python (3.12.0)
Browse
Usage
Versions
Αe d dl mZmZ d dlmZ d dlZd dlZd dlZd dlZd dl Z d dl
Z
d dl Z d dl Z d dl
Z
d dlZdZ ed Z ed Z ed Zej( j* Zej( j. Zd\ ZZeez d k( Ze d
k( rej: d Z ne Z e
j@ jC e xs e
jD Z#e
j@ jI e#d Z%e
j@ jI e#d Z&d
Z'd Z(d Z)d Z*d Z+d Z,d Z-d dZ. G d d Z/ G d de0 Z1 G d de2 Z3 G d d ejh Z5 G d d ejh Z6d Z7e d
k( r ejp yy)! )verboserequires_IEEE_754)supportNgh㈵>naninf-inf) 7yACg):@g7yAC__main__zmath_testcases.txtzcmath_testcases.txtc v t j dt j d| d }|dk r|dz }|S )a Convert a non-NaN float x to an integer, in such a way that
adjacent floats are converted to adjacent integers. Then
abs(ulps(x) - ulps(y)) gives the difference in ulps between two
floats.
The results from this function will only make sense on platforms
where native doubles are represented in IEEE 754 binary64 format.
Note: 0.0 and -0.0 are converted to 0 and -1, respectively.
z<qz<dr l )structunpackpack)xns B/BuggyBox/python/3.12.0/bootstrap/lib/python3.12/test/test_math.pyto_ulpsr ( s;
dFKKa 01!4A1ugJ H c 2 | rdt | | dz
z z S dS )zANumber of '1' bits in binary expansion of a nonnnegative integer. r )count_set_bits)r s r r r N s! ,-1~a!a%i( (414r c h || z
dz }|sy|dk( r| S | |z dz }t | | t || z S )zProduct of integers in range(start, stop, 2), computed recursively.
start and stop should both be odd, with start <= stop.
r )partial_product)startstop
numfactorsmids r r r R sL
,1$J q z!Q& uc*_S$-GGGr c dx}}t t | j D ]+ }|t | |dz z dz dz | |z dz dz z }||z }- || t | z
z S )zFactorial of nonnegative integer n, via "Binary Split Factorial Formula"
described at http://www.luschny.de/math/factorial/binarysplitfact.html
r )reversedrange
bit_lengthr r )r innerouteris r py_factorialr$ ` s}
EE
eALLN+
,
!q1u*!1A!5Q!|a7GHH
Q ** ++r c t t | t | z
}t | |z
}||k s||k ryd}|j |||| S )zGiven finite floats `expected` and `got`, check that they're
approximately equal to within the given number of ulps or the
given absolute tolerance, whichever is bigger.
Returns None on success and an error message on failure.
NzAerror = {:.3g} ({:d} ulps); permitted error = {:.3g} or {:d} ulps)absr format)expectedgotulp_tolabs_tol ulp_error abs_errorfmts r
ulp_abs_checkr/ k sZ GH% 45IHsN#I GyG 37zz)YAAr c # l K t | d 5 }|D ] }d|v r|d|j d }|j s,|j d \ }}|j \ }}}|j }|d } |dd }
||t | t | |
f ddd y# 1 sw Y yxY ww)zParse a file with test values
-- starts a comment
blank lines, or lines containing only a comment, are ignored
other lines are expected to have the form
id fn arg -> expected [flag]*
utf-8encoding--N->r r )openindexstripsplitfloat) fnamefplinelhsrhsidfnarg
rhs_piecesexpflagss r parse_mtestfilerF } s
eg & :"
:Dt| -TZZ -.::<zz$'HC ))+KBC J Q-C qrNEr5:uSz59 9
:: : :s B4BB( B4(B1-B4c
# K t | d 5 }|D ] }|j d s|j s%|j d \ }}|j \ }}}}|j } | d | d } }
| dd } ||t | t | t |
t | | f ddd y# 1 sw Y yxY ww) zParse a file with test values
Empty lines or lines starting with -- are ignored
yields id, fn, arg_real, arg_imag, exp_real, exp_imag
r1 r2 r4 r5 r r N)r6
startswithr8 r9 r: )
r; r< r= r> r? r@ rA arg_realarg_imagrC exp_realexp_imagrE s
r parse_testfilerN s
eg & " Dt$DJJLzz$'HC), &BHh J!+A
1
hH qrNEr?E(O?E(O
s CB!B;2 C;C Cc & || k( ryd}t | t r t |t r t | }n+t |t rt | t r t | } t | t rvt |t rft j | rt j | rd}n9t j
| st j
| rnt
| ||| }|*d}|j | | }|dj | z
}|S y)a Compare arguments expected and got, as floats, if either
is a float, using a tolerance expressed in multiples of
ulp(expected) or absolutely (if given and greater).
