Revision 1a416fbbb7edb6eefb801fbd17c767db086dc51a authored by Jeff Bezanson on 15 January 2018, 02:32:46 UTC, committed by GitHub on 15 January 2018, 02:32:46 UTC
also rename `HasOrder` to `Ordered` and `ArithmeticOverflows` to `ArithmeticWraps`
1 parent 1c68f8a
mpfr.jl
# This file is a part of Julia. License is MIT: https://julialang.org/license
module MPFR
export
BigFloat,
setprecision
import
Base: *, +, -, /, <, <=, ==, >, >=, ^, ceil, cmp, convert, copysign, div,
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,
gamma, lgamma, log1p,
eps, signbit, sin, cos, sincos, tan, sec, csc, cot, acos, asin, atan,
cosh, sinh, tanh, sech, csch, coth, acosh, asinh, atanh, atan2,
cbrt, typemax, typemin, unsafe_trunc, realmin, realmax, rounding,
setrounding, maxintfloat, widen, significand, frexp, tryparse, iszero,
isone, big
import Base.Rounding: rounding_raw, setrounding_raw
import Base.GMP: ClongMax, CulongMax, CdoubleMax, Limb
import Base.Math.lgamma_r
import Base.FastMath.sincos_fast
version() = VersionNumber(unsafe_string(ccall((:mpfr_get_version,:libmpfr), Ptr{Cchar}, ())))
patches() = split(unsafe_string(ccall((:mpfr_get_patches,:libmpfr), Ptr{Cchar}, ())),' ')
function __init__()
try
# set exponent to full range by default
set_emin!(get_emin_min())
set_emax!(get_emax_max())
catch ex
Base.showerror_nostdio(ex, "WARNING: Error during initialization of module MPFR")
end
end
const ROUNDING_MODE = Ref{Cint}(0)
const DEFAULT_PRECISION = Ref(256)
# Basic type and initialization definitions
"""
BigFloat <: AbstractFloat
Arbitrary precision floating point number type.
"""
mutable struct BigFloat <: AbstractFloat
prec::Clong
sign::Cint
exp::Clong
d::Ptr{Limb}
function BigFloat()
prec = precision(BigFloat)
z = new(zero(Clong), zero(Cint), zero(Clong), C_NULL)
ccall((:mpfr_init2,:libmpfr), Cvoid, (Ref{BigFloat}, Clong), z, prec)
finalizer(cglobal((:mpfr_clear, :libmpfr)), z)
return z
end
# Not recommended for general use:
function BigFloat(prec::Clong, sign::Cint, exp::Clong, d::Ptr{Cvoid})
new(prec, sign, exp, d)
end
end
"""
BigFloat(x)
Create an arbitrary precision floating point number. `x` may be an [`Integer`](@ref), a
[`Float64`](@ref) or a [`BigInt`](@ref). The usual mathematical operators are defined for
this type, and results are promoted to a [`BigFloat`](@ref).
Note that because decimal literals are converted to floating point numbers when parsed,
`BigFloat(2.1)` may not yield what you expect. You may instead prefer to initialize
constants from strings via [`parse`](@ref), or using the `big` string literal.
```jldoctest
julia> BigFloat(2.1)
2.100000000000000088817841970012523233890533447265625
julia> big"2.1"
2.099999999999999999999999999999999999999999999999999999999999999999999999999986
```
"""
BigFloat(x)
widen(::Type{Float64}) = BigFloat
widen(::Type{BigFloat}) = BigFloat
BigFloat(x::BigFloat) = x
# convert to BigFloat
for (fJ, fC) in ((:si,:Clong), (:ui,:Culong))
@eval begin
function BigFloat(x::($fC))
z = BigFloat()
ccall(($(string(:mpfr_set_,fJ)), :libmpfr), Int32, (Ref{BigFloat}, $fC, Int32), z, x, ROUNDING_MODE[])
return z
end
end
end
function BigFloat(x::Float64)
z = BigFloat()
ccall((:mpfr_set_d, :libmpfr), Int32, (Ref{BigFloat}, Float64, Int32), z, x, ROUNDING_MODE[])
if isnan(x) && signbit(x) != signbit(z)
# for some reason doing mpfr_neg in-place doesn't work here
return -z
end
return z
end
function BigFloat(x::BigInt)
z = BigFloat()
ccall((:mpfr_set_z, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigInt}, Int32), z, x, ROUNDING_MODE[])
return z
end
BigFloat(x::Integer) = BigFloat(BigInt(x))
BigFloat(x::Union{Bool,Int8,Int16,Int32}) = BigFloat(convert(Clong, x))
BigFloat(x::Union{UInt8,UInt16,UInt32}) = BigFloat(convert(Culong, x))
BigFloat(x::Union{Float16,Float32}) = BigFloat(Float64(x))
BigFloat(x::Rational) = BigFloat(numerator(x)) / BigFloat(denominator(x))
function tryparse(::Type{BigFloat}, s::AbstractString, base::Int=0)
!isempty(s) && isspace(s[end]) && return tryparse(BigFloat, rstrip(s), base)
z = BigFloat()
err = ccall((:mpfr_set_str, :libmpfr), Int32, (Ref{BigFloat}, Cstring, Int32, Int32), z, s, base, ROUNDING_MODE[])
err == 0 ? z : nothing
end
Rational(x::BigFloat) = convert(Rational{BigInt}, x)
AbstractFloat(x::BigInt) = BigFloat(x)
float(::Type{BigInt}) = BigFloat
# generic constructor with arbitrary precision:
"""
BigFloat(x, prec::Int)
Create a representation of `x` as a [`BigFloat`](@ref) with precision `prec`.
