From 1a6937862f21a9a0b512a2defa2f7cfd38461583 Mon Sep 17 00:00:00 2001
From: Philipp Imhof <52650214+PhilippImhof@users.noreply.github.com>
Date: Sun, 7 Dec 2025 15:09:32 +0100
Subject: [PATCH 1/9] convert numeric strings to numbers for output

---
 classes/local/evaluator.php | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/classes/local/evaluator.php b/classes/local/evaluator.php
index c2247829..584543b0 100644
--- a/classes/local/evaluator.php
+++ b/classes/local/evaluator.php
@@ -163,6 +163,13 @@ public function substitute_variables_in_text(string $text, bool $skiplists = tru
                 if ($skiplists && in_array($result->type, [token::LIST, token::SET])) {
                     continue;
                 }
+                // If the result is a numeric string, we convert it back to a number, in order for
+                // the standard PHP formatting to apply: numbers with an absolute value ≥ 1e14
+                // or < 0.0001 would normally be printed in scientific notation.
+                if ($result->type === token::STRING && is_numeric($result->value)) {
+                    $result->type = token::NUMBER;
+                    $result->value = floatval($result->value);
+                }
                 // If the result is a number, we try to localize it, unless the admin settings do not
                 // allow the decimal comma.
                 if ($result->type === token::NUMBER) {

From 5db6eb91770757e1800321c82bf6c26998f2fd8e Mon Sep 17 00:00:00 2001
From: Philipp Imhof <52650214+PhilippImhof@users.noreply.github.com>
Date: Sun, 7 Dec 2025 20:35:42 +0100
Subject: [PATCH 2/9] add test case

---
 tests/evaluator_test.php | 16 ++++++++++++++++
 1 file changed, 16 insertions(+)

diff --git a/tests/evaluator_test.php b/tests/evaluator_test.php
index 92e64d30..14d31167 100644
--- a/tests/evaluator_test.php
+++ b/tests/evaluator_test.php
@@ -1348,6 +1348,22 @@ public function test_substitute_variables_in_text(): void {
         self::assertEquals($expected, $output);
     }
 
+    public function test_substitute_variables_in_text_with_sigfig(): void {
+        // Define, parse and evaluate some variables.
+        $vars = 'a=0.3; b=sigfig(a, 2); c=0.000005; d=sigfig(c, 8); e=fact(19); f=sigfig(e, 3)';
+        $parser = new parser($vars);
+        $statements = $parser->get_statements();
+        $evaluator = new evaluator();
+        $evaluator->evaluate($statements);
+
+        // We only test the correct replacement of the numbers; correct interpretation of
+        // placeholders is covered in another test.
+        $text = '{a} -- {b} -- {c} -- {d} -- {e} -- {f}';
+        $output = $evaluator->substitute_variables_in_text($text);
+        $expected = '0.3 -- 0.3 -- 5.0E-6 -- 5.0E-6 -- 1.2164510040883E+17 -- 1.22E+17';
+        self::assertEquals($expected, $output);
+    }
+
     public function test_substitute_variables_in_algebraic_formula(): void {
         // Define, parse and evaluate some variables.
         $vars = 'a=1; b=[2,3,4]; c={1,2,3}; x={1:10}; y={1:10}; k = [[1,2],[3,4]];';

From b764a44d31b3c088942cfaddfb2c081b95849b38 Mon Sep 17 00:00:00 2001
From: Philipp Imhof <52650214+PhilippImhof@users.noreply.github.com>
Date: Sun, 7 Dec 2025 20:56:09 +0100
Subject: [PATCH 3/9] add test case

