iKj% ddlZddlZddlmZdededefdZddd ded ed ed edef d ZGddejZ Gdde Z Gdde Z GddZ y)N)clampdftreturnc^t|tsJ|dkrtd||dk(ryt|}d||z|z z}|dzdk(r|t j |z }t j |}|dkDr:d}d}d}||dz kr!||dz ||zz z}||z }|dz }||dz kr!|||z|z z }|dtjz z}nMd}d}d}||dz kr!||dz ||zz z}||z }|dz }||dz kr!||zt j ||zz }|d krdd|zz Sdd|zzS) zxStudent's t CDF for integer df >= 1, evaluated at t. Closed-form finite sum from Abramowitz & Stegun 26.7.7-8. z$stdtr requires integer df >= 1, got ??g@r) isinstanceint ValueErrorabsmathsqrtatanpi) rrabs_tzupftzjs c/home/oem/CyberBrain26-unified/.venv/lib/python3.12/site-packages/hypothesis/internal/statistics.pystdtrrs b#   Av?tDEECx FE eemb  A Av{ DIIbM ! IIaL 6ABArAv+q1uQ''RQrAv+ QNA S477]   26k 1q5QU# #B GA FA26k I !b&) )E3q=4sS1W}4g|=2)epsmax_iterrr!r"c|dkrtd||dk(ryd|cxkrdksntd||dk(r|dkDrStjtjd|z ztjtjd|z zz Stjtj|z tjtj|zz S|dk(r'd|zdz tj d|zd|z zz S|dkDrdnd}|dkDr|nd|z }d \}}t |||kr|dz}t |||krtjd|dzzdtj|tjzzz tjd|zz }d||zz} t|D]} t || } | |kr| }n| }|d|dzztj| | z|z zz } tj| } | dk(r d||zz} n#| | |z | z z }||cxkr|krnn|nd||zz} ||z |dt| zzks|| zS|| zS) uJInverse Student's t CDF (quantile) for integer df >= 1. df ∈ {1, 2}: closed-form analytic quantile (Shaw 2006, eq 35-36). df >= 3: bracketed Newton iteration on stdtr — doubling search from t=1 to bracket the target, then Newton steps with bisection fallback. Always converges; ~5-10 iterations typical. rz&stdtrit requires integer df >= 1, got r r r z stdtrit requires 0 < p < 1, got r g)r r ) rrcosrsinrrlgammalograngelog1pexpr)rrr!r"signqlohilog_normr_Flog_frt_newtons rstdtritr4?sk AvA"FGGCx =S=;A3?@@ Qw s788DGGq1u-.$''QU:K1LL L1%%1(=== QwA TYYq1uA777c'3tD W!a%A FB B-!  a B-!  C26N# dgg& & ' ++cBh   rBwA 8_ "aL q5BB3"q&>DJJq1urz,BBB HHUO 8rBwAAEQ;H(0b0cR"WoA 7SAAJ' '  !8O !8OrceZdZejdedefdZejdedefdZejdedefdZy) _DistributionxrctNNotImplementedErrorselfr7s rcdfz_Distribution.cdf!!rrctr9r:r=rs r inverse_cdfz_Distribution.inverse_cdfr?rctr9r:r<s rpdfz_Distribution.pdfr?rN) __name__ __module__ __qualname__abcabstractmethodfloatr>rBrDrrr6r6sx"U"u"" "U"u"" "U"u""rr6cPeZdZdZdeddfdZdedefdZdedefd Zdedefd Zy) UniformDistributionz2Uniform distribution on [-half_width, half_width]. half_widthrNc||_yr9rN)r=rNs r__init__zUniformDistribution.