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+#! /usr/bin/env python
+#
+# Copyright (C) 2014 Intel Corporation
+#
+# Permission is hereby granted, free of charge, to any person obtaining a
+# copy of this software and associated documentation files (the "Software"),
+# to deal in the Software without restriction, including without limitation
+# the rights to use, copy, modify, merge, publish, distribute, sublicense,
+# and/or sell copies of the Software, and to permit persons to whom the
+# Software is furnished to do so, subject to the following conditions:
+#
+# The above copyright notice and this permission notice (including the next
+# paragraph) shall be included in all copies or substantial portions of the
+# Software.
+#
+# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
+# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+# FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
+# IN THE SOFTWARE.
+#
+# Authors:
+# Jason Ekstrand (jason@jlekstrand.net)
+
+import nir_algebraic
+
+# Convenience variables
+a = 'a'
+b = 'b'
+c = 'c'
+d = 'd'
+
+# Written in the form (<search>, <replace>) where <search> is an expression
+# and <replace> is either an expression or a value. An expression is
+# defined as a tuple of the form (<op>, <src0>, <src1>, <src2>, <src3>)
+# where each source is either an expression or a value. A value can be
+# either a numeric constant or a string representing a variable name.
+#
+# Variable names are specified as "[#]name[@type]" where "#" inicates that
+# the given variable will only match constants and the type indicates that
+# the given variable will only match values from ALU instructions with the
+# given output type.
+#
+# For constants, you have to be careful to make sure that it is the right
+# type because python is unaware of the source and destination types of the
+# opcodes.
+
+optimizations = [
+ (('fneg', ('fneg', a)), a),
+ (('ineg', ('ineg', a)), a),
+ (('fabs', ('fabs', a)), ('fabs', a)),
+ (('fabs', ('fneg', a)), ('fabs', a)),
+ (('iabs', ('iabs', a)), ('iabs', a)),
+ (('iabs', ('ineg', a)), ('iabs', a)),
+ (('fadd', a, 0.0), a),
+ (('iadd', a, 0), a),
+ (('fmul', a, 0.0), 0.0),
+ (('imul', a, 0), 0),
+ (('fmul', a, 1.0), a),
+ (('imul', a, 1), a),
+ (('fmul', a, -1.0), ('fneg', a)),
+ (('imul', a, -1), ('ineg', a)),
+ (('ffma', 0.0, a, b), b),
+ (('ffma', a, 0.0, b), b),
+ (('ffma', a, b, 0.0), ('fmul', a, b)),
+ (('ffma', a, 1.0, b), ('fadd', a, b)),
+ (('ffma', 1.0, a, b), ('fadd', a, b)),
+ (('flrp', a, b, 0.0), a),
+ (('flrp', a, b, 1.0), b),
+ (('flrp', a, a, b), a),
+ (('flrp', 0.0, a, b), ('fmul', a, b)),
+ (('ffma', a, b, c), ('fadd', ('fmul', a, b), c), 'options->lower_ffma'),
+ (('fadd', ('fmul', a, b), c), ('ffma', a, b, c), '!options->lower_ffma'),
+ # Comparison simplifications
+ (('inot', ('flt', a, b)), ('fge', a, b)),
+ (('inot', ('fge', a, b)), ('flt', a, b)),
+ (('inot', ('ilt', a, b)), ('ige', a, b)),
+ (('inot', ('ige', a, b)), ('ilt', a, b)),
+ (('flt', ('fadd', a, b), 0.0), ('flt', a, ('fneg', b))),
+ (('fge', ('fadd', a, b), 0.0), ('fge', a, ('fneg', b))),
+ (('feq', ('fadd', a, b), 0.0), ('feq', a, ('fneg', b))),
+ (('fne', ('fadd', a, b), 0.0), ('fne', a, ('fneg', b))),
+ (('fge', ('fneg', ('fabs', a)), 0.0), ('feq', a, 0.0)),
+ (('bcsel', ('flt', a, b), a, b), ('fmin', a, b)),
+ (('bcsel', ('flt', a, b), b, a), ('fmax', a, b)),
+ (('bcsel', ('inot', 'a@bool'), b, c), ('bcsel', a, c, b)),
+ (('bcsel', a, ('bcsel', a, b, c), d), ('bcsel', a, b, d)),
+ (('fmin', ('fmax', a, 0.0), 1.0), ('fsat', a), '!options->lower_fsat'),
+ (('fsat', a), ('fmin', ('fmax', a, 0.0), 1.0), 'options->lower_fsat'),
+ (('fsat', ('fsat', a)), ('fsat', a)),
+ (('fmin', ('fmax', ('fmin', ('fmax', a, 0.0), 1.0), 0.0), 1.0), ('fmin', ('fmax', a, 0.0), 1.0)),
+ # Comparison with the same args. Note that these are not done for
+ # the float versions because NaN always returns false on float
+ # inequalities.
