}Gj@\ddlZGddZdZdZdZdZdZd Zd Z d Z d Z d Z y)NcFeZdZdZdZdZdZedZedZ dZ y) RANArraya Array-valued Rational-Addition Number: elementwise a/b + c, where a, b, c are numpy arrays (or broadcastable). Same algebra as the scalar RAN(a,b,c) class, but every operation acts on the whole array at once via numpy instead of looping over Python RAN objects one scalar at a time. Collapse is still only performed where the original code performed it (relu's sign check, softmax boundary). abcctj|tj|_tj|tj|_tj|tj|_yN)dtype)npasarrayfloat64rrr)selfrrrs @/home/per/Documents/rational-addition-number-system/ran_array.py__init__zRANArray.__init__sDARZZ0ARZZ0ARZZ0cN|j|jz |jzSNrrs rcollapsezRANArray.collapsesvv''rct|jj|jj|jjSr)rrTrrrs rrz RANArray.Ts)$&&((DFFHH55rctj|j|j|jj Sr)r broadcastrrrshapers rrzRANArray.shapes'||DFFDFFDFF3999rc"d|jdS)NzRANArray(shape=))rrs r__repr__zRANArray.__repr__s  A..rN) __name__ __module__ __qualname____doc__ __slots__rrpropertyrrrrrrrsE I1 (66::/rrc|j|jz|j|jzz}|j|jz}|j|jz}t|||Sr)rrrrxyrrrs rran_addr*'sU acc ACC!##IA acc A acc A Aq! rc\t|j |j|j Sr)rrrr)r(s rran_negr,.s! QSSD!##t $$rc,t|t|Sr)r*r,)r(r)s rran_subr.2s 1gaj !!rcN|j|jz|j|jz|jzz|j|jz|jzz}|j|jz}|j|jz}t|||Sr)rrrrr's rran_mulr06sv acc ACC!##IO#accACCi!##o5A acc A acc A Aq! rctj|tj}t|tj|tj |Sr )r r rr ones_like zeros_likevaluevs r const_ranr7Es6 5 +A Ar||A a(8 99rctj|tj}ttj|tj ||Sr )r r rrr3r2r4s rreal_ranr9Js6 5 +A BMM!$bll1oq 99rctj|tj}t|tj||j Sr )r zerosrrr2copy)rzs rzero_ranr>Os3 bjj)A Ar||A 11rcVtj||d}tj||d}tj||d}|jddkDr|jd}|dz}|d||d||d|}}}||d|z||d|z||d|z} } } || z|| zz} || z} || z}|dzdk(rTtj| |ddgd} tj| |ddgd} tj||ddgd}| | |}}}|jddkDr|d|d|dfS)Nraxis)r moveaxisr concatenate)rrrrDnhalfa1b1c1a2b2c2nanbncs r_tree_reduce_addrR[s` AtQA AtQA AtQA ''!*q. GGAJAvuXq$x5DBtAH%qa$h'74D9IB "WrBw  "W "W q5A:QrsV 15BQrsV 15BQrsV 15Bb"a1 ''!*q. Q41qt rctj|jdk(rtj|jdk(r|j|jz|j|jzz|j|jzz}|j|jz}tj |jj d|jj df}t|||S|jdddddf}|jdddddf}|jdddddf}|jdddddf}|jdddddf} |jdddddf} ||z|| z| zz||z|zz} || z} || z} t| | | d\}}}t|||S)a x: RANArray, components shaped (N, D) w: RANArray, components shaped (D, H) returns: RANArray, components shaped (N, H) Equivalent to sum_d ran_mul(x[:, d], w[d, :]), i.e. a RAN-space matrix product where each individual term is still formed with the real RAN multiply/add formulas (no rounding is done early). Fast path: in this network b is provably 1 for every RAN value at every step (weights/biases are built as RAN(v,1,0) or RAN(0,1,0), inputs as RAN(0,1,x), and __truediv__ -- the only op that changes b -- is never used). With b == e == 1 everywhere, the general ran_mul/ran_add reduction collapses algebraically to two ordinary linear sums, which lets us use BLAS matmuls instead of a Python-level reduction -- same exact numbers, much faster. If that invariant is ever broken (e.g. division gets introduced), we fall back to the general, slower tree reduction so results stay correct either way. r@rNrC) r allrrronesrrrR)r(wrrrxaxbxcwawbwcpapbpcs r ran_matmulr`psw( vvaccQhBFF133!8, CC!##Iacc !ACC!##I - CC!##I GGQSSYYq\13399Q<0 11a  Q4ZB Q4ZB Q4ZB T1aZB T1aZB T1aZB b27R< "r'B, .B bB bBr2r2GAq! Aq! rctj|jdk(ruttj|j dtj |j jdtj|jdSt|j |j|jd\}}}t|||S)zSum a RANArray along axis 0 (used for bias gradients). Same fast-path reasoning as ran_matmul: with b == 1 throughout, RAN addition of a column is just np.sum on `a` and on `c` separately.r@rrC) r rTrrsumrrUrrrR)r(rrrs rran_sum0rcs vvaccQhqss+RWWQSSYYq\-BBFF133UVDWXXqssACC15GAq! Aq! r) numpyr rr*r,r.r0r7r9r>rRr`rcr%rrresF//F%": : 2*&Rr