nir_opt_algebraic.py 35.5 KB
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#
# 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
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import itertools
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# 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
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# defined as a tuple of the form ([~]<op>, <src0>, <src1>, <src2>, <src3>)
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# where each source is either an expression or a value.  A value can be
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# either a numeric constant or a string representing a variable name.
#
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# If the opcode in a search expression is prefixed by a '~' character, this
# indicates that the operation is inexact.  Such operations will only get
# applied to SSA values that do not have the exact bit set.  This should be
# used by by any optimizations that are not bit-for-bit exact.  It should not,
# however, be used for backend-requested lowering operations as those need to
# happen regardless of precision.
#
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# Variable names are specified as "[#]name[@type][(cond)]" where "#" inicates
# that the given variable will only match constants and the type indicates that
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# the given variable will only match values from ALU instructions with the
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# given output type, and (cond) specifies an additional condition function
# (see nir_search_helpers.h).
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#
# 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
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# opcodes.
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#
# All expression types can have a bit-size specified.  For opcodes, this
# looks like "op@32", for variables it is "a@32" or "a@uint32" to specify a
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# type and size, and for literals, you can write "2.0@32".  In the search half
# of the expression this indicates that it should only match that particular
# bit-size.  In the replace half of the expression this indicates that the
# constructed value should have that bit-size.
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optimizations = [
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   (('imul', a, '#b@32(is_pos_power_of_two)'), ('ishl', a, ('find_lsb', b))),
   (('imul', a, '#b@32(is_neg_power_of_two)'), ('ineg', ('ishl', a, ('find_lsb', ('iabs', b))))),
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   (('udiv', a, 1), a),
   (('idiv', a, 1), a),
   (('umod', a, 1), 0),
   (('imod', a, 1), 0),
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   (('udiv', a, '#b@32(is_pos_power_of_two)'), ('ushr', a, ('find_lsb', b))),
   (('idiv', a, '#b@32(is_pos_power_of_two)'), ('imul', ('isign', a), ('ushr', ('iabs', a), ('find_lsb', b))), 'options->lower_idiv'),
   (('idiv', a, '#b@32(is_neg_power_of_two)'), ('ineg', ('imul', ('isign', a), ('ushr', ('iabs', a), ('find_lsb', ('iabs', b))))), 'options->lower_idiv'),
   (('umod', a, '#b(is_pos_power_of_two)'),    ('iand', a, ('isub', b, 1))),

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   (('fneg', ('fneg', a)), a),
   (('ineg', ('ineg', a)), a),
   (('fabs', ('fabs', a)), ('fabs', a)),
   (('fabs', ('fneg', a)), ('fabs', a)),
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   (('fabs', ('u2f32', a)), ('u2f32', a)),
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   (('iabs', ('iabs', a)), ('iabs', a)),
   (('iabs', ('ineg', a)), ('iabs', a)),
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   (('~fadd', a, 0.0), a),
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   (('iadd', a, 0), a),
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   (('usadd_4x8', a, 0), a),
   (('usadd_4x8', a, ~0), ~0),
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   (('~fadd', ('fmul', a, b), ('fmul', a, c)), ('fmul', a, ('fadd', b, c))),
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   (('iadd', ('imul', a, b), ('imul', a, c)), ('imul', a, ('iadd', b, c))),
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   (('~fadd', ('fneg', a), a), 0.0),
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   (('iadd', ('ineg', a), a), 0),
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   (('iadd', ('ineg', a), ('iadd', a, b)), b),
   (('iadd', a, ('iadd', ('ineg', a), b)), b),
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   (('~fadd', ('fneg', a), ('fadd', a, b)), b),
   (('~fadd', a, ('fadd', ('fneg', a), b)), b),
   (('~fmul', a, 0.0), 0.0),
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   (('imul', a, 0), 0),
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   (('umul_unorm_4x8', a, 0), 0),
   (('umul_unorm_4x8', a, ~0), a),
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   (('fmul', a, 1.0), a),
   (('imul', a, 1), a),
   (('fmul', a, -1.0), ('fneg', a)),
   (('imul', a, -1), ('ineg', a)),
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   (('~ffma', 0.0, a, b), b),
   (('~ffma', a, 0.0, b), b),
   (('~ffma', a, b, 0.0), ('fmul', a, b)),
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   (('ffma', a, 1.0, b), ('fadd', a, b)),
   (('ffma', 1.0, a, b), ('fadd', a, b)),
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   (('~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)),
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   (('~flrp', a, b, ('b2f', c)), ('bcsel', c, b, a), 'options->lower_flrp32'),
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   (('~flrp', a, 0.0, c), ('fadd', ('fmul', ('fneg', a), c), a)),
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   (('flrp@32', a, b, c), ('fadd', ('fmul', c, ('fsub', b, a)), a), 'options->lower_flrp32'),
   (('flrp@64', a, b, c), ('fadd', ('fmul', c, ('fsub', b, a)), a), 'options->lower_flrp64'),
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   (('ffract', a), ('fsub', a, ('ffloor', a)), 'options->lower_ffract'),
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   (('~fadd', ('fmul', a, ('fadd', 1.0, ('fneg', ('b2f', c)))), ('fmul', b, ('b2f', c))), ('bcsel', c, b, a), 'options->lower_flrp32'),
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   (('~fadd@32', ('fmul', a, ('fadd', 1.0, ('fneg',         c ))), ('fmul', b,         c )), ('flrp', a, b, c), '!options->lower_flrp32'),
   (('~fadd@64', ('fmul', a, ('fadd', 1.0, ('fneg',         c ))), ('fmul', b,         c )), ('flrp', a, b, c), '!options->lower_flrp64'),
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   (('~fadd', a, ('fmul', ('b2f', c), ('fadd', b, ('fneg', a)))), ('bcsel', c, b, a), 'options->lower_flrp32'),
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   (('~fadd@32', a, ('fmul',         c , ('fadd', b, ('fneg', a)))), ('flrp', a, b, c), '!options->lower_flrp32'),
   (('~fadd@64', a, ('fmul',         c , ('fadd', b, ('fneg', a)))), ('flrp', a, b, c), '!options->lower_flrp64'),
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   (('ffma', a, b, c), ('fadd', ('fmul', a, b), c), 'options->lower_ffma'),
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   (('~fadd', ('fmul', a, b), c), ('ffma', a, b, c), 'options->fuse_ffma'),
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   (('fdot4', ('vec4', a, b,   c,   1.0), d), ('fdph',  ('vec3', a, b, c), d)),
   (('fdot4', ('vec4', a, 0.0, 0.0, 0.0), b), ('fmul', a, b)),
   (('fdot4', ('vec4', a, b,   0.0, 0.0), c), ('fdot2', ('vec2', a, b), c)),
   (('fdot4', ('vec4', a, b,   c,   0.0), d), ('fdot3', ('vec3', a, b, c), d)),

