fix setvl. not setting CR0 properly
[openpower-isa.git] / src / openpower / decoder / isa / test_caller_svp64_dct.py
index ccdae2367cf536ef061c51ce957543c2606f2eda..ce64cd2d85b1056240c2906bb0565bb4647fa2be 100644 (file)
@@ -1,5 +1,5 @@
 from nmigen import Module, Signal
-from nmigen.back.pysim import Simulator, Delay, Settle
+from nmigen.sim import Simulator, Delay, Settle
 from nmutil.formaltest import FHDLTestCase
 from openpower.decoder.power_decoder import (create_pdecode)
 from openpower.simulator.program import Program
@@ -9,7 +9,7 @@ from openpower.decoder.isa.test_caller import run_tst
 from openpower.sv.trans.svp64 import SVP64Asm
 from copy import deepcopy
 from openpower.decoder.helpers import fp64toselectable, SINGLE
-from openpower.decoder.isafunctions.double2single import DOUBLE2SINGLE
+from openpower.decoder.isafunctions.double2single import ISACallerFnHelper
 from openpower.decoder.isa.remap_dct_yield import (halfrev2, reverse_bits,
                                          iterate_dct_inner_butterfly_indices,
                                          iterate_dct_outer_butterfly_indices,
@@ -18,6 +18,10 @@ from openpower.decoder.isa.fastdctlee import inverse_transform_iter
 import unittest
 import math
 
+# really bad hack.  need to access the DOUBLE2SINGLE function auto-generated
+# from pseudo-code.
+fph = ISACallerFnHelper(XLEN=64)
+
 
 def transform_inner_radix2_dct(vec, ctable):
 
@@ -249,7 +253,7 @@ class DCTTestCase(FHDLTestCase):
             self.assertEqual(sim.gpr(i), SelectableInt(expected[i], 64))
 
     def test_sv_ffadds_dct(self):
-        """>>> lst = ["sv.fdmadds 0.v, 0.v, 0.v, 8.v"
+        """>>> lst = ["sv.fdmadds *0, *0, *0, *8"
                         ]
             four in-place vector adds, four in-place vector mul-subs
 
@@ -260,7 +264,7 @@ class DCTTestCase(FHDLTestCase):
                 fadds FRT   , FRB, FRA
                 fsubs FRT+vl, FRA, FRB+vl
         """
-        lst = SVP64Asm(["sv.fdmadds 0.v, 0.v, 0.v, 8.v"
+        lst = SVP64Asm(["sv.fdmadds *0, *0, *0, *8"
                         ])
         lst = list(lst)
 
@@ -281,11 +285,11 @@ class DCTTestCase(FHDLTestCase):
             # and FPSUB32 directly to be honest.
             t = a + b
             diff = (a - b)
-            diff = DOUBLE2SINGLE(fp64toselectable(diff)) # FP32 round
+            diff = fph.DOUBLE2SINGLE(fp64toselectable(diff)) # FP32 round
             diff = float(diff)
             u = diff * c
-            tc = DOUBLE2SINGLE(fp64toselectable(t)) # convert to Power single
-            uc = DOUBLE2SINGLE(fp64toselectable(u)) # from double
+            tc = fph.DOUBLE2SINGLE(fp64toselectable(t)) # cvt to Power single
+            uc = fph.DOUBLE2SINGLE(fp64toselectable(u)) # from double
             res.append((uc, tc))
             print ("DCT", i, "in", a, b, "c", c, "res", t, u)
 
@@ -312,7 +316,7 @@ class DCTTestCase(FHDLTestCase):
     def test_sv_remap_fpmadds_dct_inner_4(self):
         """>>> lst = ["svshape 4, 1, 1, 2, 0",
                      "svremap 27, 1, 0, 2, 0, 1, 0",
-                        "sv.fdmadds 0.v, 0.v, 0.v, 8.v"
+                        "sv.fdmadds *0, *0, *0, *8"
                      ]
             runs a full in-place 4-long O(N log2 N) inner butterfly schedule
             for DCT
@@ -326,7 +330,7 @@ class DCTTestCase(FHDLTestCase):
         """
         lst = SVP64Asm( ["svshape 4, 1, 1, 2, 0",
                          "svremap 27, 1, 0, 2, 0, 1, 0",
-                         "sv.fdmadds 0.v, 0.v, 0.v, 8.v"
+                         "sv.fdmadds *0, *0, *0, *8"
                         ])
         lst = list(lst)
 
