Increase String::num default decimal precision

Fixes #34541

Renamed MAX_DIGITS to MAX_DECIMALS, since it only changes the
amount of digits after the decimal point.

Increased MAX_DECIMALS to 32, and made String::num use
MAX_DECIMALS consistently. If -1 is passed as
decimal precision to String::num, it now gets changed to
the correct precision based on the number's magnitude,
instead of using printf default(which is 6)

String::num_real also calculates the correct precision now.

Also made the types used in floating-point math more
consistent in a few places.

7 files changed, 47 insertions, 22 deletions

diff --git a/core/core_bind.cpp b/core/core_bind.cpp
index b8c448dc82..c3e4066c4b 100644
--- a/core/core_bind.cpp
+++ b/core/core_bind.cpp
@@ -2415,12 +2415,12 @@ Variant JSONParseResult::get_result() const {
 }
 
 void _JSON::_bind_methods() {
-	ClassDB::bind_method(D_METHOD("print", "value", "indent", "sort_keys"), &_JSON::print, DEFVAL(String()), DEFVAL(false));
+	ClassDB::bind_method(D_METHOD("print", "value", "indent", "sort_keys", "full_precision"), &_JSON::print, DEFVAL(String()), DEFVAL(false), DEFVAL(false));
 	ClassDB::bind_method(D_METHOD("parse", "json"), &_JSON::parse);
 }
 
-String _JSON::print(const Variant &p_value, const String &p_indent, bool p_sort_keys) {
-	return JSON::print(p_value, p_indent, p_sort_keys);
+String _JSON::print(const Variant &p_value, const String &p_indent, bool p_sort_keys, bool p_full_precision) {
+	return JSON::print(p_value, p_indent, p_sort_keys, p_full_precision);
 }
 
 Ref<JSONParseResult> _JSON::parse(const String &p_json) {
diff --git a/core/core_bind.h b/core/core_bind.h
index be8b30b38d..3c63304488 100644
--- a/core/core_bind.h
+++ b/core/core_bind.h
@@ -705,7 +705,7 @@ protected:
 public:
 	static _JSON *get_singleton() { return singleton; }
 
-	String print(const Variant &p_value, const String &p_indent = "", bool p_sort_keys = false);
+	String print(const Variant &p_value, const String &p_indent = "", bool p_sort_keys = false, bool p_full_precision = false);
 	Ref<JSONParseResult> parse(const String &p_json);
 
 	_JSON() { singleton = this; }
diff --git a/core/io/json.cpp b/core/io/json.cpp
index 394cf216e8..e3e9d6158b 100644
--- a/core/io/json.cpp
+++ b/core/io/json.cpp
@@ -55,7 +55,7 @@ static String _make_indent(const String &p_indent, int p_size) {
 	return indent_text;
 }
 
-String JSON::_print_var(const Variant &p_var, const String &p_indent, int p_cur_indent, bool p_sort_keys) {
+String JSON::_print_var(const Variant &p_var, const String &p_indent, int p_cur_indent, bool p_sort_keys, bool p_full_precision) {
 	String colon = ":";
 	String end_statement = "";
 
@@ -71,8 +71,17 @@ String JSON::_print_var(const Variant &p_var, const String &p_indent, int p_cur_
 			return p_var.operator bool() ? "true" : "false";
 		case Variant::INT:
 			return itos(p_var);
-		case Variant::FLOAT:
-			return rtos(p_var);
+		case Variant::FLOAT: {
+			double num = p_var;
+			if (p_full_precision) {
+				// Store unreliable digits (17) instead of just reliable
+				// digits (14) so that the value can be decoded exactly.
+				return String::num(num, 17 - (int)floor(log10(num)));
+			} else {
+				// Store only reliable digits (14) by default.
+				return String::num(num, 14 - (int)floor(log10(num)));
+			}
+		}
 		case Variant::PACKED_INT32_ARRAY:
 		case Variant::PACKED_INT64_ARRAY:
 		case Variant::PACKED_FLOAT32_ARRAY:
@@ -121,8 +130,8 @@ String JSON::_print_var(const Variant &p_var, const String &p_indent, int p_cur_
 	}
 }
 
-String JSON::print(const Variant &p_var, const String &p_indent, bool p_sort_keys) {
-	return _print_var(p_var, p_indent, 0, p_sort_keys);
+String JSON::print(const Variant &p_var, const String &p_indent, bool p_sort_keys, bool p_full_precision) {
+	return _print_var(p_var, p_indent, 0, p_sort_keys, p_full_precision);
 }
 
 Error JSON::_get_token(const char32_t *p_str, int &index, int p_len, Token &r_token, int &line, String &r_err_str) {
diff --git a/core/io/json.h b/core/io/json.h
index 537477666e..f2711d8c54 100644
--- a/core/io/json.h
+++ b/core/io/json.h
@@ -62,7 +62,7 @@ class JSON {
 
 	static const char *tk_name[TK_MAX];
 