---
 tests/evaluator_test.php | 11 +++++++++++
 tests/renderer_test.php  | 27 +++++++++++++++++++++++++++
 2 files changed, 38 insertions(+)

diff --git a/tests/evaluator_test.php b/tests/evaluator_test.php
index 14d31167..af5d8786 100644
--- a/tests/evaluator_test.php
+++ b/tests/evaluator_test.php
@@ -1349,6 +1349,9 @@ public function test_substitute_variables_in_text(): void {
     }
 
     public function test_substitute_variables_in_text_with_sigfig(): void {
+        $this->resetAfterTest();
+        $this->setAdminUser();
+
         // Define, parse and evaluate some variables.
         $vars = 'a=0.3; b=sigfig(a, 2); c=0.000005; d=sigfig(c, 8); e=fact(19); f=sigfig(e, 3)';
         $parser = new parser($vars);
@@ -1362,6 +1365,14 @@ public function test_substitute_variables_in_text_with_sigfig(): void {
         $output = $evaluator->substitute_variables_in_text($text);
         $expected = '0.3 -- 0.3 -- 5.0E-6 -- 5.0E-6 -- 1.2164510040883E+17 -- 1.22E+17';
         self::assertEquals($expected, $output);
+
+        // Setting the localised decimal separator, but disallow the decimal comma in the admin settings.
+        qtype_formulas_test_helper::define_local_decimal_separator();
+        set_config('allowdecimalcomma', 1, 'qtype_formulas');
+        self::assertEquals('1', get_config('qtype_formulas', 'allowdecimalcomma'));
+        $output = $evaluator->substitute_variables_in_text($text);
+        $expected = '0,3 -- 0,3 -- 5,0E-6 -- 5,0E-6 -- 1,2164510040883E+17 -- 1,22E+17';
+        self::assertEquals($expected, $output);
     }
 
     public function test_substitute_variables_in_algebraic_formula(): void {
diff --git a/tests/renderer_test.php b/tests/renderer_test.php
index 82a52e6b..c72bd334 100644
--- a/tests/renderer_test.php
+++ b/tests/renderer_test.php
@@ -336,6 +336,33 @@ public function test_substitution_of_local_variables(): void {
         $this->check_output_does_not_contain_stray_placeholders();
     }
 
+    public function test_right_answer_feedback_uses_appropriate_decimal_separator(): void {
+        // Setting the localised decimal separator, but disallow the decimal comma in the admin settings.
+        qtype_formulas_test_helper::define_local_decimal_separator();
+        self::assertEquals('0', get_config('qtype_formulas', 'allowdecimalcomma'));
+
+        $q = $this->get_test_formulas_question('testsinglenum');
+        $q->parts[0]->answer = '3.5';
+
+        $this->start_attempt_at_question($q, 'immediatefeedback', 1);
+        $this->process_submission(['0_0' => '42', '-submit' => 1]);
+        $this->check_output_contains_lang_string('correctansweris', 'qtype_formulas', '3.5');
+
+        // Now allowing the decimal comma to be used.
+        set_config('allowdecimalcomma', 1, 'qtype_formulas');
+        $this->start_attempt_at_question($q, 'immediatefeedback', 1);
+        $this->process_submission(['0_0' => '42', '-submit' => 1]);
+        $this->check_output_contains_lang_string('correctansweris', 'qtype_formulas', '3,5');
+
+        // Make sure the decimal comma is also applied for numbers that are string tokens.
+        // Note that we *should* have 3,50 as the model answer, but as we are converting
+        // the string output from sigfig() back to a number, trailing zeroes will be lost.
+        $q = $this->get_test_formulas_question('testsinglenum');
+        $q->parts[0]->answer = 'sigfig(3.5, 3)';
+        $this->process_submission(['0_0' => '42', '-submit' => 1]);
+        $this->check_output_contains_lang_string('correctansweris', 'qtype_formulas', '3,5');
+    }
+
     public function test_render_question_with_separate_unit_field(): void {
         $q = $this->get_test_formulas_question('testsinglenumunitsep');
         $q->parts[0]->unitpenalty = 0.5;

From e7948b40bb28b5369e41ac5703a5cbc4826ea9ff Mon Sep 17 00:00:00 2001
From: Philipp Imhof <52650214+PhilippImhof@users.noreply.github.com>
Date: Sat, 1 Aug 2026 10:21:50 +0200
Subject: [PATCH 4/9] better solution, keeping trailing zeroes