@@ -366,7 +370,7 @@ class DCTTestCase(FHDLTestCase):
                 print ("i", i, float(sim.fpr(i)), "expected", expected)
             for i, expected in enumerate(res):
                 # convert to Power single
-                expected = DOUBLE2SINGLE(fp64toselectable(expected))
+                expected = fph.DOUBLE2SINGLE(fp64toselectable(expected))
                 expected = float(expected)
                 actual = float(sim.fpr(i))
                 # approximate error calculation, good enough test
@@ -379,7 +383,7 @@ class DCTTestCase(FHDLTestCase):
     def test_sv_remap_fpmadds_idct_inner_4(self):
         """>>> lst = ["svshape 4, 1, 1, 10, 0",
                       "svremap 27, 0, 1, 2, 1, 0, 0",
-                      "sv.ffmadds 0.v, 0.v, 0.v, 8.v"
+                      "sv.ffmadds *0, *0, *0, *8"
                      ]
             runs a full in-place 4-long O(N log2 N) inner butterfly schedule
             for inverse-DCT
@@ -393,7 +397,7 @@ class DCTTestCase(FHDLTestCase):
         """
         lst = SVP64Asm( ["svshape 4, 1, 1, 10, 0",
                          "svremap 27, 0, 1, 2, 1, 0, 0",
-                         "sv.ffmadds 0.v, 0.v, 0.v, 8.v"
+                         "sv.ffmadds *0, *0, *0, *8"
                         ])
         lst = list(lst)
 
@@ -428,7 +432,7 @@ class DCTTestCase(FHDLTestCase):
                 print ("i", i, float(sim.fpr(i)), "expected", expected)
             for i, expected in enumerate(res):
                 # convert to Power single
-                expected = DOUBLE2SINGLE(fp64toselectable(expected))
+                expected = fph.DOUBLE2SINGLE(fp64toselectable(expected))
                 expected = float(expected)
                 actual = float(sim.fpr(i))
                 # approximate error calculation, good enough test
@@ -441,7 +445,7 @@ class DCTTestCase(FHDLTestCase):
     def test_sv_remap_fpmadds_idct_outer_8(self):
         """>>> lst = ["svshape 8, 1, 1, 11, 0",
                      "svremap 27, 0, 1, 2, 1, 0, 0",
-                         "sv.fadds 0.v, 0.v, 0.v"
+                         "sv.fadds *0, *0, *0"
                      ]
             runs a full in-place 8-long O(N log2 N) outer butterfly schedule
             for inverse-DCT, does the iterative overlapped ADDs
@@ -450,7 +454,7 @@ class DCTTestCase(FHDLTestCase):
         """
         lst = SVP64Asm( ["svshape 8, 1, 1, 11, 0", # outer butterfly
                          "svremap 27, 0, 1, 2, 1, 0, 0",
-                         "sv.fadds 0.v, 0.v, 0.v"
+                         "sv.fadds *0, *0, *0"
                         ])
         lst = list(lst)
 
@@ -486,7 +490,7 @@ class DCTTestCase(FHDLTestCase):
                 print ("i", i, float(sim.fpr(i)), "expected", expected)
             for i, expected in enumerate(res):
                 # convert to Power single
-                expected = DOUBLE2SINGLE(fp64toselectable(expected))
+                expected = fph.DOUBLE2SINGLE(fp64toselectable(expected))
                 expected = float(expected)
                 actual = float(sim.fpr(i))
                 # approximate error calculation, good enough test
@@ -499,7 +503,7 @@ class DCTTestCase(FHDLTestCase):
     def test_sv_remap_fpmadds_dct_outer_8(self):
         """>>> lst = ["svshape 8, 1, 1, 3, 0",
                      "svremap 27, 1, 0, 2, 0, 1, 0",
-                         "sv.fadds 0.v, 0.v, 0.v"
+                         "sv.fadds *0, *0, *0"
                      ]
             runs a full in-place 8-long O(N log2 N) outer butterfly schedule
             for DCT, does the iterative overlapped ADDs
@@ -508,7 +512,7 @@ class DCTTestCase(FHDLTestCase):
         """
         lst = SVP64Asm( ["svshape 8, 1, 1, 3, 0",
                          "svremap 27, 1, 0, 2, 0, 1, 0",
-                         "sv.fadds 0.v, 0.v, 0.v"
+                         "sv.fadds *0, *0, *0"
                         ])
         lst = list(lst)
 
