File size: 2,457 Bytes
9b8659b | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 | """Generate DROM fixed-point math lookup tables (`graphcalc_tables.h`) and bignum print sleds (`sled.S`)."""
import math
import sys
from pathlib import Path
def write_tables(hdr_path: Path) -> None:
one32 = 1 << 32
lines = [
"// Auto-generated Q32.32 constants and CORDIC / log tables in DROM (.rodata).",
"#pragma once",
"#include <stdint.h>",
"",
f"#define Q32_ONE ({one32}LL)",
f"#define Q32_PI ({round(math.pi * one32)}LL)",
f"#define Q32_TWO_PI ({round(2.0 * math.pi * one32)}LL)",
f"#define Q32_INV_TWO_PI ({round((1.0 / (2.0 * math.pi)) * one32)}LL)",
f"#define Q32_HALF_PI ({round(0.5 * math.pi * one32)}LL)",
f"#define Q32_E ({round(math.e * one32)}LL)",
f"#define Q32_LN2 ({round(math.log(2.0) * one32)}LL)",
f"#define Q32_INV_LN2 ({round((1.0 / math.log(2.0)) * one32)}LL)",
f"#define Q32_LN10 ({round(math.log(10.0) * one32)}LL)",
"",
]
# CORDIC gain K = prod_{i=0}^{29} 1 / sqrt(1 + 2^{-2i})
k_gain = 1.0
atan_vals = []
for i in range(30):
k_gain /= math.hypot(1.0, 2.0 ** (-i))
atan_vals.append(round(math.atan(2.0 ** (-i)) * one32))
lines.append(f"#define CORDIC_K ({round(k_gain * one32)}LL)")
lines.append("static const int64_t CORDIC_ATAN[30] = {")
for i in range(0, 30, 5):
chunk = ", ".join(f"{v}LL" for v in atan_vals[i : i + 5])
lines.append(f" {chunk},")
lines.append("};\n")
# Shifted log table: ln(1 + 2^{-i}) for i = 1..30 in Q32.32
ln1p_vals = [0] + [round(math.log1p(2.0 ** (-i)) * one32) for i in range(1, 31)]
lines.append("static const int64_t LN1P_POW2[31] = {")
for i in range(0, 31, 5):
chunk = ", ".join(f"{v}LL" for v in ln1p_vals[i : i + 5])
lines.append(f" {chunk},")
lines.append("};\n")
hdr_path.write_text("\n".join(lines), encoding="utf-8")
def write_sled(sled_path: Path) -> None:
out = [" .section .text", " .globl bn_sleds"]
for r in range(8):
out += [f"bn_sled{r}:"] + [f" .insn i 0x2B, 0, x{r}, x0, {k}" for k in range(127, -1, -1)]
out += [" ret"]
out += [" .section .rodata", " .align 2", "bn_sleds:"]
out += [f" .word bn_sled{r}" for r in range(8)]
sled_path.write_text("\n".join(out) + "\n", encoding="utf-8")
if __name__ == "__main__":
write_tables(Path(sys.argv[1]))
write_sled(Path(sys.argv[2]))
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