.0f}); + } + + llama_token_data_array candidates_p = { candidates.data(), candidates.size(), false }; + + // Apply penalties + float nl_logit = logits[llama_token_nl()]; + auto last_n_repeat = std::min(std::min((int)last_n_tokens.size(), repeat_last_n), n_ctx); + llama_sample_repetition_penalty(ctx, &candidates_p, + last_n_tokens.data() + last_n_tokens.size() - last_n_repeat, + last_n_repeat, repeat_penalty); + llama_sample_frequency_and_presence_penalties(ctx, &candidates_p, + last_n_tokens.data() + last_n_tokens.size() - last_n_repeat, + last_n_repeat, alpha_frequency, alpha_presence); + if (!penalize_nl) { + logits[llama_token_nl()] = nl_logit; + } + + if (temp <= 0) { + // Greedy sampling + id = llama_sample_token_greedy(ctx, &candidates_p); + } else { + if (mirostat == 1) { + static float mirostat_mu = 2.0f * mirostat_tau; + const int mirostat_m = 100; + llama_sample_temperature(ctx, &candidates_p, temp); + id = llama_sample_token_mirostat(ctx, &candidates_p, mirostat_tau, mirostat_eta, mirostat_m, &mirostat_mu); + } else if (mirostat == 2) { + static float mirostat_mu = 2.0f * mirostat_tau; + llama_sample_temperature(ctx, &candidates_p, temp); + id = llama_sample_token_mirostat_v2(ctx, &candidates_p, mirostat_tau, mirostat_eta, &mirostat_mu); + } else { + // Temperature sampling + llama_sample_top_k(ctx, &candidates_p, top_k); + llama_sample_tail_free(ctx, &candidates_p, tfs_z); + llama_sample_typical(ctx, &candidates_p, typical_p); + llama_sample_top_p(ctx, &candidates_p, top_p); + llama_sample_temperature(ctx, &candidates_p, temp); + id = llama_sample_token(ctx, &candidates_p); + } + } + // printf("`%d`", candidates_p.size); last_n_tokens.erase(last_n_tokens.begin()); last_n_tokens.push_back(id); diff --git a/examples/save-load-state/save-load-state.cpp b/examples/save-load-state/save-load-state.cpp index 39aa7f82c..07dfa2c74 100644 --- a/examples/save-load-state/save-load-state.cpp +++ b/examples/save-load-state/save-load-state.cpp @@ -64,14 +64,15 @@ int main(int argc, char ** argv) { // first run printf("\n%s", params.prompt.c_str()); for (auto i = 0; i < params.n_predict; i++) { - auto next_token = llama_sample_top_p_top_k( - ctx, - &last_n_tokens_data.back() - params.repeat_last_n, - params.repeat_last_n, - 40, - 1.0, - 1.0, - 1.1); + auto logits = llama_get_logits(ctx); + auto n_vocab = llama_n_vocab(ctx); + std::vector candidates; + candidates.reserve(n_vocab); + for (llama_token token_id = 0; token_id < n_vocab; token_id++) { + candidates.emplace_back(llama_token_data{token_id, logits[token_id], 0.0f}); + } + llama_token_data_array candidates_p = { candidates.data(), candidates.size(), false }; + auto next_token = llama_sample_token(ctx, &candidates_p); auto next_token_str = llama_token_to_str(ctx, next_token); last_n_tokens_data.push_back(next_token); printf("%s", next_token_str); @@ -106,14 +107,15 @@ int main(int argc, char ** argv) { // second run for (auto i = 0; i < params.n_predict; i++) { - auto next_token = llama_sample_top_p_top_k( - ctx2, - &last_n_tokens_data.back() - params.repeat_last_n, - params.repeat_last_n, - 40, - 1.0, - 1.0, - 1.1); + auto logits = llama_get_logits(ctx2); + auto n_vocab = llama_n_vocab(ctx2); + std::vector candidates; + candidates.reserve(n_vocab); + for (llama_token token_id = 0; token_id < n_vocab; token_id++) { + candidates.emplace_back(llama_token_data{token_id, logits[token_id], 0.0f}); + } + llama_token_data_array candidates_p = { candidates.data(), candidates.size(), false }; + auto next_token = llama_sample_token(ctx2, &candidates_p); auto next_token_str = llama_token_to_str(ctx2, next_token); last_n_tokens_data.push_back(next_token); printf("%s", next_token_str); diff --git a/llama.cpp b/llama.cpp index 4699e5cf1..1032fb9fa 100644 --- a/llama.cpp +++ b/llama.cpp @@ -28,6 +28,7 @@ #include #include #include +#include #define LLAMA_USE_SCRATCH #define LLAMA_MAX_SCRATCH_BUFFERS 16 @@ -1475,109 +1476,402 @@ static std::vector llama_tokenize(const llama_vocab & vocab, co // sampling // -static void sample_top_k(std::vector> & logits_id, int top_k) { - // find the top k tokens - std::partial_sort( - logits_id.begin(), - logits_id.begin() + top_k, logits_id.end(), - [](const std::pair & a, const std::pair & b) { - return