@@ -537,7 +541,7 @@ class DCTTestCase(FHDLTestCase):
                 print ("i", i, float(sim.fpr(i)), "expected", expected)
             for i, expected in enumerate(res):
                 # convert to Power single
-                expected = DOUBLE2SINGLE(fp64toselectable(expected))
+                expected = fph.DOUBLE2SINGLE(fp64toselectable(expected))
                 expected = float(expected)
                 actual = float(sim.fpr(i))
                 # approximate error calculation, good enough test
@@ -550,18 +554,18 @@ class DCTTestCase(FHDLTestCase):
     def test_sv_remap_fpmadds_idct_8(self):
         """>>> lst = ["svremap 27, 1, 0, 2, 0, 1, 1",
                          "svshape 8, 1, 1, 11, 0",
-                         "sv.fadds 0.v, 0.v, 0.v",
+                         "sv.fadds *0, *0, *0",
                          "svshape 8, 1, 1, 10, 0",
-                         "sv.ffmadds 0.v, 0.v, 0.v, 8.v"
+                         "sv.ffmadds *0, *0, *0, *8"
                      ]
             runs a full in-place 8-long O(N log2 N) inverse-DCT, both
             inner and outer butterfly "REMAP" schedules.
         """
         lst = SVP64Asm( ["svremap 27, 0, 1, 2, 1, 0, 1",
                          "svshape 8, 1, 1, 11, 0",
-                         "sv.fadds 0.v, 0.v, 0.v",
+                         "sv.fadds *0, *0, *0",
                          "svshape 8, 1, 1, 10, 0",
-                         "sv.ffmadds 0.v, 0.v, 0.v, 8.v"
+                         "sv.ffmadds *0, *0, *0, *8"
                         ])
         lst = list(lst)
 
@@ -619,7 +623,7 @@ class DCTTestCase(FHDLTestCase):
                 print ("i", i, float(sim.fpr(i)), "expected", expected)
             for i, expected in enumerate(res):
                 # convert to Power single
-                expected = DOUBLE2SINGLE(fp64toselectable(expected))
+                expected = fph.DOUBLE2SINGLE(fp64toselectable(expected))
                 expected = float(expected)
                 actual = float(sim.fpr(i))
                 # approximate error calculation, good enough test
@@ -632,18 +636,18 @@ class DCTTestCase(FHDLTestCase):
     def test_sv_remap_fpmadds_dct_8(self):
         """>>> lst = ["svremap 27, 1, 0, 2, 0, 1, 1",
                       "svshape 8, 1, 1, 2, 0",
-                      "sv.fdmadds 0.v, 0.v, 0.v, 8.v"
+                      "sv.fdmadds *0, *0, *0, *8"
                       "svshape 8, 1, 1, 3, 0",
-                      "sv.fadds 0.v, 0.v, 0.v"
+                      "sv.fadds *0, *0, *0"
                      ]
             runs a full in-place 8-long O(N log2 N) DCT, both
             inner and outer butterfly "REMAP" schedules.
         """
         lst = SVP64Asm( ["svremap 27, 1, 0, 2, 0, 1, 1",
                          "svshape 8, 1, 1, 2, 0",
-                         "sv.fdmadds 0.v, 0.v, 0.v, 8.v",
+                         "sv.fdmadds *0, *0, *0, *8",
                          "svshape 8, 1, 1, 3, 0",
-                         "sv.fadds 0.v, 0.v, 0.v"
+                         "sv.fadds *0, *0, *0"
                         ])
         lst = list(lst)
 