   (('fdot3', ('vec3', a, 0.0, 0.0), b), ('fmul', a, b)),
   (('fdot3', ('vec3', a, b,   0.0), c), ('fdot2', ('vec2', a, b), c)),

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   # (a * #b + #c) << #d
   # ((a * #b) << #d) + (#c << #d)
   # (a * (#b << #d)) + (#c << #d)
   (('ishl', ('iadd', ('imul', a, '#b'), '#c'), '#d'),
    ('iadd', ('imul', a, ('ishl', b, d)), ('ishl', c, d))),

   # (a * #b) << #c
   # a * (#b << #c)
   (('ishl', ('imul', a, '#b'), '#c'), ('imul', a, ('ishl', b, c))),

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   # Comparison simplifications
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   (('~inot', ('flt', a, b)), ('fge', a, b)),
   (('~inot', ('fge', a, b)), ('flt', a, b)),
   (('~inot', ('feq', a, b)), ('fne', a, b)),
   (('~inot', ('fne', a, b)), ('feq', a, b)),
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   (('inot', ('ilt', a, b)), ('ige', a, b)),
   (('inot', ('ige', a, b)), ('ilt', a, b)),
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   (('inot', ('ieq', a, b)), ('ine', a, b)),
   (('inot', ('ine', a, b)), ('ieq', a, b)),
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   # 0.0 >= b2f(a)
   # b2f(a) <= 0.0
   # b2f(a) == 0.0 because b2f(a) can only be 0 or 1
   # inot(a)
   (('fge', 0.0, ('b2f', a)), ('inot', a)),

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   (('fge', ('fneg', ('b2f', a)), 0.0), ('inot', a)),

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   (('~flt', ('fadd', a, b), a), ('flt', b, 0.0)),
   (('~fge', ('fadd', a, b), a), ('fge', b, 0.0)),
   (('~feq', ('fadd', a, b), a), ('feq', b, 0.0)),
   (('~fne', ('fadd', a, b), a), ('fne', b, 0.0)),

   # Cannot remove the addition from ilt or ige due to overflow.
   (('ieq', ('iadd', a, b), a), ('ieq', b, 0)),
   (('ine', ('iadd', a, b), a), ('ine', b, 0)),

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   # fmin(-b2f(a), b) >= 0.0
   # -b2f(a) >= 0.0 && b >= 0.0
   # -b2f(a) == 0.0 && b >= 0.0    -b2f can only be 0 or -1, never >0
   # b2f(a) == 0.0 && b >= 0.0
   # a == False && b >= 0.0
   # !a && b >= 0.0
   #
   # The fge in the second replacement is not a typo.  I leave the proof that
   # "fmin(-b2f(a), b) >= 0 <=> fmin(-b2f(a), b) == 0" as an exercise for the
   # reader.
   (('fge', ('fmin', ('fneg', ('b2f', a)), b), 0.0), ('iand', ('inot', a), ('fge', b, 0.0))),
   (('feq', ('fmin', ('fneg', ('b2f', a)), b), 0.0), ('iand', ('inot', a), ('fge', b, 0.0))),

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   # 0.0 < fabs(a)
   # fabs(a) > 0.0
   # fabs(a) != 0.0 because fabs(a) must be >= 0
   # a != 0.0
   (('flt', 0.0, ('fabs', a)), ('fne', a, 0.0)),

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   (('fmax',                        ('b2f(is_used_once)', a),           ('b2f', b)),           ('b2f', ('ior', a, b))),
   (('fmax', ('fneg(is_used_once)', ('b2f(is_used_once)', a)), ('fneg', ('b2f', b))), ('fneg', ('b2f', ('ior', a, b)))),
   (('fmin',                        ('b2f(is_used_once)', a),           ('b2f', b)),           ('b2f', ('iand', a, b))),
   (('fmin', ('fneg(is_used_once)', ('b2f(is_used_once)', a)), ('fneg', ('b2f', b))), ('fneg', ('b2f', ('iand', a, b)))),

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   # fmin(b2f(a), b)
   # bcsel(a, fmin(b2f(a), b), fmin(b2f(a), b))
   # bcsel(a, fmin(b2f(True), b), fmin(b2f(False), b))
   # bcsel(a, fmin(1.0, b), fmin(0.0, b))
   #
   # Since b is a constant, constant folding will eliminate the fmin and the
   # fmax.  If b is > 1.0, the bcsel will be replaced with a b2f.
   (('fmin', ('b2f', a), '#b'), ('bcsel', a, ('fmin', b, 1.0), ('fmin', b, 0.0))),

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   # ignore this opt when the result is used by a bcsel or if so we can make
   # use of conditional modifiers on supported hardware.
   (('flt(is_not_used_by_conditional)', ('fadd(is_used_once)', a, ('fneg', b)), 0.0), ('flt', a, b)),

