o
    1&iG                    @   s
  d Z ddlZddlZddlZddlmZ ddlmZm	Z	 ddl
mZmZmZ ddlmZ ddlmZ ddlmZmZ dd	lmZ dd
lmZ edZejZedZedZdd Ze Z dZ!e"ee!Z#e$ee%ee!ee egZ&e'e&Z(dd Z)dd Z*dd Z+dd Z,dd Z-dd Z.dd Z/dd  Z0d!d" Z1d#d$ Z2d%d& Z3d'd( Z4eej5d)d* Z6eejj5d+d* Z6d,d- Z7eejd.d/ Z8eejjeejj9eejj:eejj;d0d1 Z<eejjeejj9eejj:eejj;dd2d3Z=eej>eej?d4d5 Z@eejjAeejjBd6d7 ZCeejjBd8d9 ZDeejjBd:d; ZEeejjAd<d= ZFeejjBd>d? ZGd@dA ZHdBdC ZIdDdE ZJeejKdFdG ZLdHdI ZMeejNdJdK ZOeejNdLdM ZPdNdO ZQeejNdPdQ ZReejSdRdS ZTeejjSdTdU ZUeejjSdVdW ZVeejjSdXdY ZWeejjXdZd[ ZYeejXd\d] ZZeejjXd^d_ Z[d`da Z\eejjXdbdc Z]eej^ddde Z_eej^dfdg Z`eejj^dhdg Z`eejj^ddidjZaeejbdkdl Zceejjdeejjedmdn Zfeejjedodp Zgdqdr Zheejjedsdt Zieejjddudv Zjeejkdwdx Zleejjmdydz Znd{d| Zoeejjmd}d~ Zpeejqdd Zreejjsdd Zteejjsdd Zteejjueejjsdd Zteejjudd Zveejjwdd Zxeejjwdd Zyeejjwdd Zzeejjwdd Z{eej|dd Z}dd Z~eejdd Zeejjdd Zeejjdd Zeejdd Zeejjdd Zeejjdd Zeejdd Zeejjdd Zdd Zeejjdd Zeejjdd Zeejjdd Zeejjdd Zeejjdd Zeejjdd Zeejjdd Zeejjdd Zeejjdd Zeejjdd Zeejjdd Zeejjdd Zeejjdd Zeejjdd Zeejjdd Zeejjdd Zeejjdd Zdd ZeejjddĄ ZeejjddƄ ZeejjddȄ Zeejjddʄ Zdd̄ Zdd΄ ZeejjddЄ ZeejjddЄ Zeejjddӄ ZeejjddՄ Zeejjddׄ Zeejjddل Zeejjddۄ Zeejjddۄ Zeejjddބ Zeejjdd Zeejjdd Zeejjdd Zeejjdd Zeejjdd Zeejjdd Zeejjdd Zeejjdd Zeejjdd Zeejjdd Zdd Zeejdd Zeejjdd Zeejjădd Zeejjƃdd Zeejjǃdd ZeejjȃdddZeejjɃdd dZeejjʃdd ZeejjʃdddZedd Zeejj̃dd Zeejj̃dd	dZed
d Zedd ZdS (  z6
Implement the random and np.random module functions.
    N)ir)is_nonelikeis_empty_tuple)	intrinsicoverloadregister_jitable)Registry	signature)typescgutils)NumbaTypeError)LONG_MAXZ
randomimpl    @   c                 C   s   t t| S N)r   Constantint32_tx r   CC:\wamp64\www\opt\env\Lib\site-packages\numba/cpython/randomimpl.py	const_int      r   ip  c                 C   sT   |dv sJ d| }t td}t|j||}|jd |jd ||dS )z
    Get a pointer to the given thread-local random state
    (depending on *name*: "py" or "np").
    If the state isn't initialized, it is lazily initialized with
    system entropy.
    )pynpinternalznumba_get_%s_random_stater   ZreadnoneZnounwind)	r   FunctionTypernd_state_ptr_tr   get_or_insert_functionmodule
attributesaddcall)contextbuildername	func_namefntyfnr   r   r   get_state_ptr2   s   r*   c                 C      t | |dS )z@
    Get a pointer to the thread-local Python random state.
    r   r*   r$   r%   r   r   r   get_py_state_ptrC      r.   c                 C   r+   )z?
    Get a pointer to the thread-local Numpy random state.
    r   r,   r-   r   r   r   get_np_state_ptrI   r/   r0   c                 C   r+   )zB
    Get a pointer to the thread-local internal random state.
    r   r,   r-   r   r   r   get_internal_state_ptrO   r/   r1   c                 C   s   t | |ddS Nr   r   gep_inboundsr%   	state_ptrr   r   r   get_index_ptrV      r7   c                 C      t | |ddS Nr      r3   r5   r   r   r   get_array_ptrY   r8   r<   c                 C   r9   )Nr      r3   r5   r   r   r   get_has_gauss_ptr\   r8   r>   c                 C   r9   )Nr      r3   r5   r   r   r   get_gauss_ptr_   r8   r@   c                 C   s8   t t  tf}t| jj|d}|jd 	d |S )z<
    Get the internal function to shuffle the MT taste.
    Znumba_rnd_shuffler   Z	nocapture)
r   r   VoidTyper   r   r   functionr    argsZadd_attribute)r%   r(   r)   r   r   r   get_rnd_shuffleb   s   rD   c           	   
   C   s6  t ||}||}|d|t}t|| t|}|||f |t	d| W d   n1 s5w   Y  ||}t
||}|t||d|}||t	d}||| ||||t	d}|||||t	dt	d}|||||t	dt	d	}||||t	d
}|S )zB
    Get the next int32 generated by the PRNG at *state_ptr*.
    >=r   Nr;         l   VX:    l     _    )r7   loadicmp_unsignedN_constr   if_unlikelyrD   r#   storer   r<   r4   r"   xorlshrand_shl)	r$   r%   r6   ZidxptridxZneed_reshuffler)   Z	array_ptryr   r   r   get_next_int32m   s,   



rU   c                 C   st   | t| ||td}| t| ||td}||t}||t}|||||t	tdt	tdS )zC
    Get the next double generated by the PRNG at *state_ptr*.
          g      Ag      @C)
rP   rU   r   uitofpdoubleZfdivfaddfmulr   r   )r$   r%   r6   abr   r   r   get_next_double   s   
r^   c                    sL  t |jd fdd}t t td} d|} |r\}}	| ||}
  	|
t| W d   n1 sEw   Y  |	> rW| 
|}t }
sg| 
|}  	|
t  	|tt td} || W d   n1 sw   Y  W d   n1 sw   Y   |S )z2
    Get the next integer with width *nbits*.
    r   c                    s     | }t }| jj|jjk r ||j}n| jj|jjkr+ ||j}rC t|jd} 	||} 
||S  	||S r2   )subrU   typewidthzexttruncnot_r   r   rP   rQ   )nbitsshiftrT   maskr%   Zc32r$   is_numpyr6   r   r   get_shifted_int   s   z%get_next_int.<locals>.get_shifted_intr   <=N)r   r   r`   r   Zalloca_once_valueint64_trK   if_elserN   rb   r_   rU   r"   rR   rJ   )r$   r%   r6   re   ri   rj   retZis_32bZifsmallZiflargelowhightotalr   rh   r   get_next_int   s4   


