mpfr.jl
# This file is a part of Julia. License is MIT: http://julialang.org/license
module MPFR
export
BigFloat,
setprecision,
big_str
import
Base: (*), +, -, /, <, <=, ==, >, >=, ^, besselj, besselj0, besselj1, bessely,
bessely0, bessely1, 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, round, show,
sum, sqrt, string, print, trunc, precision, exp10, expm1,
gamma, lgamma, digamma, erf, erfc, zeta, eta, log1p, airyai,
eps, signbit, sin, cos, 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
import Base.Rounding: rounding_raw, setrounding_raw
import Base.GMP: ClongMax, CulongMax, CdoubleMax
import Base.Math.lgamma_r
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 = Cint[0]
const DEFAULT_PRECISION = [256]
# Basic type and initialization definitions
type BigFloat <: AbstractFloat
prec::Clong
sign::Cint
exp::Clong
d::Ptr{Culong}
function BigFloat()
N = precision(BigFloat)
z = new(zero(Clong), zero(Cint), zero(Clong), C_NULL)
ccall((:mpfr_init2,:libmpfr), Void, (Ptr{BigFloat}, Clong), &z, N)
finalizer(z, Base.GMP._mpfr_clear_func)
return z
end
# Not recommended for general use
function BigFloat(prec::Clong, sign::Cint, exp::Clong, d::Ptr{Void})
new(prec, sign, exp, d)
end
end
widen(::Type{Float64}) = BigFloat
widen(::Type{BigFloat}) = BigFloat
convert(::Type{BigFloat}, x::BigFloat) = x
# convert to BigFloat
for (fJ, fC) in ((:si,:Clong), (:ui,:Culong), (:d,:Float64))
@eval begin
function convert(::Type{BigFloat}, x::($fC))
z = BigFloat()
ccall(($(string(:mpfr_set_,fJ)), :libmpfr), Int32, (Ptr{BigFloat}, ($fC), Int32), &z, x, ROUNDING_MODE[end])
return z
end
end
end
function convert(::Type{BigFloat}, x::BigInt)
z = BigFloat()
ccall((:mpfr_set_z, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigInt}, Int32), &z, &x, ROUNDING_MODE[end])
return z
end
convert(::Type{BigFloat}, x::Integer) = BigFloat(BigInt(x))
convert(::Type{BigFloat}, x::Union{Bool,Int8,Int16,Int32}) = BigFloat(convert(Clong,x))
convert(::Type{BigFloat}, x::Union{UInt8,UInt16,UInt32}) = BigFloat(convert(Culong,x))
convert(::Type{BigFloat}, x::Union{Float16,Float32}) = BigFloat(Float64(x))
convert(::Type{BigFloat}, x::Rational) = BigFloat(num(x)) / BigFloat(den(x))
function tryparse(::Type{BigFloat}, s::AbstractString, base::Int=0)
z = BigFloat()
err = ccall((:mpfr_set_str, :libmpfr), Int32, (Ptr{BigFloat}, Cstring, Int32, Int32), &z, s, base, ROUNDING_MODE[end])
err == 0 ? Nullable(z) : Nullable{BigFloat}()
end
convert(::Type{Rational}, x::BigFloat) = convert(Rational{BigInt}, x)
convert(::Type{AbstractFloat}, x::BigInt) = BigFloat(x)
## BigFloat -> Integer
function unsafe_cast(::Type{Int64}, x::BigFloat, ri::Cint)
ccall((:__gmpfr_mpfr_get_sj,:libmpfr), Cintmax_t,
(Ptr{BigFloat}, Cint), &x, ri)
end
function unsafe_cast(::Type{UInt64}, x::BigFloat, ri::Cint)
ccall((:__gmpfr_mpfr_get_uj,:libmpfr), Cuintmax_t,
(Ptr{BigFloat}, Cint), &x, ri)
end
function unsafe_cast{T<:Signed}(::Type{T}, x::BigFloat, ri::Cint)
unsafe_cast(Int64, x, ri) % T
end
function unsafe_cast{T<:Unsigned}(::Type{T}, x::BigFloat, ri::Cint)
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, (Ptr{BigInt}, Ptr{BigFloat}, Int32),
&z, &x, ri)