---
 classes/local/functions.php | 17 ++++++++++++++++-
 1 file changed, 16 insertions(+), 1 deletion(-)

diff --git a/classes/local/functions.php b/classes/local/functions.php
index 487961fe..7661782c 100644
--- a/classes/local/functions.php
+++ b/classes/local/functions.php
@@ -657,7 +657,22 @@ public static function sigfig($number, $precision): string {
         // We only request decimals if $digitsafter is greater than zero.
         $digitsafter = max(0, $digitsafter);
 
-        return number_format($number, $digitsafter, '.', '');
+        // If absolute value of the number is >= 1e-4 and < 1e14, we can format it and return
+        // a string.
+        if (abs($number) >= 1e-4 && abs($number) < 1e14) {
+            return number_format($number, $digitsafter, '.', '');
+        }
+
+        // For numbers with an absolute value >= 1e14, we must use the scientific notation,
+        // because that's how PHP would output the number, if it had not been formatted. Using
+        // the E format will give scientific notation with E, like the default behaviour.
+        if (abs($number) >= 1e14) {
+            return sprintf("%.{$precision}E", $number);
+        }
+
+        // Finally, if the absolute value is < 1e-4, we must reduce the precision by 1, because
+        // there will be one figure before the decimal point.
+        return sprintf('%.' . ($precision - 1) . 'E', $number);
     }
 
     /**

From a8ac66e326735d4eb1bb3c6ac45151cc68ab84a5 Mon Sep 17 00:00:00 2001
From: Philipp Imhof <52650214+PhilippImhof@users.noreply.github.com>
Date: Sat, 1 Aug 2026 10:24:08 +0200
Subject: [PATCH 5/9] remove old approach

---
 classes/local/evaluator.php | 7 -------
 1 file changed, 7 deletions(-)

diff --git a/classes/local/evaluator.php b/classes/local/evaluator.php
index 584543b0..c2247829 100644
--- a/classes/local/evaluator.php
+++ b/classes/local/evaluator.php
@@ -163,13 +163,6 @@ public function substitute_variables_in_text(string $text, bool $skiplists = tru
                 if ($skiplists && in_array($result->type, [token::LIST, token::SET])) {
                     continue;
                 }
-                // If the result is a numeric string, we convert it back to a number, in order for
-                // the standard PHP formatting to apply: numbers with an absolute value ≥ 1e14
-                // or < 0.0001 would normally be printed in scientific notation.
-                if ($result->type === token::STRING && is_numeric($result->value)) {
-                    $result->type = token::NUMBER;
-                    $result->value = floatval($result->value);
-                }
                 // If the result is a number, we try to localize it, unless the admin settings do not
                 // allow the decimal comma.
                 if ($result->type === token::NUMBER) {

From 7b5cf17c523d695d5ba7eab5a421a254958cecbc Mon Sep 17 00:00:00 2001
From: Philipp Imhof <52650214+PhilippImhof@users.noreply.github.com>
Date: Sat, 1 Aug 2026 13:23:28 +0200
Subject: [PATCH 6/9] fix implementation, add test cases

---
 classes/local/functions.php | 21 ++++++++++---------
 tests/evaluator_test.php    |  4 ++--
 tests/functions_test.php    | 42 +++++++++++++++++++++++++++++++++++++
 tests/renderer_test.php     |  2 +-
 4 files changed, 56 insertions(+), 13 deletions(-)

diff --git a/classes/local/functions.php b/classes/local/functions.php
index 7661782c..b8498dd4 100644
--- a/classes/local/functions.php
+++ b/classes/local/functions.php
@@ -636,6 +636,7 @@ public static function sigfig($number, $precision): string {
             get_string('error_func_second_posint', 'qtype_formulas', 'sigfig()'),
             self::POSITIVE | self::INTEGER
         );
+        $originalnumber = $number;
         $number = floatval($number);
         $precision = intval($precision);
 
