from nmigen import Module, Signal
from nmigen.back.pysim import Simulator, Delay, Settle
from nmutil.formaltest import FHDLTestCase
-import unittest
from openpower.decoder.power_decoder import (create_pdecode)
from openpower.simulator.program import Program
from openpower.decoder.isa.caller import SVP64State
from copy import deepcopy
from openpower.decoder.helpers import fp64toselectable, SINGLE
from openpower.decoder.isafunctions.double2single import DOUBLE2SINGLE
+from openpower.decoder.isa.remap_dct_yield import (halfrev2, reverse_bits,
+ iterate_dct_inner_butterfly_indices,
+ iterate_dct_outer_butterfly_indices,
+ transform2, inverse_transform2)
+from openpower.decoder.isa.fastdctlee import inverse_transform_iter
+import unittest
+import math
+
+
+def transform_inner_radix2_dct(vec, ctable):
+
+ # Initialization
+ n = len(vec)
+ print ()
+ print ("transform2", n)
+ levels = n.bit_length() - 1
+
+ # reference (read/write) the in-place data in *reverse-bit-order*
+ ri = list(range(n))
+ ri = [ri[reverse_bits(i, levels)] for i in range(n)]
+
+ # and pretend we LDed data in half-swapped *and* bit-reversed order as well
+ # TODO: merge these two
+ vec = halfrev2(vec, False)
+ vec = [vec[ri[i]] for i in range(n)]
+
+ ################
+ # INNER butterfly
+ ################
+ xdim = n
+ ydim = 0
+ zdim = 0
+
+ # set up an SVSHAPE
+ class SVSHAPE:
+ pass
+ # j schedule
+ SVSHAPE0 = SVSHAPE()
+ SVSHAPE0.lims = [xdim, 2, zdim]
+ SVSHAPE0.mode = 0b01
+ SVSHAPE0.submode2 = 0b01
+ SVSHAPE0.skip = 0b00
+ SVSHAPE0.offset = 0 # experiment with different offset, here
+ SVSHAPE0.invxyz = [1,0,0] # inversion if desired
+ # j+halfstep schedule
+ SVSHAPE1 = SVSHAPE()
+ SVSHAPE1.lims = [xdim, 2, zdim]
+ SVSHAPE1.mode = 0b01
+ SVSHAPE1.submode2 = 0b01
+ SVSHAPE1.skip = 0b01
+ SVSHAPE1.offset = 0 # experiment with different offset, here
+ SVSHAPE1.invxyz = [1,0,0] # inversion if desired
+
+ # enumerate over the iterator function, getting new indices
+ i0 = iterate_dct_inner_butterfly_indices(SVSHAPE0)
+ i1 = iterate_dct_inner_butterfly_indices(SVSHAPE1)
+ for k, ((jl, jle), (jh, jhe)) in enumerate(zip(i0, i1)):
+ t1, t2 = vec[jl], vec[jh]
+ coeff = ctable[k]
+ vec[jl] = t1 + t2
+ vec[jh] = (t1 - t2) * (1.0/coeff)
+ print ("coeff", "ci", k,
+ "jl", jl, "jh", jh,
+ "i/n", (k+0.5), 1.0/coeff,
+ "t1, t2", t1, t2, "res", vec[jl], vec[jh],
+ "end", bin(jle), bin(jhe))
+ if jle == 0b111: # all loops end
+ break
+
+ return vec
+
+
+def transform_outer_radix2_dct(vec):
+
+ # Initialization
+ n = len(vec)
+ print ()
+ print ("transform2", n)
+ levels = n.bit_length() - 1
+
+ # outer butterfly
+ xdim = n
+ ydim = 0
+ zdim = 0
+
+ # j schedule
+ class SVSHAPE:
+ pass
+ SVSHAPE0 = SVSHAPE()
+ SVSHAPE0.lims = [xdim, 3, zdim]
+ SVSHAPE0.submode2 = 0b100
+ SVSHAPE0.mode = 0b01
+ SVSHAPE0.skip = 0b00
+ SVSHAPE0.offset = 0 # experiment with different offset, here
+ SVSHAPE0.invxyz = [0,0,0] # inversion if desired
+ # j+halfstep schedule
+ SVSHAPE1 = SVSHAPE()
+ SVSHAPE1.lims = [xdim, 3, zdim]
+ SVSHAPE1.mode = 0b01
+ SVSHAPE1.submode2 = 0b100
+ SVSHAPE1.skip = 0b01
+ SVSHAPE1.offset = 0 # experiment with different offset, here
+ SVSHAPE1.invxyz = [0,0,0] # inversion if desired
