[libcxx][NFC] Tidy up calculation of __nbuf in num_put::do_put, and add comments

[DanielMcIntosh-IBM]

Summary

In 07ef8e679621 and 3ed9f6ebdeeb, __nbuf started to diverge from the amount
of space that was actually needed for the buffer. For 32-bit longs for example,
we allocate a buffer that is one larger than needed. Moreover, it is no longer
clear exactly where the extra +1 or +2 comes from - they're just numbers pulled
from thin air. This PR cleans up how __nbuf is calculated, and adds comments
to further clarify where each part comes from.

Specifically, it corrects the underestimation of the max size buffer needed
that the above two commits had to compensate for. The root cause looks to be
the use of signed type parameters to numeric_limits<>::digits. Since digits
only counts non-sign bits, the calculation was acting as though (for a signed
64-bit type) the longest value we would print was 2^63 in octal. However,
printing in octal treats values as unsigned, so it is actually 2^64. Thus,
using unsigned types and changing the final +2 to a +1 is probably a better
option.

[Mordante]

Nice catch! Can you rebase the patch to rerun the CI?

libcxx/include/locale

1466

Wouldn't it look better to do the rounded up character determination in one step?
((numeric_limits<unsigned long>::digits + 2) / 3)

[ldionne]

Thanks for fixing this! The CI is failing due to something that has been fixed now. Please rebase onto main and re-upload your diff, that will run CI again and everything should be green.

libcxx/include/locale

1466

IMO it's easier to read as-is since the + 2 trick isn't immediately obvious (to me at least).

[Mordante]

libcxx/include/locale

1466

I thought this was very common idiom for rounding up. But if it's not obvious for everybody, then I'm in favour of keeping the code as is.

[DanielMcIntosh-IBM]

rebase

[Mordante]

In D103339#2792317, @DanielMcIntosh-IBM wrote:

rebase

Thanks, LGTM!

libcxx/include/locale

 _OutputIterator
 num_put<_CharT, _OutputIterator>::do_put(iter_type __s, ios_base& __iob,
                                          char_type __fl, long __v) const
 {
     // Stage 1 - Get number in narrow char
     char __fmt[6] = {'%', 0};
     const char* __len = "l";
     this->__format_int(__fmt+1, __len, true, __iob.flags());
-    const unsigned __nbuf = (numeric_limits<long>::digits / 3)
-                          + ((numeric_limits<long>::digits % 3) != 0)
-                          + ((__iob.flags() & ios_base::showbase) != 0)
-                          + 2;
+    // Worst case is octal, with showbase enabled. Note that octal is always
+    // printed as an unsigned value.
+    const unsigned __nbuf = (numeric_limits<unsigned long>::digits / 3)          // 1 char per 3 bits
+                            + ((numeric_limits<unsigned long>::digits % 3) != 0) // round up
+                            + ((__iob.flags() & ios_base::showbase) != 0)        // base prefix
+                            + 1;                                                 // terminating null character
     char __nar[__nbuf];
     int __nc = __libcpp_snprintf_l(__nar, sizeof(__nar), _LIBCPP_GET_C_LOCALE, __fmt, __v);
     char* __ne = __nar + __nc;
     char* __np = this->__identify_padding(__nar, __ne, __iob);
     // Stage 2 - Widen __nar while adding thousands separators
     char_type __o[2*(__nbuf-1) - 1];
     char_type* __op;  // pad here
     char_type* __oe;  // end of output
     this->__widen_and_group_int(__nar, __np, __ne, __o, __op, __oe, __iob.getloc());
     // [__o, __oe) contains thousands_sep'd wide number
     // Stage 3 & 4
     return __pad_and_output(__s, __o, __op, __oe, __iob, __fl);
 }
 