As a convenience, when neither argument is a float, and for
non-finite floats, exact equality is demanded. Also, nan==nan
as far as this function is concerned.
Returns None on success and an error message on failure.
Nz not equalzexpected {!r}, got {!r}z ({}))
isinstancer: intmathisnanisinfr/ r' )r( r) r* r+ failurefail_fmtfail_msgs r result_checkrX s hG (E"z#s';Cj C Jx$=?(E"z#u'= ::h DJJsOG
ZZ
!TZZ_ $Hc7GDG ,??8S1GNN7++r c e Zd Zd Zd Zy) FloatLikec || _ y Nvalueselfr^ s r __init__zFloatLike.__init__
r c | j S r\ r] r` s r __float__zFloatLike.__float__ zzr N)__name__
__module__ __qualname__ra re r r rZ rZ r rZ c e Zd Zy) IntSubclassNrg rh ri rj r r rm rm s r rm c e Zd Zd Zd Zy) MyIndexablec || _ y r\ r] r_ s r ra zMyIndexable.__init__ rb r c | j S r\ r] rd s r __index__zMyIndexable.__index__ rf r Nrg rh ri ra rs rj r r rp rp rk r rp c T e Zd ZdQdZd Zd Zd Zd Zd Zd Z d Z
d
Z d Z d Z
ed
Zd Z ej$ ej( dk( xr ej* dv d d Zd Zd Zd Zd Zd Zd Z e j< d Z d Z d Z!d Z"e ej$ e#d d Z$d Z%d Z&e ej$ e#d! d" Z'd# Z(d$ Z)d% Z*d& Z+d' Z,d( Z-d) Z.ed* Z/e e j` d+d d, Z1d- Z2d. Z3e ej$ e#d/ e j< d0 Z4 e jj d1 d2 Z6e ej$ e#d/ e j< e jj d1 d3 Z7d4 Z8d5 Z9d6 Z:ed7 Z;d8 Z<d9 Z=d: Z>d; Z?d< Z@ed= ZAd> ZBd? ZCd@ ZDdA ZEdB ZFdC ZG ej eIdD dE ZJedF ZKedG ZLdH ZMdI ZNdJ ZOedK ZPedL ZQdM ZRdN ZSdO ZTyP)R MathTests c h t |||| }|"| j dj || yy)aa Compare arguments expected and got, as floats, if either
is a float, using a tolerance expressed in multiples of
ulp(expected) or absolutely, whichever is greater.
As a convenience, when neither argument is a float, and for
non-finite floats, exact equality is demanded. Also, nan==nan
in this function.
