Revision a121721f975fc4105ed24ebd0ad1020d08d07a38 authored by Shuhei Kadowaki on 01 November 2021, 10:49:07 UTC, committed by GitHub on 01 November 2021, 10:49:07 UTC
* inference: form `PartialStruct` for extra type information propagation This commit forms `PartialStruct` whenever there is any type-level refinement available about a field, even if it's not "constant" information. In Julia "definitions" are allowed to be abstract whereas "usages" (i.e. callsites) are often concrete. The basic idea is to allow inference to make more use of such precise callsite type information by encoding it as `PartialStruct`. This may increase optimization possibilities of "unidiomatic" Julia code, which may contain poorly-typed definitions, like this very contrived example: ```julia struct Problem n; s; c; t end function main(args...) prob = Problem(args...) s = 0 for i in 1:prob.n m = mod(i, 3) s += m == 0 ? sin(prob.s) : m == 1 ? cos(prob.c) : tan(prob.t) end return prob, s end main(10000, 1, 2, 3) ``` One of the obvious limitation is that this extra type information can be propagated inter-procedurally only as a const-propagation. I'm not sure this kind of "just a type-level" refinement can often make constant-prop' successful (i.e. shape-up a method body and allow it to be inlined, encoding the extra type information into the generated code), thus I didn't not modify any part of const-prop' heuristics. So the improvements from this change might not be very useful for general inter-procedural analysis currently, but they should definitely improve the accuracy of local analysis and very simple inter-procedural analysis.
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fastmath.jl
# This file is a part of Julia. License is MIT: https://julialang.org/license
# Support for @fastmath
# This module provides versions of math functions that may violate
# strict IEEE semantics.
# This allows the following transformations. For more information see
# http://llvm.org/docs/LangRef.html#fast-math-flags:
# nnan: No NaNs - Allow optimizations to assume the arguments and
# result are not NaN. Such optimizations are required to retain
# defined behavior over NaNs, but the value of the result is
# undefined.
# ninf: No Infs - Allow optimizations to assume the arguments and
# result are not +/-Inf. Such optimizations are required to
# retain defined behavior over +/-Inf, but the value of the
# result is undefined.
# nsz: No Signed Zeros - Allow optimizations to treat the sign of a
# zero argument or result as insignificant.
# arcp: Allow Reciprocal - Allow optimizations to use the reciprocal
# of an argument rather than perform division.
# fast: Fast - Allow algebraically equivalent transformations that may
# dramatically change results in floating point (e.g.
# reassociate). This flag implies all the others.
module FastMath
export @fastmath
import Core.Intrinsics: sqrt_llvm_fast, neg_float_fast,
add_float_fast, sub_float_fast, mul_float_fast, div_float_fast, rem_float_fast,
eq_float_fast, ne_float_fast, lt_float_fast, le_float_fast
const fast_op =
Dict(# basic arithmetic
:+ => :add_fast,
:- => :sub_fast,
:* => :mul_fast,
:/ => :div_fast,
:(==) => :eq_fast,
:!= => :ne_fast,
:< => :lt_fast,
:<= => :le_fast,
:abs => :abs_fast,
:abs2 => :abs2_fast,
:cmp => :cmp_fast,
