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Correct exponent_max to conform to IEEE754-2008 #24978

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Correct exponent_max to conform to IEEE754-2008 #24978

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1fbeb37
Exponent exponent_max returns actual maximum exponent, not the sentinel.
mschauer Dec 7, 2017
0c506de
Clarify doc-string of `exponent_max`.
mschauer Sep 5, 2019
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21 changes: 18 additions & 3 deletions base/math.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -37,13 +37,28 @@ end
"Complex(x)^y, or similar.")))
end

"""
exponent_max(T)

Maximum value of [`exponent`](@ref) for a real floating point number of type `T`.
for example 1023 for `Float64`. `exponent_max(T) + 1` is a possible value of
the exponent field with bias, but it is used as sentinel value for `Inf` and `NaN`.
"""
function exponent_max end

"""
exponent_raw_max(T)

The maximum value of the exponent field of floating point type `T` without bias,
that is the maximum integer value representable by `exponent_bits(T)` bits.
"""
function exponent_raw_max end

for T in (Float16, Float32, Float64)
@eval significand_bits(::Type{$T}) = $(trailing_ones(significand_mask(T)))
@eval exponent_bits(::Type{$T}) = $(sizeof(T)*8 - significand_bits(T) - 1)
@eval exponent_bias(::Type{$T}) = $(Int(exponent_one(T) >> significand_bits(T)))
# maximum float exponent
@eval exponent_max(::Type{$T}) = $(Int(exponent_mask(T) >> significand_bits(T)) - exponent_bias(T))
# maximum float exponent without bias
@eval exponent_max(::Type{$T}) = $(Int(exponent_mask(T) >> significand_bits(T)) - exponent_bias(T) - 1)
@eval exponent_raw_max(::Type{$T}) = $(Int(exponent_mask(T) >> significand_bits(T)))
end

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2 changes: 1 addition & 1 deletion base/special/exp.jl
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Expand Up @@ -116,7 +116,7 @@ function exp(x::T) where T<:Union{Float32,Float64}
# scale back
if k > -significand_bits(T)
# multiply by 2.0 first to prevent overflow, which helps extends the range
k == exponent_max(T) && return y * T(2.0) * T(2.0)^(exponent_max(T) - 1)
k == exponent_max(T) + 1 && return y * T(2.0) * T(2.0)^exponent_max(T)
twopk = reinterpret(T, rem(exponent_bias(T) + k, uinttype(T)) << significand_bits(T))
return y*twopk
else
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2 changes: 1 addition & 1 deletion base/special/exp10.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -118,7 +118,7 @@ function exp10(x::T) where T<:Union{Float32,Float64}
# scale back
if k > -significand_bits(T)
# multiply by 2.0 first to prevent overflow, extending the range
k == exponent_max(T) && return y * T(2.0) * T(2.0)^(exponent_max(T) - 1)
k == exponent_max(T) + 1 && return y * T(2.0) * T(2.0)^exponent_max(T)
twopk = reinterpret(T, rem(exponent_bias(T) + k, uinttype(T)) << significand_bits(T))
return y*twopk
else
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