__init__s $rr7c||j kry||jkDry||jzd|jzz S)Nr r r rPr<s rr>zUniformDistribution.cdfs@   t DOO#DOO(;<rBrDrKrrrMrMsQ<%e%%=U=u=:U:u:UurrMcxeZdZdZej dZdededdfdZ dedefd Z d edefd Z dedefd Z y) LogStudentTDistributionaStudent's t distribution, in the transformed domain of log_2(x). Y = sign(x) * log_2(1 + |x|) ~ scale_bits * t(df). Note that we only support integer df. This is to reduce surface area in the vendored mathematical functions, which are simpler when df is an integer. There is no fundamental difficulty to supporting float df, other than the necessary due diligence for the vendored code. r scale_bitsrrNc||_||_tj|dzdz tj|tj ztj|dz zz |_yNrr )rXrrgammarr_t_coef)r=rXrs rrQz LogStudentTDistribution.__init__sS$zz26Q,/ IIb477l #djja&8 8  rr7ctjtjdt|z||jz }t t |j|S)Nr)rcopysignlog2rrXrJrr)r=r7ys rr>zLogStudentTDistribution.cdfsB MM$))AAJ/ 3doo EU477A&''rrc|jtt|j|z}t d|d}t j t jt||jz|S)Nii) rXrJr4rrrr^expm1rLN2)r=rr`s rrBz#LogStudentTDistribution.inverse_cdfsW OOeGDGGQ$78 8 %D !}}TZZA(9:A>>rcHtjtjdt|z||jz }|j d||z|j z z|j dz dz zz}||jdt|zz|jzz SrZ)rr^r_rrXr\rrc)r=r7r`f_ts rrDzLogStudentTDistribution.pdfs MM$))AAJ/ 3doo Ella!a%$''/11~7IJJdooSV4txx?@@r) rErFrGrUrr'rcrJrrQr>rBrDrKrrrWrWsn $((1+C e   (U(u(?U?u?AUAuArrWcHeZdZdZdedededdfdZdedefd Zd edefd Zy) PiecewiseDistributionuTwo-region splice: `inner` on (-switchover, switchover), `outer` on |x| >= switchover. Each region is normalized so that the resulting density is continuous at ±switchover and integrates to 1. Both inner and outer must be symmetric around 0. innerouter switchoverrNch||_||_||_|j| |_|j||_|j| |_|j||_d|j|j z z }|j |jz }|j|}|j|}|dk7s Jd|dd||z|z |zz |_ |j|z|z |_ |j|z|_ |j|j z|_ y)Nrrzinner.pdf(switchover=zF) == 0; cannot density-match. inner must have support at the boundary.) rhrirjr> _inner_g_neg _inner_g_pos _outer_g_neg _outer_g_posrD_alpha_beta _inner_mass _left_mass)r=rhrirjouter_outer_massinner_inner_mass inner_pdf outer_pdfs rrQzPiecewiseDistribution.__init__s2   $!IIzk2!IIj1!IIzk2!IIj1 1 1D4E4E EF,,t/@/@@IIj) IIj) A~ #J<01 1 ~9'77)CFVVW [[9,y8 ::(88++(9(99rr7c||j kr(|j|jj|zS||jkrB|j|j |j j||jz zzS|j|jz|j|jj||jz zzSr9) rjrprir>rsrqrhrlrrror<s rr>zPiecewiseDistribution.cdfs  ;;!22 2 t ??TZZ q!D$5$55&  OO kkTZZ^^A.1B1BBC D rrc||jkr(|jj||jz S||j|jzkrD|j ||jz |j z z}|jj|S|jj||jz |jz |jz |jzSr9) rsrirBrprrrlrqrhro)r=rtargets rrBz!PiecewiseDistribution.inverse_cdfs  ::))!dkk/: : t!1!11 1&&!doo*=)KKF::))&1 1zz%%  4#3#3 3t{{ BTEVEV V  r) rErFrGrUr6rJrQr>rBrKrrrgrgsR:%:.;:IN: :8  U  u   U u rrg) rHrhypothesis.internal.floatsrrrJrr4ABCr6rMrWrgrKrrr}s ,$5c$5e$5$5P(-b6 66$68;6 6B "CGG "-,$Am$AN9 9 r