a.first > b.first; - }); +void llama_sample_softmax(struct llama_context * ctx, llama_token_data_array * candidates) { + assert(candidates->size > 0); - logits_id.resize(top_k); + const int64_t t_start_sample_us = ggml_time_us(); + + // Sort the logits in descending order + if (!candidates->sorted) { + std::sort(candidates->data, candidates->data + candidates->size, [](const llama_token_data & a, const llama_token_data & b) { + return a.logit > b.logit; + }); + candidates->sorted = true; + } + + float max_l = candidates->data[0].logit; + float cum_sum = 0.0f; + for (size_t i = 0; i < candidates->size; ++i) { + float p = expf(candidates->data[i].logit - max_l); + candidates->data[i].p = p; + cum_sum += p; + } + for (size_t i = 0; i < candidates->size; ++i) { + candidates->data[i].p /= cum_sum; + } + + if (ctx) { + ctx->t_sample_us += ggml_time_us() - t_start_sample_us; + } } -static llama_vocab::id llama_sample_top_p_top_k( - llama_context & lctx, - const std::vector & last_n_tokens, - int top_k, - float top_p, - float temp, - float repeat_penalty) { - auto & rng = lctx.rng; +void llama_sample_top_k(struct llama_context * ctx, llama_token_data_array * candidates, int k, size_t min_keep) { + const int64_t t_start_sample_us = ggml_time_us(); - const int n_logits = lctx.model.hparams.n_vocab; + k = std::max(k, (int) min_keep); + k = std::min(k, (int) candidates->size); - const auto & logits = lctx.logits; - const auto * plogits = logits.data() + logits.size() - n_logits; - - if (temp <= 0) { - // select the token with the highest logit directly - float max_logit = plogits[0]; - llama_vocab::id max_id = 0; - - for (int i = 1; i < n_logits; ++i) { - if (plogits[i] > max_logit) { - max_logit = plogits[i]; - max_id = i; - } + // Sort scores in descending order + if (!candidates->sorted) { + auto comp = [](const llama_token_data & a, const llama_token_data & b) { + return a.logit > b.logit; + }; + if (k == (int) candidates->size) { + std::sort(candidates->data, candidates->data + candidates->size, comp); + } else { + std::partial_sort(candidates->data, candidates->data + k, candidates->data + candidates->size, comp); } - return max_id; + candidates->sorted = true; + } + candidates->size = k; + + if (ctx) { + ctx->t_sample_us += ggml_time_us() - t_start_sample_us; + } +} + +void llama_sample_top_p(struct llama_context * ctx, llama_token_data_array * candidates, float p, size_t min_keep) { + if (p >= 1.0f) { + return; } - std::vector> logits_id; - logits_id.reserve(n_logits); + const int64_t t_start_sample_us = ggml_time_us(); - { - const float scale = 1.0f/temp; - for (int i = 0; i < n_logits; ++i) { - // repetition penalty from ctrl paper (https://arxiv.org/abs/1909.05858) - // credit https://github.com/facebookresearch/llama/compare/main...shawwn:llama:main - if (std::find(last_n_tokens.begin(), last_n_tokens.end(), i) != last_n_tokens.end()) { - // if score < 0 then repetition penalty has to multiplied to reduce the previous token probability - if (plogits[i] < 0.0f) { - logits_id.push_back(std::make_pair(plogits[i]*scale*repeat_penalty, i)); - } else { - logits_id.push_back(std::make_pair(plogits[i]*scale/repeat_penalty, i)); - } - } else { - logits_id.push_back(std::make_pair(plogits[i]*scale, i)); - } + llama_sample_softmax(ctx, candidates); + + // Compute the cumulative probabilities + float cum_sum = 0.0f; + size_t last_idx = candidates->size; + + for (size_t i = 0; i < candidates->size; ++i) { + cum_sum += candidates->data[i].p; + + // Check if the running sum is greater than p or if we have kept at least min_keep tokens + if (cum_sum > p && i >= min_keep) { + last_idx = i; + break; } } - sample_top_k(logits_id, top_k > 0 ? std::min(top_k, n_logits) : n_logits); + // Resize the output vector to keep only the top-p tokens + candidates->size = last_idx; + + if (ctx) { + ctx->t_sample_us += ggml_time_us() - t_start_sample_us; + } +} + +void llama_sample_tail_free(struct llama_context * ctx, llama_token_data_array * candidates, float z, size_t min_keep) { + if (z >= 1.0f || candidates->size <= 2) { + return; + } + + const int64_t t_start_sample_us = ggml_time_us(); + + llama_sample_softmax(nullptr, candidates); + + // Compute the first and second derivatives + std::vector