@@ -688,7 +692,7 @@ class DCTTestCase(FHDLTestCase):
                 print ("i", i, float(sim.fpr(i)), "expected", expected)
             for i, expected in enumerate(res):
                 # convert to Power single
-                expected = DOUBLE2SINGLE(fp64toselectable(expected))
+                expected = fph.DOUBLE2SINGLE(fp64toselectable(expected))
                 expected = float(expected)
                 actual = float(sim.fpr(i))
                 # approximate error calculation, good enough test
@@ -710,22 +714,22 @@ class DCTTestCase(FHDLTestCase):
         """
         lst = SVP64Asm(["svshape 8, 1, 1, 2, 0",
                         "svremap 0, 0, 0, 2, 0, 1, 1",
-                        "sv.svstep 4.v, 4, 1", # svstep get vector of ci
-                        "sv.svstep 16.v, 3, 1", # svstep get vector of step
+                        "sv.svstep *4, 4, 1", # svstep get vector of ci
+                        "sv.svstep *16, 3, 1", # svstep get vector of step
                         "addi 1, 0, 0x0000",
                         "setvl 0, 0, 12, 0, 1, 1",
-                        "sv.std 4.v, 0(1)",
-                        "sv.lfd  64.v, 0(1)",
-                        "sv.fcfids 48.v, 64.v",
+                        "sv.std *4, 0(1)",
+                        "sv.lfd  *64, 0(1)",
+                        "sv.fcfids *48, *64",
                         "addi 1, 0, 0x0060",
-                        "sv.std 16.v, 0(1)",
-                        "sv.lfd  12.v, 0(1)",
-                        "sv.fcfids 24.v, 12.v",
-                        "sv.fadds 0.v, 24.v, 43", # plus 0.5
-                        "sv.fmuls 0.v, 0.v, 41", # times PI
-                        "sv.fdivs 0.v, 0.v, 48.v", # div size
-                        "sv.fcoss 80.v, 0.v",
-                        "sv.fdivs 80.v, 43, 80.v", # div 0.5 / x
+                        "sv.std *16, 0(1)",
+                        "sv.lfd  *12, 0(1)",
+                        "sv.fcfids *24, *12",
+                        "sv.fadds *0, *24, 43", # plus 0.5
+                        "sv.fmuls *0, *0, 41", # times PI
+                        "sv.fdivs *0, *0, *48", # div size
+                        "sv.fcoss *80, *0",
+                        "sv.fdivs *80, 43, *80", # div 0.5 / x
                      ])
         lst = list(lst)
 
@@ -784,22 +788,22 @@ class DCTTestCase(FHDLTestCase):
         """
         lst = SVP64Asm(["svshape 8, 1, 1, 5, 0",
                         "svremap 0, 0, 0, 2, 0, 1, 1",
-                        "sv.svstep 4.v, 3, 1", # svstep get vector of ci
-                        "sv.svstep 16.v, 2, 1", # svstep get vector of step
+                        "sv.svstep *4, 3, 1", # svstep get vector of ci
+                        "sv.svstep *16, 2, 1", # svstep get vector of step
                         "addi 1, 0, 0x0000",
                         "setvl 0, 0, 7, 0, 1, 1",
-                        "sv.std 4.v, 0(1)",
-                        "sv.lfd  64.v, 0(1)",
-                        "sv.fcfids 48.v, 64.v",
+                        "sv.std *4, 0(1)",
+                        "sv.lfd  *64, 0(1)",
+                        "sv.fcfids *48, *64",
                         "addi 1, 0, 0x0060",
-                        "sv.std 16.v, 0(1)",
-                        "sv.lfd  12.v, 0(1)",
-                        "sv.fcfids 24.v, 12.v",
-                        "sv.fadds 0.v, 24.v, 43", # plus 0.5
-                        "sv.fmuls 0.v, 0.v, 41", # times PI
-                        "sv.fdivs 0.v, 0.v, 48.v", # div size
-                        "sv.fcoss 80.v, 0.v",
-                        "sv.fdivs 80.v, 43, 80.v", # div 0.5 / x
+                        "sv.std *16, 0(1)",
+                        "sv.lfd  *12, 0(1)",
+                        "sv.fcfids *24, *12",
+                        "sv.fadds *0, *24, 43", # plus 0.5
+                        "sv.fmuls *0, *0, 41", # times PI
+                        "sv.fdivs *0, *0, *48", # div size
+                        "sv.fcoss *80, *0",
+                        "sv.fdivs *80, 43, *80", # div 0.5 / x
                      ])
         lst = list(lst)
 