"""
function BigFloat(x, prec::Int)
setprecision(BigFloat, prec) do
BigFloat(x)
end
end
"""
BigFloat(x, prec::Int, rounding::RoundingMode)
Create a representation of `x` as a [`BigFloat`](@ref) with precision `prec` and
rounding mode `rounding`.
"""
function BigFloat(x, prec::Int, rounding::RoundingMode)
setrounding(BigFloat, rounding) do
BigFloat(x, prec)
end
end
"""
BigFloat(x, rounding::RoundingMode)
Create a representation of `x` as a [`BigFloat`](@ref) with the current global precision
and rounding mode `rounding`.
"""
function BigFloat(x::Union{Integer, AbstractFloat, String}, rounding::RoundingMode)
BigFloat(x, precision(BigFloat), rounding)
end
"""
BigFloat(x::String)
Create a representation of the string `x` as a [`BigFloat`](@ref).
"""
BigFloat(x::String) = parse(BigFloat, x)
## BigFloat -> Integer
function unsafe_cast(::Type{Int64}, x::BigFloat, ri::Cint)
ccall((:__gmpfr_mpfr_get_sj,:libmpfr), Cintmax_t, (Ref{BigFloat}, Cint), x, ri)
end
function unsafe_cast(::Type{UInt64}, x::BigFloat, ri::Cint)
ccall((:__gmpfr_mpfr_get_uj,:libmpfr), Cuintmax_t, (Ref{BigFloat}, Cint), x, ri)
end
function unsafe_cast(::Type{T}, x::BigFloat, ri::Cint) where T<:Signed
unsafe_cast(Int64, x, ri) % T
end
function unsafe_cast(::Type{T}, x::BigFloat, ri::Cint) where T<:Unsigned
unsafe_cast(UInt64, x, ri) % T
end
function unsafe_cast(::Type{BigInt}, x::BigFloat, ri::Cint)
# actually safe, just keep naming consistent
z = BigInt()
ccall((:mpfr_get_z, :libmpfr), Int32, (Ref{BigInt}, Ref{BigFloat}, Int32), z, x, ri)
return z
end
unsafe_cast(::Type{Int128}, x::BigFloat, ri::Cint) = Int128(unsafe_cast(BigInt, x, ri))
unsafe_cast(::Type{UInt128}, x::BigFloat, ri::Cint) = UInt128(unsafe_cast(BigInt, x, ri))
unsafe_cast(::Type{T}, x::BigFloat, r::RoundingMode) where {T<:Integer} = unsafe_cast(T, x, to_mpfr(r))
unsafe_trunc(::Type{T}, x::BigFloat) where {T<:Integer} = unsafe_cast(T, x, RoundToZero)
function trunc(::Type{T}, x::BigFloat) where T<:Union{Signed,Unsigned}
(typemin(T) <= x <= typemax(T)) || throw(InexactError(:trunc, T, x))
unsafe_cast(T, x, RoundToZero)
end
function floor(::Type{T}, x::BigFloat) where T<:Union{Signed,Unsigned}
(typemin(T) <= x <= typemax(T)) || throw(InexactError(:floor, T, x))
unsafe_cast(T, x, RoundDown)
end
function ceil(::Type{T}, x::BigFloat) where T<:Union{Signed,Unsigned}
(typemin(T) <= x <= typemax(T)) || throw(InexactError(:ceil, T, x))
unsafe_cast(T, x, RoundUp)
end
function round(::Type{T}, x::BigFloat) where T<:Union{Signed,Unsigned}
(typemin(T) <= x <= typemax(T)) || throw(InexactError(:round, T, x))
unsafe_cast(T, x, ROUNDING_MODE[])
end
trunc(::Type{BigInt}, x::BigFloat) = unsafe_cast(BigInt, x, RoundToZero)
floor(::Type{BigInt}, x::BigFloat) = unsafe_cast(BigInt, x, RoundDown)
ceil(::Type{BigInt}, x::BigFloat) = unsafe_cast(BigInt, x, RoundUp)
round(::Type{BigInt}, x::BigFloat) = unsafe_cast(BigInt, x, ROUNDING_MODE[])
# convert/round/trunc/floor/ceil(Integer, x) should return a BigInt
trunc(::Type{Integer}, x::BigFloat) = trunc(BigInt, x)
floor(::Type{Integer}, x::BigFloat) = floor(BigInt, x)
ceil(::Type{Integer}, x::BigFloat) = ceil(BigInt, x)
round(::Type{Integer}, x::BigFloat) = round(BigInt, x)
function Bool(x::BigFloat)
iszero(x) && return false
isone(x) && return true
throw(InexactError(:Bool, Bool, x))
end
function BigInt(x::BigFloat)
isinteger(x) || throw(InexactError(:BigInt, BigInt, x))
trunc(BigInt, x)
end
function (::Type{T})(x::BigFloat) where T<:Integer
isinteger(x) || throw(InexactError(Symbol(string(T)), T, x))
trunc(T,x)
end
## BigFloat -> AbstractFloat
_cpynansgn(x::AbstractFloat, y::BigFloat) = isnan(x) && signbit(x) != signbit(y) ? -x : x
Float64(x::BigFloat) =
_cpynansgn(ccall((:mpfr_get_d,:libmpfr), Float64, (Ref{BigFloat}, Int32), x, ROUNDING_MODE[]), x)
Float32(x::BigFloat) =
_cpynansgn(ccall((:mpfr_get_flt,:libmpfr), Float32, (Ref{BigFloat}, Int32), x, ROUNDING_MODE[]), x)
# TODO: avoid double rounding
Float16(x::BigFloat) = Float16(Float32(x))
Float64(x::BigFloat, r::RoundingMode) =
_cpynansgn(ccall((:mpfr_get_d,:libmpfr), Float64, (Ref{BigFloat}, Int32), x, to_mpfr(r)), x)
Float32(x::BigFloat, r::RoundingMode) =