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   (('fge', ('fneg', ('fabs', a)), 0.0), ('feq', a, 0.0)),
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   (('~bcsel', ('flt', b, a), b, a), ('fmin', a, b)),
   (('~bcsel', ('flt', a, b), b, a), ('fmax', a, b)),
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   (('~bcsel', ('fge', a, b), b, a), ('fmin', a, b)),
   (('~bcsel', ('fge', b, a), b, a), ('fmax', a, b)),
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   (('bcsel', ('inot', a), b, c), ('bcsel', a, c, b)),
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   (('bcsel', a, ('bcsel', a, b, c), d), ('bcsel', a, b, d)),
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   (('bcsel', a, True, 'b@bool'), ('ior', a, b)),
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   (('fmin', a, a), a),
   (('fmax', a, a), a),
   (('imin', a, a), a),
   (('imax', a, a), a),
   (('umin', a, a), a),
   (('umax', a, a), a),
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   (('fmin', a, ('fneg', a)), ('fneg', ('fabs', a))),
   (('imin', a, ('ineg', a)), ('ineg', ('iabs', a))),
   (('fmin', a, ('fneg', ('fabs', a))), ('fneg', ('fabs', a))),
   (('imin', a, ('ineg', ('iabs', a))), ('ineg', ('iabs', a))),
   (('fmin', a, ('fabs', a)), a),
   (('imin', a, ('iabs', a)), a),
   (('fmax', a, ('fneg', ('fabs', a))), a),
   (('imax', a, ('ineg', ('iabs', a))), a),
   (('fmax', a, ('fabs', a)), ('fabs', a)),
   (('imax', a, ('iabs', a)), ('iabs', a)),
   (('fmax', a, ('fneg', a)), ('fabs', a)),
   (('imax', a, ('ineg', a)), ('iabs', a)),
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   (('~fmin', ('fmax', a, 0.0), 1.0), ('fsat', a), '!options->lower_fsat'),
   (('~fmax', ('fmin', a, 1.0), 0.0), ('fsat', a), '!options->lower_fsat'),
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   (('fsat', a), ('fmin', ('fmax', a, 0.0), 1.0), 'options->lower_fsat'),
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   (('fsat', ('fsat', a)), ('fsat', a)),
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   (('fmin', ('fmax', ('fmin', ('fmax', a, b), c), b), c), ('fmin', ('fmax', a, b), c)),
   (('imin', ('imax', ('imin', ('imax', a, b), c), b), c), ('imin', ('imax', a, b), c)),
   (('umin', ('umax', ('umin', ('umax', a, b), c), b), c), ('umin', ('umax', a, b), c)),
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   (('fmax', ('fsat', a), '#b@32(is_zero_to_one)'), ('fsat', ('fmax', a, b))),
   (('fmin', ('fsat', a), '#b@32(is_zero_to_one)'), ('fsat', ('fmin', a, b))),
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   (('extract_u8', ('imin', ('imax', a, 0), 0xff), 0), ('imin', ('imax', a, 0), 0xff)),
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   (('~ior', ('flt(is_used_once)', a, b), ('flt', a, c)), ('flt', a, ('fmax', b, c))),
   (('~ior', ('flt(is_used_once)', a, c), ('flt', b, c)), ('flt', ('fmin', a, b), c)),
   (('~ior', ('fge(is_used_once)', a, b), ('fge', a, c)), ('fge', a, ('fmin', b, c))),
   (('~ior', ('fge(is_used_once)', a, c), ('fge', b, c)), ('fge', ('fmax', a, b), c)),
   (('~ior', ('flt', a, '#b'), ('flt', a, '#c')), ('flt', a, ('fmax', b, c))),
   (('~ior', ('flt', '#a', c), ('flt', '#b', c)), ('flt', ('fmin', a, b), c)),
   (('~ior', ('fge', a, '#b'), ('fge', a, '#c')), ('fge', a, ('fmin', b, c))),
   (('~ior', ('fge', '#a', c), ('fge', '#b', c)), ('fge', ('fmax', a, b), c)),
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   (('~iand', ('flt(is_used_once)', a, b), ('flt', a, c)), ('flt', a, ('fmin', b, c))),
   (('~iand', ('flt(is_used_once)', a, c), ('flt', b, c)), ('flt', ('fmax', a, b), c)),
   (('~iand', ('fge(is_used_once)', a, b), ('fge', a, c)), ('fge', a, ('fmax', b, c))),
   (('~iand', ('fge(is_used_once)', a, c), ('fge', b, c)), ('fge', ('fmin', a, b), c)),
   (('~iand', ('flt', a, '#b'), ('flt', a, '#c')), ('flt', a, ('fmin', b, c))),
   (('~iand', ('flt', '#a', c), ('flt', '#b', c)), ('flt', ('fmax', a, b), c)),
   (('~iand', ('fge', a, '#b'), ('fge', a, '#c')), ('fge', a, ('fmax', b, c))),
   (('~iand', ('fge', '#a', c), ('fge', '#b', c)), ('fge', ('fmin', a, b), c)),
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   (('ior', ('ilt(is_used_once)', a, b), ('ilt', a, c)), ('ilt', a, ('imax', b, c))),
   (('ior', ('ilt(is_used_once)', a, c), ('ilt', b, c)), ('ilt', ('imin', a, b), c)),
   (('ior', ('ige(is_used_once)', a, b), ('ige', a, c)), ('ige', a, ('imin', b, c))),
   (('ior', ('ige(is_used_once)', a, c), ('ige', b, c)), ('ige', ('imax', a, b), c)),
   (('ior', ('ult(is_used_once)', a, b), ('ult', a, c)), ('ult', a, ('umax', b, c))),
   (('ior', ('ult(is_used_once)', a, c), ('ult', b, c)), ('ult', ('umin', a, b), c)),
   (('ior', ('uge(is_used_once)', a, b), ('uge', a, c)), ('uge', a, ('umin', b, c))),
   (('ior', ('uge(is_used_once)', a, c), ('uge', b, c)), ('uge', ('umax', a, b), c)),
   (('iand', ('ilt(is_used_once)', a, b), ('ilt', a, c)), ('ilt', a, ('imin', b, c))),
   (('iand', ('ilt(is_used_once)', a, c), ('ilt', b, c)), ('ilt', ('imax', a, b), c)),
   (('iand', ('ige(is_used_once)', a, b), ('ige', a, c)), ('ige', a, ('imax', b, c))),
   (('iand', ('ige(is_used_once)', a, c), ('ige', b, c)), ('ige', ('imin', a, b), c)),
   (('iand', ('ult(is_used_once)', a, b), ('ult', a, c)), ('ult', a, ('umin', b, c))),
   (('iand', ('ult(is_used_once)', a, c), ('ult', b, c)), ('ult', ('umax', a, b), c)),
   (('iand', ('uge(is_used_once)', a, b), ('uge', a, c)), ('uge', a, ('umax', b, c))),
   (('iand', ('uge(is_used_once)', a, c), ('uge', b, c)), ('uge', ('umin', a, b), c)),

