arb_get_str() & arb_set_str() does not preserve value

[saraedum]

Consider the following C program.

$ cat roundtrip.c
#include <arb.h>

int main() {
  arb_t a;
  arb_init(a);

  arb_load_str(a, "2bb573849d73 -2c 800031b 365d");

  arb_printn(a, 1024, ARB_STR_MORE);

  arb_set_str(a, arb_get_str(a, 1024, ARB_STR_MORE), 1024);

  arb_printn(a, 1024, ARB_STR_MORE);
}

When run (with Arb 2.22.1 from conda-forge) it prints:

[+/- 3.65e+4197][+/- 3.66e+4197]

I understand that arb_get_str() can introduce imprecision and I also understand that I should probably use arb_dump_str to serialize an arb_t; but shouldn't arb_set_str() preserve the radius?

[albinahlback]

Neither arb_get_str nor arb_set_str says in their documentation that they preserve the radius. It only states that the old interval is contained in the new interval.

[saraedum]

@albinahlback Thanks, I am aware of that. I am not saying that the implementation breaks the documentation.

[albinahlback]

Then what is your issue? You asked if arb_set_str preserves the radius, for which I gave an answer.

[saraedum]

My question was: Shouldn't arb_set_str() try to preserve the radius here?

[saraedum]

Note that this is somewhat related to flintlib/arb#391. In flintlib/arb#391 arb_get_str introduces an error, here arb_set_str introduces an error.

I wonder if both methods could be more careful when it's possible not to introduce any error.

[JeffreySarnoff]

I have been trying to get this right for a while, testing various approaches and they all end like this:

using Serialization, ArbNumerics
using Serialization: serialize_type
using ArbNumerics: @libarb, @libflint

function Serialization.serialize(s::AbstractSerializer, x::ArbFloat)
Serialization.serialize_type(s, typeof(x))
unsafestr = ccall(@libarb(arf_dump_str), Cstring, (Ref{ArbFloat},), x)
len = Int64(ccall(:strlen, Csize_t, (Cstring,), unsafestr)) + 1
write(s.io, len)
unsafe_write(s.io, pointer(unsafestr), len)
ccall(@libflint(flint_free), Cvoid, (Cstring,), unsafestr)
return nothing
end

function Serialization.deserialize(s::AbstractSerializer, ::Type{ArbFloat{P}}) where {P}
len = read(s.io, Int64)::Int64
str = Serialization.deserialize_string(s, Int(len))
# TODO: call arb_load_str to constuct arb_t from str
x = ArbFloat{P}(0)
ccall(@libarb(arf_load_str), Int, (Ref{ArbFloat{P}}, Ref{Cstring}), x, str)
return x
end

low_precision = 53
high_precision = 320

setworkingprecision(low_precision)

arf_val = log(ArbFloat(17))

2.83321334405621608

serialize_buffer = Serializer(IOBuffer())

Serializer{IOBuffer}(IOBuffer(data=UInt8[...], readable=true, writable=true, seekable=true, append=false,

size=0, maxsize=Inf, ptr=1, mark=-1), 0, IdDict{Any, Any}(),

Int64[], Dict{UInt64, Any}(), 26)

serialize(serialize_buffer, arf_val)

Serializer{IOBuffer}(IOBuffer(data=UInt8[...], readable=true, writable=true, seekable=true, append=false,

size=82, maxsize=Inf, ptr=83, mark=-1), 3, IdDict{Any, Any}(:ArbNumerics => 2, ArbFloat{64} => 0, :ArbFloat => 1),

Int64[], Dict{UInt64, Any}(), 26)

arf_val_recovered = deserialize(serialize_buffer, typeof(arf_val))
ERROR: EOFError: read end of file

[albinahlback]

@fredrik-johansson can you transfer this issue to FLINT?

[albinahlback]

@JeffreySarnoff can you provide a MWE in C for your issue? Also, please use code blocks to format the code.

[albinahlback]

@saraedum So the issue is that when you use string methods, you convert between a binary and a decimal representation on an inexact ring. This forces a loss of information.