Nz{}: {})rX failr' )r` namer) r( r* r+ rU s r ftestzMathTests.ftest s6 xgw? IIhoodG4 5 r c | j dt j d | j dt j d | j t j
dt j z y )Npig-DT! @egiW
@rH )r{ rR r} r~ assertEqualtaurd s r
testConstantszMathTests.testConstants sH
4"<=
3 :; 1TWW9-r c 8 | j t t j | j dt j d t j
| j dt j d t j
dz | j dt j d d | j t t j t | j t t j t | j t t j dt z | j t t j dt z
| j t j t j t y )Nzacos(-1)zacos(0)r rH zacos(1)r )
assertRaises TypeErrorrR acosr{ r}
ValueErrorINFNINFeps
assertTruerS NANrd s r testAcoszMathTests.testAcos s )TYY/
:tyy}dgg6
9diilDGGAI6
9diilA. *dii5 *dii6 *diiS9 *diic:
499S>23r c | j t t j | j dt j d d | j dt j d d | j t
t j d | j t
t j d | j
t j t t | j t
t j t | j t j t j t y )Nzacosh(1)r r zacosh(2)rH g5qB?r ) r r rR acoshr{ r r r r r rS r rd s r testAcoshzMathTests.testAcosh s )TZZ0
:tzz!}a0
:tzz!}.@A *djj!4 *djj"5 C #. *djj$7
4::c?34r c @ | j t t j | j dt j d t j
dz | j dt j d d | j dt j d t j
dz | j t t j t | j t t j t | j t t j dt z | j t t j dt z
| j t j t j t y )Nzasin(-1)r rH zasin(0)r zasin(1)r )
r r rR asinr{ r} r r r r r rS r rd s r testAsinzMathTests.testAsin s )TYY/
:tyy}twwhqj9
9diilA.
9diilDGGAI6 *dii5 *dii6 *diiS9 *diic:
499S>23r c Z | j t t j | j dt j d d | j dt j d d | j dt j d d | j t j t t | j t j t t | j t j t j t y ) Nzasinh(0)r zasinh(1)r g'ya64?z asinh(-1)r g'ya64) r r rR asinhr{ r r r r rS r rd s r testAsinhzMathTests.testAsinh# s )TZZ0
:tzz!}a0
:tzz!}.AB
;
20DE C #. D)40
4::c?34r c | j t t j | j dt j d t j
dz | j dt j d d | j dt j d t j
dz | j dt j t t j
d z | j d
t j t t j
d z | j t j t j t y ) Nzatan(-1)r zatan(0)r zatan(1)r z atan(inf)rH z
atan(-inf)) r r rR atanr{ r} r r r rS r rd s r testAtanzMathTests.testAtan, s )TYY/
:tyy}twwhqj9
9diilA.
9diilDGGAI6
; # :
<4 477(1*=
499S>23r c | j t t j | j dt j
d d | j dt j
d d | j dt j
d d | j t t j
d | j t t j
d
| j t t j
t | j t t j
t | j t j t j
t y ) Nzatanh(0)r z
atanh(0.5) ?g z?z atanh(-0.5) g zr r ) r r rR r r{ atanhr r r r rS r rd s r testAtanhzMathTests.testAtanh5 s )TYY/
:tzz!}a0
<C 2EF
=$**T"24HI *djj!4 *djj"5 *djj#6 *djj$7
4::c?34r c 2 | j t t j | j dt j dd t j
dz | j dt j dd t j
dz | j dt j dd d | j d t j dd t j
dz | j d
t j dd t j
dz | j d t j d t t j
| j d
t j d d t j
| j dt j d d t j