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   # These patterns can result when (a < b || a < c) => (a < min(b, c))
   # transformations occur before constant propagation and loop-unrolling.
   (('~flt', a, ('fmax', b, a)), ('flt', a, b)),
   (('~flt', ('fmin', a, b), a), ('flt', b, a)),
   (('~fge', a, ('fmin', b, a)), True),
   (('~fge', ('fmax', a, b), a), True),
   (('~flt', a, ('fmin', b, a)), False),
   (('~flt', ('fmax', a, b), a), False),

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   (('ilt', a, ('imax', b, a)), ('ilt', a, b)),
   (('ilt', ('imin', a, b), a), ('ilt', b, a)),
   (('ige', a, ('imin', b, a)), True),
   (('ige', ('imax', a, b), a), True),
   (('ult', a, ('umax', b, a)), ('ult', a, b)),
   (('ult', ('umin', a, b), a), ('ult', b, a)),
   (('uge', a, ('umin', b, a)), True),
   (('uge', ('umax', a, b), a), True),

   (('ilt', '#a', ('imin', '#b', c)), ('iand', ('ilt', a, b), ('ilt', a, c))),
   (('ilt', ('imax', '#a', b), '#c'), ('iand', ('ilt', a, c), ('ilt', b, c))),
   (('ige', '#a', ('imax', '#b', c)), ('iand', ('ige', a, b), ('ige', a, c))),
   (('ige', ('imin', '#a', b), '#c'), ('iand', ('ige', a, c), ('ige', b, c))),
   (('ult', '#a', ('umin', '#b', c)), ('iand', ('ult', a, b), ('ult', a, c))),
   (('ult', ('umax', '#a', b), '#c'), ('iand', ('ult', a, c), ('ult', b, c))),
   (('uge', '#a', ('umax', '#b', c)), ('iand', ('uge', a, b), ('uge', a, c))),
   (('uge', ('umin', '#a', b), '#c'), ('iand', ('uge', a, c), ('uge', b, c))),

