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【ニューラルネットワーク】fpgaに組み込む

概要

tensorflow.jsで学習したモデルをfpgaに組み込む手順を共有する。
モデルは、xor分類器です。
入力 0,0なら0、1,0なら1、1,0なら1、1,1なら0を返します。

①tensorflow.jsで学習する。

https://qiita.com/ohisama@github/items/57d2dd342dcb99d47959

https://qiita.com/ohisama@github/items/dd443bb0835eac1f195d

②ウェイトとバイアスを取り出す。

let w1 = [[-3.4681022, 0.379121, -1.4711456, 2.2247136, 2.3135107, 2.7624693, -1.83576, -1.1545312], [2.1978209, 0.2895245, 2.0881913, -1.3450832, -1.4154571, 1.9255028, 3.2867477, 1.956522]];
    let b1 = [-0.6591252, 0.3864409, 0.4982838, 0.3707547, 0.3982254, -0.3612466, 0.4284867, 0.2701645];
    let w2 = [[1.4324994 ], [0.7911373], [-2.3011343],  [-1.7614117], [-2.4442003], [3.9701838], [-1.837263], [-1.3641325]];
    let b2 = [0.9285715];

③スクラッチで関数を書いて、ウェイトとバイアス入れて、同じ結果を得る。

fn tanh(x: f64) -> f64 {
    let a: f64 = (x).exp();
    let b: f64 = (-x).exp();
    return (a - b) / (a + b);
}
fn sigmoid(x: f64) -> f64 {
    return 1.0 / (1.0 + (-x).exp());
}
fn main() {
    let w1 = [[-3.4681022, 0.379121, -1.4711456, 2.2247136, 2.3135107, 2.7624693, -1.83576, -1.1545312], [2.1978209, 0.2895245, 2.0881913, -1.3450832, -1.4154571, 1.9255028, 3.2867477, 1.956522]];
    let b1 = [-0.6591252, 0.3864409, 0.4982838, 0.3707547, 0.3982254, -0.3612466, 0.4284867, 0.2701645];
    let w2 = [[1.4324994 ], [0.7911373], [-2.3011343],  [-1.7614117], [-2.4442003], [3.9701838], [-1.837263], [-1.3641325]];
    let b2 = [0.9285715];
    for i in 0..4
    {
        let mut x = [0.0, 0.0];   
        let mut y = [0.0];
        let mut h = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0];
        if i == 0
        {
            x = [1.0, 0.0];
            print!("1, 0 = ");
        }
        if i == 1
        {
            x = [0.0, 1.0];
            print!("0, 1 = ");
        }
        if i == 2
        {  
            x = [1.0, 1.0];
            print!("1, 1 = ");
        }
        if i == 3
        {
            x = [0.0, 0.0];
            print!("0, 0 = ");
        }
        for k in 0..2
        {
            for l in 0..8
            {
                h[l] += x[k] * w1[k][l];
            }
        }
        for l in 0..8
        {
            h[l] += b1[l];
            h[l] = tanh(h[l]);
        }
        for k in 0..8
        {
            for l in 0..1
            {
                y[l] += h[k] * w2[k][l];
            }
        }
        for k in 0..1
        {
            y[k] += b2[k];
            y[k] = sigmoid(y[k]);
        }
        println!("{} ", y[0]);
    }
}


④高位合成する。

必要な回路は、以下になる。
高位合成言語polyphonyを使う。

○浮動小数点の大小比較。

https://qiita.com/ohisama@github/items/dcc0e968d5508727259e

○浮動小数点の加算。

https://qiita.com/ohisama@github/items/c987caa25caaba5a8e95

○浮動小数点の乗算。

https://qiita.com/ohisama@github/items/071cc3579e805dcd0e38

○浮動小数点のtanh関数。

https://qiita.com/ohisama@github/items/8ad3f59d8bd948b5c2a3

○浮動小数点のsigmoid関数。

https://qiita.com/ohisama@github/items/4b41c085017d8e35647d

サンプルコード

import polyphony
from polyphony import testbench, module, is_worker_running
from polyphony.io import Port
from polyphony.typing import bit, bit32, bit23, bit24, bit25