| j t j d d d | j t j d d d | j t j d t d | j t j t j d t | j dt j dt t j
| j dt j dd t j
| j dt j dd t j
| j t j dd d | j t j dd d | j t j dt d | j t j t j dt | j dt j t t t j
dz dz | j dt j t d t j
dz | j dt j t d t j
dz | j dt j t d t j
dz | j dt j t d t j
dz | j dt j t t t j
dz | j t j t j t t | j d t j t t t j
dz dz | j d t j t d t j
dz | j d t j t d t j
dz | j d t j t d t j
dz | j d t j t d t j
dz | j d!t j t t t j
dz | j t j t j t t | j d"t j dt t j
| j d#t j dd t j
dz | j d$t j dd t j
dz | j t j dt d | j t j t j dt | j d%t j dt t j
| j d&t j dd t j
dz | j d't j dd t j
dz | j t j dt d | j t j t j dt | j t j t j t t | j t j t j t d | j t j t j t d | j t j t j t d | j t j t j t d | j t j t j t t | j t j t j t t y )(Nz atan2(-1, 0)r r rH z atan2(-1, 1)r r z atan2(0, 1)z atan2(1, 1)z atan2(1, 0)zatan2(0., -inf) zatan2(0., -2.3)ffffffzatan2(0., -0.) ffffff@zatan2(-0., -inf)zatan2(-0., -2.3)zatan2(-0., -0.)zatan2(inf, -inf) zatan2(inf, -2.3)zatan2(inf, -0.)zatan2(inf, 0.)zatan2(inf, 2.3)zatan2(inf, inf)zatan2(-inf, -inf)zatan2(-inf, -2.3)zatan2(-inf, -0.)zatan2(-inf, 0.)zatan2(-inf, 2.3)zatan2(-inf, inf)zatan2(2.3, -inf)zatan2(2.3, -0.)zatan2(2.3, 0.)zatan2(-2.3, -inf)zatan2(-2.3, -0.)zatan2(-2.3, 0.)) r r rR atan2r{ r} r r r r rS r rd s r testAtan2zMathTests.testAtan2@ s )TZZ0
>4::b!#4twwhqjA
>4::b!#4twwhqjA
=$**Q"2A6
=$**Q"2DGGAI>
=$**Q"2DGGAI>
$djjT&:DGGD
$djjT&:DGGD
#TZZC%8$''B B+R0 B,b1 B,b1
4::b##678
%tzz#t'<twwhG
%tzz#t'<twwhG
$djjc&:TWWHE C,c2 C-s3 C-s3
4::c3#789
%tzz#t'<dggaikJ
%tzz#t'<dggaiH
$djjd&;TWWQYG
#TZZS%947719E
$djjc&:DGGAIF
$djjc&:DGGAIF
4::c3#789
&
4(>
1 M
&
4(>
K
%tzz$'=xzJ
$djjs&;dggXaZH
%tzz$'<twwhqjI
%tzz$'<twwhqjI
4::dC#89:
%tzz#t'<dggF
$djjc&:DGGAIF
#TZZR%8$''!)D C-r2
4::c3#789
&
4(>I
%tzz$'<twwhqjI
$djjr&:TWWHQJG D#.4
4::dC#89:
4::c4#89:
4::c4#89:
4::c3#789
4::c2#678
4::c3#789
4::c3#789
4::c3#789r c n | j t t j | j dt j d d | j dt j d d | j dt j d d | j dt j d d | j d
t j d d | j d t j d
d | j dt j d d | j dt j d d | j dt j d d | j dt j d d | j t j t t | j t j t t | j t j t j t y )Nzcbrt(0)r zcbrt(1)r zcbrt(8) rH z cbrt(0.0)r z
cbrt(-0.0)r z cbrt(1.2)g333333?ggAE ?z
cbrt(-2.6)ggL]6H zcbrt(27) r zcbrt(-1)r z cbrt(-27)i) r r rR cbrtr{ r r r r rS r rd s r testCbrtzMathTests.testCbrt} sU )TYY/
9diilA.
9diilA.
9diilA.