:conj => :conj_fast,
:inv => :inv_fast,
:rem => :rem_fast,
:sign => :sign_fast,
:isfinite => :isfinite_fast,
:isinf => :isinf_fast,
:isnan => :isnan_fast,
:issubnormal => :issubnormal_fast,
# math functions
:^ => :pow_fast,
:acos => :acos_fast,
:acosh => :acosh_fast,
:angle => :angle_fast,
:asin => :asin_fast,
:asinh => :asinh_fast,
:atan => :atan_fast,
:atanh => :atanh_fast,
:cbrt => :cbrt_fast,
:cis => :cis_fast,
:cos => :cos_fast,
:cosh => :cosh_fast,
:exp10 => :exp10_fast,
:exp2 => :exp2_fast,
:exp => :exp_fast,
:expm1 => :expm1_fast,
:hypot => :hypot_fast,
:log10 => :log10_fast,
:log1p => :log1p_fast,
:log2 => :log2_fast,
:log => :log_fast,
:max => :max_fast,
:min => :min_fast,
:minmax => :minmax_fast,
:sin => :sin_fast,
:sincos => :sincos_fast,
:sinh => :sinh_fast,
:sqrt => :sqrt_fast,
:tan => :tan_fast,
:tanh => :tanh_fast)
const rewrite_op =
Dict(:+= => :+,
:-= => :-,
:*= => :*,
:/= => :/,
:^= => :^)
function make_fastmath(expr::Expr)
if expr.head === :quote
return expr
elseif expr.head === :call && expr.args[1] === :^ && expr.args[3] isa Integer
# mimic Julia's literal_pow lowering of literal integer powers
return Expr(:call, :(Base.FastMath.pow_fast), make_fastmath(expr.args[2]), Val{expr.args[3]}())
end
op = get(rewrite_op, expr.head, :nothing)
if op !== :nothing
var = expr.args[1]
rhs = expr.args[2]
if isa(var, Symbol)
# simple assignment
expr = :($var = $op($var, $rhs))
elseif isa(var, Expr) && var.head === :ref
var = var::Expr
# array reference
arr = var.args[1]
inds = var.args[2:end]
arrvar = gensym()
indvars = Any[gensym() for _ in inds]
expr = quote
$(Expr(:(=), arrvar, arr))
$(Expr(:(=), Base.exprarray(:tuple, indvars), Base.exprarray(:tuple, inds)))
$arrvar[$(indvars...)] = $op($arrvar[$(indvars...)], $rhs)
end
end
end
Base.exprarray(make_fastmath(expr.head), Base.mapany(make_fastmath, expr.args))
end
function make_fastmath(symb::Symbol)
fast_symb = get(fast_op, symb, :nothing)
if fast_symb === :nothing
return symb
end
:(Base.FastMath.$fast_symb)
end
make_fastmath(expr) = expr
"""
@fastmath expr
Execute a transformed version of the expression, which calls functions that
may violate strict IEEE semantics. This allows the fastest possible operation,
but results are undefined -- be careful when doing this, as it may change numerical
results.
This sets the [LLVM Fast-Math flags](http://llvm.org/docs/LangRef.html#fast-math-flags),
and corresponds to the `-ffast-math` option in clang. See [the notes on performance
annotations](@ref man-performance-annotations) for more details.
# Examples
```jldoctest
julia> @fastmath 1+2
3
julia> @fastmath(sin(3))
0.1411200080598672
```
"""
macro fastmath(expr)
make_fastmath(esc(expr))
end
# Basic arithmetic
const FloatTypes = Union{Float16,Float32,Float64}
sub_fast(x::FloatTypes) = neg_float_fast(x)
add_fast(x::T, y::T) where {T<:FloatTypes} = add_float_fast(x, y)
sub_fast(x::T, y::T) where {T<:FloatTypes} = sub_float_fast(x, y)
mul_fast(x::T, y::T) where {T<:FloatTypes} = mul_float_fast(x, y)
div_fast(x::T, y::T) where {T<:FloatTypes} = div_float_fast(x, y)
rem_fast(x::T, y::T) where {T<:FloatTypes} = rem_float_fast(x, y)
add_fast(x::T, y::T, zs::T...) where {T<:FloatTypes} =
add_fast(add_fast(x, y), zs...)
mul_fast(x::T, y::T, zs::T...) where {T<:FloatTypes} =
mul_fast(mul_fast(x, y), zs...)