rr   c                    s,   t | tjrttd  fdd}|S d S )Nr   c                        | S r   r   r\   r)   r   r   impl   s   zseed_impl.<locals>.impl)
isinstancer   Integerr   
_seed_impl)r\   rv   r   ru   r   	seed_impl   s
   rz   c                 C   s   t | tjr
tdS d S Nr   )rw   r   rx   ry   seedr   r   r   rz         c                    s   t fdd  fddS )Nc                    s    fdd}t tjtj|fS )Nc                    sR   |\}t t  ttf}t|jj|d}|	|t
| | |f | tjd S )NZnumba_rnd_init)r   r   rA   r   r   r   r   rB   r    r#   r*   Zget_constantr   none)r$   r%   sigrC   Z
seed_valuer(   r)   
state_typer   r   codegen   s   z*_seed_impl.<locals>._impl.<locals>.codegen)r
   r   ZvoidZuint32)typingcontextr}   r   r   r   r   _impl   s   z_seed_impl.<locals>._implc                    rs   r   r   r|   r   r   r   <lambda>       z_seed_impl.<locals>.<lambda>r   r   r   )r   r   r   ry      s   
ry   c                         t dd   fddS )Nc                 S      dd }t tj|fS )Nc                 S      t | |d}t| ||S Nr   r*   r^   r$   r%   r   rC   r6   r   r   r   r         z+random_impl.<locals>._impl.<locals>.codegen)r
   r   rY   r   r   r   r   r   r         zrandom_impl.<locals>._implc                           S r   r   r   r   r   r   r          zrandom_impl.<locals>.<lambda>r   r   r   r   r   random_impl   s   
r   c                      r   )Nc                 S   r   )Nc                 S   r   r{   r   r   r   r   r   r      r   z,random_impl0.<locals>._impl.<locals>.codegen)r
   r   float64r   r   r   r   r      r   zrandom_impl0.<locals>._implc                      r   r   r   r   r   r   r   r      r   zrandom_impl0.<locals>.<lambda>r   r   r   r   r   random_impl0   s   
r   c                 C   s`   t | r	dddS t| rdddS t| tjs%t| tjr,t| jtjr.ddd}|S d S d S )Nc                 S   
   t j S r   r   randomsizer   r   r   r        
 zrandom_impl1.<locals>.<lambda>c                 S   s   t t j S r   )r   arrayr   r   r   r   r   r         c                 S   s2   t | }|j}t|jD ]	}t j ||< q|S r   )r   emptyflatranger   r   r   outout_flatrS   r   r   r   r   
  
   
zrandom_impl1.<locals>._implr   r   r   rw   r   rx   UniTupledtyper   r   r   r   r   random_impl1   s   


r   c                    D   t | tjtjfrt |tjtjfr tdd   fddS d S d S )Nc                 S   *   t |}t |}ttj||td||fS r   _double_preprocessorr
   r   r   _gauss_impl)r   musigmaloc_preprocessorscale_preprocessorr   r   r   r     
   
zgauss_impl.<locals>._implc                    
    | |S r   r   r   r   r   r   r   r     r   zgauss_impl.<locals>.<lambda>rw   r   Floatrx   r   r   r   r   r   
gauss_impl  s   
r   c                   C      dd S )Nc                   S      t jddS N              ?r   r   normalr   r   r   r   r   $      z np_gauss_impl0.<locals>.<lambda>r   r   r   r   r   np_gauss_impl0!  s   r   c                 C      t | tjtjfrdd S d S )Nc                 S      t j| dS Nr   r   locr   r   r   r   *  r   z np_gauss_impl1.<locals>.<lambda>rw   r   r   rx   r   r   r   r   np_gauss_impl1'     r   c                    r   )Nc                 S   r   r{   r   )r   r   scaler   r   r   r   r   r   1  r   znp_gauss_impl2.<locals>._implc                    r   r   r   r   r   r   r   r   r   7  r   z np_gauss_impl2.<locals>.<lambda>r   r   r   r   r   np_gauss_impl2-     
r   c                 C   Z   t | rdd S t| rdd S t| tjs#t| tjr)t| jtjr+dd }|S d S d S )Nc                 S   
   t j S r   r   r   standard_normalr   r   r   r   r   =  r   z'standard_normal_impl1.<locals>.<lambda>c                 S      t t j S r   )r   r   r   r   r   r   r   r   r   @  r   c                 S   2   t | }|j}t|jD ]	}t j ||< q|S r   )r   r   r   r   r   r   r   r   r   r   r   r   D  r   z$standard_normal_impl1.<locals>._implr   r   r   r   r   standard_normal_impl1:     r   c                 C      t | tjtjfrt |tjtjfrt|rdd S t | tjtjfr4t |tjtjfr4t|r4dd S t | tjtjfr_t |tjtjfrat |tjsYt |tjrct |jtjredd }|S d S d S d S d S )Nc                 S      t j| |S r   r   r   r   r   r   r   r   r   R  r   z np_gauss_impl3.<locals>.<lambda>c                 S      t t j| |S r   )r   r   r   r   r   r   r   r   r   W      c                 S   6   t |}|j}t|jD ]}t j| |||< q|S r   )r   r   r   r   r   r   r   r   r   r   r   r   rS   r   r   r   r   ]  
   
znp_gauss_impl3.<locals>._implrw   r   r   rx   r   r   r   r   r   r   r   r   r   r   r   np_gauss_impl3M  s4   

r   c                        fdd}|S )Nc                     sj   	 d   d } d   d }| |  ||  }|dk r |dkr nqt dt | | }||  || fS )zG
        Compute a pair of numbers on the normal distribution.
        T       @r   r          )mathsqrtlog)x1Zx2r2f_randomr   r   compute_gauss_pairg  s   z,_gauss_pair_impl.<locals>.compute_gauss_pairr   )r   r   r   r   r   _gauss_pair_implf  s   r   c                        fdd}|S )Nc                    s  |j }| |}tjtjjd }t| |}tj||dd}t||}	t||}
t	||
|
}||l\}}| ||
|	| |td|
 W d    n1 sYw   Y  |5 | |t|tt|dd}t||d\}}|||	 ||| |td|
 W d    n1 sw   Y  W d    n1 sw   Y  |\}}| ||||||
|S )N)r   r   resultr&   r   r=   r   r;   )return_typeZget_data_typer   r   r*   r   alloca_oncer@   r>   Zis_truerJ   rm   rN   r   compile_internalr   r
   r   r   Zunpack_tuplerZ   r[   )r$   r%   r   rC   tyZlltyr   r6   rn   Z	gauss_ptrZhas_gauss_ptrZ	has_gaussZthenZ	otherwisepairfirstsecondr   r   r   r   stater   r   r   y  sH   


z_gauss_impl.<locals>._implr   )r   r   r   r   r   r   r   r   x  s   $r   c                    sj   t j  t| tjr| jr fddS  fddS t| tjr/| jdkr+ fddS dd S td|  )Nc                       |  | S r   )Zsitofpr%   vr   r   r   r         z&_double_preprocessor.<locals>.<lambda>c                    r   r   )rX   r   r   r   r   r     r   r   c                    r   r   )Zfpextr   r   r   r   r     r   c                 S      |S r   r   )_builderr   r   r   r   r         z(Cannot convert {} to floating point type)	r   r   
DoubleTyperw   rx   signedr   bitwidthr   )valuer   r   r   r     s   

r   c                    s(   t | tjrtdd   fddS d S )Nc                 S   s   dd }t tj||fS )Nc           	      S   s   |\}| d|td}| d|td}t|||| d}| j|t|f W d    n1 s5w   Y  t| |d}t	| |||dS )NrE   A   ==r   z getrandbits() limited to 64 bitsr   F)
rK   r   r   rM   or_	call_convreturn_user_excOverflowErrorr*   rr   )	r$   r%   r   rC   re   	too_largeZ	too_smallmsgr6   r   r   r   r     s   
z0getrandbits_impl.<locals>._impl.<locals>.codegen)r
   r   Zuint64)r   kr   r   r   r   r     s   zgetrandbits_impl.<locals>._implc                    rs   r   r   r  r   r   r   r     r   z"getrandbits_impl.<locals>.<lambda>)rw   r   rx   r   r  r   r   r   getrandbits_impl  s
   
