How does postgresql cast float to numeric? - postgresql

Question

I was wondering how Postgresql converts floating point (float4) values to NUMERIC.
I chose 0.1 as a testing value. This value is not accurately representable in base2, see https://float.exposed/0x3dcccccd for a visualization. So the stored value 0x3dcccccd in hex for a float4 is actually not 0.1 but 0.100000001490116119385.
However, I do not understand the output of the following commands:
mydb=# SELECT '0.100000001490116119385'::float4::numeric(50,50);
numeric
------------------------------------------------------
0.10000000000000000000000000000000000000000000000000
(1 row)
mydb=# SELECT '0.1'::float4::numeric(50,50);
numeric
------------------------------------------------------
0.10000000000000000000000000000000000000000000000000
mydb=# SELECT '0.10000000000000000000000000000000001'::float4::numeric(50,50);
numeric
------------------------------------------------------
0.10000000000000000000000000000000000000000000000000
Why (and how) do I get 0.1 as a result in all cases? Both, 0.1 and 0.10000000000000000000000000000000001 cannot be accurately stored in a float4. The value that can be stored is 0.100000001490116119385 which is also the closest float4 value in both cases, but that's not what I get when casting to numeric. Why?

Answer 1

From the source code:
Datum
float4_numeric(PG_FUNCTION_ARGS)
{
float4 val = PG_GETARG_FLOAT4(0);
Numeric res;
NumericVar result;
char buf[FLT_DIG + 100];
if (isnan(val))
PG_RETURN_NUMERIC(make_result(&const_nan));
if (isinf(val))
{
if (val < 0)
PG_RETURN_NUMERIC(make_result(&const_ninf));
else
PG_RETURN_NUMERIC(make_result(&const_pinf));
}
snprintf(buf, sizeof(buf), "%.*g", FLT_DIG, val);
init_var(&result);
/* Assume we need not worry about leading/trailing spaces */
(void) set_var_from_str(buf, buf, &result);
res = make_result(&result);
free_var(&result);
PG_RETURN_NUMERIC(res);
}

Answer 2

Further explanation of Frank Heikens's answer
source code idea is get the float4 input. convert to char string, then convert to numeric.
Key function is
snprintf(buf, sizeof(buf), "%.*g", FLT_DIG, val);
FLT_DIG is equal to 6.
https://pubs.opengroup.org/onlinepubs/7908799/xsh/fprintf.html
An optional precision that gives the minimum number of digits to
appear for the d, i, o, u, x and X conversions; the number of digits
to appear after the radix character for the e, E and f conversions;
the maximum number of significant digits for the g and G conversions;
or the maximum number of bytes to be printed from a string in s and S
conversions. The precision takes the form of a period (.) followed
either by an asterisk (*), described below, or an optional decimal
digit string, where a null digit string is treated as 0. If a
precision appears with any other conversion character, the behaviour
is undefined.
float convert to text then to numeric processs: the text after decimal delimiter can only have 6 digits precision!
snprintf example: https://legacy.cplusplus.com/reference/cstdio/snprintf/
further post: Avoid trailing zeroes in printf()