o i @sHddlZdededefddZd ded ed edeeeeffd d ZdS)Njneg_hreturncsJtdkr dt|Stfddt|D}t||S)u1 Compute φⱼ(z) where z = -h (negative step size in log-space) φ₁(z) = (e^z - 1) / z φ₂(z) = (e^z - 1 - z) / z² φⱼ(z) = (e^z - Σₖ₌₀^(j-1) zᵏ/k!) / zʲ These functions naturally appear when solving: dx/dt = A*x + g(x,t) (linear drift + nonlinear part) g|=g?c3s"|] }|t|VqdS)N)math factorial).0krJ/home/ubuntu/LTX-2/packages/ltx-pipelines/src/ltx_pipelines/utils/res2s.py s zphi..)absrrsumrangeexp)rr remainderr r r phis r?h phi_cachec2c sjdtdtdtffdd }| |}|d|}||}| }|d|}||} |d|} | | } || | fS)a Compute res_2s Runge-Kutta coefficients for a given step size. Args: h: Step size in log-space = log(sigma / sigma_next) phi_cache: Dictionary to cache phi function results. Cache key: (j, neg_h) c2: Substep position (default 0.5 = midpoint) Returns: a21: Coefficient for computing intermediate x b1, b2: Coefficients for final combination rrrcs.||f}|vr |St||}||<|S)zGet phi value with caching.)r)rr cache_keyresultrr r get_phi%s  z'get_res2s_coefficients..get_phi)intfloat) rrrrneg_h_c2phi_1_c2a21 neg_h_full phi_2_fullb2 phi_1_fullb1r rr get_res2s_coefficientss    r')r)rrrrdicttupler'r r r r s*