r  c              	      s  t  td}td}	tj dd}
  |||
   d||!  	 	 
|
||	} || |
 W d    n1 sRw   Y    d||	!   	 
|
||	} || |
 W d    n1 sw   Y   
|
t  d| d}j t|f W d    n1 sw   Y  ttjjg}t jj|d	 }d
krԈ |	n}  ||tjgt ttjtj dd fdd}d
krU  d|	9\}}|  | W d    n	1 s)w   Y  | |  W d    n	1 s?w   Y  W d    n	1 sOw   Y  n|   	|  
|S )Nr   r;   nr   <>rk   zempty range for randrange()zllvm.ctlz.%sr   rc                     s~     d}   d} |   |  t dk} |} d|} || |  |  | d S )Nwhilez	while.endr   rE   )append_basic_blockbranchposition_at_endrr   rc   icmp_signedZcbranchrN   )Zbbwhilebbendr  r  r%   r$   r  re   Zrptrr   r6   r   r   r   get_num  s   




z _randrange_impl.<locals>.get_numr	  )r*   r   r   r   r   rN   r_   if_thenr  r"   rJ   ZsdivrM   r  r  
ValueErrorr   Ztrue_bitr`   r   rB   r    rc   r#   r   ra   rm   mul)r$   r%   startstopstepr   r  r   zerooneZnptrwr  r(   r)   Znm1r  Zis_oneZ
is_not_oner   r  r   _randrange_impl  sT   


r(  c                 C      t | tjr
dd S d S )Nc                 S   s   t d| dS r:   r   	randranger"  r   r   r   r     r   z"randrange_impl_1.<locals>.<lambda>rw   r   rx   r,  r   r   r   randrange_impl_1  r~   r.  c                 C   (   t | tjrt |tjrdd S d S d S )Nc                 S   s   t | |dS Nr;   r*  r"  r#  r   r   r   r     r   z"randrange_impl_2.<locals>.<lambda>r-  r1  r   r   r   randrange_impl_2     r2  c                 C   s(   |j | kr|jrtjjS tjjS dd S )Nc                 S   r  r   r   )r  r   Z_tyr   r   r   r     r  z)_randrange_preprocessor.<locals>.<lambda>)r  r  r   Z	IRBuilderZsextrb   )r  r   r   r   r   _randrange_preprocessor  s
   
r4  c                    s   t | tjrRt |tjrTt |tjrVt| j|j|jt| j|j|j}tj|t|t	|| t	||t	||t
fdd  fddS d S d S d S )Nc                    s&   fdd}t  ||||fS )Nc              	      sD   |\}}}|| }|| }|| }t | |||| dS r   )r(  r$   r%   r   rC   r"  r#  r$  )	llvm_typer  start_preprocessorstep_preprocessorstop_preprocessorr   r   r   /  s   
z0randrange_impl_3.<locals>._impl.<locals>.codegenr	   )r   r"  r#  r$  r   )int_tyr6  r  r7  r8  r9  r   r   r   -  s   zrandrange_impl_3.<locals>._implc                    s    | ||S r   r   )r"  r#  r$  r   r   r   r   8  r   z"randrange_impl_3.<locals>.<lambda>rw   r   rx   maxr  r  Zfrom_bitwidthr   IntTyper4  r   )r"  r#  r$  r  r   )r   r:  r6  r  r7  r8  r9  r   randrange_impl_3   s   





r>  c                 C   r/  )Nc                 S   s   t | |d dS r0  r*  r\   r]   r   r   r   r   >      z randint_impl_1.<locals>.<lambda>r-  r?  r   r   r   randint_impl_1;  r3  rA  c                 C   r)  )Nc                 S   s   t jd| S r2   r   r   randintro   r   r   r   r   D  r   z#np_randint_impl_1.<locals>.<lambda>r-  rD  r   r   r   np_randint_impl_1A  r~   rE  c                    s   t | tjrBt |tjrDt| j|jt| j|j}tj|t|t	|| t	||t
fdd  fddS d S d S )Nc                    s"   fdd}t  |||fS )Nc              	      sB   |\}}|| }|| }t  d}t| |||| dS )Nr;   r   )r   r   r(  r5  )r6  r  r7  r9  r   r   r   T  s   z1np_randint_impl_2.<locals>._impl.<locals>.codegenr	   )r   ro   rp   r   )r:  r6  r  r7  r9  r   r   r   R  s   z np_randint_impl_2.<locals>._implc                    r   r   r   ro   rp   r   r   r   r   ]  r   z#np_randint_impl_2.<locals>.<lambda>r;  )ro   rp   r  r   )r   r:  r6  r  r7  r9  r   np_randint_impl_2G  s   



rG  c                    s   t | tjrt |tjrt|rdd S t | tjr(t |tjr(t|r(dd S t | tjr^t |tjr`t |tjsGt |tjrbt |jtjrdt| j|j}t	t
d|   fdd}|S d S d S d S d S )Nc                 S   r   r   rB  ro   rp   r   r   r   r   r   d  r   z#np_randint_impl_3.<locals>.<lambda>c                 S   r   r   )r   r   r   rC  rH  r   r   r   r   h  r   intc                    s:   t j| d}|j}t|jD ]}t j| |||< q|S N)r   )r   r   r   r   r   r   rC  ro   rp   r   r   r   rS   Zresult_typer   r   r   p  s
   z np_randint_impl_3.<locals>._impl)rw   r   rx   r   r   r   r   r<  r  getattrr   )ro   rp   r   r  r   r   rL  r   np_randint_impl_3`  s,   

rN  c                   C   r   )Nc                   S   r   r   r   r   uniformr   r   r   r   r   {  r   z"np_uniform_impl0.<locals>.<lambda>r   r   r   r   r   np_uniform_impl0y     rQ  c                    r   )Nc                 S   r   r   r   r
   r   r   uniform_impl)r   r\   r]   low_preprocessorhigh_preprocessorr   r   r   r     
   zuniform_impl2.<locals>._implc                    r   r   r   r?  r   r   r   r     r   zuniform_impl2.<locals>.<lambda>r   r?  r   r   r   uniform_impl2~  r   rX  c                    r   )Nc                 S   r   r{   rS  )r   ro   rp   rU  rV  r   r   r   r     rW  znp_uniform_impl2.<locals>._implc                    r   r   r   rF  r   r   r   r     r   z"np_uniform_impl2.<locals>.<lambda>r   rF  r   r   r   np_uniform_impl2  r   rY  c                    r   )Nc           	         sT   t | |}|\}} ||}||}|||}t| ||}|||||S r   )r*   Zfsubr^   rZ   r[   )	r$   r%   r   rC   r6   r\   r]   ra   r  a_preprocessorb_preprocessorr   r   r   rv     s   

zuniform_impl.<locals>.implr   )r   r[  r\  rv   r   rZ  r   rT    s   rT  c                 C   r   )Nc                 S   r   r   rO  rH  r   r   r   r     r   z"np_uniform_impl3.<locals>.<lambda>c                 S   r   r   )r   r   r   rP  rH  r   r   r   r     r   c                 S   r   r   )r   r   r   r   r   r   rP  rK  r   r   r   r     r   znp_uniform_impl3.<locals>._implr   )ro   rp   r   r   r   r   r   np_uniform_impl3  s4   