_cpynansgn(ccall((:mpfr_get_flt,:libmpfr), Float32, (Ref{BigFloat}, Int32), x, to_mpfr(r)), x)
# TODO: avoid double rounding
Float16(x::BigFloat, r::RoundingMode) = Float16(Float32(x, r))
promote_rule(::Type{BigFloat}, ::Type{<:Real}) = BigFloat
promote_rule(::Type{BigInt}, ::Type{<:AbstractFloat}) = BigFloat
promote_rule(::Type{BigFloat}, ::Type{<:AbstractFloat}) = BigFloat
big(::Type{<:AbstractFloat}) = BigFloat
function (::Type{Rational{BigInt}})(x::AbstractFloat)
isnan(x) && return zero(BigInt) // zero(BigInt)
isinf(x) && return copysign(one(BigInt),x) // zero(BigInt)
iszero(x) && return zero(BigInt) // one(BigInt)
s = max(precision(x) - exponent(x), 0)
BigInt(ldexp(x,s)) // (BigInt(1) << s)
end
# Basic arithmetic without promotion
for (fJ, fC) in ((:+,:add), (:*,:mul))
@eval begin
# BigFloat
function ($fJ)(x::BigFloat, y::BigFloat)
z = BigFloat()
ccall(($(string(:mpfr_,fC)),:libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, Int32), z, x, y, ROUNDING_MODE[])
return z
end
# Unsigned Integer
function ($fJ)(x::BigFloat, c::CulongMax)
z = BigFloat()
ccall(($(string(:mpfr_,fC,:_ui)), :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Culong, Int32), z, x, c, ROUNDING_MODE[])
return z
end
($fJ)(c::CulongMax, x::BigFloat) = ($fJ)(x,c)
# Signed Integer
function ($fJ)(x::BigFloat, c::ClongMax)
z = BigFloat()
ccall(($(string(:mpfr_,fC,:_si)), :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Clong, Int32), z, x, c, ROUNDING_MODE[])
return z
end
($fJ)(c::ClongMax, x::BigFloat) = ($fJ)(x,c)
# Float32/Float64
function ($fJ)(x::BigFloat, c::CdoubleMax)
z = BigFloat()
ccall(($(string(:mpfr_,fC,:_d)), :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Cdouble, Int32), z, x, c, ROUNDING_MODE[])
return z
end
($fJ)(c::CdoubleMax, x::BigFloat) = ($fJ)(x,c)
# BigInt
function ($fJ)(x::BigFloat, c::BigInt)
z = BigFloat()
ccall(($(string(:mpfr_,fC,:_z)), :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigInt}, Int32), z, x, c, ROUNDING_MODE[])
return z
end
($fJ)(c::BigInt, x::BigFloat) = ($fJ)(x,c)
end
end
for (fJ, fC) in ((:-,:sub), (:/,:div))
@eval begin
# BigFloat
function ($fJ)(x::BigFloat, y::BigFloat)
z = BigFloat()
ccall(($(string(:mpfr_,fC)),:libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, Int32), z, x, y, ROUNDING_MODE[])
return z
end
# Unsigned Int
function ($fJ)(x::BigFloat, c::CulongMax)
z = BigFloat()
ccall(($(string(:mpfr_,fC,:_ui)), :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Culong, Int32), z, x, c, ROUNDING_MODE[])
return z
end
function ($fJ)(c::CulongMax, x::BigFloat)
z = BigFloat()
ccall(($(string(:mpfr_,:ui_,fC)), :libmpfr), Int32, (Ref{BigFloat}, Culong, Ref{BigFloat}, Int32), z, c, x, ROUNDING_MODE[])
return z
end
# Signed Integer
function ($fJ)(x::BigFloat, c::ClongMax)
z = BigFloat()
ccall(($(string(:mpfr_,fC,:_si)), :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Clong, Int32), z, x, c, ROUNDING_MODE[])
return z
end
function ($fJ)(c::ClongMax, x::BigFloat)
z = BigFloat()
ccall(($(string(:mpfr_,:si_,fC)), :libmpfr), Int32, (Ref{BigFloat}, Clong, Ref{BigFloat}, Int32), z, c, x, ROUNDING_MODE[])
return z
end
# Float32/Float64
function ($fJ)(x::BigFloat, c::CdoubleMax)
z = BigFloat()
ccall(($(string(:mpfr_,fC,:_d)), :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Cdouble, Int32), z, x, c, ROUNDING_MODE[])
return z
end
function ($fJ)(c::CdoubleMax, x::BigFloat)
z = BigFloat()
ccall(($(string(:mpfr_,:d_,fC)), :libmpfr), Int32, (Ref{BigFloat}, Cdouble, Ref{BigFloat}, Int32), z, c, x, ROUNDING_MODE[])
return z
end
# BigInt
function ($fJ)(x::BigFloat, c::BigInt)
z = BigFloat()
ccall(($(string(:mpfr_,fC,:_z)), :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigInt}, Int32), z, x, c, ROUNDING_MODE[])
return z
end
# no :mpfr_z_div function
end
end
function -(c::BigInt, x::BigFloat)
z = BigFloat()
ccall((:mpfr_z_sub, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigInt}, Ref{BigFloat}, Int32), z, c, x, ROUNDING_MODE[])
return z
end
function fma(x::BigFloat, y::BigFloat, z::BigFloat)
r = BigFloat()
ccall(("mpfr_fma",:libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, Int32), r, x, y, z, ROUNDING_MODE[])