first_derivatives(candidates->size - 1); + std::vector second_derivatives(candidates->size - 2); + + for (size_t i = 0; i < first_derivatives.size(); ++i) { + first_derivatives[i] = candidates->data[i].p - candidates->data[i + 1].p; + } + for (size_t i = 0; i < second_derivatives.size(); ++i) { + second_derivatives[i] = first_derivatives[i] - first_derivatives[i + 1]; + } + + // Calculate absolute value of second derivatives + for (size_t i = 0; i < second_derivatives.size(); ++i) { + second_derivatives[i] = abs(second_derivatives[i]); + } + + // Normalize the second derivatives + float second_derivatives_sum = std::accumulate(second_derivatives.begin(), second_derivatives.end(), 0.0f); + for (float & value : second_derivatives) { + value /= second_derivatives_sum; + } + + float cum_sum = 0.0f; + size_t last_idx = candidates->size; + for (size_t i = 0; i < second_derivatives.size(); ++i) { + cum_sum += second_derivatives[i]; + + // Check if the running sum is greater than z or if we have kept at least min_keep tokens + if (cum_sum > z && i >= min_keep) { + last_idx = i; + break; + } + } + + // Resize the output vector to keep only the tokens above the tail location + candidates->size = last_idx; + + if (ctx) { + ctx->t_sample_us += ggml_time_us() - t_start_sample_us; + } +} + + +void llama_sample_typical(struct llama_context * ctx, llama_token_data_array * candidates, float p, size_t min_keep) { + // Reference implementation: + // https://github.com/huggingface/transformers/compare/main...cimeister:typical-sampling:typical-pr + if (p >= 1.0f) { + return; + } + + const int64_t t_start_sample_us = ggml_time_us(); + + // Compute the softmax of logits and calculate entropy + llama_sample_softmax(nullptr, candidates); + + float entropy = 0.0f; + for (size_t i = 0; i < candidates->size; ++i) { + entropy += -candidates->data[i].p * logf(candidates->data[i].p); + } + + // Compute the absolute difference between negative log probability and entropy for each candidate + std::vector shifted_scores; + for (size_t i = 0; i < candidates->size; ++i) { + float shifted_score = fabsf(-logf(candidates->data[i].p) - entropy); + shifted_scores.push_back(shifted_score); + } + + // Sort tokens based on the shifted_scores and their corresponding indices + std::vector indices(candidates->size); + std::iota(indices.begin(), indices.end(), 0); + + std::sort(indices.begin(), indices.end(), [&](size_t a, size_t b) { + return shifted_scores[a] < shifted_scores[b]; + }); + + // Compute the cumulative probabilities + float cum_sum = 0.0f; + size_t last_idx = indices.size(); + + for (size_t i = 0; i < indices.size(); ++i) { + size_t idx = indices[i]; + cum_sum += candidates->data[idx].p; + + // Check if the running sum is greater than typical or if we have kept at least min_keep tokens + if (cum_sum > p && i >= min_keep - 1) { + last_idx = i + 1; + break; + } + } + + // Resize the output vector to keep only the locally typical tokens + std::vector new_candidates; + for (size_t i = 0; i < last_idx; ++i) { + size_t idx = indices[i]; + new_candidates.push_back(candidates->data[idx]); + } + + // Replace the data in candidates with the new_candidates data + std::copy(new_candidates.begin(), new_candidates.end(), candidates->data); + candidates->size = new_candidates.size(); + + if (ctx) { + ctx->t_sample_us += ggml_time_us() - t_start_sample_us; + } +} + +void llama_sample_temperature(struct llama_context * ctx, llama_token_data_array * candidates_p, float temp) { + const int64_t t_start_sample_us = ggml_time_us(); + + for (size_t i = 0; i < candidates_p->size; ++i) { + candidates_p->data[i].logit /= temp; + } + + if (ctx) { + ctx->t_sample_us += ggml_time_us() - t_start_sample_us; + } +} + +void llama_sample_repetition_penalty(struct llama_context * ctx, llama_token_data_array * candidates, llama_token * last_tokens, size_t last_tokens_size, float penalty) { + if (last_tokens_size == 0 || penalty == 1.0f) { + return; + } + + const int64_t t_start_sample_us = ggml_time_us(); + + for (size_t i = 0; i < candidates->size; ++i) { + auto token_iter = std::find(last_tokens, last_tokens + last_tokens_size, candidates->data[i].id); + if (token_iter == last_tokens + last_tokens_size) { + continue; + } + + // The