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{T<:Integer}(::Type{T}, x::BigFloat, r::RoundingMode) = unsafe_cast(T,x,to_mpfr(r))
unsafe_trunc{T<:Integer}(::Type{T}, x::BigFloat) = unsafe_cast(T,x,RoundToZero)
function trunc{T<:Union{Signed,Unsigned}}(::Type{T}, x::BigFloat)
(typemin(T) <= x <= typemax(T)) || throw(InexactError())
unsafe_cast(T,x,RoundToZero)
end
function floor{T<:Union{Signed,Unsigned}}(::Type{T}, x::BigFloat)
(typemin(T) <= x <= typemax(T)) || throw(InexactError())
unsafe_cast(T,x,RoundDown)
end
function ceil{T<:Union{Signed,Unsigned}}(::Type{T}, x::BigFloat)
(typemin(T) <= x <= typemax(T)) || throw(InexactError())
unsafe_cast(T,x,RoundUp)
end
function round{T<:Union{Signed,Unsigned}}(::Type{T}, x::BigFloat)
(typemin(T) <= x <= typemax(T)) || throw(InexactError())
unsafe_cast(T,x,ROUNDING_MODE[end])
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[end])
# 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)
convert(::Type{Bool}, x::BigFloat) = x==0 ? false : x==1 ? true : throw(InexactError())
function convert(::Type{BigInt},x::BigFloat)
isinteger(x) || throw(InexactError())
trunc(BigInt,x)
end
function convert{T<:Integer}(::Type{T},x::BigFloat)
isinteger(x) || throw(InexactError())
trunc(T,x)
end
## BigFloat -> AbstractFloat
convert(::Type{Float64}, x::BigFloat) =
ccall((:mpfr_get_d,:libmpfr), Float64, (Ptr{BigFloat},Int32), &x, ROUNDING_MODE[end])
convert(::Type{Float32}, x::BigFloat) =
ccall((:mpfr_get_flt,:libmpfr), Float32, (Ptr{BigFloat},Int32), &x, ROUNDING_MODE[end])
# TODO: avoid double rounding
convert(::Type{Float16}, x::BigFloat) = convert(Float16, convert(Float32, x))
call(::Type{Float64}, x::BigFloat, r::RoundingMode) =
ccall((:mpfr_get_d,:libmpfr), Float64, (Ptr{BigFloat},Int32), &x, to_mpfr(r))
call(::Type{Float32}, x::BigFloat, r::RoundingMode) =
ccall((:mpfr_get_flt,:libmpfr), Float32, (Ptr{BigFloat},Int32), &x, to_mpfr(r))
# TODO: avoid double rounding
call(::Type{Float16}, x::BigFloat, r::RoundingMode) =
convert(Float16, call(Float32, x, r))
promote_rule{T<:Real}(::Type{BigFloat}, ::Type{T}) = BigFloat
promote_rule{T<:AbstractFloat}(::Type{BigInt},::Type{T}) = BigFloat
promote_rule{T<:AbstractFloat}(::Type{BigFloat},::Type{T}) = BigFloat
function convert(::Type{Rational{BigInt}}, x::AbstractFloat)
if isnan(x); return zero(BigInt)//zero(BigInt); end
if isinf(x); return copysign(one(BigInt),x)//zero(BigInt); end
if x == 0; return zero(BigInt) // one(BigInt); end
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(($(string(:mpfr_,fC)),:libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Ptr{BigFloat}, Int32), &z, &x, &y, ROUNDING_MODE[end])
return z
end
# Unsigned Integer
function ($fJ)(x::BigFloat, c::CulongMax)
z = BigFloat()
ccall(($(string(:mpfr_,fC,:_ui)), :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Culong, Int32), &z, &x, c, ROUNDING_MODE[end])
return z
end
($fJ)(c::CulongMax, x::BigFloat) = ($fJ)(x,c)
# Signed Integer
function ($fJ)(x::BigFloat, c::ClongMax)
z = BigFloat()
ccall(($(string(:mpfr_,fC,:_si)), :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Clong, Int32), &z, &x, c, ROUNDING_MODE[end])
return z