@@ -657,21 +658,21 @@ public static function sigfig($number, $precision): string {
         // We only request decimals if $digitsafter is greater than zero.
         $digitsafter = max(0, $digitsafter);
 
-        // If absolute value of the number is >= 1e-4 and < 1e14, we can format it and return
-        // a string.
-        if (abs($number) >= 1e-4 && abs($number) < 1e14) {
+        // If the absolute value of the *original* number is >= 1e-4 and < 1e14, we can format
+        // it and return a string.
+        if (abs($originalnumber) >= 1e-4 && abs($originalnumber) < 1e14) {
             return number_format($number, $digitsafter, '.', '');
         }
 
-        // For numbers with an absolute value >= 1e14, we must use the scientific notation,
-        // because that's how PHP would output the number, if it had not been formatted. Using
-        // the E format will give scientific notation with E, like the default behaviour.
-        if (abs($number) >= 1e14) {
-            return sprintf("%.{$precision}E", $number);
+        // If the absolute value of the original number was below 1e-4, but just reached that
+        // limit after rounding, it should be output as 0.0001, plus possibly some trailing zeroes.
+        if (abs($originalnumber) < 1e-4 && abs($number) == 1e-4) {
+            return sprintf("%.{$precision}H", $number);
         }
 
-        // Finally, if the absolute value is < 1e-4, we must reduce the precision by 1, because
-        // there will be one figure before the decimal point.
+        // For all other cases, we force scientific notation. Note that we have to subtract 1
+        // from the requested precision, because with the E format, the parameter indicates
+        // the number of places *after* the decimal comma.
         return sprintf('%.' . ($precision - 1) . 'E', $number);
     }
 
diff --git a/tests/evaluator_test.php b/tests/evaluator_test.php
index af5d8786..d972f547 100644
--- a/tests/evaluator_test.php
+++ b/tests/evaluator_test.php
@@ -1363,7 +1363,7 @@ public function test_substitute_variables_in_text_with_sigfig(): void {
         // placeholders is covered in another test.
         $text = '{a} -- {b} -- {c} -- {d} -- {e} -- {f}';
         $output = $evaluator->substitute_variables_in_text($text);
-        $expected = '0.3 -- 0.3 -- 5.0E-6 -- 5.0E-6 -- 1.2164510040883E+17 -- 1.22E+17';
+        $expected = '0.3 -- 0.30 -- 5.0E-6 -- 5.0000000E-6 -- 1.2164510040883E+17 -- 1.22E+17';
         self::assertEquals($expected, $output);
 
         // Setting the localised decimal separator, but disallow the decimal comma in the admin settings.
@@ -1371,7 +1371,7 @@ public function test_substitute_variables_in_text_with_sigfig(): void {
         set_config('allowdecimalcomma', 1, 'qtype_formulas');
         self::assertEquals('1', get_config('qtype_formulas', 'allowdecimalcomma'));
         $output = $evaluator->substitute_variables_in_text($text);
-        $expected = '0,3 -- 0,3 -- 5,0E-6 -- 5,0E-6 -- 1,2164510040883E+17 -- 1,22E+17';
+        $expected = '0,3 -- 0,30 -- 5,0E-6 -- 5,0000000E-6 -- 1,2164510040883E+17 -- 1,22E+17';
         self::assertEquals($expected, $output);
     }
 