return r
end
# div
# BigFloat
function div(x::BigFloat, y::BigFloat)
z = BigFloat()
ccall((:mpfr_div,:libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, Int32), z, x, y, to_mpfr(RoundToZero))
ccall((:mpfr_trunc, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}), z, z)
return z
end
# Unsigned Int
function div(x::BigFloat, c::CulongMax)
z = BigFloat()
ccall((:mpfr_div_ui, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Culong, Int32), z, x, c, to_mpfr(RoundToZero))
ccall((:mpfr_trunc, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}), z, z)
return z
end
function div(c::CulongMax, x::BigFloat)
z = BigFloat()
ccall((:mpfr_ui_div, :libmpfr), Int32, (Ref{BigFloat}, Culong, Ref{BigFloat}, Int32), z, c, x, to_mpfr(RoundToZero))
ccall((:mpfr_trunc, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}), z, z)
return z
end
# Signed Integer
function div(x::BigFloat, c::ClongMax)
z = BigFloat()
ccall((:mpfr_div_si, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Clong, Int32), z, x, c, to_mpfr(RoundToZero))
ccall((:mpfr_trunc, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}), z, z)
return z
end
function div(c::ClongMax, x::BigFloat)
z = BigFloat()
ccall((:mpfr_si_div, :libmpfr), Int32, (Ref{BigFloat}, Clong, Ref{BigFloat}, Int32), z, c, x, to_mpfr(RoundToZero))
ccall((:mpfr_trunc, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}), z, z)
return z
end
# Float32/Float64
function div(x::BigFloat, c::CdoubleMax)
z = BigFloat()
ccall((:mpfr_div_d, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Cdouble, Int32), z, x, c, to_mpfr(RoundToZero))
ccall((:mpfr_trunc, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}), z, z)
return z
end
function div(c::CdoubleMax, x::BigFloat)
z = BigFloat()
ccall((:mpfr_d_div, :libmpfr), Int32, (Ref{BigFloat}, Cdouble, Ref{BigFloat}, Int32), z, c, x, to_mpfr(RoundToZero))
ccall((:mpfr_trunc, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}), z, z)
return z
end
# BigInt
function div(x::BigFloat, c::BigInt)
z = BigFloat()
ccall((:mpfr_div_z, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigInt}, Int32), z, x, c, to_mpfr(RoundToZero))
ccall((:mpfr_trunc, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}), z, z)
return z
end
# More efficient commutative operations
for (fJ, fC, fI) in ((:+, :add, 0), (:*, :mul, 1))
@eval begin
function ($fJ)(a::BigFloat, b::BigFloat, c::BigFloat)
z = BigFloat()
ccall(($(string(:mpfr_,fC)), :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, Int32), z, a, b, ROUNDING_MODE[])
ccall(($(string(:mpfr_,fC)), :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, Int32), z, z, c, ROUNDING_MODE[])
return z
end
function ($fJ)(a::BigFloat, b::BigFloat, c::BigFloat, d::BigFloat)
z = BigFloat()
ccall(($(string(:mpfr_,fC)), :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, Int32), z, a, b, ROUNDING_MODE[])
ccall(($(string(:mpfr_,fC)), :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, Int32), z, z, c, ROUNDING_MODE[])
ccall(($(string(:mpfr_,fC)), :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, Int32), z, z, d, ROUNDING_MODE[])
return z
end
function ($fJ)(a::BigFloat, b::BigFloat, c::BigFloat, d::BigFloat, e::BigFloat)
z = BigFloat()
ccall(($(string(:mpfr_,fC)), :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, Int32), z, a, b, ROUNDING_MODE[])
ccall(($(string(:mpfr_,fC)), :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, Int32), z, z, c, ROUNDING_MODE[])
ccall(($(string(:mpfr_,fC)), :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, Int32), z, z, d, ROUNDING_MODE[])
ccall(($(string(:mpfr_,fC)), :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, Int32), z, z, e, ROUNDING_MODE[])
return z
end
end
end
function -(x::BigFloat)
z = BigFloat()
ccall((:mpfr_neg, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Int32), z, x, ROUNDING_MODE[])
return z
end
function sqrt(x::BigFloat)
isnan(x) && return x
z = BigFloat()
ccall((:mpfr_sqrt, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Int32), z, x, ROUNDING_MODE[])
isnan(z) && throw(DomainError(x, "NaN result for non-NaN input."))