@@ -851,9 +855,9 @@ class DCTTestCase(FHDLTestCase):
     def test_sv_remap_fpmadds_dct_8_mode_4(self):
         """>>> lst = ["svremap 31, 1, 0, 2, 0, 1, 1",
                       "svshape 8, 1, 1, 4, 0",
-                      "sv.fdmadds 0.v, 0.v, 0.v, 8.v"
+                      "sv.fdmadds *0, *0, *0, *8"
                       "svshape 8, 1, 1, 3, 0",
-                      "sv.fadds 0.v, 0.v, 0.v"
+                      "sv.fadds *0, *0, *0"
                      ]
             runs a full in-place 8-long O(N log2 N) DCT, both
             inner and outer butterfly "REMAP" schedules.
@@ -861,9 +865,9 @@ class DCTTestCase(FHDLTestCase):
         """
         lst = SVP64Asm( ["svremap 31, 1, 0, 2, 0, 1, 1",
                          "svshape 8, 1, 1, 4, 0",
-                         "sv.fdmadds 0.v, 0.v, 0.v, 8.v",
+                         "sv.fdmadds *0, *0, *0, *8",
                          "svshape 8, 1, 1, 3, 0",
-                         "sv.fadds 0.v, 0.v, 0.v"
+                         "sv.fadds *0, *0, *0"
                         ])
         lst = list(lst)
 
@@ -907,7 +911,7 @@ class DCTTestCase(FHDLTestCase):
                 print ("i", i, float(sim.fpr(i)), "expected", expected)
             for i, expected in enumerate(res):
                 # convert to Power single
-                expected = DOUBLE2SINGLE(fp64toselectable(expected))
+                expected = fph.DOUBLE2SINGLE(fp64toselectable(expected))
                 expected = float(expected)
                 actual = float(sim.fpr(i))
                 # approximate error calculation, good enough test
@@ -920,15 +924,15 @@ class DCTTestCase(FHDLTestCase):
     def test_sv_remap_fpmadds_ldbrev_dct_8_mode_4(self):
         """>>> lst = [# LOAD bit-reversed with half-swap
                       "svshape 8, 1, 1, 6, 0",
-                      "svremap 1, 0, 0, 0, 0, 0, 0, 1",
-                      "sv.lfsbr 0.v, 4(1), 2",
+                      "svremap 1, 0, 0, 0, 0, 0, 0",
+                      "sv.lfs/els *0, 4(1)",
                       # Inner butterfly, twin +/- MUL-ADD-SUB
                       "svremap 31, 1, 0, 2, 0, 1, 1",
                       "svshape 8, 1, 1, 4, 0",
-                      "sv.fdmadds 0.v, 0.v, 0.v, 8.v"
+                      "sv.fdmadds *0, *0, *0, *8"
                       # Outer butterfly, iterative sum
                       "svshape 8, 1, 1, 3, 0",
-                      "sv.fadds 0.v, 0.v, 0.v"
+                      "sv.fadds *0, *0, *0"
                      ]
             runs a full in-place 8-long O(N log2 N) DCT, both
             inner and outer butterfly "REMAP" schedules, and using
@@ -938,13 +942,13 @@ class DCTTestCase(FHDLTestCase):
         """
         lst = SVP64Asm( ["addi 1, 0, 0x000",
                          "svshape 8, 1, 1, 6, 0",
-                         "svremap 1, 0, 0, 0, 0, 0, 0, 1",
-                         "sv.lfsbr 0.v, 4(1), 2",
+                         "svremap 1, 0, 0, 0, 0, 0, 0",
+                         "sv.lfs/els *0, 4(1)",
                          "svremap 31, 1, 0, 2, 0, 1, 1",
                          "svshape 8, 1, 1, 4, 0",
-                         "sv.fdmadds 0.v, 0.v, 0.v, 8.v",
+                         "sv.fdmadds *0, *0, *0, *8",
                          "svshape 8, 1, 1, 3, 0",
-                         "sv.fadds 0.v, 0.v, 0.v"
+                         "sv.fadds *0, *0, *0"
                         ])
         lst = list(lst)
 