+ (('ilt', a, a), False),
+ (('ige', a, a), True),
+ (('ieq', a, a), True),
+ (('ine', a, a), False),
+ (('ult', a, a), False),
+ (('uge', a, a), True),
+ # Logical and bit operations
+ (('fand', a, 0.0), 0.0),
+ (('iand', a, a), a),
+ (('iand', a, 0), 0),
+ (('ior', a, a), a),
+ (('ior', a, 0), a),
+ (('fxor', a, a), 0.0),
+ (('ixor', a, a), 0),
+ (('inot', ('inot', a)), a),
+ # DeMorgan's Laws
+ (('iand', ('inot', a), ('inot', b)), ('inot', ('ior', a, b))),
+ (('ior', ('inot', a), ('inot', b)), ('inot', ('iand', a, b))),
+ # Shift optimizations
+ (('ishl', 0, a), 0),
+ (('ishl', a, 0), a),
+ (('ishr', 0, a), 0),
+ (('ishr', a, 0), a),
+ (('ushr', 0, a), 0),
+ (('ushr', a, 0), 0),
+ # Exponential/logarithmic identities
+ (('fexp2', ('flog2', a)), a), # 2^lg2(a) = a
+ (('fexp', ('flog', a)), a), # e^ln(a) = a
+ (('flog2', ('fexp2', a)), a), # lg2(2^a) = a
+ (('flog', ('fexp', a)), a), # ln(e^a) = a
+ (('fpow', a, b), ('fexp2', ('fmul', ('flog2', a), b)), 'options->lower_fpow'), # a^b = 2^(lg2(a)*b)
+ (('fexp2', ('fmul', ('flog2', a), b)), ('fpow', a, b), '!options->lower_fpow'), # 2^(lg2(a)*b) = a^b
+ (('fexp', ('fmul', ('flog', a), b)), ('fpow', a, b), '!options->lower_fpow'), # e^(ln(a)*b) = a^b
+ (('fpow', a, 1.0), a),
+ (('fpow', a, 2.0), ('fmul', a, a)),
+ (('fpow', 2.0, a), ('fexp2', a)),
+ # Division and reciprocal
+ (('fdiv', 1.0, a), ('frcp', a)),
+ (('frcp', ('frcp', a)), a),
+ (('frcp', ('fsqrt', a)), ('frsq', a)),
+ (('fsqrt', a), ('frcp', ('frsq', a)), 'options->lower_fsqrt'),
+ (('frcp', ('frsq', a)), ('fsqrt', a), '!options->lower_fsqrt'),
+ # Boolean simplifications
+ (('ine', 'a@bool', 0), 'a'),
+ (('ieq', 'a@bool', 0), ('inot', 'a')),
+ (('bcsel', a, True, False), ('ine', a, 0)),
+ (('bcsel', a, False, True), ('ieq', a, 0)),
+ (('bcsel', True, b, c), b),
+ (('bcsel', False, b, c), c),
+ # The result of this should be hit by constant propagation and, in the
+ # next round of opt_algebraic, get picked up by one of the above two.
+ (('bcsel', '#a', b, c), ('bcsel', ('ine', 'a', 0), b, c)),
+
+ (('bcsel', a, b, b), b),
+ (('fcsel', a, b, b), b),
+
+ # Subtracts
+ (('fsub', a, ('fsub', 0.0, b)), ('fadd', a, b)),
+ (('isub', a, ('isub', 0, b)), ('iadd', a, b)),
+ (('fneg', a), ('fsub', 0.0, a), 'options->lower_negate'),
+ (('ineg', a), ('isub', 0, a), 'options->lower_negate'),
+ (('fadd', a, ('fsub', 0.0, b)), ('fsub', a, b)),
+ (('iadd', a, ('isub', 0, b)), ('isub', a, b)),
+ (('fabs', ('fsub', 0.0, a)), ('fabs', a)),
+ (('iabs', ('isub', 0, a)), ('iabs', a)),
+
+# This one may not be exact
+ (('feq', ('fadd', a, b), 0.0), ('feq', a, ('fneg', b))),
+]
+
+# Add optimizations to handle the case where the result of a ternary is
+# compared to a constant. This way we can take things like
+#
+# (a ? 0 : 1) > 0
+#
+# and turn it into
+#
+# a ? (0 > 0) : (1 > 0)
+#
+# which constant folding will eat for lunch. The resulting ternary will
+# further get cleaned up by the boolean reductions above and we will be
+# left with just the original variable "a".
+for op in ['flt', 'fge', 'feq', 'fne',
+ 'ilt', 'ige', 'ieq', 'ine', 'ult', 'uge']:
+ optimizations += [
+ ((op, ('bcsel', 'a', '#b', '#c'), '#d'),
+ ('bcsel', 'a', (op, 'b', 'd'), (op, 'c', 'd'))),
+ ((op, '#d', ('bcsel', a, '#b', '#c')),
+ ('bcsel', 'a', (op, 'd', 'b'), (op, 'd', 'c'))),
+ ]
+
+print nir_algebraic.AlgebraicPass("nir_opt_algebraic", optimizations).render()