return z
end
sqrt(x::BigInt) = sqrt(BigFloat(x))
function ^(x::BigFloat, y::BigFloat)
z = BigFloat()
ccall((:mpfr_pow, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, Int32), z, x, y, ROUNDING_MODE[])
return z
end
function ^(x::BigFloat, y::CulongMax)
z = BigFloat()
ccall((:mpfr_pow_ui, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Culong, Int32), z, x, y, ROUNDING_MODE[])
return z
end
function ^(x::BigFloat, y::ClongMax)
z = BigFloat()
ccall((:mpfr_pow_si, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Clong, Int32), z, x, y, ROUNDING_MODE[])
return z
end
function ^(x::BigFloat, y::BigInt)
z = BigFloat()
ccall((:mpfr_pow_z, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigInt}, Int32), z, x, y, ROUNDING_MODE[])
return z
end
^(x::BigFloat, y::Integer) = typemin(Clong) <= y <= typemax(Clong) ? x^Clong(y) : x^BigInt(y)
^(x::BigFloat, y::Unsigned) = typemin(Culong) <= y <= typemax(Culong) ? x^Culong(y) : x^BigInt(y)
for f in (:exp, :exp2, :exp10, :expm1, :cosh, :sinh, :tanh, :sech, :csch, :coth, :cbrt)
@eval function $f(x::BigFloat)
z = BigFloat()
ccall(($(string(:mpfr_,f)), :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Int32), z, x, ROUNDING_MODE[])
return z
end
end
function sincos_fast(v::BigFloat)
s = BigFloat()
c = BigFloat()
ccall((:mpfr_sin_cos, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, Int32), s, c, v, ROUNDING_MODE[])
return (s, c)
end
sincos(v::BigFloat) = sincos_fast(v)
# return log(2)
function big_ln2()
c = BigFloat()
ccall((:mpfr_const_log2, :libmpfr), Cint, (Ref{BigFloat}, Int32), c, MPFR.ROUNDING_MODE[])
return c
end
function ldexp(x::BigFloat, n::Clong)
z = BigFloat()
ccall((:mpfr_mul_2si, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Clong, Int32), z, x, n, ROUNDING_MODE[])
return z
end
function ldexp(x::BigFloat, n::Culong)
z = BigFloat()
ccall((:mpfr_mul_2ui, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Culong, Int32), z, x, n, ROUNDING_MODE[])
return z
end
ldexp(x::BigFloat, n::ClongMax) = ldexp(x, convert(Clong, n))
ldexp(x::BigFloat, n::CulongMax) = ldexp(x, convert(Culong, n))
ldexp(x::BigFloat, n::Integer) = x * exp2(BigFloat(n))
function factorial(x::BigFloat)
if x < 0 || !isinteger(x)
throw(DomainError(x, "Must be a non-negative integer."))
end
ui = convert(Culong, x)
z = BigFloat()
ccall((:mpfr_fac_ui, :libmpfr), Int32, (Ref{BigFloat}, Culong, Int32), z, ui, ROUNDING_MODE[])
return z
end
function hypot(x::BigFloat, y::BigFloat)
z = BigFloat()
ccall((:mpfr_hypot, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, Int32), z, x, y, ROUNDING_MODE[])
return z
end
for f in (:log, :log2, :log10)
@eval function $f(x::BigFloat)
if x < 0
throw(DomainError(x, string($f, " will only return a complex result if called ",
"with a complex argument. Try ", $f, "(complex(x)).")))
end
z = BigFloat()
ccall(($(string(:mpfr_,f)), :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Int32), z, x, ROUNDING_MODE[])
return z
end
end
function log1p(x::BigFloat)
if x < -1
throw(DomainError(x, string("log1p will only return a complex result if called ",
"with a complex argument. Try log1p(complex(x)).")))