+
+ # enumerate over the iterator function, getting new indices
+ i0 = iterate_dct_outer_butterfly_indices(SVSHAPE0)
+ i1 = iterate_dct_outer_butterfly_indices(SVSHAPE1)
+ for k, ((jl, jle), (jh, jhe)) in enumerate(zip(i0, i1)):
+ print ("itersum jr", jl, jh,
+ "end", bin(jle), bin(jhe))
+ vec[jl] += vec[jh]
+ if jle == 0b111: # all loops end
+ break
+
+ print("transform2 result", vec)
+
+ return vec
+
+
+def transform_inner_radix2_idct(vec, ctable):
+
+ # Initialization
+ n = len(vec)
+ print ()
+ print ("transform2", n)
+ levels = n.bit_length() - 1
+
+ # pretend we LDed data in half-swapped order
+ vec = halfrev2(vec, False)
+
+ ################
+ # INNER butterfly
+ ################
+ xdim = n
+ ydim = 0
+ zdim = 0
+
+ # set up an SVSHAPE
+ class SVSHAPE:
+ pass
+ # j schedule
+ SVSHAPE0 = SVSHAPE()
+ SVSHAPE0.lims = [xdim, 0b000001, 0]
+ SVSHAPE0.mode = 0b11
+ SVSHAPE0.submode2 = 0b11
+ SVSHAPE0.skip = 0b00
+ SVSHAPE0.offset = 0 # experiment with different offset, here
+ SVSHAPE0.invxyz = [0,0,0] # inversion if desired
+ # j+halfstep schedule
+ SVSHAPE1 = SVSHAPE()
+ SVSHAPE1.lims = [xdim, 0b000001, 0]
+ SVSHAPE1.mode = 0b11
+ SVSHAPE1.submode2 = 0b11
+ SVSHAPE1.skip = 0b01
+ SVSHAPE1.offset = 0 # experiment with different offset, here
+ SVSHAPE1.invxyz = [0,0,0] # inversion if desired
+
+ # enumerate over the iterator function, getting new indices
+ i0 = iterate_dct_inner_butterfly_indices(SVSHAPE0)
+ i1 = iterate_dct_inner_butterfly_indices(SVSHAPE1)
+ for k, ((jl, jle), (jh, jhe)) in enumerate(zip(i0, i1)):
+ t1, t2 = vec[jl], vec[jh]
+ coeff = ctable[k]
+ vec[jl] = t1 + t2/coeff
+ vec[jh] = t1 - t2/coeff
+ print ("coeff", "ci", k,
+ "jl", jl, "jh", jh,
+ "i/n", (k+0.5), 1.0/coeff,
+ "t1, t2", t1, t2, "res", vec[jl], vec[jh],
+ "end", bin(jle), bin(jhe))
+ if jle == 0b111: # all loops end
+ break
+
+ return vec
+
+
+def transform_outer_radix2_idct(vec):
+
+ # Initialization
+ n = len(vec)
+ print ()
+ print ("transform2-inv", n)
+ levels = n.bit_length() - 1
+
+ # outer butterfly
+ xdim = n
+ ydim = 0
+ zdim = 0
+
+ # reference (read/write) the in-place data in *reverse-bit-order*
+ ri = list(range(n))
+ ri = [ri[reverse_bits(i, levels)] for i in range(n)]
+
+ # and pretend we LDed data in half-swapped *and* bit-reversed order as well
+ # TODO: merge these two
+ vec = [vec[ri[i]] for i in range(n)]
+ vec = halfrev2(vec, True)
+
+ # j schedule
+ class SVSHAPE:
+ pass
+ SVSHAPE0 = SVSHAPE()
+ SVSHAPE0.lims = [xdim, 2, zdim]
+ SVSHAPE0.submode2 = 0b011
+ SVSHAPE0.mode = 0b11
+ SVSHAPE0.skip = 0b00
+ SVSHAPE0.offset = 0 # experiment with different offset, here
+ SVSHAPE0.invxyz = [1,0,1] # inversion if desired
+ # j+halfstep schedule
+ SVSHAPE1 = SVSHAPE()
+ SVSHAPE1.lims = [xdim, 2, zdim]
+ SVSHAPE1.mode = 0b11
+ SVSHAPE1.submode2 = 0b011
+ SVSHAPE1.skip = 0b01
+ SVSHAPE1.offset = 0 # experiment with different offset, here
+ SVSHAPE1.invxyz = [1,0,1] # inversion if desired
+
+ # enumerate over the iterator function, getting new indices
+ i0 = iterate_dct_outer_butterfly_indices(SVSHAPE0)
+ i1 = iterate_dct_outer_butterfly_indices(SVSHAPE1)
+ for k, ((jl, jle), (jh, jhe)) in enumerate(zip(i0, i1)):
+ print ("itersum jr", jl, jh,