r]  c                 C   s8   dd }t | tjtjfrt |tjtjfr|S d S d S )Nc                 S   s@   t   }d}||krd| }|| } }| ||  t||   S )N      ?r   r   r   r   )ro   rp   ucr   r   r   r     s   
z triangular_impl_2.<locals>._implr   )ro   rp   r   r   r   r   triangular_impl_2  s   rb  c                 C   N   t | tjtjfr!t |tjtjfr#t |tjtjfr%dd }|S d S d S d S )Nc                 S   s`   || kr| S t   }||  ||   }||kr#d| }d| }|| } }| ||  t||   S r   r_  )ro   rp   moder`  ra  r   r   r   r     s   
 triangular_impl_3.<locals>._implr   )ro   rp   rd  r   r   r   r   triangular_impl_3     rf  c                 C   rc  )Nc                 S   sb   || kr| S t j }||  ||   }||kr$d| }d| }|| } }| ||  t||   S r   )r   r   r   r   )leftrd  rightr`  ra  r   r   r   r     s   

re  r   )rh  rd  ri  r   r   r   r   rf    rg  c                 C   s`   t |r	dddS t|rdddS t|tjs%t|tjr,t|jtjr.ddd}|S d S d S )Nc                 S      t j| ||S r   )r   r   
triangularrh  rd  ri  r   r   r   r   r     s    z!triangular_impl.<locals>.<lambda>c                 S      t t j| ||S r   )r   r   r   rk  rl  r   r   r   r     s    c                 S   s8   t |}|j}t|jD ]}t j| ||||< q|S r   )r   r   r   r   r   r   rk  )rh  rd  ri  r   r   r   rS   r   r   r   r     s
   
ztriangular_impl.<locals>._implr   r   )rh  rd  ri  r   r   r   r   r   triangular_impl  s   


rn  c                 C   s6   t | tjtjfrt |tjtjfrttjS d S d S r   )rw   r   r   rx   _gammavariate_implr   alphabetar   r   r   gammavariate_impl
  
   
rs  c                 C   r   )Nc                 S   r   r   r   r   gammashaper   r   r   r     r   z%ol_np_random_gamma1.<locals>.<lambda>r   rw  r   r   r   ol_np_random_gamma1  s   ry  c                    sL   t | tjtjfr"t |tjtjfr$tttjj  fdd}|S d S d S )Nc                    r   r   r   )rx  r   ru   r   r   rv        
z!ol_np_random_gamma2.<locals>.impl)rw   r   r   rx   r   ro  r   r   )rx  r   rv   r   ru   r   ol_np_random_gamma2     r{  c                    r   )Nc                    s  dt d }| dks|dkrtd| dkrvt d|  d }| t d }| | }	   }d|  k r9d	k s;n q+d   }t |d|  | }| t | }	|| | }
|||  |	 }|| d|
  dksq|t |
kru|	| S q,| dkrt d    | S 	   }t j|  t j }|| }|dkr|d|   }	n
t || |   }	  }|dkr||	| d  kr	 |	| S n|t |	 kr	 |	| S q)
z1Gamma distribution.  Taken from CPython.
        r   g      @r   z*gammavariate: alpha and beta must be > 0.0r   g      @r;   gHz>gP?)r   r   r   r   expe)rq  rr  SG_MAGICCONSTainvbbbcccu1u2r   r   zr  r`  r]   pr   r   r   r   #  sL   
"z!_gammavariate_impl.<locals>._implr   r   r   r   r   r   ro  "  s   7ro  c                 C   Z   t |rdd S t|rdd S t|tjs#t|tjr)t|jtjr+dd }|S d S d S )Nc                 S   r   r   ru  rx  r   r   r   r   r   r   `  r   zgamma_impl.<locals>.<lambda>c                 S   r   r   )r   r   r   rv  r  r   r   r   r   c  r   c                 S   r   r   )r   r   r   r   r   r   rv  )rx  r   r   r   r   rS   r   r   r   r   g  r   zgamma_impl.<locals>._implr   )rx  r   r   r   r   r   r   
gamma_impl]  r   r  c                 C   Z   t |rdd S t|rdd S t|tjs#t|tjr)t|jtjr+dd }|S d S d S )Nc                 S      t j| S r   r   r   standard_gammarx  r   r   r   r   r   s  r   z%standard_gamma_impl.<locals>.<lambda>c                 S      t t j| S r   )r   r   r   r  r  r   r   r   r   v  r@  c                 S   4   t |}|j}t|jD ]
}t j| ||< q|S r   )r   r   r   r   r   r   r  )rx  r   r   r   rS   r   r   r   r   z  
   