end
z = BigFloat()
ccall((:mpfr_log1p, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Int32), z, x, ROUNDING_MODE[])
return z
end
function max(x::BigFloat, y::BigFloat)
isnan(x) && return x
isnan(y) && return y
z = BigFloat()
ccall((:mpfr_max, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, Int32), z, x, y, ROUNDING_MODE[])
return z
end
function min(x::BigFloat, y::BigFloat)
isnan(x) && return x
isnan(y) && return y
z = BigFloat()
ccall((:mpfr_min, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, Int32), z, x, y, ROUNDING_MODE[])
return z
end
function modf(x::BigFloat)
isinf(x) && return (BigFloat(NaN), x)
zint = BigFloat()
zfloat = BigFloat()
ccall((:mpfr_modf, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, Int32), zint, zfloat, x, ROUNDING_MODE[])
return (zfloat, zint)
end
function rem(x::BigFloat, y::BigFloat)
z = BigFloat()
ccall((:mpfr_fmod, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, Int32), z, x, y, ROUNDING_MODE[])
return z
end
function rem(x::BigFloat, y::BigFloat, ::RoundingMode{:Nearest})
z = BigFloat()
ccall((:mpfr_remainder, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, Int32), z, x, y, ROUNDING_MODE[])
return z
end
# TODO: use a higher-precision BigFloat(pi) here?
rem2pi(x::BigFloat, r::RoundingMode) = rem(x, 2*BigFloat(pi), r)
function sum(arr::AbstractArray{BigFloat})
z = BigFloat(0)
for i in arr
ccall((:mpfr_add, :libmpfr), Int32,
(Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, Cint), z, z, i, 0)
end
return z
end
# Functions for which NaN results are converted to DomainError, following Base
for f in (:sin, :cos, :tan, :sec, :csc, :acos, :asin, :atan, :acosh, :asinh, :atanh, :gamma)
@eval begin
function ($f)(x::BigFloat)
isnan(x) && return x
z = BigFloat()
ccall(($(string(:mpfr_,f)), :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Int32), z, x, ROUNDING_MODE[])
isnan(z) && throw(DomainError(x, "NaN result for non-NaN input."))
return z
end
end
end
# log of absolute value of gamma function
const lgamma_signp = Ref{Cint}()
function lgamma(x::BigFloat)
z = BigFloat()
ccall((:mpfr_lgamma,:libmpfr), Cint, (Ref{BigFloat}, Ref{Cint}, Ref{BigFloat}, Int32), z, lgamma_signp, x, ROUNDING_MODE[])
return z
end
lgamma_r(x::BigFloat) = (lgamma(x), lgamma_signp[])
function atan2(y::BigFloat, x::BigFloat)
z = BigFloat()
ccall((:mpfr_atan2, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, Int32), z, y, x, ROUNDING_MODE[])
return z
end
# Utility functions
==(x::BigFloat, y::BigFloat) = ccall((:mpfr_equal_p, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}), x, y) != 0
<=(x::BigFloat, y::BigFloat) = ccall((:mpfr_lessequal_p, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}), x, y) != 0
>=(x::BigFloat, y::BigFloat) = ccall((:mpfr_greaterequal_p, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}), x, y) != 0
<(x::BigFloat, y::BigFloat) = ccall((:mpfr_less_p, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}), x, y) != 0
>(x::BigFloat, y::BigFloat) = ccall((:mpfr_greater_p, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}), x, y) != 0
function cmp(x::BigFloat, y::BigInt)
isnan(x) && return 1
ccall((:mpfr_cmp_z, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigInt}), x, y)
end
function cmp(x::BigFloat, y::ClongMax)
isnan(x) && return 1
ccall((:mpfr_cmp_si, :libmpfr), Int32, (Ref{BigFloat}, Clong), x, y)
end
function cmp(x::BigFloat, y::CulongMax)
isnan(x) && return 1
ccall((:mpfr_cmp_ui, :libmpfr), Int32, (Ref{BigFloat}, Culong), x, y)
end
cmp(x::BigFloat, y::Integer) = cmp(x,big(y))
cmp(x::Integer, y::BigFloat) = -cmp(y,x)
function cmp(x::BigFloat, y::CdoubleMax)
isnan(x) && return isnan(y) ? 0 : 1
isnan(y) && return -1
ccall((:mpfr_cmp_d, :libmpfr), Int32, (Ref{BigFloat}, Cdouble), x, y)
end
cmp(x::CdoubleMax, y::BigFloat) = -cmp(y,x)
==(x::BigFloat, y::Integer) = !isnan(x) && cmp(x,y) == 0
==(x::Integer, y::BigFloat) = y == x
==(x::BigFloat, y::CdoubleMax) = !isnan(x) && !isnan(y) && cmp(x,y) == 0
==(x::CdoubleMax, y::BigFloat) = y == x
<(x::BigFloat, y::Integer) = !isnan(x) && cmp(x,y) < 0
<(x::Integer, y::BigFloat) = !isnan(y) && cmp(y,x) > 0
<(x::BigFloat, y::CdoubleMax) = !isnan(x) && !isnan(y) && cmp(x,y) < 0
<(x::CdoubleMax, y::BigFloat) = !isnan(x) && !isnan(y) && cmp(y,x) > 0
<=(x::BigFloat, y::Integer) = !isnan(x) && cmp(x,y) <= 0
<=(x::Integer, y::BigFloat) = !isnan(y) && cmp(y,x) >= 0
<=(x::BigFloat, y::CdoubleMax) = !isnan(x) && !isnan(y) && cmp(x,y) <= 0
<=(x::CdoubleMax, y::BigFloat) = !isnan(x) && !isnan(y) && cmp(y,x) >= 0
signbit(x::BigFloat) = ccall((:mpfr_signbit, :libmpfr), Int32, (Ref{BigFloat},), x) != 0
function precision(x::BigFloat) # precision of an object of type BigFloat
return ccall((:mpfr_get_prec, :libmpfr), Clong, (Ref{BigFloat},), x)
end
"""
precision(BigFloat)
Get the precision (in bits) currently used for [`BigFloat`](@ref) arithmetic.