+ "end", bin(jle), bin(jhe))
+ vec[jh] += vec[jl]
+ if jle == 0b111: # all loops end
+ break
+
+ print("transform2-inv result", vec)
+
+ return vec
class DCTTestCase(FHDLTestCase):
self.assertEqual(sim.gpr(i), SelectableInt(expected[i], 64))
def test_sv_ffadds_dct(self):
- """>>> lst = ["sv.fdmadds 0.v, 8.v, 0.v, 0.v"
+ """>>> lst = ["sv.fdmadds 0.v, 0.v, 0.v, 8.v"
]
four in-place vector adds, four in-place vector mul-subs
fadds FRT , FRB, FRA
fsubs FRT+vl, FRA, FRB+vl
"""
- lst = SVP64Asm(["sv.fdmadds 0.v, 8.v, 0.v, 0.v"
+ lst = SVP64Asm(["sv.fdmadds 0.v, 0.v, 0.v, 8.v"
])
lst = list(lst)
+ # cheat here with these values, they're selected so that
+ # rounding errors do not occur. sigh.
fprs = [0] * 32
- av = [7.0, -9.8, 2.0, -32.3] # first half of array 0..3
- bv = [-2.0, 2.0, -9.8, 32.3] # second half of array 4..7
- cv = [-1.0, 0.5, 2.3, -3.2] # coefficients
+ av = [7.0, -0.8, 2.0, -2.3] # first half of array 0..3
+ bv = [-2.0, 2.0, -0.8, 1.4] # second half of array 4..7
+ cv = [-1.0, 0.5, 2.5, -0.25] # coefficients
res = []
# work out the results with the twin add-sub
for i, (a, b, c) in enumerate(zip(av, bv, cv)):
fprs[i+0] = fp64toselectable(a)
fprs[i+4] = fp64toselectable(b)
fprs[i+8] = fp64toselectable(c)
- t = b + a
- u = (b - a) * c
- t = DOUBLE2SINGLE(fp64toselectable(t)) # convert to Power single
- u = DOUBLE2SINGLE(fp64toselectable(u)) # from double
- res.append((t, u))
- print ("FFT", i, "in", a, b, "c", c, "res", t, u)
+ # this isn't quite a perfect replication of the
+ # FP32 mul-add-sub. better really to use FPMUL32, FPADD32
+ # and FPSUB32 directly to be honest.
+ t = a + b
+ diff = (a - b)
+ diff = 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
+ res.append((uc, tc))
+ print ("DCT", i, "in", a, b, "c", c, "res", t, u)
# SVSTATE (in this case, VL=2)
svstate = SVP64State()
b = float(sim.fpr(i+4))
t = float(t)
u = float(u)
- print ("FFT", i, "in", a, b, "res", t, u)
+ print ("DCT", i, "in", a, b, "res", t, u)
for i, (t, u) in enumerate(res):
- self.assertEqual(sim.fpr(i+2), t)
- self.assertEqual(sim.fpr(i+6), u)
+ self.assertEqual(sim.fpr(i+0), t)
+ self.assertEqual(sim.fpr(i+4), u)
- def tst_sv_remap_fpmadds_dct(self):
+ def test_sv_remap_fpmadds_dct_inner_4(self):
""">>> lst = ["svshape 4, 1, 1, 2, 0",
- "svremap 31, 1, 0, 2, 0, 1, 0",
- "sv.ffmadds 0.v, 0.v, 0.v, 8.v"
+ "svremap 27, 1, 0, 2, 0, 1, 0",
+ "sv.fdmadds 0.v, 0.v, 0.v, 8.v"
]
- runs a full in-place O(N log2 N) butterfly schedule for
- DCT
+ runs a full in-place 4-long O(N log2 N) inner butterfly schedule
+ for DCT
SVP64 "REMAP" in Butterfly Mode is applied to a twin +/- FMAC
(3 inputs, 2 outputs)
+
+ Note that the coefficient (FRC) is not on a "schedule", it
+ is straight Vectorised (0123...) because DCT coefficients
+ cannot be shared between butterfly layers (due to +0.5)
"""
lst = SVP64Asm( ["svshape 4, 1, 1, 2, 0",
- "svremap 31, 1, 0, 2, 0, 1, 0",
- "sv.ffmadds 0.v, 0.v, 0.v, 8.v"
+ "svremap 27, 1, 0, 2, 0, 1, 0",
+ "sv.fdmadds 0.v, 0.v, 0.v, 8.v"
])
lst = list(lst)
# array and coefficients to test
+ n = 4
av = [7.0, -9.8, 3.0, -32.3]
- coe = [-0.25, 0.5, 3.1, 6.2, 0.1, -0.2] # 6 coefficients
+ coe = [-0.25, 0.5, 3.1, 6.2] # 4 coefficients
+
