fix: render log ticks in mathtext (#1405)

### **User description**
## Summary
- ensure log and symlog tick formatting never falls back to literal 0
for small positive powers of ten
- wrap power-of-ten tick labels in mathtext delimiters so matplotlib
renders superscripts
- update log/symlog regression tests to expect the mathtext output

## Testing
- make test
- PATH="/tmp/fortplot_shim:$PATH" make verify-artifacts


___

### **PR Type**
Bug fix


___

### **Description**
- Wrap log/symlog tick labels in mathtext delimiters (`$...$`)

- Fix zero value detection using epsilon comparison

- Update test expectations for mathtext formatting

- Improve log scale detection logic


___

### Diagram Walkthrough


```mermaid
flowchart LR
  A["Log/Symlog Ticks"] --> B["format_power_of_ten_label()"]
  B --> C["Add $...$ delimiters"]
  C --> D["Mathtext Rendered Labels"]
  E["Zero Detection"] --> F["Use epsilon() comparison"]
  F --> G["More Accurate Zero Handling"]
```



<details> <summary><h3> File Walkthrough</h3></summary>

<table><thead><tr><th></th><th align="left">Relevant
files</th></tr></thead><tbody><tr><td><strong>Bug
fix</strong></td><td><table>
<tr>
  <td>
    <details>
<summary><strong>fortplot_axes.f90</strong><dd><code>Improve log scale
detection and zero handling</code>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; </dd></summary>
<hr>

src/ui/fortplot_axes.f90

<ul><li>Add <code>is_log_scale</code> variable for cleaner scale type
checking<br> <li> Replace hardcoded epsilon with
<code>epsilon(1.0_wp)</code> for zero detection<br> <li> Add separate
zero handling for non-log scales with <code>TICK_EPS</code></ul>


</details>


  </td>
<td><a
href="https://github.com/lazy-fortran/fortplot/pull/1405/files#diff-d0c945cc3f3dbc1f92931a90eacb84df8d6ccb60169a619700703acd8d60c5f8">+8/-4</a>&nbsp;
&nbsp; &nbsp; </td>

</tr>

<tr>
  <td>
    <details>
<summary><strong>fortplot_tick_formatting.f90</strong><dd><code>Add
mathtext delimiters to power-of-ten labels</code>&nbsp; &nbsp; &nbsp;
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; </dd></summary>
<hr>

src/utilities/ticks/fortplot_tick_formatting.f90

<ul><li>Wrap power-of-ten labels in mathtext delimiters
(<code>$10^{n}$</code>)<br> <li> Apply formatting to both positive and
negative powers</ul>


</details>


  </td>
<td><a
href="https://github.com/lazy-fortran/fortplot/pull/1405/files#diff-b854d288119583f4762e92f3ee5bbc09d35ae2309e32cd9820d42cba62381ab6">+2/-2</a>&nbsp;
&nbsp; &nbsp; </td>

</tr>
</table></td></tr><tr><td><strong>Tests</strong></td><td><table>
<tr>
  <td>
    <details>
<summary><strong>test_log_symlog_ticks.f90</strong><dd><code>Update test
expectations for mathtext formatting</code>&nbsp; &nbsp; &nbsp; &nbsp;
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; </dd></summary>
<hr>

test/test_log_symlog_ticks.f90

<ul><li>Update expected tick labels from <code>10^{n}</code> to
<code>$10^{n}$</code><br> <li> Update both positive and negative power
expectations<br> <li> Maintain test logic while adjusting format
expectations</ul>


</details>


  </td>
<td><a
href="https://github.com/lazy-fortran/fortplot/pull/1405/files#diff-6b6eb24c38744dba8b05e680d94e05fc769b5bf8b5d110a8e7c056166e04b0bb">+10/-10</a>&nbsp;
</td>

</tr>

<tr>
  <td>
    <details>

<summary><strong>test_pdf_log_symlog_tick_positions.f90</strong><dd><code>Update
PDF test for mathtext tick labels</code>&nbsp; &nbsp; &nbsp; &nbsp;
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
&nbsp; &nbsp; &nbsp; </dd></summary>
<hr>

test/test_pdf_log_symlog_tick_positions.f90

<ul><li>Update label comparisons to expect <code>$10^{n}$</code>
format<br> <li> Remove trailing whitespace<br> <li> Maintain position
verification logic</ul>


</details>


  </td>
<td><a
href="https://github.com/lazy-fortran/fortplot/pull/1405/files#diff-5031fa6f40167a392d161cfc5d1f2147b10ef45ea8ce68c781e20b3d3c37ca75">+4/-5</a>&nbsp;
&nbsp; &nbsp; </td>

</tr>
</table></td></tr></tr></tbody></table>

</details>

___

Author: krystophny

src/ui/fortplot_axes.f90

@@ -156,14 +156,18 @@ function format_tick_label(value, scale_type) result(label)
         character(len=*), intent(in) :: scale_type
         character(len=20) :: label
         real(wp) :: abs_value
-        
+        logical :: is_log_scale
+
         abs_value = abs(value)
-        
-        if (abs_value < 1.0e-10_wp) then
+        is_log_scale = trim(scale_type) == 'log' .or. trim(scale_type) == 'symlog'
+
+        if (abs_value <= epsilon(1.0_wp)) then
             label = '0'
-        else if ((trim(scale_type) == 'log' .or. trim(scale_type) == 'symlog') .and. is_power_of_ten(value)) then
+        else if (is_log_scale .and. is_power_of_ten(value)) then
             ! Unify log and symlog formatting: show powers of ten with superscript
             label = format_power_of_ten_label(value)
+        else if (.not. is_log_scale .and. abs_value < TICK_EPS) then
+            label = '0'
         else if (abs_value >= SCIENTIFIC_THRESHOLD_HIGH .or. abs_value < SCIENTIFIC_THRESHOLD_LOW) then
             ! Use scientific notation for very large or very small values
             write(label, '(ES10.2)') value

src/utilities/ticks/fortplot_tick_formatting.f90

@@ -106,7 +106,7 @@ function format_log_tick_value(value) result(formatted)
         integer :: exponent
         logical :: is_power_of_ten
 