"""
precision(::Type{BigFloat}) = DEFAULT_PRECISION[] # precision of the type BigFloat itself
"""
setprecision([T=BigFloat,] precision::Int)
Set the precision (in bits) to be used for `T` arithmetic.
"""
function setprecision(::Type{BigFloat}, precision::Int)
if precision < 2
throw(DomainError(precision, "`precision` cannot be less than 2."))
end
DEFAULT_PRECISION[] = precision
end
setprecision(precision::Int) = setprecision(BigFloat, precision)
maxintfloat(x::BigFloat) = BigFloat(2)^precision(x)
maxintfloat(::Type{BigFloat}) = BigFloat(2)^precision(BigFloat)
to_mpfr(::RoundingMode{:Nearest}) = Cint(0)
to_mpfr(::RoundingMode{:ToZero}) = Cint(1)
to_mpfr(::RoundingMode{:Up}) = Cint(2)
to_mpfr(::RoundingMode{:Down}) = Cint(3)
to_mpfr(::RoundingMode{:FromZero}) = Cint(4)
function from_mpfr(c::Integer)
if c == 0
return RoundNearest
elseif c == 1
return RoundToZero
elseif c == 2
return RoundUp
elseif c == 3
return RoundDown
elseif c == 4
return RoundFromZero
else
throw(ArgumentError("invalid MPFR rounding mode code: $c"))
end
RoundingMode(c)
end
rounding_raw(::Type{BigFloat}) = ROUNDING_MODE[]
setrounding_raw(::Type{BigFloat},i::Integer) = ROUNDING_MODE[] = i
rounding(::Type{BigFloat}) = from_mpfr(rounding_raw(BigFloat))
setrounding(::Type{BigFloat},r::RoundingMode) = setrounding_raw(BigFloat,to_mpfr(r))
function copysign(x::BigFloat, y::BigFloat)
z = BigFloat()
ccall((:mpfr_copysign, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, Int32), z, x, y, ROUNDING_MODE[])
return z
end
function exponent(x::BigFloat)
if iszero(x) || !isfinite(x)
throw(DomainError(x, "`x` must be non-zero and finite."))
end
# The '- 1' is to make it work as Base.exponent
return ccall((:mpfr_get_exp, :libmpfr), Clong, (Ref{BigFloat},), x) - 1
end
function frexp(x::BigFloat)
z = BigFloat()
c = Ref{Clong}()
ccall((:mpfr_frexp, :libmpfr), Int32, (Ptr{Clong}, Ref{BigFloat}, Ref{BigFloat}, Cint), c, z, x, ROUNDING_MODE[])
return (z, c[])
end
function significand(x::BigFloat)
z = BigFloat()
c = Ref{Clong}()
ccall((:mpfr_frexp, :libmpfr), Int32, (Ptr{Clong}, Ref{BigFloat}, Ref{BigFloat}, Cint), c, z, x, ROUNDING_MODE[])
# Double the significand to make it work as Base.significand
ccall((:mpfr_mul_si, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Clong, Int32), z, z, 2, ROUNDING_MODE[])
return z
end
function isinteger(x::BigFloat)
return ccall((:mpfr_integer_p, :libmpfr), Int32, (Ref{BigFloat},), x) != 0
end
for f in (:ceil, :floor, :trunc)
@eval begin
function ($f)(x::BigFloat)
z = BigFloat()
ccall(($(string(:mpfr_,f)), :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}), z, x)
return z
end
end
end
function round(x::BigFloat)
z = BigFloat()
ccall((:mpfr_rint, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Cint), z, x, ROUNDING_MODE[])
return z
end
function round(x::BigFloat,::RoundingMode{:NearestTiesAway})
z = BigFloat()
ccall((:mpfr_round, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}), z, x)
return z
end
function isinf(x::BigFloat)
return ccall((:mpfr_inf_p, :libmpfr), Int32, (Ref{BigFloat},), x) != 0
end
function isnan(x::BigFloat)
return ccall((:mpfr_nan_p, :libmpfr), Int32, (Ref{BigFloat},), x) != 0
end
isfinite(x::BigFloat) = !isinf(x) && !isnan(x)
iszero(x::BigFloat) = x == Clong(0)
isone(x::BigFloat) = x == Clong(1)
@eval typemax(::Type{BigFloat}) = $(BigFloat(Inf))
@eval typemin(::Type{BigFloat}) = $(BigFloat(-Inf))
function nextfloat(x::BigFloat)
z = BigFloat()
ccall((:mpfr_set, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Int32),
z, x, ROUNDING_MODE[])
ccall((:mpfr_nextabove, :libmpfr), Int32, (Ref{BigFloat},), z) != 0
return z
end
function prevfloat(x::BigFloat)
z = BigFloat()
ccall((:mpfr_set, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Int32),
z, x, ROUNDING_MODE[])
ccall((:mpfr_nextbelow, :libmpfr), Int32, (Ref{BigFloat},), z) != 0
return z
end
eps(::Type{BigFloat}) = nextfloat(BigFloat(1)) - BigFloat(1)
realmin(::Type{BigFloat}) = nextfloat(zero(BigFloat))
realmax(::Type{BigFloat}) = prevfloat(BigFloat(Inf))
"""
setprecision(f::Function, [T=BigFloat,] precision::Integer)
Change the `T` arithmetic precision (in bits) for the duration of `f`.