end
($fJ)(c::ClongMax, x::BigFloat) = ($fJ)(x,c)
# Float32/Float64
function ($fJ)(x::BigFloat, c::CdoubleMax)
z = BigFloat()
ccall(($(string(:mpfr_,fC,:_d)), :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Cdouble, Int32), &z, &x, c, ROUNDING_MODE[end])
return z
end
($fJ)(c::CdoubleMax, x::BigFloat) = ($fJ)(x,c)
# BigInt
function ($fJ)(x::BigFloat, c::BigInt)
z = BigFloat()
ccall(($(string(:mpfr_,fC,:_z)), :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Ptr{BigInt}, Int32), &z, &x, &c, ROUNDING_MODE[end])
return z
end
($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(($(string(:mpfr_,fC)),:libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Ptr{BigFloat}, Int32), &z, &x, &y, ROUNDING_MODE[end])
return z
end
# Unsigned Int
function ($fJ)(x::BigFloat, c::CulongMax)
z = BigFloat()
ccall(($(string(:mpfr_,fC,:_ui)), :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Culong, Int32), &z, &x, c, ROUNDING_MODE[end])
return z
end
function ($fJ)(c::CulongMax, x::BigFloat)
z = BigFloat()
ccall(($(string(:mpfr_,:ui_,fC)), :libmpfr), Int32, (Ptr{BigFloat}, Culong, Ptr{BigFloat}, Int32), &z, c, &x, ROUNDING_MODE[end])
return z
end
# Signed Integer
function ($fJ)(x::BigFloat, c::ClongMax)
z = BigFloat()
ccall(($(string(:mpfr_,fC,:_si)), :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Clong, Int32), &z, &x, c, ROUNDING_MODE[end])
return z
end
function ($fJ)(c::ClongMax, x::BigFloat)
z = BigFloat()
ccall(($(string(:mpfr_,:si_,fC)), :libmpfr), Int32, (Ptr{BigFloat}, Clong, Ptr{BigFloat}, Int32), &z, c, &x, ROUNDING_MODE[end])
return z
end
# Float32/Float64
function ($fJ)(x::BigFloat, c::CdoubleMax)
z = BigFloat()
ccall(($(string(:mpfr_,fC,:_d)), :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Cdouble, Int32), &z, &x, c, ROUNDING_MODE[end])
return z
end
function ($fJ)(c::CdoubleMax, x::BigFloat)
z = BigFloat()
ccall(($(string(:mpfr_,:d_,fC)), :libmpfr), Int32, (Ptr{BigFloat}, Cdouble, Ptr{BigFloat}, Int32), &z, c, &x, ROUNDING_MODE[end])
return z
end
# BigInt
function ($fJ)(x::BigFloat, c::BigInt)
z = BigFloat()
ccall(($(string(:mpfr_,fC,:_z)), :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Ptr{BigInt}, Int32), &z, &x, &c, ROUNDING_MODE[end])
return z
end
# no :mpfr_z_div function
end
end
function -(c::BigInt, x::BigFloat)
z = BigFloat()
ccall((:mpfr_z_sub, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigInt}, Ptr{BigFloat}, Int32), &z, &c, &x, ROUNDING_MODE[end])
return z
end
function fma(x::BigFloat, y::BigFloat, z::BigFloat)
r = BigFloat()
ccall(("mpfr_fma",:libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Ptr{BigFloat}, Ptr{BigFloat}, Int32), &r, &x, &y, &z, ROUNDING_MODE[end])
return r
end
# div
# BigFloat
function div(x::BigFloat, y::BigFloat)
z = BigFloat()
ccall((:mpfr_div,:libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Ptr{BigFloat}, Int32), &z, &x, &y, to_mpfr(RoundToZero))
ccall((:mpfr_trunc, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}), &z, &z)
return z
end
# Unsigned Int
function div(x::BigFloat, c::CulongMax)
z = BigFloat()
ccall((:mpfr_div_ui, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Culong, Int32), &z, &x, c, to_mpfr(RoundToZero))
