Backend refactor (#120)

* remove spqlios, split cpu_ref and cpu_avx into different crates

* remove spqlios submodule

* update crate naming & add avx tests

poulpy-cpu-avx/examples/rlwe_encrypt.rs

@@ -0,0 +1,140 @@
+use itertools::izip;
+use poulpy_cpu_avx::FFT64Avx;
+use poulpy_hal::{
+    api::{
+        ModuleNew, ScratchOwnedAlloc, ScratchOwnedBorrow, SvpApplyDftToDftInplace, SvpPPolAlloc, SvpPrepare, VecZnxAddNormal,
+        VecZnxBigAddSmallInplace, VecZnxBigAlloc, VecZnxBigNormalize, VecZnxBigNormalizeTmpBytes, VecZnxBigSubSmallNegateInplace,
+        VecZnxDftAlloc, VecZnxDftApply, VecZnxFillUniform, VecZnxIdftApplyTmpA, VecZnxNormalizeInplace,
+    },
+    layouts::{Module, ScalarZnx, ScratchOwned, SvpPPol, VecZnx, VecZnxBig, VecZnxDft, ZnxInfos},
+    source::Source,
+};
+
+fn main() {
+    let n: usize = 16;
+    let base2k: usize = 18;
+    let ct_size: usize = 3;
+    let msg_size: usize = 2;
+    let log_scale: usize = msg_size * base2k - 5;
+    let module: Module<FFT64Avx> = Module::<FFT64Avx>::new(n as u64);
+
+    let mut scratch: ScratchOwned<FFT64Avx> = ScratchOwned::<FFT64Avx>::alloc(module.vec_znx_big_normalize_tmp_bytes());
+
+    let seed: [u8; 32] = [0; 32];
+    let mut source: Source = Source::new(seed);
+
+    // s <- Z_{-1, 0, 1}[X]/(X^{N}+1)
+    let mut s: ScalarZnx<Vec<u8>> = ScalarZnx::alloc(module.n(), 1);
+    s.fill_ternary_prob(0, 0.5, &mut source);
+
+    // Buffer to store s in the DFT domain
+    let mut s_dft: SvpPPol<Vec<u8>, FFT64Avx> = module.svp_ppol_alloc(s.cols());
+
+    // s_dft <- DFT(s)
+    module.svp_prepare(&mut s_dft, 0, &s, 0);
+
+    // Allocates a VecZnx with two columns: ct=(0, 0)
+    let mut ct: VecZnx<Vec<u8>> = VecZnx::alloc(
+        module.n(),
+        2,       // Number of columns
+        ct_size, // Number of small poly per column
+    );
+
+    // Fill the second column with random values: ct = (0, a)
+    module.vec_znx_fill_uniform(base2k, &mut ct, 1, &mut source);
+
+    let mut buf_dft: VecZnxDft<Vec<u8>, FFT64Avx> = module.vec_znx_dft_alloc(1, ct_size);
+
+    module.vec_znx_dft_apply(1, 0, &mut buf_dft, 0, &ct, 1);
+
+    // Applies DFT(ct[1]) * DFT(s)
+    module.svp_apply_dft_to_dft_inplace(
+        &mut buf_dft, // DFT(ct[1] * s)
+        0,            // Selects the first column of res
+        &s_dft,       // DFT(s)
+        0,            // Selects the first column of s_dft
+    );
+
+    // Alias scratch space (VecZnxDft<B> is always at least as big as VecZnxBig<B>)
+
+    // BIG(ct[1] * s) <- IDFT(DFT(ct[1] * s)) (not normalized)
+    let mut buf_big: VecZnxBig<Vec<u8>, FFT64Avx> = module.vec_znx_big_alloc(1, ct_size);
+    module.vec_znx_idft_apply_tmpa(&mut buf_big, 0, &mut buf_dft, 0);
+
+    // Creates a plaintext: VecZnx with 1 column
+    let mut m = VecZnx::alloc(
+        module.n(),
+        1,        // Number of columns
+        msg_size, // Number of small polynomials
+    );
+    let mut want: Vec<i64> = vec![0; n];
+    want.iter_mut()
+        .for_each(|x| *x = source.next_u64n(16, 15) as i64);
+    m.encode_vec_i64(base2k, 0, log_scale, &want);
+    module.vec_znx_normalize_inplace(base2k, &mut m, 0, scratch.borrow());
+
+    // m - BIG(ct[1] * s)
+    module.vec_znx_big_sub_small_negate_inplace(
+        &mut buf_big,
+        0, // Selects the first column of the receiver
+        &m,
+        0, // Selects the first column of the message
+    );
+
+    // Normalizes back to VecZnx
+    // ct[0] <- m - BIG(c1 * s)
+    module.vec_znx_big_normalize(
+        base2k,
+        &mut ct,
+        0, // Selects the first column of ct (ct[0])
+        base2k,
+        &buf_big,
+        0, // Selects the first column of buf_big
+        scratch.borrow(),
+    );
+
+    // Add noise to ct[0]
+    // ct[0] <- ct[0] + e
+    module.vec_znx_add_normal(
+        base2k,
+        &mut ct,
+        0,                // Selects the first column of ct (ct[0])
+        base2k * ct_size, // Scaling of the noise: 2^{-base2k * limbs}
+        &mut source,
+        3.2,       // Standard deviation
+        3.2 * 6.0, // Truncatation bound
+    );
+
+    // Final ciphertext: ct = (-a * s + m + e, a)
+
+    // Decryption
+
+    // DFT(ct[1] * s)
+    module.vec_znx_dft_apply(1, 0, &mut buf_dft, 0, &ct, 1);
+    module.svp_apply_dft_to_dft_inplace(
+        &mut buf_dft,
+        0, // Selects the first column of res.
+        &s_dft,
+        0,
+    );
+
+    // BIG(c1 * s) = IDFT(DFT(c1 * s))
+    module.vec_znx_idft_apply_tmpa(&mut buf_big, 0, &mut buf_dft, 0);
+
+    // BIG(c1 * s) + ct[0]
+    module.vec_znx_big_add_small_inplace(&mut buf_big, 0, &ct, 0);
+
+    // m + e <- BIG(ct[1] * s + ct[0])
+    let mut res = VecZnx::alloc(module.n(), 1, ct_size);
+    module.vec_znx_big_normalize(base2k, &mut res, 0, base2k, &buf_big, 0, scratch.borrow());
+
+    // have = m * 2^{log_scale} + e
+    let mut have: Vec<i64> = vec![i64::default(); n];
+    res.decode_vec_i64(base2k, 0, ct_size * base2k, &mut have);
+    let scale: f64 = (1 << (res.size() * base2k - log_scale)) as f64;
+    izip!(want.iter(), have.iter())
+        .enumerate()
+        .for_each(|(i, (a, b))| {
+            println!("{}: {} {}", i, a, (*b as f64) / scale);
+        });
+}