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Bugs Found During SLATEC Modernisation

This document records bugs discovered and fixed during the GOTO elimination and modernisation effort.

1. DBESK/BESK Numerical Drift (K Bessel Function)

Discovery Date: 2025-12-20 Severity: High (numerical accuracy) Affected Routines: dbsknu.f90, besknu.f90 Reference: Temme, N.M., J. Comp. Physics 19, 1975, pp. 324-337

Symptoms

  • K Bessel function values showed relative error of approximately 4×10⁻⁵
  • Example: K₄(1) computed as 44.2324 instead of correct value 44.2341

Root Cause

During GOTO elimination, the control flow for the power series computation (X ≤ 2) was incorrectly structured. The original SLATEC code used:

! After series computation
GOTO 20  ! Skip to forward recursion
...
! Coefficient/asymptotic/Miller code
...
20  ck = (dnu+dnu+2._DP)/X  ! Forward recursion

The modernised code removed the GOTO but failed to skip the coefficient/asymptotic/Miller section. This caused the already-computed series values (s1, s2) to be overwritten by the coefficient calculation code.

Fix

Added a series_done logical flag:

LOGICAL :: series_done
...
series_done = .FALSE.
...
! After series computation
series_done = .TRUE.
...
! Coefficient/asymptotic/Miller section
IF( .NOT. series_done ) THEN
  ! ... coefficient/asymptotic/Miller code ...
END IF

Verification

After the fix, the relative error dropped from ~4×10⁻⁵ to ~1×10⁻¹⁴ (machine precision).

2. DCOV/SCOV Missing BLOCK Statement

Discovery Date: 2025-12-20 Severity: Medium (compilation failure) Affected Routines: dcov.inc, scov.inc (MINPACK covariance routines)

Symptoms

Compilation error: Name 'process' in EXIT statement at (1) is unknown

Root Cause

During GOTO elimination, a named BLOCK construct was introduced to replace a labelled error exit, but the opening process: BLOCK statement was missing whilst END BLOCK process remained.

Fix

Added the missing process: BLOCK statement before the main IF block.

3. DPSORT/HPSORT/IPSORT/SPSORT Unclosed DO Loop

Discovery Date: 2025-12-20 Severity: Medium (compilation failure) Affected Routines: Data handling sort routines

Symptoms

Compilation error: Syntax error in END DO statement

Root Cause

A nested DO loop was missing its END DO statement. The code had:

main_sort: DO
  ...
  DO            ! Inner loop
    ...
  END DO main_sort  ! Wrong! This closes outer loop, not inner

Fix

Added the missing END DO for the inner loop:

main_sort: DO
  ...
  DO            ! Inner loop
    ...
  END DO        ! Closes inner loop
END DO main_sort  ! Now correctly closes outer loop

4. PCHID/PCHIA Undeclared Variable

Discovery Date: 2025-12-20 Severity: Low (compilation failure) Affected Routines: PCHIP interpolation routines

Symptoms

Compilation error: Symbol 'ierr' at (1) has no IMPLICIT type

Root Cause

During GOTO elimination, error return code assignments (Ierr = -3) were left in place but the subsequent line was changed to ERROR STOP. The variable assignment became redundant and the variable was never declared.

Fix

Removed the redundant Ierr assignments since the ERROR STOP statements make them unreachable.

Pre-existing Issues (Not Introduced by Modernisation)

The following issues were discovered but predate the modernisation effort:

  1. PCHSP.inc: Contains GOTOs (20, 50) that were never converted
  2. PCHFE.inc: Contains multiple unconverted GOTOs (100, 200, 300, 320, 350, 400, 600)
  3. Various PCHIP routines: Unused labels (100, 200) generating warnings

These require additional GOTO elimination work in the interpolation module.

Build System Issues

The following structural issues were addressed to enable compilation:

  1. Include files as .f90: Files intended for inclusion via Fortran include statements were named .f90, causing fpm to attempt standalone compilation. Renamed to .inc.

  2. Module dependencies: Several modules (blas, lapack, linpack) needed to be extracted to separate files to ensure correct compilation order.

  3. Missing USE statements: Some module files lacked explicit USE statements for their dependencies, preventing fpm from determining the correct build order.