ccall((:mpfr_trunc, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}), &z, &z)
return z
end
function div(c::CulongMax, x::BigFloat)
z = BigFloat()
ccall((:mpfr_ui_div, :libmpfr), Int32, (Ptr{BigFloat}, Culong, Ptr{BigFloat}, Int32), &z, c, &x, to_mpfr(RoundToZero))
ccall((:mpfr_trunc, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}), &z, &z)
return z
end
# Signed Integer
function div(x::BigFloat, c::ClongMax)
z = BigFloat()
ccall((:mpfr_div_si, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Clong, Int32), &z, &x, c, to_mpfr(RoundToZero))
ccall((:mpfr_trunc, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}), &z, &z)
return z
end
function div(c::ClongMax, x::BigFloat)
z = BigFloat()
ccall((:mpfr_si_div, :libmpfr), Int32, (Ptr{BigFloat}, Clong, Ptr{BigFloat}, Int32), &z, c, &x, to_mpfr(RoundToZero))
ccall((:mpfr_trunc, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}), &z, &z)
return z
end
# Float32/Float64
function div(x::BigFloat, c::CdoubleMax)
z = BigFloat()
ccall((:mpfr_div_d, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Cdouble, Int32), &z, &x, c, to_mpfr(RoundToZero))
ccall((:mpfr_trunc, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}), &z, &z)
return z
end
function div(c::CdoubleMax, x::BigFloat)
z = BigFloat()
ccall((:mpfr_d_div, :libmpfr), Int32, (Ptr{BigFloat}, Cdouble, Ptr{BigFloat}, Int32), &z, c, &x, to_mpfr(RoundToZero))
ccall((:mpfr_trunc, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}), &z, &z)
return z
end
# BigInt
function div(x::BigFloat, c::BigInt)
z = BigFloat()
ccall((:mpfr_div_z, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Ptr{BigInt}, Int32), &z, &x, &c, to_mpfr(RoundToZero))
ccall((:mpfr_trunc, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{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(($(string(:mpfr_,fC)), :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Ptr{BigFloat}, Int32), &z, &a, &b, ROUNDING_MODE[end])
ccall(($(string(:mpfr_,fC)), :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Ptr{BigFloat}, Int32), &z, &z, &c, ROUNDING_MODE[end])
return z
end
function ($fJ)(a::BigFloat, b::BigFloat, c::BigFloat, d::BigFloat)
z = BigFloat()
ccall(($(string(:mpfr_,fC)), :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Ptr{BigFloat}, Int32), &z, &a, &b, ROUNDING_MODE[end])
ccall(($(string(:mpfr_,fC)), :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Ptr{BigFloat}, Int32), &z, &z, &c, ROUNDING_MODE[end])
ccall(($(string(:mpfr_,fC)), :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Ptr{BigFloat}, Int32), &z, &z, &d, ROUNDING_MODE[end])
return z
end
function ($fJ)(a::BigFloat, b::BigFloat, c::BigFloat, d::BigFloat, e::BigFloat)
z = BigFloat()
ccall(($(string(:mpfr_,fC)), :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Ptr{BigFloat}, Int32), &z, &a, &b, ROUNDING_MODE[end])
ccall(($(string(:mpfr_,fC)), :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Ptr{BigFloat}, Int32), &z, &z, &c, ROUNDING_MODE[end])
ccall(($(string(:mpfr_,fC)), :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Ptr{BigFloat}, Int32), &z, &z, &d, ROUNDING_MODE[end])