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   (('fabs', ('slt', a, b)), ('slt', a, b)),
   (('fabs', ('sge', a, b)), ('sge', a, b)),
   (('fabs', ('seq', a, b)), ('seq', a, b)),
   (('fabs', ('sne', a, b)), ('sne', a, b)),
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   (('slt', a, b), ('b2f', ('flt', a, b)), 'options->lower_scmp'),
   (('sge', a, b), ('b2f', ('fge', a, b)), 'options->lower_scmp'),
   (('seq', a, b), ('b2f', ('feq', a, b)), 'options->lower_scmp'),
   (('sne', a, b), ('b2f', ('fne', a, b)), 'options->lower_scmp'),
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   (('fne', ('fneg', a), a), ('fne', a, 0.0)),
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   (('feq', ('fneg', a), a), ('feq', a, 0.0)),
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   # Emulating booleans
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   (('imul', ('b2i', a), ('b2i', b)), ('b2i', ('iand', a, b))),
319
   (('fmul', ('b2f', a), ('b2f', b)), ('b2f', ('iand', a, b))),
320
   (('fsat', ('fadd', ('b2f', a), ('b2f', b))), ('b2f', ('ior', a, b))),
321 322
   (('iand', 'a@bool', 1.0), ('b2f', a), '!options->lower_b2f'),
   (('b2f@32', a), ('iand', a, 1.0), 'options->lower_b2f'),
323
   # True/False are ~0 and 0 in NIR.  b2i of True is 1, and -1 is ~0 (True).
324
   (('ineg', ('b2i@32', a)), a),
325 326
   (('flt', ('fneg', ('b2f', a)), 0), a), # Generated by TGSI KILL_IF.
   (('flt', ('fsub', 0.0, ('b2f', a)), 0), a), # Generated by TGSI KILL_IF.
327 328 329 330 331 332 333 334 335
   # 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),
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   # Logical and bit operations
   (('fand', a, 0.0), 0.0),
   (('iand', a, a), a),
339
   (('iand', a, ~0), a),
340 341 342
   (('iand', a, 0), 0),
   (('ior', a, a), a),
   (('ior', a, 0), a),
343
   (('ior', a, True), True),
344 345
   (('fxor', a, a), 0.0),
   (('ixor', a, a), 0),
346
   (('ixor', a, 0), a),
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   (('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))),
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   # Shift optimizations
   (('ishl', 0, a), 0),
   (('ishl', a, 0), a),
   (('ishr', 0, a), 0),
   (('ishr', a, 0), a),
   (('ushr', 0, a), 0),
357
   (('ushr', a, 0), a),
358 359
   (('iand', 0xff, ('ushr@32', a, 24)), ('ushr', a, 24)),
   (('iand', 0xffff, ('ushr@32', a, 16)), ('ushr', a, 16)),
360
   # Exponential/logarithmic identities
361 362
   (('~fexp2', ('flog2', a)), a), # 2^lg2(a) = a
   (('~flog2', ('fexp2', a)), a), # lg2(2^a) = a
363
   (('fpow', a, b), ('fexp2', ('fmul', ('flog2', a), b)), 'options->lower_fpow'), # a^b = 2^(lg2(a)*b)
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   (('~fexp2', ('fmul', ('flog2', a), b)), ('fpow', a, b), '!options->lower_fpow'), # 2^(lg2(a)*b) = a^b
   (('~fexp2', ('fadd', ('fmul', ('flog2', a), b), ('fmul', ('flog2', c), d))),
    ('~fmul', ('fpow', a, b), ('fpow', c, d)), '!options->lower_fpow'), # 2^(lg2(a) * b + lg2(c) + d) = a^b * c^d
367 368
   (('~fexp2', ('fmul', ('flog2', a), 2.0)), ('fmul', a, a)),
   (('~fexp2', ('fmul', ('flog2', a), 4.0)), ('fmul', ('fmul', a, a), ('fmul', a, a))),
369 370 371 372 373 374 375 376 377 378 379 380 381
   (('~fpow', a, 1.0), a),
   (('~fpow', a, 2.0), ('fmul', a, a)),
   (('~fpow', a, 4.0), ('fmul', ('fmul', a, a), ('fmul', a, a))),
   (('~fpow', 2.0, a), ('fexp2', a)),
   (('~fpow', ('fpow', a, 2.2), 0.454545), a),
   (('~fpow', ('fabs', ('fpow', a, 2.2)), 0.454545), ('fabs', a)),
   (('~fsqrt', ('fexp2', a)), ('fexp2', ('fmul', 0.5, a))),
   (('~frcp', ('fexp2', a)), ('fexp2', ('fneg', a))),
   (('~frsq', ('fexp2', a)), ('fexp2', ('fmul', -0.5, a))),
   (('~flog2', ('fsqrt', a)), ('fmul', 0.5, ('flog2', a))),
   (('~flog2', ('frcp', a)), ('fneg', ('flog2', a))),
   (('~flog2', ('frsq', a)), ('fmul', -0.5, ('flog2', a))),
   (('~flog2', ('fpow', a, b)), ('fmul', b, ('flog2', a))),
382
   (('~fmul', ('fexp2(is_used_once)', a), ('fexp2(is_used_once)', b)), ('fexp2', ('fadd', a, b))),
383
   # Division and reciprocal
384
   (('~fdiv', 1.0, a), ('frcp', a)),
385
   (('fdiv', a, b), ('fmul', a, ('frcp', b)), 'options->lower_fdiv'),
386 387
   (('~frcp', ('frcp', a)), a),
   (('~frcp', ('fsqrt', a)), ('frsq', a)),
388
   (('fsqrt', a), ('frcp', ('frsq', a)), 'options->lower_fsqrt'),
389
   (('~frcp', ('frsq', a)), ('fsqrt', a), '!options->lower_fsqrt'),
390
   # Boolean simplifications
391
   (('ieq', 'a@bool', True), a),
392
   (('ine(is_not_used_by_if)', 'a@bool', True), ('inot', a)),
393
   (('ine', 'a@bool', False), a),
394
   (('ieq(is_not_used_by_if)', 'a@bool', False), ('inot', 'a')),
395 396
   (('bcsel', a, True, False), a),
   (('bcsel', a, False, True), ('inot', a)),
397 398 399 400
   (('bcsel@32', a, 1.0, 0.0), ('b2f', a)),
   (('bcsel@32', a, 0.0, 1.0), ('b2f', ('inot', a))),
   (('bcsel@32', a, -1.0, -0.0), ('fneg', ('b2f', a))),
   (('bcsel@32', a, -0.0, -1.0), ('fneg', ('b2f', ('inot', a)))),
401 402
   (('bcsel', True, b, c), b),
   (('bcsel', False, b, c), c),
403
   (('bcsel', a, ('b2f(is_used_once)', b), ('b2f', c)), ('b2f', ('bcsel', a, b, c))),
404 405 406
   # 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)),
407

408 409 410
   (('bcsel', a, b, b), b),
   (('fcsel', a, b, b), b),

411
   # Conversions
412
   (('i2b', ('b2i', a)), a),
413
   (('i2b', 'a@bool'), a),
414 415
   (('f2i32', ('ftrunc', a)), ('f2i32', a)),
   (('f2u32', ('ftrunc', a)), ('f2u32', a)),
416 417
   (('i2b', ('ineg', a)), ('i2b', a)),
   (('i2b', ('iabs', a)), ('i2b', a)),
418 419
   (('fabs', ('b2f', a)), ('b2f', a)),
   (('iabs', ('b2i', a)), ('b2i', a)),
420

421 422 423 424 425 426
   # Packing and then unpacking does nothing
   (('unpack_64_2x32_split_x', ('pack_64_2x32_split', a, b)), a),
   (('unpack_64_2x32_split_y', ('pack_64_2x32_split', a, b)), b),
   (('pack_64_2x32_split', ('unpack_64_2x32_split_x', a),
                           ('unpack_64_2x32_split_y', a)), a),

427 428 429 430 431 432
   # Byte extraction
   (('ushr', a, 24), ('extract_u8', a, 3), '!options->lower_extract_byte'),
   (('iand', 0xff, ('ushr', a, 16)), ('extract_u8', a, 2), '!options->lower_extract_byte'),
   (('iand', 0xff, ('ushr', a,  8)), ('extract_u8', a, 1), '!options->lower_extract_byte'),
   (('iand', 0xff, a), ('extract_u8', a, 0), '!options->lower_extract_byte'),

433 434 435 436
    # Word extraction
   (('ushr', a, 16), ('extract_u16', a, 1), '!options->lower_extract_word'),
   (('iand', 0xffff, a), ('extract_u16', a, 0), '!options->lower_extract_word'),

