add base keyword to precision/setprecision

NEWS.md

@@ -52,6 +52,7 @@ Standard library changes
 ------------------------
 
 * `range` accepts either `stop` or `length` as a sole keyword argument ([#39241])
+* `precision` and `setprecision` now accept a `base` keyword ([#42428]).
 * The `length` function on certain ranges of certain specific element types no longer checks for integer
   overflow in most cases. The new function `checked_length` is now available, which will try to use checked
   arithmetic to error if the result may be wrapping. Or use a package such as SaferIntegers.jl when

base/float.jl

@@ -676,17 +676,31 @@ end
 
 
 """
-    precision(num::AbstractFloat)
+    precision(num::AbstractFloat; base::Integer=2)
+    precision(T::Type; base::Integer=2)
 
 Get the precision of a floating point number, as defined by the effective number of bits in
-the significand.
+the significand, or the precision of a floating-point type `T` (its current default, if
+`T` is a variable-precision type like [`BigFloat`](@ref)).
+
+If `base` is specified, then it returns the maximum corresponding
+number of significand digits in that base.
+
+!!! compat "Julia 1.8"
+    The `base` keyword requires at least Julia 1.8.
 """
 function precision end
 
-precision(::Type{Float16}) = 11
-precision(::Type{Float32}) = 24
-precision(::Type{Float64}) = 53
-precision(::T) where {T<:AbstractFloat} = precision(T)
+_precision(::Type{Float16}) = 11
+_precision(::Type{Float32}) = 24
+_precision(::Type{Float64}) = 53
+function _precision(x, base::Integer=2)
+    base > 1 || throw(DomainError(base, "`base` cannot be less than 2."))
+    p = _precision(x)
+    return base == 2 ? Int(p) : floor(Int, p / log2(base))
+end
+precision(::Type{T}; base::Integer=2) where {T<:AbstractFloat} = _precision(T, base)
+precision(::T; base::Integer=2) where {T<:AbstractFloat} = precision(T; base)
 
 """
     uabs(x::Integer)

base/mpfr.jl

@@ -11,7 +11,7 @@ import
         inv, exp, exp2, exponent, factorial, floor, fma, hypot, isinteger,
         isfinite, isinf, isnan, ldexp, log, log2, log10, max, min, mod, modf,
         nextfloat, prevfloat, promote_rule, rem, rem2pi, round, show, float,
-        sum, sqrt, string, print, trunc, precision, exp10, expm1, log1p,
+        sum, sqrt, string, print, trunc, precision, _precision, exp10, expm1, log1p,
         eps, signbit, sign, sin, cos, sincos, tan, sec, csc, cot, acos, asin, atan,
         cosh, sinh, tanh, sech, csch, coth, acosh, asinh, atanh, lerpi,
         cbrt, typemax, typemin, unsafe_trunc, floatmin, floatmax, rounding,
@@ -181,7 +181,7 @@ widen(::Type{Float64}) = BigFloat
 widen(::Type{BigFloat}) = BigFloat
 
 function BigFloat(x::BigFloat, r::MPFRRoundingMode=ROUNDING_MODE[]; precision::Integer=DEFAULT_PRECISION[])
-    if precision == MPFR.precision(x)
+    if precision == MPFR._precision(x)
         return x
     else
         z = BigFloat(;precision=precision)
@@ -192,7 +192,7 @@ function BigFloat(x::BigFloat, r::MPFRRoundingMode=ROUNDING_MODE[]; precision::I
 end
 
 function _duplicate(x::BigFloat)
-    z = BigFloat(;precision=precision(x))
+    z = BigFloat(;precision=_precision(x))
     ccall((:mpfr_set, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Int32), z, x, 0)
     return z
 end
@@ -792,37 +792,37 @@ function sign(x::BigFloat)
     return c < 0 ? -one(x) : one(x)
 end
 
-function precision(x::BigFloat)  # precision of an object of type BigFloat
+function _precision(x::BigFloat)  # precision of an object of type BigFloat
     return ccall((:mpfr_get_prec, :libmpfr), Clong, (Ref{BigFloat},), x)
 end
+precision(x::BigFloat; base::Integer=2) = _precision(x, base)
 
-"""
-    precision(BigFloat)
-
-Get the precision (in bits) currently used for [`BigFloat`](@ref) arithmetic.
-"""
-precision(::Type{BigFloat}) = Int(DEFAULT_PRECISION[]) # precision of the type BigFloat itself
+_precision(::Type{BigFloat}) = Int(DEFAULT_PRECISION[]) # default precision of the type BigFloat itself
 
 """
-    setprecision([T=BigFloat,] precision::Int)
+    setprecision([T=BigFloat,] precision::Int; base=2)
 
-Set the precision (in bits) to be used for `T` arithmetic.
+Set the precision (in bits, by default) to be used for `T` arithmetic.
+If `base` is specified, then the precision is the minimum required to give
+at least `precision` digits in the given `base`.
 
