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80 lines
2.7 KiB
80 lines
2.7 KiB
#!/usr/bin/env python3
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"""Reproduce article arithmetic. No model, benchmark, or third-party packages."""
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import json
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import math
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import struct
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def fp16(value):
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value = float(value)
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try:
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return struct.unpack(">e", struct.pack(">e", value))[0]
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except OverflowError:
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return math.copysign(math.inf, value)
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def bf16(value):
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"""Round a finite FP32 value to BF16, nearest with ties to even."""
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bits = struct.unpack(">I", struct.pack(">f", value))[0]
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rounded = (bits + 0x7FFF + ((bits >> 16) & 1)) & 0xFFFF0000
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return struct.unpack(">f", struct.pack(">I", rounded))[0]
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def endpoint_grid(value, bits, low=-1.0, high=1.0):
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"""Teaching grid, not an implementation of GGUF/NF4/signed INT4."""
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maximum_code = (1 << bits) - 1
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step = (high - low) / maximum_code
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code = min(max(round((value - low) / step), 0), maximum_code)
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restored = low + code * step
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return {
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"bits": bits,
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"levels": maximum_code + 1,
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"step": step,
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"code": code,
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"restored": restored,
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"absolute_error": abs(value - restored),
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}
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def main():
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value = 0.1234
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report = {
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"scope": "teaching arithmetic only; not a model quality/speed benchmark",
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"parameters": 8_000_000_000,
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"weight_only_budget": [
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{"bits": bits, "GB": 8_000_000_000 * bits / 8 / 1e9,
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"GiB": 8_000_000_000 * bits / 8 / 2**30}
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for bits in (32, 16, 8, 4)
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],
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"floating_point": [
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{"original": v, "FP16": fp16(v) if math.isfinite(fp16(v)) else "+inf",
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"BF16": bf16(v)}
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for v in (1.001, 100000.0)
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],
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"scale_example": {
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"original": value, "scale": 0.02, "zero_point": 0,
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"code": round(value / 0.02), "restored": round(value / 0.02) * 0.02,
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"absolute_error": abs(value - round(value / 0.02) * 0.02),
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},
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"endpoint_grids": [endpoint_grid(value, bits) for bits in (8, 4)],
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"group_range_example": {
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"wide_step": 20 / 15, "narrow_step": 0.2 / 15,
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"note": "same 16-level teaching grid, different ranges",
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},
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"q4_0_block": {
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"weights": 32, "code_bytes": 16, "scale_bytes": 2,
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"total_bytes": 18, "bits_per_weight": 18 * 8 / 32,
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"all_8B_block_data_GB": 8_000_000_000 * (18 / 32) / 1e9,
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},
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}
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assert fp16(1.001) == 1.0009765625
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assert bf16(1.001) == 1.0 and bf16(100000) == 99840
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assert math.isinf(fp16(100000))
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assert endpoint_grid(value, 8)["code"] == 143
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assert endpoint_grid(value, 4)["code"] == 8
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assert report["q4_0_block"]["bits_per_weight"] == 4.5
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print(json.dumps(report, ensure_ascii=False, indent=2, allow_nan=False))
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if __name__ == "__main__":
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main()
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