Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

tanh 3x faster, and <1.5 ULP vs 2.0 ULP for master #38382

Merged
merged 3 commits into from
Nov 14, 2020
Merged

tanh 3x faster, and <1.5 ULP vs 2.0 ULP for master #38382

Changes from all commits
Commits
Show all changes
3 commits
Select commit Hold shift + click to select a range
086027d
tanh 3x faster, and <1.5 ULP vs 2.0 ULP for master
oscardssmith Nov 11, 2020
ceda3a7
fix whitespace, function name, and remove now incorrect attribution
oscardssmith Nov 11, 2020
b9ac57a
Fix whitespace
oscardssmith Nov 13, 2020
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
56 changes: 23 additions & 33 deletions base/special/hyperbolic.jl
View file
Open in desktop
Original file line number Diff line number Diff line change
@@ -1,6 +1,6 @@
# This file is a part of Julia. License is MIT: https://julialang.org/license

# sinh, cosh, tanh, asinh, acosh, and atanh are heavily based on FDLIBM code:
# asinh, acosh, and atanh are heavily based on FDLIBM code:
# e_sinh.c, e_sinhf, e_cosh.c, e_coshf, s_tanh.c, s_tanhf.c, s_asinh.c,
# s_asinhf.c, e_acosh.c, e_coshf.c, e_atanh.c, and e_atanhf.c
# that are made available under the following licence:
Expand Down Expand Up @@ -132,45 +132,35 @@ cosh(x::Real) = cosh(float(x))
# tanh methods
TANH_LARGE_X(::Type{Float64}) = 22.0
TANH_LARGE_X(::Type{Float32}) = 9.0f0
TANH_SMALL_X(::Type{Float64}) = 1.0
TANH_SMALL_X(::Type{Float32}) = 1.3862944f0 #2*log(2)
@inline function tanh_kernel(x::Float64)
return evalpoly(x, (1.0, -0.33333333333332904, 0.13333333333267555,
-0.05396825393066753, 0.02186948742242217,
-0.008863215974794633, 0.003591910693118715,
-0.0014542587440487815, 0.0005825521659411748,
-0.00021647574085351332, 5.5752458452673005e-5))
end
@inline function tanh_kernel(x::Float32)
return evalpoly(x, (1.0f0, -0.3333312f0, 0.13328037f0,
-0.05350336f0, 0.019975215f0, -0.0050525228f0))
end
function tanh(x::T) where T<:Union{Float32, Float64}
# Method
# mathematically tanh(x) is defined to be (exp(x)-exp(-x))/(exp(x)+exp(-x))
# 1. reduce x to non-negative by tanh(-x) = -tanh(x).
# 2. Find the branch and the expression to calculate and return it
# a) 0 <= x < H_SMALL_X
# return x
# b) H_SMALL_X <= x < 1
# -expm1(-2x)/(expm1(-2x) + 2)
# c) 1 <= x < TANH_LARGE_X
# 1 - 2/(expm1(2x) + 2)
# d) TANH_LARGE_X <= x
# Use a minimax polynomial over the range
# b) H_SMALL_X <= x < TANH_LARGE_X
# 1 - 2/(exp(2x) + 1)
# c) TANH_LARGE_X <= x
# return 1
if isnan(x)
return x
elseif isinf(x)
return copysign(T(1), x)
end

absx = abs(x)
if absx < TANH_LARGE_X(T)
# in a)
if absx < H_SMALL_X(T)
return x
end
if absx >= T(1)
# in c)
t = expm1(T(2)*absx)
z = T(1) - T(2)/(t + T(2))
else
# in b)
t = expm1(-T(2)*absx)
z = -t/(t + T(2))
end
else
# in d)
z = T(1)
end
return copysign(z, x)
abs2x = abs(2x)
abs2x >= TANH_LARGE_X(T) && return copysign(one(T), x)
abs2x <= TANH_SMALL_X(T) && return x*tanh_kernel(x*x)
k = exp(abs2x)
return copysign(1 - 2/(k+1), x)
end
tanh(x::Real) = tanh(float(x))

Expand Down