-        if (abs(value) < 1.0e-10_wp) then
+        if (abs(value) <= epsilon(1.0_wp)) then
             formatted = '0'
             return
         end if
@@ -167,9 +167,9 @@ function format_power_of_ten_label(value) result(formatted)
 
         ! Always emit mathtext-style powers of ten to mirror matplotlib output
         if (value < 0.0_wp) then
-            write(formatted, '(A, I0, A)') '-10^{', exponent, '}'
+            write(formatted, '(A, I0, A)') '$-10^{', exponent, '}$'
         else
-            write(formatted, '(A, I0, A)') '10^{', exponent, '}'
+            write(formatted, '(A, I0, A)') '$10^{', exponent, '}$'
         end if
         formatted = adjustl(formatted)
     end function format_power_of_ten_label

test/test_log_symlog_ticks.f90

@@ -58,18 +58,18 @@ subroutine test_should_format_log_ticks_as_powers_of_ten()
             stop 1
         end if
 
-        if (trim(format_tick_label(ticks(1), 'log')) /= '10^{0}') then
-            print *, 'FAIL: log tick at 1 should be formatted as 10^{0}'
+        if (trim(format_tick_label(ticks(1), 'log')) /= '$10^{0}$') then
+            print *, 'FAIL: log tick at 1 should be formatted as $10^{0}$'
             stop 1
         end if
 
-        if (trim(format_tick_label(ticks(2), 'log')) /= '10^{1}') then
-            print *, 'FAIL: log tick at 10 should be formatted as 10^{1}'
+        if (trim(format_tick_label(ticks(2), 'log')) /= '$10^{1}$') then
+            print *, 'FAIL: log tick at 10 should be formatted as $10^{1}$'
             stop 1
         end if
 
-        if (trim(format_tick_label(ticks(3), 'log')) /= '10^{2}') then
-            print *, 'FAIL: log tick at 100 should be formatted as 10^{2}'
+        if (trim(format_tick_label(ticks(3), 'log')) /= '$10^{2}$') then
+            print *, 'FAIL: log tick at 100 should be formatted as $10^{2}$'
             stop 1
         end if
     end subroutine test_should_format_log_ticks_as_powers_of_ten
@@ -114,8 +114,8 @@ subroutine test_should_include_symlog_threshold_ticks()
         do i = 1, num_ticks
             if (abs(ticks(i) + 10.0_wp) <= 1.0e-9_wp) then
                 label = trim(format_tick_label(ticks(i), 'symlog'))
-                if (label /= '-10^{1}') then
-                    print *, 'FAIL: symlog negative threshold should be -10^{1}, got', label
+                if (label /= '$-10^{1}$') then
+                    print *, 'FAIL: symlog negative threshold should be $-10^{1}$, got', label
                     stop 1
                 end if
                 if (found_negative_threshold) then
@@ -125,8 +125,8 @@ subroutine test_should_include_symlog_threshold_ticks()
                 found_negative_threshold = .true.
             else if (abs(ticks(i) - 10.0_wp) <= 1.0e-9_wp) then
                 label = trim(format_tick_label(ticks(i), 'symlog'))
-                if (label /= '10^{1}') then
-                    print *, 'FAIL: symlog positive threshold should be 10^{1}, got', label
+                if (label /= '$10^{1}$') then
+                    print *, 'FAIL: symlog positive threshold should be $10^{1}$, got', label
                     stop 1
                 end if
                 if (found_positive_threshold) then

test/test_pdf_log_symlog_tick_positions.f90

@@ -35,10 +35,10 @@ program test_pdf_log_symlog_tick_positions
         if (abs(log10(yexp) - nint(log10(yexp))) < 1.0e-12_wp) then
             idx = -1
             do i = 1, ny
-                if (trim(yl(i)) == '10^0' .and. yexp == 1.0_wp) idx = i
-                if (trim(yl(i)) == '10^1' .and. yexp == 10.0_wp) idx = i
-                if (trim(yl(i)) == '10^2' .and. yexp == 100.0_wp) idx = i
-                if (trim(yl(i)) == '10^3' .and. yexp == 1000.0_wp) idx = i
+                if (trim(yl(i)) == '$10^{0}$' .and. yexp == 1.0_wp) idx = i
+                if (trim(yl(i)) == '$10^{1}$' .and. yexp == 10.0_wp) idx = i
+                if (trim(yl(i)) == '$10^{2}$' .and. yexp == 100.0_wp) idx = i
+                if (trim(yl(i)) == '$10^{3}$' .and. yexp == 1000.0_wp) idx = i
             end do
             if (idx > 0) then
                 ymin = 1.0_wp; ymax = 1000.0_wp
@@ -79,4 +79,3 @@ program test_pdf_log_symlog_tick_positions
 
     print *, 'PASS: PDF log/symlog tick positions verified'
 end program test_pdf_log_symlog_tick_positions
-