diff --git a/sdp/challenger_sdp.py b/sdp/challenger_sdp.py
index ce60e8d..7ee13af 100644
--- a/sdp/challenger_sdp.py
+++ b/sdp/challenger_sdp.py
@@ -1,14 +1,78 @@
+import math
 import numpy as np
 
+from numba import njit
 
-def setup(Q, T):
-    return
+@njit(fastmath=True)
+def _rfft_preprocess_TQ(T, Q):
+    n = len(T)
+    m = len(Q)
+
+    Q0 = np.empty(n, dtype=np.float64)
+    Q0[:m] = Q[::-1]
+    Q0[m:] = 0.0
+
+    half_n = n // 2
+    out = np.empty((2, half_n), dtype=np.complex128)
+    
+    m_stop = m // 2
+    for i in range(m_stop):
+        out[0, i] = T[2 * i] + 1j * T[2 * i + 1]
+        out[1, i] = Q0[2 * i] + 1j * Q0[2 * i + 1]
+
+    for i in range(m_stop, half_n):
+        out[0, i] = T[2 * i] + 1j * T[2 * i + 1]
+    out[1, m_stop:] = 0.0
+        
+    return out
+
+
+@njit(fastmath=True)
+def _rfft_postprocess_TQ(TQ):
+    x_T = TQ[0]
+    x_Q = TQ[1]
+
+    n_x = len(x_T)
+    half_n_x = n_x // 2
+
+    F = np.empty(n_x + 1, dtype=np.complex128)
+
+    # 0th element, half_n_x, and n_x
+    F[0] = (x_T[0].real + x_T[0].imag) * (x_Q[0].real + x_Q[0].imag)
+    F[half_n_x] = (x_T[half_n_x] * x_Q[half_n_x]).conjugate()
+    F[n_x] = (x_T[0].real - x_T[0].imag) * (x_Q[0].real - x_Q[0].imag)
+
+    theta0 = math.pi / n_x
+    factor = math.cos(theta0) - 1j * math.sin(theta0)
+    w = 0.5j
+    for k in range(1, half_n_x):
+        w = w * factor
+
+        val_T = (x_T[k] - x_T[n_x - k].conjugate()) * (0.5 + w)
+        val_Q = (x_Q[k] - x_Q[n_x - k].conjugate()) * (0.5 + w)
+
+        F[k] = (x_T[k] - val_T) * (x_Q[k] - val_Q)
+        F[n_x - k] = (x_T[n_x - k] + val_T.conjugate()) * (x_Q[n_x - k] + val_Q.conjugate())
+
+    return F
+
+
+def _rfft_TQ(T, Q):
+    TQ = _rfft_preprocess_TQ(T, Q)
+    np.fft.fft(TQ, axis=1, out=TQ)
+    return _rfft_postprocess_TQ(TQ)
 
 
 def sliding_dot_product(Q, T):
+    n = len(T)
     m = len(Q)
-    l = T.shape[0] - m + 1
-    out = np.empty(l)
-    for i in range(l):
-        out[i] = np.dot(Q, T[i : i + m])
-    return out
+    
+    F = _rfft_TQ(T, Q)
+
+    return np.fft.irfft(F)[m - 1 : n]
+
+
+def setup(Q, T):
+    return sliding_dot_product(Q, T)
+
+
diff --git a/test.sh b/test.sh
index 7b853ba..c770552 100755
--- a/test.sh
+++ b/test.sh
@@ -1,5 +1,5 @@
 #!/bin/bash
-
+python -m pytest test_challenger.py 
 rm -rf sdp/__pycache__
 ./test.py > timing.csv
 rm -rf sdp/__pycache__
diff --git a/test_challenger.py b/test_challenger.py
new file mode 100644
index 0000000..28d11b2
--- /dev/null
+++ b/test_challenger.py
@@ -0,0 +1,27 @@
+import numpy as np
+import pytest
+
+from sdp import challenger_sdp
+
+def naive_sliding_dot_product(Q, T):
+    m = len(Q)
+    l = T.shape[0] - m + 1
+    out = np.empty(l)
+    for i in range(l):
+        out[i] = np.dot(Q, T[i : i + m])
+    return out
+
+
+def test_challenger():
+    pmin = 2
+    pmax = 10
+    for q in range(pmin, pmax):
+        for p in range(q, pmax):
+            Q = np.random.rand(2 ** q)
+            T = np.random.rand(2 ** p)
+            ref = naive_sliding_dot_product(Q, T)
+            comp = challenger_sdp.sliding_dot_product(Q, T)
+            
+            np.testing.assert_allclose(comp, ref)
+
+    return
\ No newline at end of file