-	static String _print_var(const Variant &p_var, const String &p_indent, int p_cur_indent, bool p_sort_keys);
+	static String _print_var(const Variant &p_var, const String &p_indent, int p_cur_indent, bool p_sort_keys, bool p_full_precision = false);
 
 	static Error _get_token(const char32_t *p_str, int &index, int p_len, Token &r_token, int &line, String &r_err_str);
 	static Error _parse_value(Variant &value, Token &token, const char32_t *p_str, int &index, int p_len, int &line, String &r_err_str);
@@ -70,7 +70,7 @@ class JSON {
 	static Error _parse_object(Dictionary &object, const char32_t *p_str, int &index, int p_len, int &line, String &r_err_str);
 
 public:
-	static String print(const Variant &p_var, const String &p_indent = "", bool p_sort_keys = true);
+	static String print(const Variant &p_var, const String &p_indent = "", bool p_sort_keys = true, bool p_full_precision = false);
 	static Error parse(const String &p_json, Variant &r_ret, String &r_err_str, int &r_err_line);
 };
 
diff --git a/core/string/ustring.cpp b/core/string/ustring.cpp
index 49cf171f2b..6a19baa94b 100644
--- a/core/string/ustring.cpp
+++ b/core/string/ustring.cpp
@@ -54,7 +54,7 @@
 #define snprintf _snprintf_s
 #endif
 
-#define MAX_DIGITS 6
+#define MAX_DECIMALS 32
 #define UPPERCASE(m_c) (((m_c) >= 'a' && (m_c) <= 'z') ? ((m_c) - ('a' - 'A')) : (m_c))
 #define LOWERCASE(m_c) (((m_c) >= 'A' && (m_c) <= 'Z') ? ((m_c) + ('a' - 'A')) : (m_c))
 #define IS_DIGIT(m_d) ((m_d) >= '0' && (m_d) <= '9')
@@ -1379,8 +1379,11 @@ String String::num(double p_num, int p_decimals) {
 	}
 #ifndef NO_USE_STDLIB
 
-	if (p_decimals > 16) {
-		p_decimals = 16;
+	if (p_decimals < 0) {
+		p_decimals = 14 - (int)floor(log10(p_num));
+	}
+	if (p_decimals > MAX_DECIMALS) {
+		p_decimals = MAX_DECIMALS;
 	}
 
 	char fmt[7];
@@ -1391,7 +1394,6 @@ String String::num(double p_num, int p_decimals) {
 		fmt[1] = 'l';
 		fmt[2] = 'f';
 		fmt[3] = 0;
-
 	} else if (p_decimals < 10) {
 		fmt[2] = '0' + p_decimals;
 		fmt[3] = 'l';
@@ -1458,8 +1460,9 @@ String String::num(double p_num, int p_decimals) {
 		double dec = p_num - (double)((int)p_num);
 
 		int digit = 0;
-		if (p_decimals > MAX_DIGITS)
-			p_decimals = MAX_DIGITS;
+		if (p_decimals > MAX_DECIMALS) {
+			p_decimals = MAX_DECIMALS;
+		}
 
 		int dec_int = 0;
 		int dec_max = 0;
@@ -1471,16 +1474,18 @@ String String::num(double p_num, int p_decimals) {
 			digit++;
 
 			if (p_decimals == -1) {
-				if (digit == MAX_DIGITS) //no point in going to infinite
+				if (digit == MAX_DECIMALS) { //no point in going to infinite
 					break;
+				}
 
 				if (dec - (double)((int)dec) < 1e-6) {
 					break;
 				}
 			}
 
-			if (digit == p_decimals)
+			if (digit == p_decimals) {
 				break;
+			}
 		}
 		dec *= 10;
 		int last = (int)dec % 10;
@@ -1616,7 +1621,15 @@ String String::num_real(double p_num) {
 		double dec = p_num - (double)((int)p_num);
 
 		int digit = 0;
-		int decimals = MAX_DIGITS;
+
+#if REAL_T_IS_DOUBLE
+		int decimals = 14 - (int)floor(log10(p_num));
+#else
+		int decimals = 6 - (int)floor(log10(p_num));
+#endif
+		if (decimals > MAX_DECIMALS) {
+			decimals = MAX_DECIMALS;
+		}
 
 		int dec_int = 0;
 		int dec_max = 0;
diff --git a/doc/classes/JSON.xml b/doc/classes/JSON.xml
index a9fb50c262..7baff7aa39 100644
--- a/doc/classes/JSON.xml
+++ b/doc/classes/JSON.xml
@@ -27,9 +27,12 @@
 			</argument>
 			<argument index="2" name="sort_keys" type="bool" default="false">
 			</argument>
+			<argument index="3" name="full_precision" type="bool" default="false">
+			</argument>
 			<description>
 				Converts a [Variant] var to JSON text and returns the result. Useful for serializing data to store or send over the network.
 				[b]Note:[/b] The JSON specification does not define integer or float types, but only a [i]number[/i] type. Therefore, converting a Variant to JSON text will convert all numerical values to [float] types.
+				[b]Note:[/b] If [code]full_precision[/code] is true, when printing floats, the unreliable digits are printed in addition to the reliable digits to guarantee exact decoding.
 				Use [code]indent[/code] parameter to pretty print the output.
 				[b]Example output:[/b]
 				[codeblock]
diff --git a/modules/gdscript/doc_classes/@GDScript.xml b/modules/gdscript/doc_classes/@GDScript.xml
index 9e974b6fdc..58620f2b3e 100644
--- a/modules/gdscript/doc_classes/@GDScript.xml
+++ b/modules/gdscript/doc_classes/@GDScript.xml
@@ -240,10 +240,10 @@
 		</method>
 	</methods>
 	<constants>
-		<constant name="PI" value="3.141593">
+		<constant name="PI" value="3.14159265358979">
 			Constant that represents how many times the diameter of a circle fits around its perimeter. This is equivalent to [code]TAU / 2[/code].
 		</constant>
-		<constant name="TAU" value="6.283185">
+		<constant name="TAU" value="6.28318530717959">
 			The circle constant, the circumference of the unit circle in radians.
 		</constant>
 		<constant name="INF" value="inf">