ccall(($(string(:mpfr_,fC)), :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Ptr{BigFloat}, Int32), &z, &z, &e, ROUNDING_MODE[end])
return z
end
end
end
function -(x::BigFloat)
z = BigFloat()
ccall((:mpfr_neg, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Int32), &z, &x, ROUNDING_MODE[end])
return z
end
function sqrt(x::BigFloat)
isnan(x) && return x
z = BigFloat()
ccall((:mpfr_sqrt, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Int32), &z, &x, ROUNDING_MODE[end])
if isnan(z)
throw(DomainError())
end
return z
end
sqrt(x::BigInt) = sqrt(BigFloat(x))
function ^(x::BigFloat, y::BigFloat)
z = BigFloat()
ccall((:mpfr_pow, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Ptr{BigFloat}, Int32), &z, &x, &y, ROUNDING_MODE[end])
return z
end
function ^(x::BigFloat, y::CulongMax)
z = BigFloat()
ccall((:mpfr_pow_ui, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Culong, Int32), &z, &x, y, ROUNDING_MODE[end])
return z
end
function ^(x::BigFloat, y::ClongMax)
z = BigFloat()
ccall((:mpfr_pow_si, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Clong, Int32), &z, &x, y, ROUNDING_MODE[end])
return z
end
function ^(x::BigFloat, y::BigInt)
z = BigFloat()
ccall((:mpfr_pow_z, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Ptr{BigInt}, Int32), &z, &x, &y, ROUNDING_MODE[end])
return z
end
for f in (:exp, :exp2, :exp10, :expm1, :digamma, :erf, :erfc, :zeta,
:cosh,:sinh,:tanh,:sech,:csch,:coth, :cbrt)
@eval function $f(x::BigFloat)
z = BigFloat()
ccall(($(string(:mpfr_,f)), :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Int32), &z, &x, ROUNDING_MODE[end])
return z
end
end
# return log(2)
function big_ln2()
c = BigFloat()
ccall((:mpfr_const_log2, :libmpfr), Cint, (Ptr{BigFloat}, Int32),
&c, MPFR.ROUNDING_MODE[end])
return c
end
function eta(x::BigFloat)
x == 1 && return big_ln2()
return -zeta(x) * expm1(big_ln2()*(1-x))
end
function airyai(x::BigFloat)
z = BigFloat()
ccall((:mpfr_ai, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Int32), &z, &x, ROUNDING_MODE[end])
return z
end
function ldexp(x::BigFloat, n::Clong)
z = BigFloat()
ccall((:mpfr_mul_2si, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Clong, Int32), &z, &x, n, ROUNDING_MODE[end])
return z
end
function ldexp(x::BigFloat, n::Culong)
z = BigFloat()
ccall((:mpfr_mul_2ui, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Culong, Int32), &z, &x, n, ROUNDING_MODE[end])
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 besselj0(x::BigFloat)
z = BigFloat()
ccall((:mpfr_j0, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Int32), &z, &x, ROUNDING_MODE[end])
return z
end
function besselj1(x::BigFloat)
z = BigFloat()
ccall((:mpfr_j1, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Int32), &z, &x, ROUNDING_MODE[end])
return z
end
function besselj(n::Integer, x::BigFloat)
z = BigFloat()
ccall((:mpfr_jn, :libmpfr), Int32, (Ptr{BigFloat}, Clong, Ptr{BigFloat}, Int32), &z, n, &x, ROUNDING_MODE[end])
return z
end
function bessely0(x::BigFloat)
if x < 0
throw(DomainError())
end
z = BigFloat()
ccall((:mpfr_y0, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Int32), &z, &x, ROUNDING_MODE[end])
return z
end