 !!! warning
 
     This function is not thread-safe. It will affect code running on all threads, but
     its behavior is undefined if called concurrently with computations that use the
     setting.
+
+!!! compat "Julia 1.8"
+    The `base` keyword requires at least Julia 1.8.
 """
-function setprecision(::Type{BigFloat}, precision::Integer)
-    if precision < 1
-        throw(DomainError(precision, "`precision` cannot be less than 1."))
-    end
-    DEFAULT_PRECISION[] = precision
+function setprecision(::Type{BigFloat}, precision::Integer; base::Integer=2)
+    base > 1 || throw(DomainError(base, "`base` cannot be less than 2."))
+    precision > 0 || throw(DomainError(precision, "`precision` cannot be less than 1."))
+    DEFAULT_PRECISION[] = base == 2 ? precision : ceil(Int, precision * log2(base))
     return precision
 end
 
-setprecision(precision::Integer) = setprecision(BigFloat, precision)
+setprecision(precision::Integer; base::Integer=2) = setprecision(BigFloat, precision; base)
 
 maxintfloat(x::BigFloat) = BigFloat(2)^precision(x)
 maxintfloat(::Type{BigFloat}) = BigFloat(2)^precision(BigFloat)
@@ -916,9 +916,9 @@ floatmin(::Type{BigFloat}) = nextfloat(zero(BigFloat))
 floatmax(::Type{BigFloat}) = prevfloat(BigFloat(Inf))
 
 """
-    setprecision(f::Function, [T=BigFloat,] precision::Integer)
+    setprecision(f::Function, [T=BigFloat,] precision::Integer; base=2)
 
-Change the `T` arithmetic precision (in bits) for the duration of `f`.
+Change the `T` arithmetic precision (in the given `base`) for the duration of `f`.
 It is logically equivalent to:
 
     old = precision(BigFloat)
@@ -929,19 +929,22 @@ It is logically equivalent to:
 Often used as `setprecision(T, precision) do ... end`
 
 Note: `nextfloat()`, `prevfloat()` do not use the precision mentioned by
-`setprecision`
+`setprecision`.
+
+!!! compat "Julia 1.8"
+    The `base` keyword requires at least Julia 1.8.
 """
-function setprecision(f::Function, ::Type{T}, prec::Integer) where T
+function setprecision(f::Function, ::Type{T}, prec::Integer; kws...) where T
     old_prec = precision(T)
-    setprecision(T, prec)
+    setprecision(T, prec; kws...)
     try
         return f()
     finally
         setprecision(T, old_prec)
     end
 end
 
-setprecision(f::Function, prec::Integer) = setprecision(f, BigFloat, prec)
+setprecision(f::Function, prec::Integer; base::Integer=2) = setprecision(f, BigFloat, prec; base)
 
 function string_mpfr(x::BigFloat, fmt::String)
     pc = Ref{Ptr{UInt8}}()

doc/src/base/numbers.md

@@ -122,7 +122,6 @@ and for [`BigInt`](@ref) the [GNU Multiple Precision Arithmetic Library (GMP)]
 ```@docs
 Base.MPFR.BigFloat(::Any, rounding::RoundingMode)
 Base.precision
-Base.MPFR.precision(::Type{BigFloat})
 Base.MPFR.setprecision
 Base.GMP.BigInt(::Any)
 Base.@big_str

test/mpfr.jl

@@ -1022,3 +1022,14 @@ end
         @test big(typeof(complex(x, x))) == typeof(big(complex(x, x)))
     end
 end
+
+@testset "precision base" begin
+    setprecision(53) do
+        @test precision(Float64, base=10) == precision(BigFloat, base=10) == 15
+    end
+    setprecision(100, base=10) do
+        @test precision(BigFloat, base=10) == 100
+        @test precision(BigFloat, base=100) == 50
+        @test precision(BigFloat) == precision(BigFloat, base=2) == 333
+    end
+end