; #4
<4 $7
; #0AB
<4 2DE
:tyy}a0
:tyy}b1
; #3 3 - 4 $/
499S>23r c R | j t t j | j t
t
t j d | j t j d d | j t j d d | j t j d d | j t j d d | j t j d d | j t j d
d | j t j d d | j t j d d G d
d } G d dt } G d d }| j t j | d | j t j | d | j t j t d d | j t t j | | }d |_ | j t t j | | j t t j |d y )Nr r ? ?rH r r r r r c e Zd Zd Zy)$MathTests.testCeil.<locals>.TestCeilc yN* rj rd s r __ceil__z-MathTests.testCeil.<locals>.TestCeil.__ceil__ r Nrg rh ri r rj r r TestCeilr
r r c e Zd Zd Zy)%MathTests.testCeil.<locals>.FloatCeilc yr rj rd s r r z.MathTests.testCeil.<locals>.FloatCeil.__ceil__ r r Nr rj r r FloatCeilr r r r c e Zd Zy)&MathTests.testCeil.<locals>.TestNoCeilNrn rj r r
TestNoCeilr r r r g @E@+ c | S r\ rj argss r <lambda>z$MathTests.testCeil.<locals>.<lambda> s 4 r )
r r rR ceilr rQ typer: rZ r )r` r r r ts r testCeilzMathTests.testCeil s )TYY/ d499S> 23 3 + 3 + 3 + 4 !, 4 "- 4 "- 3 + 4 !,
8:.3 9;/4 9T?3R8 )TYY
= L'
)TYY2 )TYY15r c | j t j dd d | j t j dd d | j t j dd d | j t j dd d | j t j d d
d | j t t j | j t j dd d | j t j dd
d | j t j t
d t
| j t j t
d
t | j t j t d t
| j t j t d
t | j t j dt
d | j t j dt d | j t j t
t
t
| j t j t
t t | j t j t t
t
| j t j t t t | j t j t j t d | j t j t j t t
| j t j t j t t | j t j t j t t | j t j t j t
t | j t t j d t d y )
Nr r r r ir r @ @r @) r rR copysignr r r r r rS r rT r& rd s r testCopysignzMathTests.testCopysign s q"-s3 r2.4 r3/6 q"-s3 r3/6 )T]]3 r2.3 r3/5 sB/5 sC0$7 tR0#6 tS148 r3/4 r40#6 sC0#6 sD148 tS137 tT2D9
4==b#9:;
4==c#:;<
4==d#;<=
4==c#:;<
4==c#:;< T]]2s 34b9r c X | j t t j | j dt j t j
dz dt j d | j dt j d d | j dt j t j
dz dt j d | j dt j t j
d | j t j t j t | j t j t j t | j t j t j t y # t $ rU | j t t j t | j t t j t Y w xY w)
Nz
cos(-pi/2)rH r r r+ zcos(0)z cos(pi/2)zcos(pi)r )
r r rR cosr{ r} ulpr rS r r r r rd s r testCoszMathTests.testCos sB )TXX.
<477(1*!5q$((1+
N
8TXXa[!,
; 3Q
L
9dhhtww /4 : OODJJtxx} 5 6 OODJJtxx~ 6 7
488C=12 : j$((C 8 j$((D 9 :s A6G AH)(H)win32)ARMARM64zEWindows UCRT is off by 2 ULP this test requires accuracy within 1 ULPc F | j t t j | j dt j d d | j dt j d dt j d dz z z
d | j t j t t | j t j t t | j t j t j t y )Nzcosh(0)r r zcosh(2)-2*cosh(1)**2rH r ) r r rR coshr{ r r r r rS r rd s r testCoshzMathTests.testCosh s
)TYY/
9diilA.
)499Q<$))A,/8I+I2N 3 - 4 #.
499S>23r c | j t t j | j dt j t j
d | j dt j t j
dz d | j dt j t j
dz d | j d t j d
d
y ) Nz degrees(pi)g f@z
degrees(pi/2)rH g V@zdegrees(-pi/4)r g Fz
degrees(0)r )r r rR degreesr{ r} rd s r testDegreeszMathTests.testDegrees s )T\\2
=$,,tww"7?
?DLL$;TB
#T\\477(1*%=uE
< a !4r c | j t t j | j dt j d dt j
z | j dt j d d | j dt j d t j
| j
t j t t | j
t j t d | j t j t j t | j t t j d y ) Nzexp(-1)r r zexp(0)r zexp(1)r @B )
r r rR rD r{ r~ r r r r rS r
OverflowErrorrd s r testExpzMathTests.testExp s )TXX.
9dhhrlAdffH5
8TXXa[!,
8TXXa[$&&1 # , $ ,
488C=12 -7;r c | j t t j | j dt j d d | j dt j d d | j dt j d d | j d t j d
d | j t j t t | j t j t d | j t j t j t | j t t j d
y )Nzexp2(-1)r r zexp2(0)r r zexp2(1)rH z exp2(2.3)r g){IJ@r r ) r r rR exp2r{ r r r r rS r r rd s r testExp2zMathTests.testExp2 s )TYY/
:tyy}c2
9diilA.
