FP16 added. Split-mixtral improved.

fp16.c

@@ -0,0 +1,85 @@
+#include <stdint.h>
+#include <math.h>
+
+/* This code comes originally from:
+ * https://github.com/Maratyszcza/FP16/blob/master/include/fp16/fp16.h
+ *
+ * The original code is MIT licensed. */
+
+static inline float fp32_from_bits(uint32_t w) {
+    union {
+        uint32_t as_bits;
+        float as_value;
+    } fp32;
+    fp32.as_bits = w;
+    return fp32.as_value;
+}
+
+static inline uint32_t fp32_to_bits(float f) {
+    union {
+        float as_value;
+        uint32_t as_bits;
+    } fp32;
+    fp32.as_value = f;
+    return fp32.as_bits;
+}
+
+float from_half(uint16_t h) {
+    const uint32_t w = (uint32_t) h << 16;
+    const uint32_t sign = w & UINT32_C(0x80000000);
+    const uint32_t two_w = w + w;
+
+    const uint32_t exp_offset = UINT32_C(0xE0) << 23;
+#if defined(__STDC_VERSION__) && (__STDC_VERSION__ >= 199901L) || defined(__GNUC__) && !defined(__STRICT_ANSI__)
+    const float exp_scale = 0x1.0p-112f;
+#else
+    const float exp_scale = fp32_from_bits(UINT32_C(0x7800000));
+#endif
+    const float normalized_value = fp32_from_bits((two_w >> 4) + exp_offset) * exp_scale;
+
+    const uint32_t magic_mask = UINT32_C(126) << 23;
+    const float magic_bias = 0.5f;
+    const float denormalized_value = fp32_from_bits((two_w >> 17) | magic_mask) - magic_bias;
+
+    const uint32_t denormalized_cutoff = UINT32_C(1) << 27;
+    const uint32_t result = sign |
+        (two_w < denormalized_cutoff ? fp32_to_bits(denormalized_value) : fp32_to_bits(normalized_value));
+    return fp32_from_bits(result);
+}
+
+uint16_t to_half(float f) {
+#if defined(__STDC_VERSION__) && (__STDC_VERSION__ >= 199901L) || defined(__GNUC__) && !defined(__STRICT_ANSI__)
+    const float scale_to_inf = 0x1.0p+112f;
+    const float scale_to_zero = 0x1.0p-110f;
+#else
+    const float scale_to_inf = fp32_from_bits(UINT32_C(0x77800000));
+    const float scale_to_zero = fp32_from_bits(UINT32_C(0x08800000));
+#endif
+    float base = (fabsf(f) * scale_to_inf) * scale_to_zero;
+
+    const uint32_t w = fp32_to_bits(f);
+    const uint32_t shl1_w = w + w;
+    const uint32_t sign = w & UINT32_C(0x80000000);
+    uint32_t bias = shl1_w & UINT32_C(0xFF000000);
+    if (bias < UINT32_C(0x71000000)) {
+        bias = UINT32_C(0x71000000);
+    }
+
+    base = fp32_from_bits((bias >> 1) + UINT32_C(0x07800000)) + base;
+    const uint32_t bits = fp32_to_bits(base);
+    const uint32_t exp_bits = (bits >> 13) & UINT32_C(0x00007C00);
+    const uint32_t mantissa_bits = bits & UINT32_C(0x00000FFF);
+    const uint32_t nonsign = exp_bits + mantissa_bits;
+    return (sign >> 16) | (shl1_w > UINT32_C(0xFF000000) ? UINT16_C(0x7E00) : nonsign);
+}
+
+#ifdef TEST_MAIN
+#include <stdio.h>
+int main(void) {
+    float f = 1.2345;
+    uint16_t half = to_half(f);
+    float f2 = from_half(half);
+    printf("%f %f\n", f, f2);
+    return 0;
+}
+#endif