diff --git a/tests/functions_test.php b/tests/functions_test.php
index 1e305a51..252d9741 100644
--- a/tests/functions_test.php
+++ b/tests/functions_test.php
@@ -627,6 +627,48 @@ public static function provide_sigfig_expressions(): array {
             ['-0.005', 'sigfig(-.005, 1)'],
             ['-0.0050', 'sigfig(-.005, 2)'],
             ['-0.00500', 'sigfig(-.005, 3)'],
+
+            ['9.99E-5', 'sigfig(0.0000999, 3)'],
+            ['9.990E-5', 'sigfig(0.0000999, 4)'],
+            ['1.00E-5', 'sigfig(0.0000100, 3)'],
+            ['1.000E-5', 'sigfig(0.0000100, 4)'],
+            ['-9.99E-5', 'sigfig(-0.0000999, 3)'],
+            ['-9.990E-5', 'sigfig(-0.0000999, 4)'],
+            ['-1.00E-5', 'sigfig(-0.0000100, 3)'],
+            ['-1.000E-5', 'sigfig(-0.0000100, 4)'],
+            ['1.23E-6', 'sigfig(0.000001234, 3)'],
+            ['1.2340E-6', 'sigfig(0.000001234, 5)'],
+            ['-1.23E-5', 'sigfig(-0.0000123, 3)'],
+            ['-1.230E-5', 'sigfig(-0.0000123, 4)'],
+
+            ['0.000100', 'sigfig(0.0001, 3)'],
+            ['0.0001000', 'sigfig(0.0001, 4)'],
+            ['0.0001', 'sigfig(0.00009995, 3)'],
+            ['9.995E-5', 'sigfig(0.00009995, 4)'],
+            ['-0.000100', 'sigfig(-0.0001, 3)'],
+            ['-0.0001000', 'sigfig(-0.0001, 4)'],
+            ['-0.0001', 'sigfig(-0.00009995, 3)'],
+            ['-9.995E-5', 'sigfig(-0.00009995, 4)'],
+
+            ['1.00E+14', 'sigfig(1e14, 3)'],
+            ['1.0000E+14', 'sigfig(1e14, 5)'],
+            ['1.23E+14', 'sigfig(1.23e14, 3)'],
+            ['1.2300E+14', 'sigfig(1.23e14, 5)'],
+            ['1.20E+14', 'sigfig(1.2e14, 3)'],
+            ['9.99E+14', 'sigfig(9.99e14, 3)'],
+            ['-1.230E+14', 'sigfig(-1.23e14, 4)'],
+
+            ['100000000000000', 'sigfig(99999999999999, 3)'],
+            ['100000000000000', 'sigfig(99999999999999, 5)'],
+            ['99900000000000', 'sigfig(99900000000000, 3)'],
+            ['-100000000000000', 'sigfig(-99999999999999, 3)'],
+            ['-100000000000000', 'sigfig(-99999999999999, 5)'],
+            ['-99900000000000', 'sigfig(-99900000000000, 3)'],
+
+            ['0.300', 'sigfig(0.3, 3)'],
+            ['123.00', 'sigfig(123, 5)'],
+            ['99999.0', 'sigfig(99999, 6)'],
+            ['-0.00123', 'sigfig(-0.00123, 3)'],
         ];
     }
 
diff --git a/tests/renderer_test.php b/tests/renderer_test.php
index c72bd334..e6a60296 100644
--- a/tests/renderer_test.php
+++ b/tests/renderer_test.php
@@ -360,7 +360,7 @@ public function test_right_answer_feedback_uses_appropriate_decimal_separator():
         $q = $this->get_test_formulas_question('testsinglenum');
         $q->parts[0]->answer = 'sigfig(3.5, 3)';
         $this->process_submission(['0_0' => '42', '-submit' => 1]);
-        $this->check_output_contains_lang_string('correctansweris', 'qtype_formulas', '3,5');
+        $this->check_output_contains_lang_string('correctansweris', 'qtype_formulas', '3,50');
     }
 
     public function test_render_question_with_separate_unit_field(): void {

From e53e8f6fa4b2db9a22faf8a261acc222bdbea74f Mon Sep 17 00:00:00 2001
From: Philipp Imhof <52650214+PhilippImhof@users.noreply.github.com>
Date: Sat, 1 Aug 2026 13:39:19 +0200
Subject: [PATCH 7/9] bugfix