437
   # Subtracts
438
   (('~fsub', a, ('fsub', 0.0, b)), ('fadd', a, b)),
439
   (('isub', a, ('isub', 0, b)), ('iadd', a, b)),
440 441
   (('ussub_4x8', a, 0), a),
   (('ussub_4x8', a, ~0), 0),
442 443
   (('fsub', a, b), ('fadd', a, ('fneg', b)), 'options->lower_sub'),
   (('isub', a, b), ('iadd', a, ('ineg', b)), 'options->lower_sub'),
444 445
   (('fneg', a), ('fsub', 0.0, a), 'options->lower_negate'),
   (('ineg', a), ('isub', 0, a), 'options->lower_negate'),
446
   (('~fadd', a, ('fsub', 0.0, b)), ('fsub', a, b)),
447 448 449
   (('iadd', a, ('isub', 0, b)), ('isub', a, b)),
   (('fabs', ('fsub', 0.0, a)), ('fabs', a)),
   (('iabs', ('isub', 0, a)), ('iabs', a)),
450

451 452
   # Propagate negation up multiplication chains
   (('fmul', ('fneg', a), b), ('fneg', ('fmul', a, b))),
453
   (('imul', ('ineg', a), b), ('ineg', ('imul', a, b))),
454

455 456 457 458 459 460
   # Propagate constants up multiplication chains
   (('~fmul(is_used_once)', ('fmul(is_used_once)', 'a(is_not_const)', 'b(is_not_const)'), '#c'), ('fmul', ('fmul', a, c), b)),
   (('imul(is_used_once)', ('imul(is_used_once)', 'a(is_not_const)', 'b(is_not_const)'), '#c'), ('imul', ('imul', a, c), b)),
   (('~fadd(is_used_once)', ('fadd(is_used_once)', 'a(is_not_const)', 'b(is_not_const)'), '#c'), ('fadd', ('fadd', a, c), b)),
   (('iadd(is_used_once)', ('iadd(is_used_once)', 'a(is_not_const)', 'b(is_not_const)'), '#c'), ('iadd', ('iadd', a, c), b)),

461
   # Reassociate constants in add/mul chains so they can be folded together.
462
   # For now, we mostly only handle cases where the constants are separated by
463 464 465
   # a single non-constant.  We could do better eventually.
   (('~fmul', '#a', ('fmul', b, '#c')), ('fmul', ('fmul', a, c), b)),
   (('imul', '#a', ('imul', b, '#c')), ('imul', ('imul', a, c), b)),
466 467
   (('~fadd', '#a',          ('fadd', b, '#c')),  ('fadd', ('fadd', a,          c),           b)),
   (('~fadd', '#a', ('fneg', ('fadd', b, '#c'))), ('fadd', ('fadd', a, ('fneg', c)), ('fneg', b))),
468 469
   (('iadd', '#a', ('iadd', b, '#c')), ('iadd', ('iadd', a, c), b)),

470 471 472 473 474 475 476 477 478 479 480
   # By definition...
   (('bcsel', ('ige', ('find_lsb', a), 0), ('find_lsb', a), -1), ('find_lsb', a)),
   (('bcsel', ('ige', ('ifind_msb', a), 0), ('ifind_msb', a), -1), ('ifind_msb', a)),
   (('bcsel', ('ige', ('ufind_msb', a), 0), ('ufind_msb', a), -1), ('ufind_msb', a)),

   (('bcsel', ('ine', a, 0), ('find_lsb', a), -1), ('find_lsb', a)),
   (('bcsel', ('ine', a, 0), ('ifind_msb', a), -1), ('ifind_msb', a)),
   (('bcsel', ('ine', a, 0), ('ufind_msb', a), -1), ('ufind_msb', a)),

   (('bcsel', ('ine', a, -1), ('ifind_msb', a), -1), ('ifind_msb', a)),

481
   # Misc. lowering
482 483 484
   (('fmod@32', a, b), ('fsub', a, ('fmul', b, ('ffloor', ('fdiv', a, b)))), 'options->lower_fmod32'),
   (('fmod@64', a, b), ('fsub', a, ('fmul', b, ('ffloor', ('fdiv', a, b)))), 'options->lower_fmod64'),
   (('frem', a, b), ('fsub', a, ('fmul', b, ('ftrunc', ('fdiv', a, b)))), 'options->lower_fmod32'),
485 486
   (('uadd_carry@32', a, b), ('b2i', ('ult', ('iadd', a, b), a)), 'options->lower_uadd_carry'),
   (('usub_borrow@32', a, b), ('b2i', ('ult', a, b)), 'options->lower_usub_borrow'),
487 488 489 490 491

   (('bitfield_insert', 'base', 'insert', 'offset', 'bits'),
    ('bcsel', ('ilt', 31, 'bits'), 'insert',
              ('bfi', ('bfm', 'bits', 'offset'), 'insert', 'base')),
    'options->lower_bitfield_insert'),
492 493 494 495 496 497 498 499 500 501

   (('ibitfield_extract', 'value', 'offset', 'bits'),
    ('bcsel', ('ilt', 31, 'bits'), 'value',
              ('ibfe', 'value', 'offset', 'bits')),
    'options->lower_bitfield_extract'),

   (('ubitfield_extract', 'value', 'offset', 'bits'),
    ('bcsel', ('ult', 31, 'bits'), 'value',
              ('ubfe', 'value', 'offset', 'bits')),
    'options->lower_bitfield_extract'),
502

503
   (('extract_i8', a, 'b@32'),
504 505 506
    ('ishr', ('ishl', a, ('imul', ('isub', 3, b), 8)), 24),
    'options->lower_extract_byte'),

507
   (('extract_u8', a, 'b@32'),
508 509 510
    ('iand', ('ushr', a, ('imul', b, 8)), 0xff),
    'options->lower_extract_byte'),

511
   (('extract_i16', a, 'b@32'),
512 513 514
    ('ishr', ('ishl', a, ('imul', ('isub', 1, b), 16)), 16),
    'options->lower_extract_word'),

515
   (('extract_u16', a, 'b@32'),
516 517
    ('iand', ('ushr', a, ('imul', b, 16)), 0xffff),
    'options->lower_extract_word'),
518 519 520

    (('pack_unorm_2x16', 'v'),
     ('pack_uvec2_to_uint',
521
        ('f2u32', ('fround_even', ('fmul', ('fsat', 'v'), 65535.0)))),
522 523 524 525
     'options->lower_pack_unorm_2x16'),