@fastmath begin
cmp_fast(x::T, y::T) where {T<:FloatTypes} = ifelse(x==y, 0, ifelse(x<y, -1, +1))
log_fast(b::T, x::T) where {T<:FloatTypes} = log_fast(x)/log_fast(b)
end
eq_fast(x::T, y::T) where {T<:FloatTypes} = eq_float_fast(x, y)
ne_fast(x::T, y::T) where {T<:FloatTypes} = ne_float_fast(x, y)
lt_fast(x::T, y::T) where {T<:FloatTypes} = lt_float_fast(x, y)
le_fast(x::T, y::T) where {T<:FloatTypes} = le_float_fast(x, y)
isinf_fast(x) = false
isfinite_fast(x) = true
isnan_fast(x) = false
issubnormal_fast(x) = false
# complex numbers
ComplexTypes = Union{ComplexF32, ComplexF64}
@fastmath begin
abs_fast(x::ComplexTypes) = hypot(real(x), imag(x))
abs2_fast(x::ComplexTypes) = real(x)*real(x) + imag(x)*imag(x)
conj_fast(x::T) where {T<:ComplexTypes} = T(real(x), -imag(x))
inv_fast(x::ComplexTypes) = conj(x) / abs2(x)
sign_fast(x::ComplexTypes) = x == 0 ? float(zero(x)) : x/abs(x)
add_fast(x::T, y::T) where {T<:ComplexTypes} =
T(real(x)+real(y), imag(x)+imag(y))
add_fast(x::Complex{T}, b::T) where {T<:FloatTypes} =
Complex{T}(real(x)+b, imag(x))
add_fast(a::T, y::Complex{T}) where {T<:FloatTypes} =
Complex{T}(a+real(y), imag(y))
sub_fast(x::T, y::T) where {T<:ComplexTypes} =
T(real(x)-real(y), imag(x)-imag(y))
sub_fast(x::Complex{T}, b::T) where {T<:FloatTypes} =
Complex{T}(real(x)-b, imag(x))
sub_fast(a::T, y::Complex{T}) where {T<:FloatTypes} =
Complex{T}(a-real(y), -imag(y))
mul_fast(x::T, y::T) where {T<:ComplexTypes} =
T(real(x)*real(y) - imag(x)*imag(y),
real(x)*imag(y) + imag(x)*real(y))
mul_fast(x::Complex{T}, b::T) where {T<:FloatTypes} =
Complex{T}(real(x)*b, imag(x)*b)
mul_fast(a::T, y::Complex{T}) where {T<:FloatTypes} =
Complex{T}(a*real(y), a*imag(y))
@inline div_fast(x::T, y::T) where {T<:ComplexTypes} =
T(real(x)*real(y) + imag(x)*imag(y),
imag(x)*real(y) - real(x)*imag(y)) / abs2(y)
div_fast(x::Complex{T}, b::T) where {T<:FloatTypes} =
Complex{T}(real(x)/b, imag(x)/b)
div_fast(a::T, y::Complex{T}) where {T<:FloatTypes} =
Complex{T}(a*real(y), -a*imag(y)) / abs2(y)
eq_fast(x::T, y::T) where {T<:ComplexTypes} =
(real(x)==real(y)) & (imag(x)==imag(y))
eq_fast(x::Complex{T}, b::T) where {T<:FloatTypes} =
(real(x)==b) & (imag(x)==T(0))
eq_fast(a::T, y::Complex{T}) where {T<:FloatTypes} =
(a==real(y)) & (T(0)==imag(y))
ne_fast(x::T, y::T) where {T<:ComplexTypes} = !(x==y)
# Note: we use the same comparison for min, max, and minmax, so
# that the compiler can convert between them
max_fast(x::T, y::T) where {T<:FloatTypes} = ifelse(y > x, y, x)
min_fast(x::T, y::T) where {T<:FloatTypes} = ifelse(y > x, x, y)
minmax_fast(x::T, y::T) where {T<:FloatTypes} = ifelse(y > x, (x,y), (y,x))
max_fast(x::T, y::T, z::T...) where {T<:FloatTypes} = max_fast(max_fast(x, y), z...)
min_fast(x::T, y::T, z::T...) where {T<:FloatTypes} = min_fast(min_fast(x, y), z...)
end
# fall-back implementations and type promotion
for op in (:abs, :abs2, :conj, :inv, :sign)
op_fast = fast_op[op]
@eval begin
# fall-back implementation for non-numeric types
$op_fast(xs...) = $op(xs...)
end
end
for op in (:+, :-, :*, :/, :(==), :!=, :<, :<=, :cmp, :rem, :min, :max, :minmax)
op_fast = fast_op[op]
@eval begin
# fall-back implementation for non-numeric types
$op_fast(xs...) = $op(xs...)
# type promotion
$op_fast(x::Number, y::Number, zs::Number...) =
$op_fast(promote(x,y,zs...)...)
# fall-back implementation that applies after promotion
$op_fast(x::T,ys::T...) where {T<:Number} = $op(x,ys...)