academic publication that described this technique actually just only divided, but that would cause tokens with negative logits to become more likely, which is obviously wrong. + // This is common fix for this problem, which is to multiply by the penalty instead of dividing. + if (candidates->data[i].logit <= 0) { + candidates->data[i].logit *= penalty; + } else { + candidates->data[i].logit /= penalty; + } + } + + candidates->sorted = false; + + if (ctx) { + ctx->t_sample_us += ggml_time_us() - t_start_sample_us; + } +} + +void llama_sample_frequency_and_presence_penalties(struct llama_context * ctx, llama_token_data_array * candidates, llama_token * last_tokens_p, size_t last_tokens_size, float alpha_frequency, float alpha_presence) { + if (last_tokens_size == 0 || (alpha_frequency == 0.0f && alpha_presence == 0.0f)) { + return; + } + + const int64_t t_start_sample_us = ggml_time_us(); + + // Create a frequency map to count occurrences of each token in last_tokens + std::unordered_map token_count; + for (size_t i = 0; i < last_tokens_size; ++i) { + token_count[last_tokens_p[i]]++; + } + + // Apply frequency and presence penalties to the candidates + for (size_t i = 0; i < candidates->size; ++i) { + auto token_iter = token_count.find(candidates->data[i].id); + if (token_iter == token_count.end()) { + continue; + } + + int count = token_iter->second; + candidates->data[i].logit -= float(count) * alpha_frequency + float(count > 0) * alpha_presence; + } + + candidates->sorted = false; + + if (ctx) { + ctx->t_sample_us += ggml_time_us() - t_start_sample_us; + } +} + + +llama_token llama_sample_token_mirostat(struct llama_context * ctx, llama_token_data_array * candidates, float tau, float eta, int m, float * mu) { + assert(ctx); + auto N = float(llama_n_vocab(ctx)); + int64_t t_start_sample_us; + t_start_sample_us = ggml_time_us(); + + llama_sample_softmax(nullptr, candidates); + + // Estimate s_hat using the most probable m tokens + float s_hat = 0.0; + float sum_ti_bi = 0.0; + float sum_ti_sq = 0.0; + for (size_t i = 0; i < size_t(m - 1) && i < candidates->size - 1; ++i) { + float t_i = logf(float(i + 2) / float(i + 1)); + float b_i = logf(candidates->data[i].p / candidates->data[i + 1].p); + sum_ti_bi += t_i * b_i; + sum_ti_sq += t_i * t_i; + } + s_hat = sum_ti_bi / sum_ti_sq; + + // Compute k from the estimated s_hat and target surprise value + float epsilon_hat = s_hat - 1; + float k = powf((epsilon_hat * powf(2, *mu)) / (1 - powf(N, -epsilon_hat)), 1 / s_hat); + + // Sample the next word X using top-k sampling + llama_sample_top_k(nullptr, candidates, int(k)); + if (ctx) { + ctx->t_sample_us += ggml_time_us() - t_start_sample_us; + } + llama_token X = llama_sample_token(ctx, candidates); + t_start_sample_us = ggml_time_us(); + + // Compute error as the difference between observed surprise and target surprise value + size_t X_idx = std::distance(candidates->data, std::find_if(candidates->data, candidates->data + candidates->size, [&](const llama_token_data & candidate) { + return candidate.id == X; + })); + float observed_surprise = -log2f(candidates->data[X_idx].p); + float e = observed_surprise - tau; + + // Update mu using the learning rate and error + *mu = *mu - eta * e; + + if (ctx) { + ctx->t_sample_us += ggml_time_us() - t_start_sample_us; + ctx->n_sample++; + } + return X; +} + +llama_token llama_sample_token_mirostat_v2(struct llama_context * ctx, llama_token_data_array * candidates, float tau, float eta, float * mu) { + assert(ctx); + int64_t t_start_sample_us; + t_start_sample_us = ggml_time_us(); + + llama_sample_softmax(ctx, candidates); + + // Truncate the words with surprise values greater than mu + candidates->size = std::distance(candidates->data, std::find_if(candidates->data, candidates->data + candidates->size, [&](const llama_token_data & candidate) { + return -log2f(candidate.p) > *mu; + })); + + // Normalize the probabilities of the remaining words + llama_sample_softmax(ctx, candidates); + + // Sample the next word X from the remaining words + if (ctx) { + ctx->t_sample_us += ggml_time_us() - t_start_sample_us; + } + llama_token X = llama_sample_token(ctx, candidates); + t_start_sample_us = ggml_time_us(); + + // Compute error as the difference