    (('pack_unorm_4x8', 'v'),
     ('pack_uvec4_to_uint',
526
        ('f2u32', ('fround_even', ('fmul', ('fsat', 'v'), 255.0)))),
527 528 529 530
     'options->lower_pack_unorm_4x8'),

    (('pack_snorm_2x16', 'v'),
     ('pack_uvec2_to_uint',
531
        ('f2i32', ('fround_even', ('fmul', ('fmin', 1.0, ('fmax', -1.0, 'v')), 32767.0)))),
532 533 534 535
     'options->lower_pack_snorm_2x16'),

    (('pack_snorm_4x8', 'v'),
     ('pack_uvec4_to_uint',
536
        ('f2i32', ('fround_even', ('fmul', ('fmin', 1.0, ('fmax', -1.0, 'v')), 127.0)))),
537
     'options->lower_pack_snorm_4x8'),
538 539

    (('unpack_unorm_2x16', 'v'),
540 541
     ('fdiv', ('u2f32', ('vec2', ('extract_u16', 'v', 0),
                                 ('extract_u16', 'v', 1))),
542 543 544 545
              65535.0),
     'options->lower_unpack_unorm_2x16'),

    (('unpack_unorm_4x8', 'v'),
546 547 548 549
     ('fdiv', ('u2f32', ('vec4', ('extract_u8', 'v', 0),
                                 ('extract_u8', 'v', 1),
                                 ('extract_u8', 'v', 2),
                                 ('extract_u8', 'v', 3))),
550 551 552 553
              255.0),
     'options->lower_unpack_unorm_4x8'),

    (('unpack_snorm_2x16', 'v'),
554 555
     ('fmin', 1.0, ('fmax', -1.0, ('fdiv', ('i2f32', ('vec2', ('extract_i16', 'v', 0),
                                                              ('extract_i16', 'v', 1))),
556 557 558 559
                                           32767.0))),
     'options->lower_unpack_snorm_2x16'),

    (('unpack_snorm_4x8', 'v'),
560 561 562 563
     ('fmin', 1.0, ('fmax', -1.0, ('fdiv', ('i2f32', ('vec4', ('extract_i8', 'v', 0),
                                                              ('extract_i8', 'v', 1),
                                                              ('extract_i8', 'v', 2),
                                                              ('extract_i8', 'v', 3))),
564 565
                                           127.0))),
     'options->lower_unpack_snorm_4x8'),
566 567
]

568 569 570 571 572 573 574 575
invert = {'feq': 'fne', 'fne': 'feq', 'fge': 'flt', 'flt': 'fge' }

for left, right in list(itertools.combinations(invert.keys(), 2)) + zip(invert.keys(), invert.keys()):
   optimizations.append((('inot', ('ior(is_used_once)', (left, a, b), (right, c, d))),
                         ('iand', (invert[left], a, b), (invert[right], c, d))))
   optimizations.append((('inot', ('iand(is_used_once)', (left, a, b), (right, c, d))),
                         ('ior', (invert[left], a, b), (invert[right], c, d))))

576 577 578 579 580
def fexp2i(exp, bits):
   # We assume that exp is already in the right range.
   if bits == 32:
      return ('ishl', ('iadd', exp, 127), 23)
   elif bits == 64:
581
      return ('pack_64_2x32_split', 0, ('ishl', ('iadd', exp, 1023), 20))
582 583 584 585
   else:
      assert False

def ldexp(f, exp, bits):
586 587 588 589 590 591 592 593 594 595
   # First, we clamp exp to a reasonable range.  The maximum possible range
   # for a normal exponent is [-126, 127] and, throwing in denormals, you get
   # a maximum range of [-149, 127].  This means that we can potentially have
   # a swing of +-276.  If you start with FLT_MAX, you actually have to do
   # ldexp(FLT_MAX, -278) to get it to flush all the way to zero.  The GLSL
   # spec, on the other hand, only requires that we handle an exponent value
   # in the range [-126, 128].  This implementation is *mostly* correct; it
   # handles a range on exp of [-252, 254] which allows you to create any
   # value (including denorms if the hardware supports it) and to adjust the
   # exponent of any normal value to anything you want.
596 597 598 599 600 601
   if bits == 32:
      exp = ('imin', ('imax', exp, -252), 254)
   elif bits == 64:
      exp = ('imin', ('imax', exp, -2044), 2046)
   else:
      assert False
602 603 604 605 606 607 608 609 610

   # Now we compute two powers of 2, one for exp/2 and one for exp-exp/2.
   # (We use ishr which isn't the same for -1, but the -1 case still works
   # since we use exp-exp/2 as the second exponent.)  While the spec
   # technically defines ldexp as f * 2.0^exp, simply multiplying once doesn't
   # work with denormals and doesn't allow for the full swing in exponents
   # that you can get with normalized values.  Instead, we create two powers
   # of two and multiply by them each in turn.  That way the effective range
   # of our exponent is doubled.
611 612
   pow2_1 = fexp2i(('ishr', exp, 1), bits)
   pow2_2 = fexp2i(('isub', exp, ('ishr', exp, 1)), bits)
613 614
   return ('fmul', ('fmul', f, pow2_1), pow2_2)

615
optimizations += [
616 617
   (('ldexp@32', 'x', 'exp'), ldexp('x', 'exp', 32), 'options->lower_ldexp'),
   (('ldexp@64', 'x', 'exp'), ldexp('x', 'exp', 64), 'options->lower_ldexp'),
618
]
619