@module
class xor:
    def __init__(self):
        self.a = Port(bit32, 'in')
        self.b = Port(bit32, 'in')
        self.c = Port(bit, 'out')
        self.w10:bit32 = [
            0xc05df563,
            0x3ec21c26,
            0xbfbc4e80,
            0x400e61b5,
            0x4014108f,
            0x4030cc4c,
            0xbfeafa2f,
            0xbf93c7ae
        ];
        self.w11:bit32 = [
            0x400ca919,
            0x3e943c8e,
            0x4005a4ed,
            0xbfac2bb0,
            0xbfb52db3,
            0x3ff676e0,
            0x40525a13,
            0x3ffa6f50
        ];
        self.b1:bit32 = [
            0xbf28bc6e,
            0x3ec5db95,
            0x3eff1f0e,
            0x3ebdd38f,
            0x3ecbe433,
            0xbeb8f550,
            0x3edb629c,
            0x3e8a5300
        ];
        self.w2:bit32 = [
            0x3fb75c24,
            0x3f4a87f9,
            0xc01345c9,
            0xbfe175f0,
            0xc01c6dc7,
            0x407e177e,
            0xbfeb2b6f,
            0xbfae9be5,
        ];
        self.b2:bit32 = 0x3f6db6dd;
        self.tanht:bit32 = [
            0xbf7f0bb0,
            0xbf7e8cf1,
            0xbf7dccba,
            0xbf7ca996,
            0xbf7af177,
            0xbf785a09,
            0xbf747658,
            0xbf6ea9b9,
            0xbf66197c,
            0xbf59a267,
            0xbf47dce7,
            0xbf2f433d,
            0xbf0e908f,
            0xbecabea1,
            0xbe536260,
            0xa6000000,
            0x3e536260,
            0x3ecabea1,
            0x3f0e908f,
            0x3f2f433d,
            0x3f47dce7,
            0x3f59a267,
            0x3f66197c,
            0x3f6ea9b9,
            0x3f747658,
            0x3f785a09,
            0x3f7af177,
            0x3f7ca996,
            0x3f7dccba,
            0x3f7e8cf1,
            0x3f7f0bb0
        ]
        self.sigmoidt:bit32 = [
            0x3d29ac09,
            0x3d4f341f,
            0x3d7c80d6,
            0x3d997663,
            0x3db9f86f,
            0x3de08c65,
            0x3e06fc01,
            0x3e217985,
            0x3e400a67,
            0x3e62dee1,
            0x3e84ffbc,
            0x3e9aa0af,
            0x3eb21ee3,
            0x3ecb2768,
            0x3ee54a10,
            0x3f000000,
            0x3f0d5af8,
            0x3f1a6c4c,
            0x3f26f08e,
            0x3f32afa8,
            0x3f3d8022,
            0x3f474848,
            0x3f4ffd66,
            0x3f57a19f,
            0x3f5e4100,
            0x3f63ee73,
            0x3f68c0f2,
            0x3f6cd134,
            0x3f7037f3,
            0x3f730cbe,
            0x3f75653f
        ]
        self.append_worker(self.worker)
    def float2b(self, a:bit32):
        a_sig:bit = (a >> 31) & 0x1
        a_exp:bit8 = (a >> 23) & 0xff
        a_fra:bit24 = a & 0x7fffff | 0x800000
        if a_fra == 0x800000:
            a_fra = 0x000000
        return (a_sig, a_exp, a_fra)
    def b2float(self, a_sig:bit32, a_exp:bit32, a_fra:bit32):
        return (a_sig << 31) | (a_exp << 23) | a_fra
    def gt(self, a0:bit32, b0:bit32):
        c0:bit = 0
        if (a0 < b0):
            c0 = 1
        return c0
    def add(self, a0:bit32, b0:bit32):
        (a_sig, a_exp, a_fra) = self.float2b(a0)
        (b_sig, b_exp, b_fra) = self.float2b(b0)
        if a_exp > b_exp:
            (a_sig, b_sig) = (b_sig, a_sig)
            (a_exp, b_exp) = (b_exp, a_exp)
            (a_fra, b_fra) = (b_fra, a_fra)
        if a_exp != b_exp:
            a_fra >>= (b_exp - a_exp)
        sig:bit = a_sig ^ b_sig
        fra:bit23
        frac:bit25
        if sig == 1:
            frac = a_fra - b_fra
            if frac == 0x000000:
                frac = 0
                b_exp = 0
            else:
                while ((frac & 0x800000) < 1):
                    frac <<= 1
                    b_exp -= 1
        else:
            frac = a_fra + b_fra
            if frac & 0x1000000:
                frac = frac >> 1
                b_exp += 1
        fra = frac & 0x7fffff
        c0:bit32 = self.b2float(b_sig, b_exp, fra)
        return c0
    def mul(self, a0:bit32, b0:bit32):
        if (a0 == 0x00000000):
            return a0
        if (b0 == 0x00000000):
            return b0
        (a_sig, a_exp, a_fra) = self.float2b(a0)
        (b_sig, b_exp, b_fra) = self.float2b(b0)
        b_exp = a_exp + b_exp - 127
        b_exp = b_exp & 0xff
        fra:bit23
        frac:bit48 = a_fra * b_fra
        frac = frac >> 23
        while (frac & 0xffffff000000):
            frac = frac >> 1
            b_exp += 1
        fra = frac & 0x7fffff
        b_sig = a_sig ^ b_sig
        c0:bit32 = self.b2float(b_sig, b_exp, fra)
        return c0
    def tanh(self, b0:bit32):
        b0 = self.mul(b0, 0x40A00000)
        b0 = self.add(b0, 0x41700000)
        (b_sig, b_exp, b_fra) = self.float2b(b0)
        b_exp = 127 - b_exp + 23
        b_exp = b_exp & 0xff
        frac:bit48 = b_fra
        frac = frac >> b_exp
        frac = frac & 0xffffff
        if (frac < 31):
            frac = self.tanht[frac]
        c0:bit32 = frac
        return c0
    def sigmoid(self, b0:bit32):
        b0 = self.mul(b0, 0x40A00000)
        b0 = self.add(b0, 0x41700000)
        (b_sig, b_exp, b_fra) = self.float2b(b0)
        b_exp = 127 - b_exp + 23
        b_exp = b_exp & 0xff
        frac:bit48 = b_fra
        frac = frac >> b_exp
        frac = frac & 0xffffff
        if (frac < 31):
            frac = self.sigmoidt[frac]
        c0:bit32 = frac
        return c0
    def worker(self):
        while is_worker_running():
            x0:bit32 = self.a.rd()
            x1:bit32 = self.b.rd()
            y:bit32 = 0x00000000;
            h:bit32 = [0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x0000000, 0x0000000, 0x00000000]
            for l in range(8):
                h[l] = self.add(h[l], self.mul(x0, self.w10[l]))
            for l in range(8):
                h[l] = self.add(h[l], self.mul(x1, self.w11[l]))
            for l in range(8):
                h[l] = self.add(h[l], self.b1[l])
                h[l] = self.tanh(h[l])
            for l in range(8):
                y = self.add(y, self.mul(h[l], self.w2[l]))
            y = self.add(y, self.b2)
            y = self.sigmoid(y);
            if self.gt(y, 0x3e99999a):
                self.c(0)
            else:
                self.c(1)