between observed surprise and target surprise value + size_t X_idx = std::distance(candidates->data, std::find_if(candidates->data, candidates->data + candidates->size, [&](const llama_token_data & candidate) { + return candidate.id == X; + })); + float observed_surprise = -log2f(candidates->data[X_idx].p); + float e = observed_surprise - tau; + + // Update mu using the learning rate and error + *mu = *mu - eta * e; + + if (ctx) { + ctx->t_sample_us += ggml_time_us() - t_start_sample_us; + } + return X; +} + +llama_token llama_sample_token_greedy(struct llama_context * ctx, llama_token_data_array * candidates) { + const int64_t t_start_sample_us = ggml_time_us(); + + // Find max element + auto max_iter = std::max_element(candidates->data, candidates->data + candidates->size, [](const llama_token_data & a, const llama_token_data & b) { + return a.logit < b.logit; + }); + + llama_token result = max_iter->id; + if (ctx) { + ctx->t_sample_us += ggml_time_us() - t_start_sample_us; + ctx->n_sample++; + } + return result; +} + +llama_token llama_sample_token(struct llama_context * ctx, llama_token_data_array * candidates) { + assert(ctx); + const int64_t t_start_sample_us = ggml_time_us(); + llama_sample_softmax(nullptr, candidates); - // compute probs for the top k tokens std::vector probs; - probs.reserve(logits_id.size()); - - float maxl = logits_id[0].first; - double sum = 0.0; - for (const auto & kv : logits_id) { - const float p = expf(kv.first - maxl); - probs.push_back(p); - sum += p; + probs.reserve(candidates->size); + for (size_t i = 0; i < candidates->size; ++i) { + probs.push_back(candidates->data[i].p); } - // normalize the probs - for (auto & p : probs) { - p /= sum; - } - - if (top_p < 1.0) { - double cumsum = 0.0; - for (int i = 0; i < (int) probs.size(); i++) { - cumsum += probs[i]; - if (cumsum >= top_p) { - probs.resize(i + 1); - logits_id.resize(i + 1); - break; - } - } - } - - //printf("\n"); - //for (int i = 0; i < (int) 10; i++) { - // printf("%d: '%s' %f\n", i, lctx.vocab.id_to_token.at(logits_id[i].second).tok.c_str(), probs[i]); - //} - //printf("\n\n"); - //exit(0); - std::discrete_distribution<> dist(probs.begin(), probs.end()); + auto & rng = ctx->rng; int idx = dist(rng); - return logits_id[idx].second; + llama_token result = candidates->data[idx].id; + + ctx->t_sample_us += ggml_time_us() - t_start_sample_us; + ctx->n_sample++; + return result; } // @@ -2348,33 +2642,8 @@ llama_token llama_token_eos() { return 2; } -llama_token llama_sample_top_p_top_k( - llama_context * ctx, - const llama_token * last_n_tokens_data, - int last_n_tokens_size, - int top_k, - float top_p, - float temp, - float repeat_penalty) { - const int64_t t_start_sample_us = ggml_time_us(); - - llama_token result = 0; - - // TODO: avoid this ... - const auto last_n_tokens = std::vector(last_n_tokens_data, last_n_tokens_data + last_n_tokens_size); - - result = llama_sample_top_p_top_k( - *ctx, - last_n_tokens, - top_k, - top_p, - temp, - repeat_penalty); - - ctx->t_sample_us += ggml_time_us() - t_start_sample_us; - ctx->n_sample++; - - return result; +llama_token llama_token_nl() { + return 13; } diff --git a/llama.h b/llama.h index 936c52139..34a8f5b3c 100644 --- a/llama.h +++ b/llama.h @@ -39,12 +39,16 @@ extern "C" { typedef struct llama_token_data { llama_token id; // token id - + float logit; // log-odds of the token float p; // probability of the token - float plog; // log probability of the token - } llama_token_data; + typedef struct llama_token_data_array { + llama_token_data * data; + size_t size; + bool sorted; + } llama_token_data_array; + typedef void (*llama_progress_callback)(float progress, void *ctx); struct llama_context_params { @@ -181,16 +185,52 @@ extern "C" { // Special tokens LLAMA_API llama_token llama_token_bos(); LLAMA_API llama_token llama_token_eos(); + LLAMA_API llama_token llama_token_nl(); - // TODO: improve the last_n_tokens interface ? - LLAMA_API llama_token llama_sample_top_p_top_k( - struct llama_context * ctx, - const llama_token * last_n_tokens_data, - int last_n_tokens_size, - int top_k, - float top_p, - float temp, - float repeat_penalty); + // Sampling functions + + /// @details Repetition penalty described in CTRL academic paper