z"standard_gamma_impl.<locals>._implr   )rx  r   r   r   r   r   standard_gamma_implp  r   r  c                 C   s6   t | tjtjfrt |tjtjfrttjS d S d S r   )rw   r   r   rx   _betavariate_implr   gammavariaterp  r   r   r   betavariate_impl  rt  r  c                    sL   t | tjtjfr"t |tjtjfr$tttjj  fdd}|S d S d S )Nc                    r   r   r   r?  ru   r   r   rv     rz  zol_np_random_beta.<locals>.impl)	rw   r   r   rx   r   r  r   r   rv  )r\   r]   rv   r   ru   r   ol_np_random_beta  r|  r  c                    r   )Nc                    s(    | d}|dkrdS || |d  S )z0Beta distribution.  Taken from CPython.
        r   r   r   )rq  rr  rT   rv  r   r   r     s   
z _betavariate_impl.<locals>._implr   )rv  r   r   r  r   r    s   
r  c                 C   r  )Nc                 S   r   r   )r   r   rr  r\   r]   r   r   r   r   r     r   zbeta_impl.<locals>.<lambda>c                 S   r   r   )r   r   r   rr  r  r   r   r   r     r   c                 S   r   r   )r   r   r   r   r   r   rr  )r\   r]   r   r   r   rS   r   r   r   r     r   zbeta_impl.<locals>._implr   )r\   r]   r   r   r   r   r   	beta_impl     r  c                 C      t | tjrdd }|S d S )Nc                 S   s   t dt   |  S )z;Exponential distribution.  Taken from CPython.
            r   )r   r   r   )lambdr   r   r   r     s   zexpovariate_impl.<locals>._implrw   r   r   )r  r   r   r   r   expovariate_impl  s   
r  c                 C   "   t | tjtjfrdd }|S d S )Nc                 S   s   t dtj   |  S r   r   r   r   r   r   r   r   r   r     s   exponential_impl.<locals>._implr   )r   r   r   r   r   exponential_impl  s   r  c                 C   r  )Nc                 S   r  r   )r   r   exponentialr   r   r   r   r   r     r   z"exponential_impl.<locals>.<lambda>c                 S   r  r   )r   r   r   r  r  r   r   r   r     r@  c                 S   r  r   )r   r   r   r   r   r   r  r   r   r   r   rS   r   r   r   r     r  r  r   r   r   r   r   r   r   r    r   c                  C      dd } | S )Nc                   S   s   t dtj   S r   r  r   r   r   r   r        r  r   r   r   r   r   r    s   c                 C   r   )Nc                 S   r   r   )r   r   standard_exponentialr   r   r   r   r     r   z+standard_exponential_impl.<locals>.<lambda>c                 S   r   r   )r   r   r   r  r   r   r   r   r     r   c                 S   r   r   )r   r   r   r   r   r   r  r   r   r   r   r     r   z(standard_exponential_impl.<locals>._implr   r   r   r   r   standard_exponential_impl  s   
r  c                   C   r   )Nc                   S   r   r   r   r   	lognormalr   r   r   r   r     r   z$np_lognormal_impl0.<locals>.<lambda>r   r   r   r   r   np_lognormal_impl0  rR  r  c                 C   r   )Nc                 S   r   r   r  meanr   r   r   r     r   z%np_log_normal_impl1.<locals>.<lambda>r   r  r   r   r   np_log_normal_impl1  r   r  c                    sH   t | tjtjfr t |tjtjfr"tttjj  fddS d S d S )Nc                    r   r   r   r  r   ru   r   r   r     r   z%np_log_normal_impl2.<locals>.<lambda>)	rw   r   r   rx   r   _lognormvariate_implr   r   r   r  r   ru   r   np_log_normal_impl2  s   r  c                 C   r  )Nc                 S   r   r   r  r  r   r   r   r   r   r     r   z lognormal_impl.<locals>.<lambda>c                 S   r   r   )r   r   r   r  r  r   r   r   r     r   c                 S   r   r   )r   r   r   r   r   r   r  )r  r   r   r   r   rS   r   r   r   r     r   zlognormal_impl.<locals>._implr   )r  r   r   r   r   r   r   lognormal_impl  r   r  c                    s:   t | tjrt |tjrtttj  fddS d S d S )Nc                    r   r   r   r   ru   r   r   r   '  r   z%lognormvariate_impl.<locals>.<lambda>)rw   r   r   r   r  r   gaussr   r   ru   r   lognormvariate_impl#  s   r  c                    s    fddS )Nc                    s   t  | |S r   )r   r}  r   Z_gaussr   r   r   +  r   z&_lognormvariate_impl.<locals>.<lambda>r   r  r   r  r   r  *  r   r  c                 C   r  )Nc                 S   s   dt    }d|d|    S )z)Pareto distribution.  Taken from CPython.r   )r   )rq  r`  r   r   r   r   1  s   z!paretovariate_impl.<locals>._implr  )rq  r   r   r   r   paretovariate_impl.  s   r  c                 C   r  )Nc                 S   s"   dt j  }d|d|    d S )Nr   r;   r   r\   r`  r   r   r   r   =     pareto_impl.<locals>._implr  r\   r   r   r   r   pareto_impl:  s   r  c                 C   r  )Nc                 S   r  r   )r   r   paretor\   r   r   r   r   r   H  r   zpareto_impl.<locals>.<lambda>c                 S   r  r   )r   r   r   r  r  r   r   r   r   K  r@  c                 S   r  r   )r   r   r   r   r   r   r  r\   r   r   r   rS   r   r   r   r   O  r  r  r   r\   r   r   r   r   r   r  E  r   c                 C   8   t | tjtjfrt |tjtjfrdd }|S d S d S )Nc                 S   s$   dt    }| t| d|   S )z*Weibull distribution.  Taken from CPython.r   )r   r   r   )rq  rr  r`  r   r   r   r   \  s   z"weibullvariate_impl.<locals>._implr   )rq  rr  r   r   r   r   weibullvariate_implX  s   r  c                 C   r  )Nc                 S   s"   dt j  }t| d|   S r   r   r   r   r   r  r   r   r   r   h  r  zweibull_impl.<locals>._implr   r  r   r   r   weibull_imple  s   r  c                 C   r  )Nc                 S   r  r   )r   r   weibullr  r   r   r   r   s  r   zweibull_impl2.<locals>.<lambda>c                 S   r  r   )r   r   r   r  r  r   r   r   r   v  r@  c                 S   r  r   )r   r   r   r   r   r   r  r  r   r   r   r   z  r  zweibull_impl2.<locals>._implr   r  r   r   r   weibull_impl2p  r   r  c                 C   s*   t | tjrt |tjrttjS d S d S r   )rw   r   r   _vonmisesvariate_implr   r   kappar   r   r   vonmisesvariate_impl  s   
r  c                 C   s,   t | tjrt |tjrttjjS d S d S r   )rw   r   r   r  r   r   r  r   r   r   r    s   c                    r   )Nc                    s   |dkrdt j    S d| }|t d||   }	   }t t j| }|||  }  }|d||  k sC|d| t | krDnqd| }|| d||   }	  }
|
dkrh| t |	 dt j  }|S | t |	 dt j  }|S )zCircular data distribution.  Taken from CPython.
        Note the algorithm in Python 2.6 and Numpy is different:
        http://bugs.python.org/issue17141
        gư>r   r^  r   )r   pir   cosr}  acos)r   r  sr  r  r  dr  qr   u3thetar   r   r   r     s(   &	z$_vonmisesvariate_impl.<locals>._implr   r  r   r   r   r    s   (r  c                 C   r  )Nc                 S   r   r   )r   r   vonmisesr   r  r   r   r   r   r     r   zvonmises_impl.<locals>.<lambda>c                 S   r   r   )r   r   r   r  r  r   r   r   r     r   c                 S   r   r   )r   r   r   r   r   r   r  )r   r  r   r   r   rS   r   r   r   r     r   zvonmises_impl.<locals>._implr   )r   r  r   r   r   r   r   vonmises_impl  r   r  c                 C   s2   t | tjrt |tjtjfrdd }|S d S d S )Nc                 S   s\  | dk rt dd|  krdkst d t d|dkr dS |dkr&| S |dk}|r0d| }d| }d}||  }|dkrT|d	K }| d	L } ||  }| dksPJ |dks>| | }t| |d
t|| d   }d}|dkrd}	tj }
|}|	|kr|
|kr||r| |	 n|	7 }|d8 }n|
|8 }
|	d7 }	| |	 d | | |	|  }|	|ks{|dksn|S )z
            Binomial distribution.  Numpy's variant of the BINV algorithm
            is used.
            (Numpy uses BTPE for n*p >= 30, though)
            r   zbinomial(): n <= 0r   r   zbinomial(): p outside of [0, 1]r^  r;   gx0 r=         $@)r   minr   r   r   r   )r  r  Zflippedr  ZnitersqnZnp_prodboundrq   XUZpxr   r   r   r     sP    
binomial_impl.<locals>._impl)rw   r   rx   r   r  r  r   r   r   r   binomial_impl  s   1r  c                 C   r  )Nc                 S   r   r   )r   r   binomialr  r  r   r   r   r   r   	  r   zbinomial_impl.<locals>.<lambda>c                 S   r   r   )r   r   r   r  r  r   r   r   r     r   c                 S   s<   t j|t jd}|j}t|jD ]}t j| |||< q|S rJ  )r   r   intpr   r   r   r   r  )r  r  r   r   r   rS   r   r   r   r     s
   r  r   )r  r  r   r   r   r   r   r    r  c                 C   r  )Nc                 S   s   dt j| d  S Nr   r  )dfr   r   r   r        zchisquare_impl.<locals>._implr   r  r   r   r   r   chisquare_impl  s   r  c                 C   r  )Nc                 S   r  r   r   r   	chisquarer  r   r   r   r   r   &  r   z!chisquare_impl2.<locals>.<lambda>c                 S   r  r   )r   r   r   r  r  r   r   r   r   (  r@  c                 S   r  r   )r   r   r   r   r   r   r  r  r   r   r   rS   r   r   r   r   ,  r  zchisquare_impl2.<locals>._implr   r  r   r   r   r   r   chisquare_impl2#     r  c                 C   r  )Nc                 S   s    t j| | t j||   S r   r  )dfnumdfdenr   r   r   r   9  s   f_impl.<locals>._implr   )r  r  r   r   r   r   f_impl5     r  c                 C   s   t | tjtjfrt |tjtjfrt|rdd S t | tjtjfr4t |tjtjfr4t|r4dd S t |tjsGt |tjrMt |jtjrOdd }|S d S d S )Nc                 S   r   r   )r   r   r   r  r  r   r   r   r   r   E  r   zf_impl.<locals>.<lambda>c                 S   r   r   )r   r   r   r   r  r   r   r   r   J  r   c                 S   r   r   )r   r   r   r   r   r   r   )r  r  r   r   r   rS   r   r   r   r   N  r   r  r   )r  r  r   r   r   r   r   r  @  s(   c                 C   r  )Nc                 S   s   | dks| dkrt dd|  }| dkr7td}|  }}tj }||kr5||9 }||7 }|d7 }||ks%|S ttdtj  t| S )Nr   r   z geometric(): p outside of (0, 1]gUUUUUU?r;   )r   rI  r   r   r   ceilr   )r  r  r  sumprodr  r   r   r   r   Z  s    
geometric_impl.<locals>._implr   )r  r   r   r   r   geometric_implW  s   r  c                 C   r  )Nc                 S   r  r   )r   r   	geometricr  r   r   r   r   r   r  r   z geometric_impl.<locals>.<lambda>c                 S   r  r   )r   r   r   r  r  r   r   r   r   u  r@  c                 S   :   t j|t jd}|j}t|jD ]
}t j| ||< q|S rJ  )r   r   int64r   r   r   r   r  r  r   r   r   rS   r   r   r   r   y  
   r  r   r  r   r   r   r   r   r  o  r   c                 C   r  )Nc                 S   s(   dt j  }| |tt|   S r   r  r   r   r  r   r   r   r     s   zgumbel_impl.<locals>._implr   )r   r   r   r   r   r   gumbel_impl  r  r  c                 C   r  )Nc                 S   r   r   )r   r   gumbelr   r   r   r   r     r   zgumbel_impl3.<locals>.<lambda>c                 S   r   r   )r   r   r   r  r   r   r   r   r     r   c                 S   r   r   )r   r   r   r   r   r   r  r   r   r   r   r     r   zgumbel_impl3.<locals>._implr   r   r   r   r   gumbel_impl3  r   r  c                 C   rc  )Nc                 S   s   t |t |  t | }tt|| }|}t |}|dkr=|dkr=|ttj |||   8 }|d8 }|dkr=|dks!t || }| |krMt || S |S )z'Numpy's algorithm for hypergeometric().r   r   r;   )rI  floatr  r   floorr   r   )ngoodnbadnsampleZd1Zd2YKZr   r   r   r     s    "hypergeometric_impl.<locals>._implr   )r
  r  r  r   r   r   r   hypergeometric_impl  s   r  c                 C   sZ   t |rdd S t|rdd S t|tjs#t|tjr)t|jtjr+dd }|S d S d S )Nc                 S   rj  r   )r   r   hypergeometricr
  r  r  r   r   r   r   r     r8   z%hypergeometric_impl.<locals>.<lambda>c                 S   rm  r   )r   r   r   r  r  r   r   r   r     r  c                 S   s>   t j|t jd}|j}t|jD ]}t j| ||||< q|S rJ  )r   r   r  r   r   r   r   r  )r
  r  r  r   r   r   rS   r   r   r   r     s
   r  r   )r
  r  r  r   r   r   r   r   r    s   c                   C   r   )Nc                   S   r   r   r   r   laplacer   r   r   r   r     r   zlaplace_impl0.<locals>.<lambda>r   r   r   r   r   laplace_impl0  rR  r  c                 C   r   )Nc                 S   r   r   r  r   r   r   r   r     r   zlaplace_impl1.<locals>.<lambda>r   r   r   r   r   laplace_impl1  r   r  c                 C   0   t | tjtjfrt |tjtjfrtS d S d S r   )rw   r   r   rx   laplace_implr   r   r   r   laplace_impl2  
   r  c                 C   r  )Nc                 S   r   r   r  r   r   r   r   r     r   zlaplace_impl3.<locals>.<lambda>c                 S   r   r   )r   r   r   r  r   r   r   r   r     r   c                 S   r   r   )r   r   r   r   r   r   r  r   r   r   r   r     r   zlaplace_impl3.<locals>._implr   r   r   r   r   laplace_impl3  r   r  c                 C   sB   t j }|dk r| |t||   S | |td| |   S )Nr^  r   r  r  r   r   r   r    s   
r  c                   C   r   )Nc                   S   r   r   r   r   logisticr   r   r   r   r     r   z logistic_impl0.<locals>.<lambda>r   r   r   r   r   logistic_impl0  rR  r  c                 C   r   )Nc                 S   r   r   r  r   r   r   r   r     r   z logistic_impl1.<locals>.<lambda>r   r   r   r   r   logistic_impl1  r   r   c                 C   r  r   )rw   r   r   rx   logistic_implr   r   r   r   logistic_impl2  r  r"  c                 C   r  )Nc                 S   r   r   r  r   r   r   r   r     r   z logistic_impl3.<locals>.<lambda>c                 S   r   r   )r   r   r   r  r   r   r   r   r     r   c                 S   r   r   )r   r   r   r   r   r   r  r   r   r   r   r     r   zlogistic_impl3.<locals>._implr   r   r   r   r   logistic_impl3  r   r#  c                 C   s$   t j }| |t|d|    S r   r  r  r   r   r   r!    s   
r!  c                 C   s   | dks| dkrt dtd|  }	 tj }|| krdS tj }dt||  }||| krBtdt|t|  S ||krHdS dS )z"Numpy's algorithm for logseries().r   r   z logseries(): p outside of (0, 1]r;   r=   )r   r   r   r   r   r}  r   )r  r  Vr  r  r   r   r   _logseries_impl$  s   