m = xor()

@testbench
def test(m):
    m.a.wr(0x00000000)
    m.b.wr(0x00000000)
    print("0, 0=")
    c = m.c.rd()
    print(c)
    m.a.wr(0x00000000)
    m.b.wr(0x3F800000)
    print("0, 1=")
    c = m.c.rd()
    print(c)
    m.a.wr(0x3F800000)
    m.b.wr(0x00000000)
    print("1, 0=")
    c = m.c.rd()
    print(c)
    m.a.wr(0x3F800000)
    m.b.wr(0x3F800000)
    print("1, 1=")
    c = m.c.rd()
    print(c)

test(m)




実行結果


0, 0=
0
0, 1=
1
1, 0=
1
1, 1=
0


コンパイルエラー

Traceback (most recent call last):
  File "c:\users\ore\anaconda3\lib\runpy.py", line 193, in _run_module_as_main    "__main__", mod_spec)
  File "c:\users\ore\anaconda3\lib\runpy.py", line 85, in _run_code    exec(code, run_globals)
  File "C:\Users\ore\Anaconda3\Scripts\polyphony.exe\__main__.py", line 9, in <module>
  File "c:\users\ore\anaconda3\lib\site-packages\polyphony\compiler\__main__.py", line 858, in main    compile_main(options.source, options)
  File "c:\users\ore\anaconda3\lib\site-packages\polyphony\compiler\__main__.py", line 787, in compile_main    compile_results = compile(compile_plan(), main_source, src_file)
  File "c:\users\ore\anaconda3\lib\site-packages\polyphony\compiler\__main__.py", line 780, in compile    driver.run()
  File "c:\users\ore\anaconda3\lib\site-packages\polyphony\compiler\driver.py",line 76, in run    proc(self, s)
  File "c:\users\ore\anaconda3\lib\site-packages\polyphony\compiler\__main__.py", line 380, in constopt_pre_detectrom    ConstantOptPreDetectROM().process(scope)
  File "c:\users\ore\anaconda3\lib\site-packages\polyphony\compiler\constopt.py", line 264, in process    self.visit(stm)
  File "c:\users\ore\anaconda3\lib\site-packages\polyphony\compiler\irvisitor.py", line 31, in visit    return visitor(ir)
  File "c:\users\ore\anaconda3\lib\site-packages\polyphony\compiler\constopt.py", line 176, in visit_CJUMP    self._process_unconditional_cjump(ir, [])
  File "c:\users\ore\anaconda3\lib\site-packages\polyphony\compiler\constopt.py", line 239, in _process_unconditional_cjump    remove_dominated_branch(false_blk)
  File "c:\users\ore\anaconda3\lib\site-packages\polyphony\compiler\constopt.py", line 214, in remove_dominated_branch    phi.args.pop(idx)
IndexError: pop index out of range

github

https://github.com/ktok07b6/polyphony

⑤fpgaにverilogHDLで回路を書く。

環境

windows vista 32bit
quartus ii v13.0
polyphony v0.3.6
ep2c5t144ボード

写真

CIMG2963.JPG

以上。

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