Introduce bfloat16 support

Many models on Hugging Face (e.g. Mistral, TinyLLaMA) use bfloat16 as
their canonical floating point format.

      ┌sign
      │
      │   ┌exponent
      │   │
      │   │      ┌mantissa
      │   │      │
      │┌──┴───┐┌─┴───┐
    0b0000000000000000 brain16

This encoding has the same number of exponent bits as float32. That
makes conversion relatively straightforward, even in the absence of
hardware support. For example, converting brain16 to binary32 means
simply shifting 16 bits to the left.

      ┌sign
      │
      │   ┌exponent
      │   │
      │   │      ┌mantissa
      │   │      │
      │┌──┴───┐┌─┴───────────────────┐
    0b00000000000000000000000000000000 IEEE binary32

The issue is that converting weights from bf16 to fp16 will cause 3
bits of knowledge to be lost. There is currently no way to evaluate
models like Mistral at full fidelity, without f32, using llama.cpp.

      ┌sign
      │
      │  ┌exponent
      │  │
      │  │    ┌mantissa
      │  │    │
      │┌─┴─┐┌─┴──────┐
    0b0000000000000000 IEEE binary16

This change fixes that, by adding a bf16 data type to GGML. Support
for CPU inference has been implemented along with optimizations for
the AVX2, AVX512, and AVX512BF16 ISAs. Perplexity on Mistral 7b 0.2
improves somewhere around -0.0024 to -0.0046 compared to using fp16

examples/finetune/finetune.cpp

@@ -575,7 +575,7 @@ static struct ggml_tensor * llama_build_lora_finetune_graphs(
     GGML_ASSERT(tokens_input->type == GGML_TYPE_I32);
 
     auto add_to_f32 = [] (struct ggml_context * ctx, struct ggml_tensor * a, struct ggml_tensor * b) {
-        if (ggml_is_quantized(a->type) || a->type == GGML_TYPE_F16) {
+        if (ggml_is_quantized(a->type) || a->type == GGML_TYPE_F16 || a->type == GGML_TYPE_BF16) {
             return ggml_add_cast(ctx, a, b, GGML_TYPE_F32);
         } else if (a->type == GGML_TYPE_F32) {
             return ggml_add(ctx, a, b);

examples/quantize/quantize.cpp

@@ -47,7 +47,8 @@ static const std::vector<struct quant_option> QUANT_OPTIONS = {
     { "Q5_K_M", LLAMA_FTYPE_MOSTLY_Q5_K_M, " 4.45G, +0.0122 ppl @ LLaMA-v1-7B", },
     { "Q6_K",   LLAMA_FTYPE_MOSTLY_Q6_K,   " 5.15G, +0.0008 ppl @ LLaMA-v1-7B", },
     { "Q8_0",   LLAMA_FTYPE_MOSTLY_Q8_0,   " 6.70G, +0.0004 ppl @ LLaMA-v1-7B", },
-    { "F16",    LLAMA_FTYPE_MOSTLY_F16,    "13.00G              @ 7B", },
+    { "F16",    LLAMA_FTYPE_MOSTLY_F16,    "14.00G, -0.0020 ppl @ Mistral-7B", },
+    { "BF16",   LLAMA_FTYPE_MOSTLY_BF16,   "14.00G, -0.0050 ppl @ Mistral-7B", },
     { "F32",    LLAMA_FTYPE_ALL_F32,       "26.00G              @ 7B", },
     // Note: Ensure COPY comes after F32 to avoid ftype 0 from matching.
     { "COPY",   LLAMA_FTYPE_ALL_F32,       "only copy tensors, no quantizing", },

ggml-impl.h

@@ -260,6 +260,9 @@ size_t ggml_hash_insert        (      struct ggml_hash_set hash_set, struct ggml
 // return index, asserts if table is full
 size_t ggml_hash_find_or_insert(      struct ggml_hash_set hash_set, struct ggml_tensor * key);
 
+#define GGML_FP32_TO_BF16(x) ggml_fp32_to_bf16(x)
+#define GGML_BF16_TO_FP32(x) ggml_bf16_to_fp32(x)
+
 #ifdef __cplusplus
 }
 #endif