function bessely1(x::BigFloat)
if x < 0
throw(DomainError())
end
z = BigFloat()
ccall((:mpfr_y1, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Int32), &z, &x, ROUNDING_MODE[end])
return z
end
function bessely(n::Integer, x::BigFloat)
if x < 0
throw(DomainError())
end
z = BigFloat()
ccall((:mpfr_yn, :libmpfr), Int32, (Ptr{BigFloat}, Clong, Ptr{BigFloat}, Int32), &z, n, &x, ROUNDING_MODE[end])
return z
end
function factorial(x::BigFloat)
if x < 0 || !isinteger(x)
throw(DomainError())
end
ui = convert(Culong, x)
z = BigFloat()
ccall((:mpfr_fac_ui, :libmpfr), Int32, (Ptr{BigFloat}, Culong, Int32), &z, ui, ROUNDING_MODE[end])
return z
end
function hypot(x::BigFloat, y::BigFloat)
z = BigFloat()
ccall((:mpfr_hypot, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Ptr{BigFloat}, Int32), &z, &x, &y, ROUNDING_MODE[end])
return z
end
for f in (:log, :log2, :log10)
@eval function $f(x::BigFloat)
if x < 0
throw(DomainError())
end
z = BigFloat()
ccall(($(string(:mpfr_,f)), :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Int32), &z, &x, ROUNDING_MODE[end])
return z
end
end
function log1p(x::BigFloat)
if x < -1
throw(DomainError())
end
z = BigFloat()
ccall((:mpfr_log1p, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Int32), &z, &x, ROUNDING_MODE[end])
return z
end
function max(x::BigFloat, y::BigFloat)
z = BigFloat()
ccall((:mpfr_max, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Ptr{BigFloat}, Int32), &z, &x, &y, ROUNDING_MODE[end])
return z
end
function min(x::BigFloat, y::BigFloat)
z = BigFloat()
ccall((:mpfr_min, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Ptr{BigFloat}, Int32), &z, &x, &y, ROUNDING_MODE[end])
return z
end
function modf(x::BigFloat)
if isinf(x)
return (BigFloat(NaN), x)
end
zint = BigFloat()
zfloat = BigFloat()
ccall((:mpfr_modf, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Ptr{BigFloat}, Int32), &zint, &zfloat, &x, ROUNDING_MODE[end])
return (zfloat, zint)
end
function rem(x::BigFloat, y::BigFloat)
z = BigFloat()
ccall((:mpfr_fmod, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Ptr{BigFloat}, Int32), &z, &x, &y, ROUNDING_MODE[end])
return z
end
function sum(arr::AbstractArray{BigFloat})
z = BigFloat(0)
for i in arr
ccall((:mpfr_add, :libmpfr), Int32,
(Ptr{BigFloat}, Ptr{BigFloat}, Ptr{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 ($f)(x::BigFloat)
if isnan(x)
return x
end
z = BigFloat()
ccall(($(string(:mpfr_,f)), :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Int32), &z, &x, ROUNDING_MODE[end])
if isnan(z)
throw(DomainError())
end
return z
end
end
end
# log of absolute value of gamma function
const lgamma_signp = Array(Cint, 1)
function lgamma(x::BigFloat)
z = BigFloat()
ccall((:mpfr_lgamma,:libmpfr), Cint, (Ptr{BigFloat}, Ptr{Cint}, Ptr{BigFloat}, Int32), &z, lgamma_signp, &x, ROUNDING_MODE[end])
return z
end
lgamma_r(x::BigFloat) = (lgamma(x), lgamma_signp[1])
function atan2(y::BigFloat, x::BigFloat)
z = BigFloat()
ccall((:mpfr_atan2, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Ptr{BigFloat}, Int32), &z, &y, &x, ROUNDING_MODE[end])
return z
end
# Utility functions
==(x::BigFloat, y::BigFloat) = ccall((:mpfr_equal_p, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}), &x, &y) != 0