end
end
# Math functions
exp2_fast(x::Union{Float32,Float64}) = Base.Math.exp2_fast(x)
exp_fast(x::Union{Float32,Float64}) = Base.Math.exp_fast(x)
exp10_fast(x::Union{Float32,Float64}) = Base.Math.exp10_fast(x)
# builtins
pow_fast(x::Float32, y::Integer) = ccall("llvm.powi.f32", llvmcall, Float32, (Float32, Int32), x, y)
pow_fast(x::Float64, y::Integer) = ccall("llvm.powi.f64", llvmcall, Float64, (Float64, Int32), x, y)
pow_fast(x::FloatTypes, ::Val{p}) where {p} = pow_fast(x, p) # inlines already via llvm.powi
@inline pow_fast(x, v::Val) = Base.literal_pow(^, x, v)
sqrt_fast(x::FloatTypes) = sqrt_llvm_fast(x)
sincos_fast(v::FloatTypes) = sincos(v)
@inline function sincos_fast(v::Float16)
s, c = sincos_fast(Float32(v))
return Float16(s), Float16(c)
end
sincos_fast(v::AbstractFloat) = (sin_fast(v), cos_fast(v))
sincos_fast(v::Real) = sincos_fast(float(v)::AbstractFloat)
sincos_fast(v) = (sin_fast(v), cos_fast(v))
@fastmath begin
hypot_fast(x::T, y::T) where {T<:FloatTypes} = sqrt(x*x + y*y)
# complex numbers
function cis_fast(x::T) where {T<:FloatTypes}
s, c = sincos_fast(x)
Complex{T}(c, s)
end
# See <http://en.cppreference.com/w/cpp/numeric/complex>
pow_fast(x::T, y::T) where {T<:ComplexTypes} = exp(y*log(x))
pow_fast(x::T, y::Complex{T}) where {T<:FloatTypes} = exp(y*log(x))
pow_fast(x::Complex{T}, y::T) where {T<:FloatTypes} = exp(y*log(x))
acos_fast(x::T) where {T<:ComplexTypes} =
convert(T,π)/2 + im*log(im*x + sqrt(1-x*x))
acosh_fast(x::ComplexTypes) = log(x + sqrt(x+1) * sqrt(x-1))
angle_fast(x::ComplexTypes) = atan(imag(x), real(x))
asin_fast(x::ComplexTypes) = -im*asinh(im*x)
asinh_fast(x::ComplexTypes) = log(x + sqrt(1+x*x))
atan_fast(x::ComplexTypes) = -im*atanh(im*x)
atanh_fast(x::T) where {T<:ComplexTypes} = convert(T,1)/2*(log(1+x) - log(1-x))
cis_fast(x::ComplexTypes) = exp(-imag(x)) * cis(real(x))
cos_fast(x::ComplexTypes) = cosh(im*x)
cosh_fast(x::T) where {T<:ComplexTypes} = convert(T,1)/2*(exp(x) + exp(-x))
exp10_fast(x::T) where {T<:ComplexTypes} =
exp10(real(x)) * cis(imag(x)*log(convert(T,10)))
exp2_fast(x::T) where {T<:ComplexTypes} =
exp2(real(x)) * cis(imag(x)*log(convert(T,2)))
exp_fast(x::ComplexTypes) = exp(real(x)) * cis(imag(x))
expm1_fast(x::ComplexTypes) = exp(x)-1
log10_fast(x::T) where {T<:ComplexTypes} = log(x) / log(convert(T,10))
log1p_fast(x::ComplexTypes) = log(1+x)
log2_fast(x::T) where {T<:ComplexTypes} = log(x) / log(convert(T,2))
log_fast(x::T) where {T<:ComplexTypes} = T(log(abs2(x))/2, angle(x))
log_fast(b::T, x::T) where {T<:ComplexTypes} = T(log(x)/log(b))
sin_fast(x::ComplexTypes) = -im*sinh(im*x)
sinh_fast(x::T) where {T<:ComplexTypes} = convert(T,1)/2*(exp(x) - exp(-x))
sqrt_fast(x::ComplexTypes) = sqrt(abs(x)) * cis(angle(x)/2)
tan_fast(x::ComplexTypes) = -im*tanh(im*x)
tanh_fast(x::ComplexTypes) = (a=exp(x); b=exp(-x); (a-b)/(a+b))
end
# fall-back implementations and type promotion
for f in (:acos, :acosh, :angle, :asin, :asinh, :atan, :atanh, :cbrt,
:cis, :cos, :cosh, :exp10, :exp2, :exp, :expm1,
:log10, :log1p, :log2, :log, :sin, :sinh, :sqrt, :tan,
:tanh)
f_fast = fast_op[f]
@eval begin
$f_fast(x) = $f(x)
end
end
for f in (:^, :atan, :hypot, :log)
f_fast = fast_op[f]
@eval begin
# fall-back implementation for non-numeric types
$f_fast(x, y) = $f(x, y)
# type promotion
$f_fast(x::Number, y::Number) = $f_fast(promote(x, y)...)
# fall-back implementation that applies after promotion
$f_fast(x::T, y::T) where {T<:Number} = $f(x, y)
end
end
end
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