fix(stdlib): make IS_NUM agree with STR_TO_NUM and explain conversion errors

Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>

2 files changed, 2 insertions, 2 deletions

diff --git a/doc/language/function/cpsc-function-is_num.7.md b/doc/language/function/cpsc-function-is_num.7.md
index efb5f1a..3b9641d 100644
--- a/doc/language/function/cpsc-function-is_num.7.md
+++ b/doc/language/function/cpsc-function-is_num.7.md
@@ -14,7 +14,7 @@ IS_NUM(text : STRING) RETURNS BOOLEAN
 
 Provided by the standard string library, loaded and linked by default.
 
-Return true for a nonempty string fully consumed by the runtime's numeric conversion. Leading whitespace is accepted; trailing whitespace or other trailing text is rejected.
+Return true exactly when STR_TO_NUM would succeed: a nonempty string fully consumed by `strtod`, with a value inside the REAL range. Leading whitespace, NaN, inf and hexadecimal forms are accepted; trailing whitespace, trailing text, embedded NUL bytes and overflowing values such as `1e999` are rejected. Underflow to zero or a denormal is accepted.
 
 # EXAMPLE
 
diff --git a/doc/language/function/cpsc-function-str_to_num.7.md b/doc/language/function/cpsc-function-str_to_num.7.md
index acdf60b..48d24db 100644
--- a/doc/language/function/cpsc-function-str_to_num.7.md
+++ b/doc/language/function/cpsc-function-str_to_num.7.md
@@ -14,7 +14,7 @@ STR_TO_NUM(text : STRING) RETURNS REAL
 
 Provided by the standard string library, loaded and linked by default.
 
-Return REAL, including for integer-looking text. The whole string must be consumed. Invalid text, trailing junk and values outside the REAL range throw a catchable exception. Use IS_NUM first to check numeric text without throwing for invalid input.
+Return REAL, including for integer-looking text. The whole string must be consumed. Invalid text and trailing junk throw a catchable exception reading `STR_TO_NUM: '<text>' is not a number`, and overflowing values throw `STR_TO_NUM: '<text>' is out of the REAL range`. Underflow is accepted. Use IS_NUM first to check numeric text without throwing for invalid input.
 
 # EXAMPLE