<=(x::BigFloat, y::BigFloat) = ccall((:mpfr_lessequal_p, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}), &x, &y) != 0
>=(x::BigFloat, y::BigFloat) = ccall((:mpfr_greaterequal_p, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}), &x, &y) != 0
<(x::BigFloat, y::BigFloat) = ccall((:mpfr_less_p, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}), &x, &y) != 0
>(x::BigFloat, y::BigFloat) = ccall((:mpfr_greater_p, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}), &x, &y) != 0
function cmp(x::BigFloat, y::BigInt)
isnan(x) && throw(DomainError())
ccall((:mpfr_cmp_z, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigInt}), &x, &y)
end
function cmp(x::BigFloat, y::ClongMax)
isnan(x) && throw(DomainError())
ccall((:mpfr_cmp_si, :libmpfr), Int32, (Ptr{BigFloat}, Clong), &x, y)
end
function cmp(x::BigFloat, y::CulongMax)
isnan(x) && throw(DomainError())
ccall((:mpfr_cmp_ui, :libmpfr), Int32, (Ptr{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) || isnan(y)) && throw(DomainError())
ccall((:mpfr_cmp_d, :libmpfr), Int32, (Ptr{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, (Ptr{BigFloat},), &x) != 0
function precision(x::BigFloat) # precision of an object of type BigFloat
return ccall((:mpfr_get_prec, :libmpfr), Clong, (Ptr{BigFloat},), &x)
end
precision(::Type{BigFloat}) = DEFAULT_PRECISION[end] # 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())
end
DEFAULT_PRECISION[end] = 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: $c"))
end
RoundingMode(c)
end
rounding_raw(::Type{BigFloat}) = ROUNDING_MODE[end]
setrounding_raw(::Type{BigFloat},i::Integer) = ROUNDING_MODE[end] = i
rounding(::Type{BigFloat}) = from_mpfr(rounding_raw(BigFloat))
setrounding(::Type{BigFloat},r::RoundingMode) = setrounding_raw(BigFloat,to_mpfr(r))
function copysign(x::BigFloat, y::BigFloat)
z = BigFloat()
ccall((:mpfr_copysign, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Ptr{BigFloat}, Int32), &z, &x, &y, ROUNDING_MODE[end])
return z
end
function exponent(x::BigFloat)
if x == 0 || !isfinite(x)
throw(DomainError())
end
# The '- 1' is to make it work as Base.exponent
return ccall((:mpfr_get_exp, :libmpfr), Clong, (Ptr{BigFloat},), &x) - 1
end
function frexp(x::BigFloat)
z = BigFloat()
c = Clong[0]
ccall((:mpfr_frexp, :libmpfr), Int32, (Ptr{Clong}, Ptr{BigFloat}, Ptr{BigFloat}, Cint), c, &z, &x, ROUNDING_MODE[end])
return (z, c[1])
end
function significand(x::BigFloat)
z = BigFloat()
c = Clong[0]
ccall((:mpfr_frexp, :libmpfr), Int32, (Ptr{Clong}, Ptr{BigFloat}, Ptr{BigFloat}, Cint), c, &z, &x, ROUNDING_MODE[end])
# Double the significand to make it work as Base.significand
ccall((:mpfr_mul_si, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Clong, Int32), &z, &z, 2, ROUNDING_MODE[end])
return z
end
function isinteger(x::BigFloat)
return ccall((:mpfr_integer_p, :libmpfr), Int32, (Ptr{BigFloat},), &x) != 0
end
for f in (:ceil, :floor, :trunc)
@eval begin
function ($f)(x::BigFloat)
z = BigFloat()
ccall(($(string(:mpfr_,f)), :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}), &z, &x)
return z
end
end