r%  c                 C   s   t | tjtjfrtS d S r   )rw   r   r   rx   r%  )r  r   r   r   logseries_impl9  s   r&  c                 C   r  )Nc                 S   r  r   )r   r   	logseriesr  r   r   r   r   B  r   z logseries_impl.<locals>.<lambda>c                 S   r  r   )r   r   r   r'  r  r   r   r   r   D  r@  c                 S   r  rJ  )r   r   r   r   r   r   r   r'  r  r   r   r   r   H  r  zlogseries_impl.<locals>._implr   r  r   r   r   r&  ?  r  c                 C   r  )Nc                 S   sJ   | dkrt d|dk s|dkrt dtj| d| | }tj|S )Nr   znegative_binomial(): n <= 0r   r   z(negative_binomial(): p outside of [0, 1])r   r   r   rv  poisson)r  r  r  r   r   r   r   U  s   z%negative_binomial_impl.<locals>._implr   r  r   r   r   negative_binomial_implQ  s   r)  c                   C   r   )Nc                   S      t jdS r   r   r   r(  r   r   r   r   r   b  r   zpoisson_impl0.<locals>.<lambda>r   r   r   r   r   poisson_impl0`  rR  r,  c                    s.   t | tjtjfrtdd   fddS d S )Nc                    s$   t |  fdd}ttj||fS )Nc                    s0  t | |}tj|tdd}|d}|d}|\}||}|d|ttd}	|	|	, t
tttf}
t|jj|
d}||||f}||| || W d    n1 s^w   Y  || || tjjtj  fdd	}| ||||}||| || || ||S )
Nrn   r   bbcontr  rE   r  Znumba_poisson_ptrsc                    sT   | dk rt d| dkrdS  |  }d}d}	  }||9 }||kr%|S |d7 }q)ag  Numpy's algorithm for poisson() on small *lam*.