@@ -997,7 +1001,99 @@ class DCTTestCase(FHDLTestCase):
 
             for i, expected in enumerate(res):
                 # convert to Power single
-                expected = DOUBLE2SINGLE(fp64toselectable(expected))
+                expected = fph.DOUBLE2SINGLE(fp64toselectable(expected))
+                expected = float(expected)
+                actual = float(sim.fpr(i))
+                # approximate error calculation, good enough test
+                # reason: we are comparing FMAC against FMUL-plus-FADD-or-FSUB
+                # and the rounding is different
+                err = abs((actual - expected) / expected)
+                print ("err", i, err)
+                self.assertTrue(err < 1e-5)
+
+    def test_sv_remap_fpmadds_ldbrev_idct_8_mode_4(self):
+        """>>> lst = [# LOAD bit-reversed with half-swap
+                      "svshape 8, 1, 1, 14, 0",
+                      "svremap 1, 0, 0, 0, 0, 0, 0",
+                      "sv.lfs/els *0, 4(1)",
+                      # Outer butterfly, iterative sum
+                      "svremap 31, 0, 1, 2, 1, 0, 1",
+                      "svshape 8, 1, 1, 11, 0",
+                      "sv.fadds *0, *0, *0",
+                      # Inner butterfly, twin +/- MUL-ADD-SUB
+                      "svshape 8, 1, 1, 10, 0",
+                      "sv.ffmadds *0, *0, *0, *8"
+                     ]
+            runs a full in-place 8-long O(N log2 N) Inverse-DCT, both
+            inner and outer butterfly "REMAP" schedules, and using
+            bit-reversed half-swapped LDs.
+            uses shorter pre-loaded COS tables: FRC also needs to be on a
+            Schedule in the sv.ffmadds instruction
+        """
+        lst = SVP64Asm( ["addi 1, 0, 0x000",
+                         "svshape 8, 1, 1, 14, 0",
+                         "svremap 1, 0, 0, 0, 0, 0, 0",
+                         "sv.lfs/els *0, 4(1)",
+                         "svremap 31, 0, 1, 2, 1, 0, 1",
+                         "svshape 8, 1, 1, 11, 0",
+                         "sv.fadds *0, *0, *0",
+                         "svshape 8, 1, 1, 12, 0",
+                         "sv.ffmadds *0, *0, *0, *8"
+                        ])
+        lst = list(lst)
+
+        # array and coefficients to test
+        avi = [7.0, -9.8, 3.0, -32.3, 2.1, 3.6, 0.7, -0.2]
+
+        # store in memory, in standard (expected) order, FP32s (2 per 8-bytes)
+        # LD will bring them in, in the correct order.
+        mem = {}
+        val = 0
+        for i, a in enumerate(avi):
+            if i == 0: # first element, divide by 2
+                a /= 2.0
+            a = SINGLE(fp64toselectable(a)).value
+            shift = (i % 2) == 1
+            if shift == 0:
+                val = a                         # accumulate for next iteration
+            else:
+                mem[(i//2)*8] = val | (a << 32) # even and odd 4-byte in same 8
+
+        # calculate the (shortened) COS tables, 4 2 1 not 4 2+2 1+1+1+1
+        n = len(avi)
+        ctable = []
+        size = 2
+        while size <= n:
+            halfsize = size // 2
+            for ci in range(halfsize):
+                ctable.append(math.cos((ci + 0.5) * math.pi / size) * 2.0)
+            size *= 2
+
+        # store in regfile
+        fprs = [0] * 32
+        for i, c in enumerate(ctable):
+            fprs[i+8] = fp64toselectable(1.0 / c) # invert
+
+        with Program(lst, bigendian=False) as program:
+            sim = self.run_tst_program(program, initial_fprs=fprs,
+                                                initial_mem=mem)
+            print ("spr svshape0", sim.spr['SVSHAPE0'])
+            print ("    xdimsz", sim.spr['SVSHAPE0'].xdimsz)
+            print ("    ydimsz", sim.spr['SVSHAPE0'].ydimsz)
+            print ("    zdimsz", sim.spr['SVSHAPE0'].zdimsz)
+            print ("spr svshape1", sim.spr['SVSHAPE1'])
+            print ("spr svshape2", sim.spr['SVSHAPE2'])
+            print ("spr svshape3", sim.spr['SVSHAPE3'])
+
+            # outer iterative sum
+            res = inverse_transform2(avi)
+
+            for i, expected in enumerate(res):
+                print ("i", i, float(sim.fpr(i)), "expected", expected)
+
+            for i, expected in enumerate(res):
+                # convert to Power single
+                expected = fph.DOUBLE2SINGLE(fp64toselectable(expected))
                 expected = float(expected)
                 actual = float(sim.fpr(i))
                 # approximate error calculation, good enough test