more informative flint_printf of arb objects, especially for debugging?

[mezzarobba]

I've tripped myself up multiple times forgetting that flint_printf prints arb balls in a way that doesn't reflect their accuracy. For instance, I've repeatedly overlooked precision losses, misinterpreted things like [0.5 +/- 1.42e-6] as 0.5±1e-30 while the actual value was something like 0.49999999937898754567876543456±1e-30, etc.

It would be great if there was a simple way of having the actual order of magnitude of the radius show in the output—ideally without having to think of adding a flag to every printf call, though, on the other hand, I am not sure changing the default output format would be a good idea. For what it's worth I'm currently using a quick and dirty patch similar to the one below to get something like [0.4999... +/- 1.23e-30] in the above example.

diff --git src/arb/get_str.c src/arb/get_str.c
index e71446223..efc8786d1 100644
--- src/arb/get_str.c
+++ src/arb/get_str.c
@@ -33,7 +33,7 @@ _arb_condense_digits(char * s, slong n)
             for (j = 0; isdigit(s[i + j]); j++)
                 run++;

-            if (run > 3 * n)
+            if (run > 2 * n)
             {
                 for (j = 0; j < n; j++)
                 {
@@ -41,13 +41,13 @@ _arb_condense_digits(char * s, slong n)
                     out++;
                 }

-                out += flint_sprintf(res + out, "{...%wd digits...}", run - 2 * n);
+                out += flint_sprintf(res + out, "...", run - 2 * n);

-                for (j = run - n; j < run; j++)
-                {
-                    res[out] = s[i + j];
-                    out++;
-                }
+                // for (j = run - n; j < run; j++)
+                // {
+                //     res[out] = s[i + j];
+                //     out++;
+                // }
             }
             else
             {
diff --git src/generic_files/io_vprintf_impl.h src/generic_files/io_vprintf_impl.h
index 1ab812d73..a7dabed09 100644
--- src/generic_files/io_vprintf_impl.h
+++ src/generic_files/io_vprintf_impl.h
@@ -927,7 +927,7 @@ static size_t __arb_print(FLINT_VPRINTF_OUT_T * out, arb_srcptr ip, int flag)
         else
             ip2 = *ip;

-        str = arb_get_str(&ip2, DIGITS, 0);
+        str = arb_get_str(&ip2, 1000, 6*ARB_STR_CONDENSE);
         res = FLINT_VPRINTF_WRITE(str, strlen(str), out);

         flint_free(str);

[fredrik-johansson]

We could add another flag to arb_get_str to support the above style which I agree is convenient.

The default format of arb, acb etc. in flint_printf is not necessarily ideal. The default should maybe be (up to) 6 accurate digits without radius which is more compact for typical debug-style printing and less likely to lead the user to mistake the printed radius for the internal radius?

It would also be useful for flint_printf to accept formatting options. At minimum the number of digits, but also options supported by arb_get_str, option to show the exact internal representation, etc.

[albinahlback]

I think formatting options would be the best alternative.