                    This method is invoked only if the parameter lambda of the
                    distribution is small ( < 10 ). The algorithm used is
                    described in "Knuth, D. 1969. 'Seminumerical Algorithms.
                    The Art of Computer Programming' vol 2.
                    r   zpoisson(): lambda < 0r   r   r;   r   )lamZenlamr  r  r  _expr   r   r   poisson_impl  s   
zCpoisson_impl1.<locals>._impl.<locals>.codegen.<locals>.poisson_impl)r0   r   r   rl   r  Zfcmp_orderedr   r   rY   r  r   r   r   rB   r    r#   rN   r  r  r   r   r   r}  r   rJ   )r$   r%   r   rC   r6   Zretptrr-  r  r/  Zbig_lamr(   r)   rn   r2  Zlam_preprocessorr0  r   r   l  s:   










z-poisson_impl1.<locals>._impl.<locals>.codegen)r   r
   r   r   )r   r/  r   r   r3  r   r   h  s   7zpoisson_impl1.<locals>._implc                    rs   r   r   r/  r   r   r   r     r   zpoisson_impl1.<locals>.<lambda>r   r4  r   r   r   poisson_impl1e  s
   
;r5  c                 C   s   t | tjtjfrt|rdd S t | tjtjfr"t|r"dd S t | tjtjfrDt |tjs>t |tjrFt |jtjrHdd }|S d S d S d S )Nc                 S   r  r   r+  r/  r   r   r   r   r     r   zpoisson_impl2.<locals>.<lambda>c                 S   r  r   )r   r   r   r(  r6  r   r   r   r     r@  c                 S   r  rJ  )r   r   r  r   r   r   r   r(  )r/  r   r   r   rS   r   r   r   r     r  zpoisson_impl2.<locals>._implr   )r/  r   r   r   r   r   poisson_impl2  s    

r7  c                 C   r  )Nc                 S   s2   | dkrt dtdttj   d|  S )Nr   zpower(): a <= 0r;   r   )r   r   powr}  r   r   r  rt   r   r   r   r     s
   power_impl.<locals>._implr   r  r   r   r   
power_impl     r:  c                 C   r  )Nc                 S   r  r   )r   r   powerr  r   r   r   r     r   zpower_impl.<locals>.<lambda>c                 S   r  r   )r   r   r   r<  r  r   r   r   r     r@  c                 S   r  r   )r   r   r   r   r   r   r<  r  r   r   r   r     r  r9  r   r  r   r   r   r:    r   c                   C   r   )Nc                   S   r*  r   r   r   rayleighr   r   r   r   r     r   z rayleigh_impl0.<locals>.<lambda>r   r   r   r   r   rayleigh_impl0  rR  r?  c                 C   r  )Nc              	   S   s2   | dkrt d| tdtdtj    S )Nr   zrayleigh(): scale <= 0r   r   )r   r   r   r   r   r   r  r   r   r   rv     s   "zrayleigh_impl1.<locals>.implr   )r   rv   r   r   r   rayleigh_impl1     r@  c                 C   r  )Nc                 S   r  r   r=  r  r   r   r   r     r   z rayleigh_impl2.<locals>.<lambda>c                 S   r  r   )r   r   r   r>  r  r   r   r   r     r@  c                 S   r  r   )r   r   r   r   r   r   r>  r  r   r   r   r     r  zrayleigh_impl2.<locals>._implr   r  r   r   r   rayleigh_impl2  r   rB  c                  C   r  )Nc                   S   s   t j t j  S r   r   r   r   r   r   r     r  zcauchy_impl.<locals>._implr   r   r   r   r   cauchy_impl  s   rC  c                 C   r   )Nc                 S   r   r   )r   r   standard_cauchyr   r   r   r   r   
  r   z&standard_cauchy_impl.<locals>.<lambda>c                 S   r   r   )r   r   r   rD  r   r   r   r   r     r   c                 S   r   r   )r   r   r   r   r   r   rD  r   r   r   r   r     r   z#standard_cauchy_impl.<locals>._implr   r   r   r   r   standard_cauchy_impl  r   rE  c                 C   r  )Nc                 S   s:   t j }t j| d }t| d | t| }|S r  )r   r   r   r  r   r   )r  NGr  r   r   r   r     s   
zstandard_t_impl.<locals>._implr   r  r   r   r   standard_t_impl  r;  rH  c                 C   r  )Nc                 S   r  r   )r   r   
standard_tr  r   r   r   r   )  r   z"standard_t_impl2.<locals>.<lambda>c                 S   r  r   )r   r   r   rI  r  r   r   r   r   +  r@  c                 S   r  r   )r   r   r   r   r   r   rI  r  r   r   r   r   /  r  zstandard_t_impl2.<locals>._implr   r  r   r   r   standard_t_impl2&  r  rJ  c                 C   s,   t | tjrt |tjrdd }|S d S d S )Nc                 S   s   | dkrt d|dkrt d| d|  }tj }| | | }| ||td| | ||     }tj }|| | |  krC|S | |  | S )Nr   zwald(): mean <= 0zwald(): scale <= 0r      )r   r   r   r   r   r   )r  r   Zmu_2lr  r  r  r   r   r   r   ;  s   
&
zwald_impl.<locals>._implr  )r  r   r   r   r   r   	wald_impl8  s   rL  c                 C   r  )Nc                 S   r   r   )r   r   waldr  r   r   r   r   r   r   P  r   zwald_impl2.<locals>.<lambda>c                 S   r   r   )r   r   r   rM  rN  r   r   r   r   S  r   c                 S   r   r   )r   r   r   r   r   r   rM  )r  r   r   r   r   rS   r   r   r   r   W  r   zwald_impl2.<locals>._implr   )r  r   r   r   r   r   r   
wald_impl2M  r   rO  c                 C   r  )Nc                 S   s   | dkrt d| d }d| }	 dtj  }tj }tt|d|  }|tks0|dk r1qdd|  | }|dkrO|| |d  |d  || krO|S q)Nr   zzipf(): a <= 1r   r;   g      )r   r   r   rI  r   r	  r   )r\   Zam1r]   r  r$  r  Tr   r   r   r   c  s   
(zipf_impl.<locals>._implr  r  r   r   r   	zipf_impl`  s   rR  c                 C   r  )Nc                 S   r  r   )r   r   zipfr  r   r   r   r   z  r   zzipf_impl.<locals>.<lambda>c                 S   r  r   )r   r   r   rS  r  r   r   r   r   }  r@  c                 S   r  rJ  )r   r   r  r   r   r   r   rS  r  r   r   r   r     r  rQ  r   r  r   r   r   rR  w  r   c                    sb   t | tjsd}t||dkrtjj n|dkrtj | jdkr) fdd}|S  fdd}|S )Nz1The argument to shuffle() should be a buffer typer   r   r;   c                    sT   | j d d }|dkr( |d }| | | | | |< | |< |d8 }|dksd S d S r:   rw  r   ijrandr   r   rv     s   zdo_shuffle_impl.<locals>.implc                    s`   | j d d }|dkr. |d }t| | t| | | |< | |< |d8 }|dksd S d S r:   )rx  r   copyrT  rW  r   r   rv     s   &)	rw   r   ZBufferr   r   r   rC  r+  ndim)r   rngr  rv   r   rW  r   do_shuffle_impl  s   