9diilA.
; #0AB 3 - 4 "-
499S>23 -G<r c 0 | j t t j | j dt j d d | j dt j d d | j dt j d d y )Nzfabs(-1)r r zfabs(0)r zfabs(1))r r rR fabsr{ rd s r testFabszMathTests.testFabs s^ )TYY/
:tyy}a0
9diilA.
9diilA.r c | j t j d d d}t dd D ]Z }||z }| j t j | | | j t j | t | \ | j t t j d | j t t j ddz y )Nr r r
d )r rR factorialr r$ r r )r` totalr# s r
testFactorialzMathTests.testFactorial
s *A.q$ AA QJE T^^A . 6 T^^A . Q @ A
*dnnb9 *dnnr3wh?r c V | j t t j d | j t t j d | j t t j d | j t t j d | j t t j t j
d | j t t j t j
d | j t t j d y )N @g@r }Ô%I5z5.2)r r rR r decimalDecimalrd s r testFactorialNonIntegersz"MathTests.testFactorialNonIntegers s )T^^S9 )T^^S9 )T^^T: )T^^V< )T^^W__S5IJ )T^^W__U5KL )T^^S9r c | j t t j ddz | j t t j d y )Nr r }Ô%IT)r r rR r r rd s r testFactorialHugeInputsz!MathTests.testFactorialHugeInputs s4
- SA )T^^U;r c | j t t j | j t
t
t j d | j t j d d | j t j d d | j t j d d | j t j d d | j t j d d | j t j d d
G d d } G d
dt } G d d }| j t j | d | j t j | d | j t j t d d | j t t j | | }d |_ | j t t j | | j t t j |d y )Nr r r r r r r r r c e Zd Zd Zy)&MathTests.testFloor.<locals>.TestFloorc yr rj rd s r __floor__z0MathTests.testFloor.<locals>.TestFloor.__floor__3 r r Nrg rh ri r rj r r TestFloorr 2 r r r c e Zd Zd Zy)'MathTests.testFloor.<locals>.FloatFloorc yr rj rd s r r z1MathTests.testFloor.<locals>.FloatFloor.__floor__6 r r Nr rj r r
FloatFloorr 5 r r r c e Zd Zy)(MathTests.testFloor.<locals>.TestNoFloorNrn rj r r TestNoFloorr 8 r r r r g33333D@) c | S r\ rj r s r r z%MathTests.testFloor.<locals>.<lambda>@ s D r )
r r rR floorr rQ r r: rZ r )r` r r r r s r testFloorzMathTests.testFloor% s )TZZ0 d4::c? 34 C !, C !, C !, D)2. D)2. D)2.
IK0"5 JL126 IdO4b9 )TZZ ? M( )TZZ3 )TZZA6r c | j t t j | j dt j dd d | j dt j dd d | j dt j dd d | j d
t j d d d | j d
t j d d d | j dt j d d d | j t j t j t d | j t j t j d t | j t j t j t t | j t t j d d | j t t j t d | j t t j t d | j t t j t d | j t j dt d | j t j dt d | j t j dt d | j t j dt d | j t j dd d | j t j dt d y )Nz fmod(10, 1)r r r z
fmod(10, 0.5)r z
fmod(10, 1.5)r r z fmod(-10, 1)r zfmod(-10, 0.5)zfmod(-10, 1.5)r r ) r r rR fmodr{ r rS r r r r r rd s r testFmodzMathTests.testFmodD s )TYY/
=$))B"2C8
?DIIb#$6<
?DIIb#$6<
>499S!#4d;
#TYYsC%8$?
#TYYsC%8$?