It is logically equivalent to:
old = precision(BigFloat)
setprecision(BigFloat, precision)
f()
setprecision(BigFloat, old)
Often used as `setprecision(T, precision) do ... end`
"""
function setprecision(f::Function, ::Type{T}, prec::Integer) where T
old_prec = precision(T)
setprecision(T, prec)
try
return f()
finally
setprecision(T, old_prec)
end
end
setprecision(f::Function, precision::Integer) = setprecision(f, BigFloat, precision)
function string_mpfr(x::BigFloat, fmt::String)
buf = Base.StringVector(0)
s = _calculate_buffer_size!(buf, fmt, x)
resize!(buf, s)
_fill_buffer!(buf, fmt, x)
String(buf)
end
function _calculate_buffer_size!(buf, fmt, x::BigFloat)
ccall((:mpfr_snprintf,:libmpfr),
Int32, (Ptr{UInt8}, Culong, Ptr{UInt8}, Ref{BigFloat}...),
buf, 0, fmt, x)
end
function _fill_buffer!(buf, fmt, x::BigFloat)
s = length(buf)
# we temporarily need one more item in buffer to capture null termination
resize!(buf, s + 1)
n = ccall((:mpfr_sprintf,:libmpfr), Int32, (Ptr{UInt8}, Ptr{UInt8}, Ref{BigFloat}...), buf, fmt, x)
@assert n + 1 == length(buf)
@assert last(buf) == 0x00
resize!(buf, s)
end
function _prettify_bigfloat(s::String)::String
mantissa, exponent = split(s, 'e')
if !contains(mantissa, '.')
mantissa = string(mantissa, '.')
end
mantissa = rstrip(mantissa, '0')
if endswith(mantissa, '.')
mantissa = string(mantissa, '0')
end
if exponent == "+00"
mantissa
else
string(mantissa, 'e', exponent)
end
end
function _string(x::BigFloat, fmt::String)::String
isfinite(x) || return string(Float64(x))
_prettify_bigfloat(string_mpfr(x, fmt))
end
_string(x::BigFloat) = _string(x, "%.Re")
_string(x::BigFloat, k::Integer) = _string(x, "%.$(k)Re")
string(b::BigFloat) = _string(b)
print(io::IO, b::BigFloat) = print(io, string(b))
function show(io::IO, b::BigFloat)
if get(io, :compact, false)
print(io, _string(b, 5))
else
print(io, _string(b))
end
end
# get/set exponent min/max
get_emax() = ccall((:mpfr_get_emax, :libmpfr), Clong, ())
get_emax_min() = ccall((:mpfr_get_emax_min, :libmpfr), Clong, ())
get_emax_max() = ccall((:mpfr_get_emax_max, :libmpfr), Clong, ())
get_emin() = ccall((:mpfr_get_emin, :libmpfr), Clong, ())
get_emin_min() = ccall((:mpfr_get_emin_min, :libmpfr), Clong, ())
get_emin_max() = ccall((:mpfr_get_emin_max, :libmpfr), Clong, ())
set_emax!(x) = ccall((:mpfr_set_emax, :libmpfr), Cvoid, (Clong,), x)
set_emin!(x) = ccall((:mpfr_set_emin, :libmpfr), Cvoid, (Clong,), x)
function Base.deepcopy_internal(x::BigFloat, stackdict::ObjectIdDict)
haskey(stackdict, x) && return stackdict[x]
prec = precision(x)
y = BigFloat(zero(Clong), zero(Cint), zero(Clong), C_NULL)
ccall((:mpfr_init2,:libmpfr), Cvoid, (Ref{BigFloat}, Clong), y, prec)
finalizer(cglobal((:mpfr_clear, :libmpfr)), y)
ccall((:mpfr_set, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Int32), y, x, ROUNDING_MODE[])
stackdict[x] = y
return y
end
function Base.lerpi(j::Integer, d::Integer, a::BigFloat, b::BigFloat)
t = BigFloat(j)/d
fma(t, b, fma(-t, a, a))
end
end #module
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