Optimize hypoStiff: cache repeated exponent computations

[patrickstaubach]

Motivation

The hypoStiff subroutine computes the same expensive power and exponential operations multiple times per call. This contributes significantly to the overall UMAT evaluation cost during FEM integration. Caching these intermediate values avoids redundant floating-point operations without changing the mathematical behavior.

Approach

In the hypoStiff subroutine, the expression (3.0d0*Stressp/MatP%bauerHs)**MatP%bauerN is computed three times to derive edi, eci, and eii. Similarly, the derivative (3.0d0*Stressp/MatP%bauerHs)**(MatP%bauerN-1.0d0) is computed once for mtd.

Changes made:

• Introduced temporary variables x, xpow, and xpow_m1 in the hypoStiff declarations
• Compute x = 3.0d0*Stressp/MatP%bauerHs once, then cache xpow = x**MatP%bauerN and xpow_m1 = x**(MatP%bauerN-1.0d0)
• Reuse cached values in all three exponential expressions and the mtd calculation
• Added tests/bench_hypo.f90 minimal benchmark program for runtime verification

Impact

• Reduces redundant pow/exp calls in hot path
• Improves numerical consistency (same value used throughout)
• Minimal code footprint; no algorithmic changes
• Expected improvement: 5-10% on a hypoStiff-dominated workload (architecture and compiler dependent)

Testing

Compile benchmark with available Fortran compiler (Intel ifort, gfortran):

ifort -extend-source src/tools.f src/HPP_Staubach_explicit.f tests/bench_hypo.f90 -o bench_hypo.exe
./bench_hypo.exe

Compare elapsed time and output summation against baseline (compile original version without this commit).

Notes

• Temporary .obj and .mod files committed; consider adding to .gitignore for production builds
• No changes to UMAT main loop or adaptive stepping logic
• Fully backward-compatible; only internal state variable reuse