[tests] add test case based on PocketFFT test

tests/config.nims

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+switch("path", "$projectDir/../src")

tests/test_fft.nim

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+import ../impulse/fft/pocketfft
+import std / [random, math]
+
+## The test case in this file is based on the tests part of PocketFFT
+
+static: doAssert defined(c), "This test must be run on the C backend!"
+
+const maxlen = 8192
+
+proc fill_random(data: var openArray[float]) =
+  for i in 0 ..< data.len:
+    data[i] = rand(-0.5 .. 0.5)
+
+proc errcalc(data, odata: openArray[float], length: int): float =
+  var
+    sum = 0.0
+    errsum = 0.0
+  for m in 0 ..< length:
+    #echo "Data ", data[m], " vs ", odata[m]
+    errsum += (data[m]-odata[m])*(data[m]-odata[m])
+    sum += odata[m]*odata[m]
+  result = sqrt(errsum / sum)
+
+proc errcalc(data, odata: Tensor[float], length: int): float =
+  result = errcalc(toOpenArray(data.toUnsafeView(), 0, length),
+                   toOpenArray(odata.toUnsafeView(), 0, length),
+                   length)
+
+proc test_real(): int =
+  var data: array[maxlen, float]
+  var odata: array[maxlen, float]
+  const epsilon = 2e-15
+  var ret = 0
+  fill_random(odata)
+  odata[0] = 0.340188
+  var errsum = 0.0
+  for length in 1 ..< maxlen:
+    copyMem(data[0].addr, odata[0].addr, length * sizeof(float))
+    var plan = make_rfft_plan(length.csize_t)
+    discard rfft_forward(plan, data[0].addr, 1.0);
+    discard rfft_backward(plan, data[0].addr, 1.0 / length.float);
+    destroy_rfft_plan(plan);
+    var err = errcalc(data, odata, length)
+    if err > epsilon:
+      echo "problem at real length ", length, " : ", err
+      ret = 1
+    errsum += err;
+  echo "errsum: ", errsum
+  result = ret
+
+proc test_real_hl(): int =
+  var data: array[maxlen, float]
+  var odata: array[maxlen, float]
+  fill_random(odata)
+  const epsilon = 2e-15
+  var ret = 0
+  var errsum = 0.0
+  for length in 1 ..< maxlen:
+    data = odata
+    fft(toOpenArray(data, 0, length), forward = true)
+    fft(toOpenArray(data, 0, length), forward = false)
+    var err = errcalc(data, odata, length)
+    if err > epsilon:
+      echo "problem at real length ", length, " : ", err
+      ret = 1
+    errsum += err;
+  echo "errsum: ", errsum
+  result = ret
+
+proc test_real_hl_seq(): int =
+  const epsilon = 2e-15
+  var ret = 0
+  var errsum = 0.0
+  for length in 1 ..< maxlen:
+    var data: seq[float]
+    var odata = newSeq[float](length)
+    fill_random(odata)
+    data = odata
+
+    fft(data, forward = true)
+    fft(data, forward = false)
+
+    let err = errcalc(data, odata, length)
+    if err > epsilon:
+      echo "problem at real length ", length, " : ", err
+      ret = 1
+    errsum += err;
+  echo "errsum: ", errsum
+  result = ret
+
+proc test_real_hl_tensor(): int =
+  const epsilon = 2e-15
+  var ret = 0
+  var errsum = 0.0
+  for length in 1 ..< maxlen:
+    var data: Tensor[float]
+    var odata = randomTensor[float](length, -0.5 .. 0.5)
+    data = odata.clone()
+
+    fft(data, forward = true)
+    fft(data, forward = false)
+
+    let err = errcalc(data, odata, length)
+    if err > epsilon:
+      echo "problem at real length ", length, " : ", err
+      ret = 1
+    errsum += err;
+  echo "errsum: ", errsum
+  result = ret
+
+doAssert test_real() == 0
+doAssert test_real_hl() == 0
+doAssert test_real_hl_seq() == 0
+doAssert test_real_hl_tensor() == 0