---
 classes/local/evaluator.php | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/classes/local/evaluator.php b/classes/local/evaluator.php
index c2247829..ff674704 100644
--- a/classes/local/evaluator.php
+++ b/classes/local/evaluator.php
@@ -163,9 +163,9 @@ public function substitute_variables_in_text(string $text, bool $skiplists = tru
                 if ($skiplists && in_array($result->type, [token::LIST, token::SET])) {
                     continue;
                 }
-                // If the result is a number, we try to localize it, unless the admin settings do not
+                // If the result is a number or a numeric string, we try to localize it, unless the admin settings do not
                 // allow the decimal comma.
-                if ($result->type === token::NUMBER) {
+                if ($result->type === token::NUMBER || ($result->type === token::STRING && is_numeric($result->value))) {
                     $result = qtype_formulas::format_float($result->value);
                 }
 

From d2227254c634dcc503c94730ec5b830ede4dc936 Mon Sep 17 00:00:00 2001
From: Philipp Imhof <52650214+PhilippImhof@users.noreply.github.com>
Date: Sat, 1 Aug 2026 14:36:33 +0200
Subject: [PATCH 8/9] fix bad test

---
 tests/renderer_test.php | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/tests/renderer_test.php b/tests/renderer_test.php
index e6a60296..e9ac96e8 100644
--- a/tests/renderer_test.php
+++ b/tests/renderer_test.php
@@ -355,10 +355,9 @@ public function test_right_answer_feedback_uses_appropriate_decimal_separator():
         $this->check_output_contains_lang_string('correctansweris', 'qtype_formulas', '3,5');
 
         // Make sure the decimal comma is also applied for numbers that are string tokens.
-        // Note that we *should* have 3,50 as the model answer, but as we are converting
-        // the string output from sigfig() back to a number, trailing zeroes will be lost.
         $q = $this->get_test_formulas_question('testsinglenum');
         $q->parts[0]->answer = 'sigfig(3.5, 3)';
+        $this->start_attempt_at_question($q, 'immediatefeedback', 1);
         $this->process_submission(['0_0' => '42', '-submit' => 1]);
         $this->check_output_contains_lang_string('correctansweris', 'qtype_formulas', '3,50');
     }

From 01b24b98635d4e467cc3ddb1c55fa070f6f993e5 Mon Sep 17 00:00:00 2001
From: Philipp Imhof <52650214+PhilippImhof@users.noreply.github.com>
Date: Sun, 2 Aug 2026 10:20:00 +0200
Subject: [PATCH 9/9] special case for zero

---
 classes/local/functions.php | 4 ++--
 tests/functions_test.php    | 1 +
 2 files changed, 3 insertions(+), 2 deletions(-)

diff --git a/classes/local/functions.php b/classes/local/functions.php
index b8498dd4..52885da0 100644
--- a/classes/local/functions.php
+++ b/classes/local/functions.php
@@ -659,8 +659,8 @@ public static function sigfig($number, $precision): string {
         $digitsafter = max(0, $digitsafter);
 
         // If the absolute value of the *original* number is >= 1e-4 and < 1e14, we can format
-        // it and return a string.
-        if (abs($originalnumber) >= 1e-4 && abs($originalnumber) < 1e14) {
+        // it and return a string. The same is true if the rounded number is zero.
+        if ($number == 0 || (abs($originalnumber) >= 1e-4 && abs($originalnumber) < 1e14)) {
             return number_format($number, $digitsafter, '.', '');
         }
 
diff --git a/tests/functions_test.php b/tests/functions_test.php
index 252d9741..8c74b01a 100644
--- a/tests/functions_test.php
+++ b/tests/functions_test.php
@@ -669,6 +669,7 @@ public static function provide_sigfig_expressions(): array {
             ['123.00', 'sigfig(123, 5)'],
             ['99999.0', 'sigfig(99999, 6)'],
             ['-0.00123', 'sigfig(-0.00123, 3)'],
+            ['0.00', 'sigfig(0, 3)'],
         ];
     }