https://arxiv.org/abs/1909.05858, with negative logit fix. + LLAMA_API void llama_sample_repetition_penalty(struct llama_context * ctx, llama_token_data_array * candidates, llama_token * last_tokens, size_t last_tokens_size, float penalty); + + /// @details Frequency and presence penalties described in OpenAI API https://platform.openai.com/docs/api-reference/parameter-details. + LLAMA_API void llama_sample_frequency_and_presence_penalties(struct llama_context * ctx, llama_token_data_array * candidates, llama_token * last_tokens, size_t last_tokens_size, float alpha_frequency, float alpha_presence); + + /// @details Sorts candidate tokens by their logits in descending order and calculate probabilities based on logits. + LLAMA_API void llama_sample_softmax(struct llama_context * ctx, llama_token_data_array * candidates); + + /// @details Top-K sampling described in academic paper "The Curious Case of Neural Text Degeneration" https://arxiv.org/abs/1904.09751 + LLAMA_API void llama_sample_top_k(struct llama_context * ctx, llama_token_data_array * candidates, int k, size_t min_keep = 1); + + /// @details Nucleus sampling described in academic paper "The Curious Case of Neural Text Degeneration" https://arxiv.org/abs/1904.09751 + LLAMA_API void llama_sample_top_p(struct llama_context * ctx, llama_token_data_array * candidates, float p, size_t min_keep = 1); + + /// @details Tail Free Sampling described in https://www.trentonbricken.com/Tail-Free-Sampling/. + LLAMA_API void llama_sample_tail_free(struct llama_context * ctx, llama_token_data_array * candidates, float z, size_t min_keep = 1); + + /// @details Locally Typical Sampling implementation described in the paper https://arxiv.org/abs/2202.00666. + LLAMA_API void llama_sample_typical(struct llama_context * ctx, llama_token_data_array * candidates, float p, size_t min_keep = 1); + LLAMA_API void llama_sample_temperature(struct llama_context * ctx, llama_token_data_array * candidates, float temp); + + /// @details Mirostat 1.0 algorithm described in the paper https://arxiv.org/abs/2007.14966. Uses tokens instead of words. + /// @param candidates A vector of `llama_token_data` containing the candidate tokens, their probabilities (p), and log-odds (logit) for the current position in the generated text. + /// @param tau The target cross-entropy (or surprise) value you want to achieve for the generated text. A higher value corresponds to more surprising or less predictable text, while a lower value corresponds to less surprising or more predictable text. + /// @param eta The learning rate used to update `mu` based on the error between the target and observed surprisal of the sampled word. A larger learning rate will cause `mu` to be updated more quickly, while a smaller learning rate will result in slower updates. + /// @param m The number of tokens considered in the estimation of `s_hat`. This is an arbitrary value that is used to calculate `s_hat`, which in turn helps to calculate the value of `k`. In the paper, they use `m = 100`, but you can experiment with different values to see how it affects the performance of the algorithm. + /// @param mu Maximum cross-entropy. This value is initialized to be twice the target cross-entropy (`2 * tau`) and is updated in the algorithm based on the error between the target and observed surprisal. + LLAMA_API llama_token llama_sample_token_mirostat(struct llama_context * ctx, llama_token_data_array * candidates, float tau, float eta, int m, float * mu); + + /// @details Mirostat 2.0 algorithm described in the paper https://arxiv.org/abs/2007.14966. Uses tokens instead of words. + /// @param candidates A vector of `llama_token_data` containing the candidate tokens, their probabilities (p), and log-odds (logit) for the current position in the generated text. + /// @param tau The target cross-entropy (or surprise) value you want to achieve for the generated text. A higher value corresponds to more surprising or less predictable text, while a lower value corresponds to less surprising or more predictable text. + /// @param eta The learning rate used to update `mu` based on the error between the target and observed surprisal of the sampled word. A larger learning rate will cause `mu` to be updated