+ levels = n.bit_length() - 1
+ ri = list(range(n))
+ ri = [ri[reverse_bits(i, levels)] for i in range(n)]
+ avi = [7.0, -0.8, 2.0, -2.3] # first half of array 0..3
+ av = halfrev2(avi, False)
+ av = [av[ri[i]] for i in range(n)]
# store in regfile
fprs = [0] * 32
for i, c in enumerate(coe):
- fprs[i+8] = fp64toselectable(c)
+ fprs[i+8] = fp64toselectable(1.0 / c) # invert
for i, a in enumerate(av):
fprs[i+0] = fp64toselectable(a)
print ("spr svshape2", sim.spr['SVSHAPE2'])
print ("spr svshape3", sim.spr['SVSHAPE3'])
- return
+ # work out the results with the twin mul/add-sub
+ res = transform_inner_radix2_dct(avi, coe)
+
+ 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 = 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-6)
+
+ 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"
+ ]
+ runs a full in-place 4-long O(N log2 N) inner butterfly schedule
+ for inverse-DCT
+
+ SVP64 "REMAP" in Butterfly Mode is applied to a twin +/- FMAC
+ (3 inputs, 2 outputs)
+
+ Note that the coefficient (FRC) is not on a "schedule", it
+ is straight Vectorised (0123...) because DCT coefficients
+ cannot be shared between butterfly layers (due to +0.5)
+ """
+ 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"
+ ])
+ lst = list(lst)
+
+ # array and coefficients to test
+ n = 4
+ levels = n.bit_length() - 1
+ coe = [-0.25, 0.5, 3.1, 6.2] # 4 coefficients
+ avi = [7.0, -0.8, 2.0, -2.3] # first half of array 0..3
+ av = halfrev2(avi, False)
+
+ # store in regfile
+ fprs = [0] * 32
+ for i, c in enumerate(coe):
+ fprs[i+8] = fp64toselectable(1.0 / c) # invert
+ for i, a in enumerate(av):
+ fprs[i+0] = fp64toselectable(a)
+
+ with Program(lst, bigendian=False) as program:
+ sim = self.run_tst_program(program, initial_fprs=fprs)
+ 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'])
# work out the results with the twin mul/add-sub
- res = transform_radix2(av, coe)
+ res = transform_inner_radix2_idct(avi, coe)
+
+ 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 = 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-6)
+
+ 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"
+ ]
+ runs a full in-place 8-long O(N log2 N) outer butterfly schedule
+ for inverse-DCT, does the iterative overlapped ADDs
+
+ SVP64 "REMAP" in Butterfly Mode.
+ """
+ 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"
+ ])
+ 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]
+
+ n = len(avi)
+ levels = n.bit_length() - 1
+ ri = list(range(n))
+ ri = [ri[reverse_bits(i, levels)] for i in range(n)]
+ av = [avi[ri[i]] for i in range(n)]
+ av = halfrev2(av, True)
+
+ # store in regfile
+ fprs = [0] * 32
+ for i, a in enumerate(av):
+ fprs[i+0] = fp64toselectable(a)
+
+ with Program(lst, bigendian=False) as program:
+ sim = self.run_tst_program(program, initial_fprs=fprs)
+ 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 = transform_outer_radix2_idct(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 = 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-6)
+
+ 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"
+ ]
+ runs a full in-place 8-long O(N log2 N) outer butterfly schedule
+ for DCT, does the iterative overlapped ADDs
+
+ SVP64 "REMAP" in Butterfly Mode.