r\  c                 C   
   t | dS r   r\  r   r   r   r   shuffle_impl     
r_  c                 C   r]  r{   r^  r   r   r   r   r_    r`  c                 C   s8   t | tjrdd }|S t | tjrdd }|S d }|S )Nc                 S   s   t | }t j| |S r   )r   aranger   shuffle)r   rT   r   r   r   permutation_impl  s   
z*permutation_impl.<locals>.permutation_implc                 S   s   |   }tj| |S r   )rY  r   r   rb  )r   Zarr_copyr   r   r   rc    s   )rw   r   rx   Array)r   rc  r   r   r   rc    s   rc  c                  G   $   t | dkrdd }|S dd }|S )Nr   c                  W   r   r   r   r   r   r   r   	rand_impl  rz  zrand.<locals>.rand_implc                  W   s   t j| S r   r   r   r   r   r   rf    r   len)r   rf  r   r   r   rX    
   rX  c                  G   re  )Nr   c                  W   r   r   r   r   r   r   r   
randn_impl  rz  zrandn.<locals>.randn_implc                  W   r  r   r   r   r   r   r   rj    r   rg  )r   rj  r   r   r   randn  ri  rk  Tc                    s   t | tjr#| jdksJ | j tdd tdd }tdd n#t | tjr?tj tdd td	d }td
d nt	d| f |d tj
fv rWdfdd	}|S d fdd	}|S )Nr;   c                 S   s   t | S r   rg  rt   r   r   r   get_source_size  rR  zchoice.<locals>.get_source_sizec                 S   s   |   S r   )rY  rt   r   r   r   copy_source  rR  zchoice.<locals>.copy_sourcec                 S   s   | | S r   r   r\   Za_ir   r   r   getitem  rR  zchoice.<locals>.getitemc                 S   s   | S r   r   rt   r   r   r   rl       c                 S   s
   t | S r   )r   ra  rt   r   r   r   rm    r`  c                 S   r  r   r   rn  r   r   r   ro    rp  z@np.random.choice() first argument should be int or array, got %sTc                    s     | }t jd|}| |S )zs
            choice() implementation returning a single sample
            (note *replace* is ignored)
            r   rB  )r\   r   replacer  rU  )rl  ro  r   r   choice_impl  s   
zchoice.<locals>.choice_implc           	         s   | }|r(t | }|j}tt|D ]}t jd|}| |||< q|S t | }|j|kr7tdt j	| }|j}tt|D ]}|| ||< qF|S )zO
            choice() implementation returning an array of samples
            r   z@Cannot take a larger sample than population when 'replace=False')
r   r   r   r   rh  r   rC  r   r   permutation)	r\   r   rq  r  r   flrU  rV  Z
permuted_ar   rl  ro  r   r   rr    s    
NT)rw   r   rd  rZ  r   r   rx   r   r  r   r   )r\   r   rq  rm  rr  r   ru  r   choice  s2   



(rw  c                    s   t j tdd t| tjstd| f t|tjtjfs&td|f |d tj	fv r7d
 fdd	}|S t|tjrGd
 fdd	}|S t|tj
rWd
 fdd	}|S td	|f )Nc                 S   s   |j }|j}t|}td||D ]=}d}| }td|d D ]#}	||	 }
tj||
|  }|||	 < ||8 }|dkr< n||
8 }q|dkrM|||| d < qd S )Nr   r   r;   )r   r   rh  r   r   r   r  )r  pvalsr   rt  szplenrU  Zp_sumZn_experimentsrV  Zp_jZn_jr   r   r   multinomial_innerA  s"   
z&multinomial.<locals>.multinomial_innerz7np.random.multinomial(): n should be an integer, got %szEnp.random.multinomial(): pvals should be an array or sequence, got %sc                    s    t t| }| || |S )z5
            multinomial(..., size=None)
            r   Zzerosrh  r  rx  r   r   r   r{  r   r   multinomial_impli  s   z%multinomial.<locals>.multinomial_implc                    s$   t |t|f }| || |S )z4
            multinomial(..., size=int)
            r|  r}  r~  r   r   r  r  s   c                    s&   t |t|f  }| || |S )z6
            multinomial(..., size=tuple)
            r|  r}  r~  r   r   r  {  s   zDnp.random.multinomial(): size should be int or tuple or None, got %sr   )r   r  r   rw   r   rx   r   Sequencerd  r   Z	BaseTuple)r  rx  r   r  r   r~  r   multinomial<  s.   
r  c                 C   r  )Nc                 S   s   t t| }t| | |S r   r   r   rh  dirichlet_arr)rq  r   r   r   r   dirichlet_impl     
!dirichlet.<locals>.dirichlet_impl)rw   r   r  rd  )rq  r  r   r   r   	dirichlet  rA  r  c                 C   s   t | tjtjfstd| f |d tjfv st|r"ddd}|S t |tjr/ddd}|S t |tjrCt |j	tjrCddd}|S td| )NzCnp.random.dirichlet(): alpha should be an array or sequence, got %sc                 S   s   t t| }t| | |S r   r  rq  r   r   r   r   r   r    r  r  c                 S   s    t |t| f}t| | |S )z2
            dirichlet(..., size=int)
            r  r  r   r   r   r    s   
c                 S   s"   t |t| f }t| | |S )z4
            dirichlet(..., size=tuple)
            r  r  r   r   r   r    s   
zJnp.random.dirichlet(): size should be int or tuple of ints or None, got %sr   )
rw   r   r  rd  r   r   r   rx   r   r   )rq  r   r  r   r   r   r    s,   


c           
      C   s   t | D ]
}|dkrtdqt| }|j}|j}td||D ]5}d}t| D ]\}}	tj	|	d||| < ||||  
 7 }q't| D ]\}}	|||   |  < qEqd S )Nr   zdirichlet: alpha must be > 0.0r;   )iterr   rh  r   r   r   	enumerater   r   rv  item)
rq  r   Za_valZa_lenr   r   rU  Znormr  r'  r   r   r   r    s    r  c                 C   r  )Nc                 S      t | | t| |S r   #validate_noncentral_chisquare_inputnoncentral_chisquare_singler  noncr   r   r   noncentral_chisquare_impl     

7noncentral_chisquare.<locals>.noncentral_chisquare_implr   )r  r  r  r   r   r   noncentral_chisquare  r  r  c                 C   sr   |d t jfv rddd}|S t|rddd}|S t|t js,t|t jr3t|jt jr3ddd}|S td| )Nc                 S   r  r   r  r  r  r   r   r   r   r    r  r  c                 S   s   t | | tt| |S r   )r  r   r   r  r  r   r   r   r    s   
c                 S   s<   t | | t|}|j}t|jD ]	}t| |||< q|S r   )r  r   r   r   r   r   r  )r  r  r   r   r   rS   r   r   r   r    s   

zUnp.random.noncentral_chisquare(): size should be int or tuple of ints or None, got %sr   )r   r   r   rw   rx   r   r   r   )r  r  r   r  r   r   r   r    s$   


c                 C   sl   t |rt jS d| k r$t j| d }t j t | }|||  S t j|d }t j| d|  S )Nr;   r   r=   )r   isnannanr   r  r   r   r(  )r  r  Zchi2r  rU  r   r   r   r  	  s   
r  c                 C   s$   | dkrt d|dk rt dd S )Nr   zdf <= 0znonc < 0r.  r  r   r   r   r  	  s
   r  r   rv  )__doc__r   r   numpyr   Zllvmliter   Znumba.core.cgutilsr   r   Znumba.core.extendingr   r   r   Znumba.core.imputilsr   Znumba.core.typingr
   Z
numba.corer   r   Znumba.core.errorsr   Znumba.np.random._constantsr   registrylowerr=  r   rl   r   r  rY   rF  r   rL   ZLiteralStructType	ArrayTypeZrnd_state_tZPointerTyper   r*   r.   r0   r1   r7   r<   r>   r@   rD   rU   r^   rr   r}   rz   ry   r   Zrandom_samplesampleZranfr   r   r  normalvariater   r   r   r   r   r   r   r   r   r   r   getrandbitsr  r(  r+  r.  r2  r4  r>  rC  rA  rE  rG  rN  rP  rQ  rX  rY  rT  r]  rk  rb  rf  rn  r  rs  r  rv  ry  r{  ro  r  r  betavariater  rr  r  r  r  expovariater  r  r  r  r  r  r  r  r  r  lognormvariater  r  paretovariater  r  r  weibullvariater  r  r  r  vonmisesvariater  r  r  r  r  r  r  r  r  r   r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r"  r#  r!  r%  r'  r&  Znegative_binomialr)  r(  r,  r5  r7  r<  r:  r>  r?  r@  rB  rD  rC  rE  rI  rH  rJ  rM  rL  rO  rS  rR  r\  rb  r_  rs  rc  rX  rk  rw  r  r  r  r  r  r  r   r   r   r   <module>   s.   
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