620 621 622 623 624 625 626 627 628 629
# Unreal Engine 4 demo applications open-codes bitfieldReverse()
def bitfield_reverse(u):
    step1 = ('ior', ('ishl', u, 16), ('ushr', u, 16))
    step2 = ('ior', ('ishl', ('iand', step1, 0x00ff00ff), 8), ('ushr', ('iand', step1, 0xff00ff00), 8))
    step3 = ('ior', ('ishl', ('iand', step2, 0x0f0f0f0f), 4), ('ushr', ('iand', step2, 0xf0f0f0f0), 4))
    step4 = ('ior', ('ishl', ('iand', step3, 0x33333333), 2), ('ushr', ('iand', step3, 0xcccccccc), 2))
    step5 = ('ior', ('ishl', ('iand', step4, 0x55555555), 1), ('ushr', ('iand', step4, 0xaaaaaaaa), 1))

    return step5

630
optimizations += [(bitfield_reverse('x@32'), ('bitfield_reverse', 'x'))]
631

632 633 634 635 636 637 638 639
# For any float comparison operation, "cmp", if you have "a == a && a cmp b"
# then the "a == a" is redundant because it's equivalent to "a is not NaN"
# and, if a is a NaN then the second comparison will fail anyway.
for op in ['flt', 'fge', 'feq']:
   optimizations += [
      (('iand', ('feq', a, a), (op, a, b)), (op, a, b)),
      (('iand', ('feq', a, a), (op, b, a)), (op, b, a)),
   ]
640

641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661
# 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'))),
   ]

662 663 664 665 666 667 668 669 670 671 672 673 674 675 676

# For example, this converts things like
#
#    1 + mix(0, a - 1, condition)
#
# into
#
#    mix(1, (a-1)+1, condition)
#
# Other optimizations will rearrange the constants.
for op in ['fadd', 'fmul', 'iadd', 'imul']:
   optimizations += [
      ((op, ('bcsel(is_used_once)', a, '#b', c), '#d'), ('bcsel', a, (op, b, d), (op, c, d)))
   ]

677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697
# This section contains "late" optimizations that should be run before
# creating ffmas and calling regular optimizations for the final time.
# Optimizations should go here if they help code generation and conflict
# with the regular optimizations.
before_ffma_optimizations = [
   # Propagate constants down multiplication chains
   (('~fmul(is_used_once)', ('fmul(is_used_once)', 'a(is_not_const)', '#b'), 'c(is_not_const)'), ('fmul', ('fmul', a, c), b)),
   (('imul(is_used_once)', ('imul(is_used_once)', 'a(is_not_const)', '#b'), 'c(is_not_const)'), ('imul', ('imul', a, c), b)),
   (('~fadd(is_used_once)', ('fadd(is_used_once)', 'a(is_not_const)', '#b'), 'c(is_not_const)'), ('fadd', ('fadd', a, c), b)),
   (('iadd(is_used_once)', ('iadd(is_used_once)', 'a(is_not_const)', '#b'), 'c(is_not_const)'), ('iadd', ('iadd', a, c), b)),

   (('~fadd', ('fmul', a, b), ('fmul', a, c)), ('fmul', a, ('fadd', b, c))),
   (('iadd', ('imul', a, b), ('imul', a, c)), ('imul', a, ('iadd', b, c))),
   (('~fadd', ('fneg', a), a), 0.0),
   (('iadd', ('ineg', a), a), 0),
   (('iadd', ('ineg', a), ('iadd', a, b)), b),
   (('iadd', a, ('iadd', ('ineg', a), b)), b),
   (('~fadd', ('fneg', a), ('fadd', a, b)), b),
   (('~fadd', a, ('fadd', ('fneg', a), b)), b),
]

698 699 700 701 702
# This section contains "late" optimizations that should be run after the
# regular optimizations have finished.  Optimizations should go here if
# they help code generation but do not necessarily produce code that is
# more easily optimizable.
late_optimizations = [
703 704
   # Most of these optimizations aren't quite safe when you get infinity or
   # Nan involved but the first one should be fine.
705 706 707 708
   (('flt',          ('fadd', a, b),  0.0), ('flt',          a, ('fneg', b))),
   (('flt', ('fneg', ('fadd', a, b)), 0.0), ('flt', ('fneg', a),         b)),
   (('~fge',          ('fadd', a, b),  0.0), ('fge',          a, ('fneg', b))),
   (('~fge', ('fneg', ('fadd', a, b)), 0.0), ('fge', ('fneg', a),         b)),
709 710 711
   (('~feq', ('fadd', a, b), 0.0), ('feq', a, ('fneg', b))),
   (('~fne', ('fadd', a, b), 0.0), ('fne', a, ('fneg', b))),

712 713
   (('~fge', ('fmin(is_used_once)', ('fadd(is_used_once)', a, b), ('fadd', c, d)), 0.0), ('iand', ('fge', a, ('fneg', b)), ('fge', c, ('fneg', d)))),

714 715 716
   (('fdot2', a, b), ('fdot_replicated2', a, b), 'options->fdot_replicates'),
   (('fdot3', a, b), ('fdot_replicated3', a, b), 'options->fdot_replicates'),
   (('fdot4', a, b), ('fdot_replicated4', a, b), 'options->fdot_replicates'),
717
   (('fdph', a, b), ('fdph_replicated', a, b), 'options->fdot_replicates'),
718 719 720

   (('b2f(is_used_more_than_once)', ('inot', a)), ('bcsel', a, 0.0, 1.0)),
   (('fneg(is_used_more_than_once)', ('b2f', ('inot', a))), ('bcsel', a, -0.0, -1.0)),
721 722 723 724

   # we do these late so that we don't get in the way of creating ffmas
   (('fmin', ('fadd(is_used_once)', '#c', a), ('fadd(is_used_once)', '#c', b)), ('fadd', c, ('fmin', a, b))),
   (('fmax', ('fadd(is_used_once)', '#c', a), ('fadd(is_used_once)', '#c', b)), ('fadd', c, ('fmax', a, b))),
725 726
]

727
print nir_algebraic.AlgebraicPass("nir_opt_algebraic", optimizations).render()
728 729
print nir_algebraic.AlgebraicPass("nir_opt_algebraic_before_ffma",
                                  before_ffma_optimizations).render()
730 731
print nir_algebraic.AlgebraicPass("nir_opt_algebraic_late",
                                  late_optimizations).render()