+ """
+ lst = SVP64Asm( ["svshape 8, 1, 1, 3, 0",
+ "svremap 27, 1, 0, 2, 0, 1, 0",
+ "sv.fadds 0.v, 0.v, 0.v"
+ ])
+ lst = list(lst)
+
+ # array and coefficients to test
+ av = [7.0, -9.8, 3.0, -32.3, 2.1, 3.6, 0.7, -0.2]
+
+ # store in regfile
+ fprs = [0] * 32
+ for i, a in enumerate(av):
+ fprs[i+0] = fp64toselectable(a)
+
+ with Program(lst, bigendian=False) as program:
+ sim = self.run_tst_program(program, initial_fprs=fprs)
+ 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 = transform_outer_radix2_dct(av)
+
+ 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 = 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-6)
+
+ 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",
+ "svshape 8, 1, 1, 10, 0",
+ "sv.ffmadds 0.v, 0.v, 0.v, 8.v"
+ ]
+ 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",
+ "svshape 8, 1, 1, 10, 0",
+ "sv.ffmadds 0.v, 0.v, 0.v, 8.v"
+ ])
+ 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]
+ n = len(avi)
+ levels = n.bit_length() - 1
+ ri = list(range(n))
+ ri = [ri[reverse_bits(i, levels)] for i in range(n)]
+ av = [avi[ri[i]] for i in range(n)]
+ av = halfrev2(av, True)
+
+ # divide first value by 2.0, manually. rev and halfrev should
+ # not have moved it
+ av[0] /= 2.0
+ #avi[0] /= 2.0
+
+ print ("input data pre idct", av)
+
+ ctable = []
+ size = 2
+ while size <= n:
+ halfsize = size // 2
+ for i in range(n//size):
+ 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, a in enumerate(av):
+ fprs[i+0] = fp64toselectable(a)
+ 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)
+ 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'])
+
+ # inverse DCT
+ expected = [-15.793373940443367, 27.46969091937703,
+ -24.712331606496313, 27.03601462756265]
+
+ #res = inverse_transform_iter(avi)
+ res = inverse_transform2(avi)
+ #res = transform_outer_radix2_idct(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 = 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_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"
+ "svshape 8, 1, 1, 3, 0",
+ "sv.fadds 0.v, 0.v, 0.v"
+ ]
+ 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",
+ "svshape 8, 1, 1, 3, 0",
+ "sv.fadds 0.v, 0.v, 0.v"
+ ])
+ 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]
+ n = len(avi)
+ levels = n.bit_length() - 1
+ ri = list(range(n))
+ ri = [ri[reverse_bits(i, levels)] for i in range(n)]
+ av = halfrev2(avi, False)
+ av = [av[ri[i]] for i in range(n)]
+ ctable = []
+ size = n
+ while size >= 2:
+ halfsize = size // 2
+ for i in range(n//size):
+ 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, a in enumerate(av):
+ fprs[i+0] = fp64toselectable(a)
+ 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)
+ 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 = transform2(avi)
for i, expected in enumerate(res):
print ("i", i, float(sim.fpr(i)), "expected", expected)
# 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
- self.assertTrue(err < 1e-7)
+ err = abs((actual - expected) / expected)
+ print ("err", i, err)
+ self.assertTrue(err < 1e-5)
+
+ def test_sv_remap_dct_cos_precompute_8(self):
+ """pre-computes a DCT COS table, deliberately using a lot of
+ registers so as to be able to see what is going on (dumping all
+ regs after the run).
+
+ the simpler (scalar) version is in test_caller_transcendentals.py
+ (test_fp_coss_cvt), this is the SVP64 variant. TODO: really
+ need the new version of fcfids which doesn't spam memory with
+ LD/STs.
+ """
+ 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
+ "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",
+ "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
+ ])
+ lst = list(lst)
+
+ gprs = [0] * 32
+ fprs = [0] * 128
+ # constants
+ fprs[43] = fp64toselectable(0.5) # 0.5
+ fprs[41] = fp64toselectable(math.pi) # pi
+ fprs[44] = fp64toselectable(2.0) # 2.0
+
+ n = 8
+
+ ctable = []
+ size = n
+ while size >= 2:
+ halfsize = size // 2
+ for i in range(n//size):
+ for ci in range(halfsize):
+ ctable.append(math.cos((ci + 0.5) * math.pi / size) * 2.0)
+ size //= 2
+
+ with Program(lst, bigendian=False) as program:
+ sim = self.run_tst_program(program, gprs, initial_fprs=fprs)
+ print ("MEM")
+ sim.mem.dump()
+ print ("ci FP")
+ for i in range(len(ctable)):
+ actual = float(sim.fpr(i+24))
+ print ("i", i, actual)
+ print ("size FP")
+ for i in range(len(ctable)):
+ actual = float(sim.fpr(i+48))
+ print ("i", i, actual)
+ print ("temps")
+ for i in range(len(ctable)):
+ actual = float(sim.fpr(i))
+ print ("i", i, actual)
+ for i in range(len(ctable)):
+ expected = 1.0/ctable[i]
+ actual = float(sim.fpr(i+80))
+ err = abs((actual - expected) / expected)
+ print ("i", i, actual, "1/expect", 1/expected,
+ "expected", expected,
+ "err", err)
+ self.assertTrue(err < 1e-6)
+
+ def test_sv_remap_dct_cos_precompute_inner_8(self):
+ """pre-computes a DCT COS table, using the shorter costable
+ indices schedule. turns out, some COS values are repeated
+ in each layer of the DCT butterfly.