 template <class _CharT, class _OutputIterator>
 _OutputIterator
 num_put<_CharT, _OutputIterator>::do_put(iter_type __s, ios_base& __iob,
                                          char_type __fl, long long __v) const
 {
     // Stage 1 - Get number in narrow char
     char __fmt[8] = {'%', 0};
     const char* __len = "ll";
     this->__format_int(__fmt+1, __len, true, __iob.flags());
-    const unsigned __nbuf = (numeric_limits<long long>::digits / 3)
-                          + ((numeric_limits<long long>::digits % 3) != 0)
-                          + ((__iob.flags() & ios_base::showbase) != 0)
-                          + 2;
+    // Worst case is octal, with showbase enabled. Note that octal is always
+    // printed as an unsigned value.
+    const unsigned __nbuf = (numeric_limits<unsigned long long>::digits / 3)          // 1 char per 3 bits
+                            + ((numeric_limits<unsigned long long>::digits % 3) != 0) // round up
+                            + ((__iob.flags() & ios_base::showbase) != 0)             // base prefix
+                            + 1;                                                      // terminating null character
     char __nar[__nbuf];
     int __nc = __libcpp_snprintf_l(__nar, sizeof(__nar), _LIBCPP_GET_C_LOCALE, __fmt, __v);
     char* __ne = __nar + __nc;
     char* __np = this->__identify_padding(__nar, __ne, __iob);
     // Stage 2 - Widen __nar while adding thousands separators
     char_type __o[2*(__nbuf-1) - 1];
     char_type* __op;  // pad here
     char_type* __oe;  // end of output
     this->__widen_and_group_int(__nar, __np, __ne, __o, __op, __oe, __iob.getloc());
     // [__o, __oe) contains thousands_sep'd wide number
     // Stage 3 & 4
     return __pad_and_output(__s, __o, __op, __oe, __iob, __fl);
 }
 
 template <class _CharT, class _OutputIterator>
 _OutputIterator
 num_put<_CharT, _OutputIterator>::do_put(iter_type __s, ios_base& __iob,
                                          char_type __fl, unsigned long __v) const
 {
     // Stage 1 - Get number in narrow char
     char __fmt[6] = {'%', 0};
     const char* __len = "l";
     this->__format_int(__fmt+1, __len, false, __iob.flags());
-    const unsigned __nbuf = (numeric_limits<unsigned long>::digits / 3)
-                          + ((numeric_limits<unsigned long>::digits % 3) != 0)
-                          + ((__iob.flags() & ios_base::showbase) != 0)
-                          + 1;
+    // Worst case is octal, with showbase enabled.
+    const unsigned __nbuf = (numeric_limits<unsigned long>::digits / 3)          // 1 char per 3 bits
+                            + ((numeric_limits<unsigned long>::digits % 3) != 0) // round up
+                            + ((__iob.flags() & ios_base::showbase) != 0)        // base prefix
+                            + 1;                                                 // terminating null character
     char __nar[__nbuf];
     int __nc = __libcpp_snprintf_l(__nar, sizeof(__nar), _LIBCPP_GET_C_LOCALE, __fmt, __v);
     char* __ne = __nar + __nc;
     char* __np = this->__identify_padding(__nar, __ne, __iob);
     // Stage 2 - Widen __nar while adding thousands separators
     char_type __o[2*(__nbuf-1) - 1];
     char_type* __op;  // pad here
     char_type* __oe;  // end of output
     this->__widen_and_group_int(__nar, __np, __ne, __o, __op, __oe, __iob.getloc());
     // [__o, __oe) contains thousands_sep'd wide number
     // Stage 3 & 4
     return __pad_and_output(__s, __o, __op, __oe, __iob, __fl);
 }
 
 template <class _CharT, class _OutputIterator>
 _OutputIterator
 num_put<_CharT, _OutputIterator>::do_put(iter_type __s, ios_base& __iob,
                                          char_type __fl, unsigned long long __v) const
 {
     // Stage 1 - Get number in narrow char
     char __fmt[8] = {'%', 0};
     const char* __len = "ll";
     this->__format_int(__fmt+1, __len, false, __iob.flags());
-    const unsigned __nbuf = (numeric_limits<unsigned long long>::digits / 3)
-                          + ((numeric_limits<unsigned long long>::digits % 3) != 0)
-                          + ((__iob.flags() & ios_base::showbase) != 0)
-                          + 1;
+    // Worst case is octal, with showbase enabled.
+    const unsigned __nbuf = (numeric_limits<unsigned long long>::digits / 3)          // 1 char per 3 bits
+                            + ((numeric_limits<unsigned long long>::digits % 3) != 0) // round up
+                            + ((__iob.flags() & ios_base::showbase) != 0)             // base prefix
+                            + 1;                                                      // terminating null character
     char __nar[__nbuf];
     int __nc = __libcpp_snprintf_l(__nar, sizeof(__nar), _LIBCPP_GET_C_LOCALE, __fmt, __v);
     char* __ne = __nar + __nc;
     char* __np = this->__identify_padding(__nar, __ne, __iob);
     // Stage 2 - Widen __nar while adding thousands separators
     char_type __o[2*(__nbuf-1) - 1];
     char_type* __op;  // pad here
     char_type* __oe;  // end of output