more quickly, while a smaller learning rate will result in slower updates. + /// @param mu Maximum cross-entropy. This value is initialized to be twice the target cross-entropy (`2 * tau`) and is updated in the algorithm based on the error between the target and observed surprisal. + LLAMA_API llama_token llama_sample_token_mirostat_v2(struct llama_context * ctx, llama_token_data_array * candidates, float tau, float eta, float * mu); + + /// @details Selects the token with the highest probability. + LLAMA_API llama_token llama_sample_token_greedy(struct llama_context * ctx, llama_token_data_array * candidates); + + /// @details Randomly selects a token from the candidates based on their probabilities. + LLAMA_API llama_token llama_sample_token(struct llama_context * ctx, llama_token_data_array * candidates); // Performance information LLAMA_API void llama_print_timings(struct llama_context * ctx); diff --git a/tests/CMakeLists.txt b/tests/CMakeLists.txt index 81eadbc4d..645648585 100644 --- a/tests/CMakeLists.txt +++ b/tests/CMakeLists.txt @@ -8,4 +8,5 @@ endfunction() # llama_add_test(test-double-float.c) # SLOW llama_add_test(test-quantize-fns.cpp) llama_add_test(test-quantize-perf.cpp) +llama_add_test(test-sampling.cpp) llama_add_test(test-tokenizer-0.cpp ${CMAKE_CURRENT_SOURCE_DIR}/../models/ggml-vocab.bin) diff --git a/tests/test-sampling.cpp b/tests/test-sampling.cpp new file mode 100644 index 000000000..7eee4f6d3 --- /dev/null +++ b/tests/test-sampling.cpp @@ -0,0 +1,199 @@ +#include "llama.h" +#include "ggml.h" +#include +#include +#include +#include +#include +#include +#include + + +void dump(const llama_token_data_array * candidates) { + for (size_t i = 0; i < candidates->size; i++) { + printf("%d: %f (%f)\n", candidates->data[i].id, candidates->data[i].p, candidates->data[i].logit); + } +} + +#define DUMP(__candidates) do { printf("%s:%d (%s)\n", __FILE__, __LINE__, __func__); dump((__candidates)); printf("-\n"); } while(0) + + +void test_top_k(const std::vector & probs, + const std::vector & expected_probs, + int k) { + size_t n_vocab = probs.size(); + std::vector candidates; + candidates.reserve(n_vocab); + for (llama_token token_id = 0; token_id < (llama_token)n_vocab; token_id++) { + float logit = log(probs[token_id]); + candidates.emplace_back(llama_token_data{token_id, logit, 0.0f}); + } + + llama_token_data_array candidates_p = { candidates.data(), candidates.size(), false }; + llama_sample_softmax(nullptr, &candidates_p); + DUMP(&candidates_p); + llama_sample_top_k(nullptr, &candidates_p, k); + DUMP(&candidates_p); + + assert(candidates_p.size == expected_probs.size()); + for (size_t i = 0; i < candidates_p.size; i++) { + assert(fabs(candidates_p.data[i].p - expected_probs[i]) < 1e-5); + } +} + + +void test_top_p(const std::vector & probs, + const std::vector & expected_probs, + float p) { + + size_t n_vocab = probs.size(); + std::vector candidates; + candidates.reserve(n_vocab); + for (llama_token token_id = 0; token_id < (llama_token)n_vocab; token_id++) { + float logit = log(probs[token_id]); + candidates.emplace_back(llama_token_data{token_id, logit, 0.0f}); + } + + llama_token_data_array candidates_p = { candidates.data(), candidates.size(), false }; + llama_sample_softmax(nullptr, &candidates_p); + DUMP(&candidates_p); + llama_sample_top_p(nullptr, &candidates_p, p); + DUMP(&candidates_p); + + assert(candidates_p.size == expected_probs.size()); + for (size_t i = 0; i < candidates_p.size; i++) { + assert(fabs(candidates_p.data[i].p - expected_probs[i]) < 1e-3); + } +} + + +void test_tfs(const std::vector & probs, + const std::vector & expected_probs, + float z) { + size_t n_vocab = probs.size(); + std::vector candidates; + candidates.reserve(n_vocab); + for (llama_token token_id = 0; token_id < (llama_token)n_vocab; token_id++) { + float logit = log(probs[token_id]); + candidates.emplace_back(llama_token_data{token_id, logit, 0.0f}); + } + + llama_token_data_array candidates_p = { candidates.data(), candidates.size(), false }; + DUMP(&candidates_p); + llama_sample_tail_free(nullptr, &candidates_p, z); + DUMP(&candidates_p); + + assert(candidates_p.size == expected_probs.size()); + for (size_t i = 0; i < candidates_p.size; i++) { + assert(fabs(candidates_p.data[i].p - expected_probs[i]) < 1e-3); + } +} + + +void test_typical(const std::vector & probs, + const std::vector & expected_probs, + float p) { + size_t n_vocab = probs.size(); + std::vector candidates; + candidates.reserve(n_vocab); + for (llama_token token_id = 0; token_id < (llama_token)n_vocab; token_id++) { + float logit = log(probs[token_id]); + candidates.emplace_back(llama_token_data{token_id, logit, 0.0f}); + } + + llama_token_data_array candidates_p = { candidates.data(), candidates.size(), false }; + DUMP(&candidates_p); + llama_sample_typical(nullptr, &candidates_p, p); + DUMP(&candidates_p); + + assert(candidates_p.size == expected_probs.size()); + for (size_t i = 0; i < candidates_p.size; i++) { + assert(fabs(candidates_p.data[i].p - expected_probs[i]) < 1e-3); + } +} + + +void test_repetition_penalty( + const std::vector & probs, + const std::vector & last_tokens, + const std::vector & expected_probs, + float penalty) { + assert(probs.size() == expected_probs.size()); + + size_t n_vocab = probs.size(); + std::vector candidates; + candidates.reserve(n_vocab); + for (llama_token token_id = 0; token_id < (llama_token)n_vocab; token_id++) { + float logit = log(probs[token_id]); + candidates.emplace_back(llama_token_data{token_id, logit, 0.0f}); + } + + llama_token_data_array candidates_p = { candidates.data(), candidates.size(), false }; + llama_sample_softmax(nullptr, &candidates_p); + DUMP(&candidates_p); + llama_sample_repetition_penalty(nullptr, &candidates_p, (llama_token *)last_tokens.data(), last_tokens.size(), penalty); + llama_sample_softmax(nullptr, &candidates_p); + DUMP(&candidates_p); + + assert(candidates_p.size == expected_probs.size()); + for (size_t i = 0; i < candidates_p.size; i++) { + assert(fabs(candidates_p.data[i].p - expected_probs[i]) < 1e-6); + } +} + + +void test_frequency_presence_penalty( + const std::vector & probs, + const std::vector & last_tokens, + const std::vector & expected_probs, + float alpha_frequency, float alpha_presence) { + assert(probs.size() == expected_probs.size()); + + size_t n_vocab = probs.size(); + std::vector candidates; + candidates.reserve(n_vocab); + for (llama_token token_id = 0; token_id < (llama_token)n_vocab; token_id++) { + float logit = log(probs[token_id]); + candidates.emplace_back(llama_token_data{token_id, logit, 0.0f}); + } + + llama_token_data_array candidates_p = { candidates.data(), candidates.size(), false }; + llama_sample_softmax(nullptr, &candidates_p); + // DUMP(&candidates_p); + llama_sample_frequency_and_presence_penalties(nullptr, &candidates_p, (llama_token *)last_tokens.data(), last_tokens.size(), alpha_frequency, alpha_presence); + llama_sample_softmax(nullptr, &candidates_p); + // DUMP(&candidates_p); + + assert(candidates_p.size == expected_probs.size()); + for (size_t i = 0; i < candidates_p.size; i++) { + assert(fabs(candidates_p.data[i].p - expected_probs[i]) < 1e-3); + } +} + +int main(void) { + ggml_time_init(); + + test_top_k({0.1, 0.2, 0.3, 0.4}, {0.4}, 1); + test_top_k({0.1, 0.2, 0.3, 0.4}, {0.4, 0.3, 0.2}, 3); + + test_top_p({0.1, 0.2, 0.3, 0.4}, {0.4}, 0); + test_top_p({0.1, 0.2, 0.3, 0.4}, {0.4, 0.3}, 0.7); + test_top_p({0.1, 0.2, 0.3, 0.4}, {0.4, 0.3, 0.2, 0.1}, 1); + + test_tfs({0.1, 0.15, 0.2, 0.25, 0.3}, {0.3}, 0.25); + test_tfs({0.1, 0.15, 0.2, 0.25, 0.3}, {0.3, 0.25}, 0.75); + test_tfs({0.1, 0.15, 0.2, 0.25, 0.3}, {0.3, 0.25}, 0.99); + + test_typical({0.97, 0.01, 0.01, 0.01}, {0.97}, 0.5); + test_typical({0.4, 0.2, 0.2, 0.2}, {0.2, 0.2, 0.2}, 0.5); + + test_repetition_penalty({0.2, 0.2, 0.2, 0.2, 0.2}, {0}, {0.25, 0.25, 0.25, 0.25, 0}, 50.0); + test_repetition_penalty({0.2, 0.2, 0.2, 0.2, 0.2}, {0, 1, 2}, {0.5, 0.5, 0, 0, 0}, 50.0); + test_repetition_penalty({0.2, 0.2, 0.2, 0.2, 0.2}, {0, 1, 2, 0, 0}, {0.5, 0.5, 0, 0, 0}, 50.0); + + test_frequency_presence_penalty({0.2, 0.2, 0.2, 0.2, 0.2}, {0}, {0.249997, 0.249997, 0.249997, 0.249997, 0.000011}, 5.0, 5.0); + test_frequency_presence_penalty({0.2, 0.2, 0.2, 0.2, 0.2}, {0, 1, 2}, {0.499966, 0.499966, 0.000023, 0.000023, 0.000023}, 5.0, 5.0); + test_frequency_presence_penalty({0.2, 0.2, 0.2, 0.2, 0.2}, {0, 1, 2, 0, 0}, {0.499977, 0.499977, 0.000023, 0.000023, 0.000000}, 5.0, 5.0); + + printf("OK\n"); +}