+
+ the simpler (scalar) version is in test_caller_transcendentals.py
+ (test_fp_coss_cvt), this is the SVP64 variant. TODO: really
+ need the new version of fcfids which doesn't spam memory with
+ LD/STs.
+ """
+ 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
+ "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",
+ "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
+ ])
+ lst = list(lst)
+
+ gprs = [0] * 32
+ fprs = [0] * 128
+ # constants
+ fprs[43] = fp64toselectable(0.5) # 0.5
+ fprs[41] = fp64toselectable(math.pi) # pi
+ fprs[44] = fp64toselectable(2.0) # 2.0
+
+ n = 8
+
+ ctable = []
+ size = n
+ while size >= 2:
+ halfsize = size // 2
+ for ci in range(halfsize):
+ coeff = math.cos((ci + 0.5) * math.pi / size) * 2.0
+ ctable.append(coeff)
+ print ("coeff", "ci", ci, "size", size,
+ "i/n", (ci+0.5), 1.0/coeff)
+ size //= 2
+
+ with Program(lst, bigendian=False) as program:
+ sim = self.run_tst_program(program, gprs, initial_fprs=fprs)
+ print ("MEM")
+ sim.mem.dump()
+ print ("ci FP")
+ for i in range(len(ctable)):
+ actual = float(sim.fpr(i+24))
+ print ("i", i, actual)
+ print ("size FP")
+ for i in range(len(ctable)):
+ actual = float(sim.fpr(i+48))
+ print ("i", i, actual)
+ print ("temps")
+ for i in range(len(ctable)):
+ actual = float(sim.fpr(i))
+ print ("i", i, actual)
+ for i in range(len(ctable)):
+ expected = 1.0/ctable[i]
+ actual = float(sim.fpr(i+80))
+ err = abs((actual - expected) / expected)
+ print ("i", i, actual, "1/expect", 1/expected,
+ "expected", expected,
+ "err", err)
+ self.assertTrue(err < 1e-6)
+
+ 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"
+ "svshape 8, 1, 1, 3, 0",
+ "sv.fadds 0.v, 0.v, 0.v"
+ ]
+ runs a full in-place 8-long O(N log2 N) DCT, both
+ inner and outer butterfly "REMAP" schedules.
+ uses shorter tables: FRC also needs to be on a Schedule
+ """
+ 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",
+ "svshape 8, 1, 1, 3, 0",
+ "sv.fadds 0.v, 0.v, 0.v"
+ ])
+ 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]
+ n = len(avi)
+ levels = n.bit_length() - 1
+ ri = list(range(n))
+ ri = [ri[reverse_bits(i, levels)] for i in range(n)]
+ av = halfrev2(avi, False)
+ av = [av[ri[i]] for i in range(n)]
+ ctable = []
+ size = n
+ while size >= 2:
+ 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, a in enumerate(av):
+ fprs[i+0] = fp64toselectable(a)
+ 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)
+ 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 = 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 = 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_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",
+ # 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"
+ # Outer butterfly, iterative sum
+ "svshape 8, 1, 1, 3, 0",
+ "sv.fadds 0.v, 0.v, 0.v"
+ ]
+ runs a full in-place 8-long O(N log2 N) 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
+ """
+ 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 31, 1, 0, 2, 0, 1, 1",
+ "svshape 8, 1, 1, 4, 0",
+ "sv.fdmadds 0.v, 0.v, 0.v, 8.v",
+ "svshape 8, 1, 1, 3, 0",
+ "sv.fadds 0.v, 0.v, 0.v"
+ ])
+ 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):
+ 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 = n
+ while size >= 2:
+ 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 = 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 = 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 run_tst_program(self, prog, initial_regs=None,
svstate=None,
projects / openpower-isa.git / blobdiff