end
function round(x::BigFloat)
z = BigFloat()
ccall((:mpfr_rint, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Cint), &z, &x, ROUNDING_MODE[end])
return z
end
function round(x::BigFloat,::RoundingMode{:NearestTiesAway})
z = BigFloat()
ccall((:mpfr_round, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}), &z, &x)
return z
end
function isinf(x::BigFloat)
return ccall((:mpfr_inf_p, :libmpfr), Int32, (Ptr{BigFloat},), &x) != 0
end
function isnan(x::BigFloat)
return ccall((:mpfr_nan_p, :libmpfr), Int32, (Ptr{BigFloat},), &x) != 0
end
isfinite(x::BigFloat) = !isinf(x) && !isnan(x)
@eval typemax(::Type{BigFloat}) = $(BigFloat( Inf))
@eval typemin(::Type{BigFloat}) = $(BigFloat(-Inf))
function nextfloat(x::BigFloat)
z = BigFloat()
ccall((:mpfr_set, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Int32),
&z, &x, ROUNDING_MODE[end])
ccall((:mpfr_nextabove, :libmpfr), Int32, (Ptr{BigFloat},), &z) != 0
return z
end
function prevfloat(x::BigFloat)
z = BigFloat()
ccall((:mpfr_set, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Int32),
&z, &x, ROUNDING_MODE[end])
ccall((:mpfr_nextbelow, :libmpfr), Int32, (Ptr{BigFloat},), &z) != 0
return z
end
eps(::Type{BigFloat}) = nextfloat(BigFloat(1)) - BigFloat(1)
realmin(::Type{BigFloat}) = nextfloat(zero(BigFloat))
realmax(::Type{BigFloat}) = prevfloat(BigFloat(Inf))
"""
setprecision(f::Function, [T=BigFloat,] precision::Integer)
Change the `T` arithmetic precision (in bits) for the duration of `f`.
It is logically equivalent to:
old = precision(BigFloat)
setprecision(BigFloat, precision)
f()
setprecision(BigFloat, old)
Often used as `setprecision(T, precision) do ... end`
"""
function setprecision{T}(f::Function, ::Type{T}, prec::Integer)
old_prec = precision(T)
setprecision(T, prec)
try
return f()
finally
setprecision(T, old_prec)
end
end
setprecision(f::Function, precision::Integer) = setprecision(f, BigFloat, precision)
function string(x::BigFloat)
# In general, the number of decimal places needed to read back the number exactly
# is, excluding the most significant, ceil(log(10, 2^precision(x)))
k = ceil(Int32, precision(x) * 0.3010299956639812)
lng = k + Int32(8) # Add space for the sign, the most significand digit, the dot and the exponent
buf = Array(UInt8, lng + 1)
# format strings are guaranteed to contain no NUL, so we don't use Cstring
lng = ccall((:mpfr_snprintf,:libmpfr), Int32, (Ptr{UInt8}, Culong, Ptr{UInt8}, Ptr{BigFloat}...), buf, lng + 1, "%.Re", &x)
if lng < k + 5 # print at least k decimal places
lng = ccall((:mpfr_sprintf,:libmpfr), Int32, (Ptr{UInt8}, Ptr{UInt8}, Ptr{BigFloat}...), buf, "%.$(k)Re", &x)
elseif lng > k + 8
buf = Array(UInt8, lng + 1)
lng = ccall((:mpfr_snprintf,:libmpfr), Int32, (Ptr{UInt8}, Culong, Ptr{UInt8}, Ptr{BigFloat}...), buf, lng + 1, "%.Re", &x)
end
return bytestring(pointer(buf), (1 <= x < 10 || -10 < x <= -1 || x == 0) ? lng - 4 : lng)
end
print(io::IO, b::BigFloat) = print(io, string(b))
show(io::IO, b::BigFloat) = print(io, string(b))
# 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), Void, (Clong,), x)
set_emin!(x) = ccall((:mpfr_set_emin, :libmpfr), Void, (Clong,), x)
end #module