499S"#567
499R#567
499S##678 *diiR8 *diib9 *diir: *diib9 3,c2 4-t4 3-s3 4.5 3,c2 3-s3r c | j t t j fd} |dt j d d |dt j d d |dt j d d
|d t j d d
j t j t
d t
j t j t d t j t j t j t d y )Nc ||c\ }}\ }}t ||z
t kD s||k7 rj | d|d| y y Nz
returned z , expected r& r ry )rz resultr( mantrD emanteexpr` s r testfrexpz&MathTests.testFrexp.<locals>.testfrexp] sJ )/ &KT3 %4:$t 3 4 )4r z frexp(-1)r )r r zfrexp(0)r r r zfrexp(1)r )r r zfrexp(2)rH )r rH )
r r rR frexpr r r r rS r )r` r s ` r testFrexpzMathTests.testFrexpZ s )TZZ0 4 +tzz"~y9*djjmV4*djjmX6*djjmX6 C +S1 D)!,d3
4::c?1#567r z2fsum is not exact on machines with double roundingc 0 ddl m} |j |j z
fd}g dfdgdfg ddfg ddfg d d
fg d d fg d
dft dd D cg c] }d|z c}t
j
d ft dd D cg c]
}d|z |z c}t
j
d fg ddfg ddft ddd D cg c] }d|z d|d z z z
d|d z z z c}d gz t
j
d fg }t d D cg c] }d |z }}|j t d! D cg c] }||dz || z
c}|d! gz |d f t | D ]0 \ }\ }} t j | } | j | 2 dd$lm}
m} m} t d! D ] }
g d%d&z }d}t d' D ], } | d |
d(z |z
}||z
}|j | . | | || }| j || t j | y c c}w c c}w c c}w c c}w c c}w # t $ r | j d"|||fz Y t $ r | j d#|||fz Y
w xY w))Nr )
float_infoc d\ }}| D ][ }t j | \ }}t t j | | z
}}||kD r |||z
z }|}n|||z
z }||z
}] t t t
t | dz
z
|z
}|dkD r1d|dz
z }|d|z z t ||z xr |d|z dz
z z }||z
}t j || S )zFull precision summation. Compute sum(iterable) without any
intermediate accumulation of error. Based on the 'lsum' function
at http://code.activestate.com/recipes/393090/
r rH r r r ) rR r rQ ldexpmaxlenbinr& bool)
iterabletmanttexpr r rD tailhetinymant_digs
r msumz MathTests.testFsum.<locals>.msum s KE4
JJqM c
4 : ;S8^c#:d3h&E DSX%D
s3s5z?+A-8%$,GDax$q&M !A#eai.IEAaCEM)JJ ::eT* *r r )r r r 0.++gd~QJr gd~Qr2 ) @Cr g g?C)r3 r 9g @C)g @Cr r4 g @C)g?Cr g <g?Cr i r z0x1.df11f45f4e61ap+2r z-0x1.62a2af1bd3624p-1)r r 缉ؗҜ<g7yAC)g7yACg?g7yAgi rH r 2 4 g z0x1.5555555555555p+970g333333?r zDtest %d failed: got OverflowError, expected %r for math.fsum(%.100r)zAtest %d failed: got ValueError, expected %r for math.fsum(%.100r))randomgaussshuffle) r ir gh$.5g#B ;r r< )sysr# r0 min_expr r: fromhexappend enumeraterR fsumr ry r r r9 r: r; )r` r# r1 r test_valuesr# termsvalsr( actualr9 r: r; jsvr/ r0 s @@r testFsumzMathTests.testFsuml s # &&""X- +8 IUCL
<f E
' 5
& 4
+\ :
); 7 !!TN
+qbd
+
]]1
2
4"'4.
1QsQhqj
1
]]2
3
5
3 4
=s C7<UC7K
L!b!eb1R4j 2":-
L[
]]3
4
6 * "'t-Aa--,1$K 8qU1Q3Z%(
" 8U4[L> I
1XI
$-[#9 / A h
I 4
VX . / 21t
:A82=DA3Z
!VX&!+a/Q A
DMT
A T$Z4 9
:? ,
1
M . 8 !
I 256$4GH I
I 256$4GH I
Is6 H7 H< I I6I 5I J2 JJc t j }| j |dd d | j |dd d | j |dd d | j |dd d | j |dd d | j |dd d | j |dd d | j |dd d | j |dd d | j |dd
d | j |d d d
d}d}dD ] }||z }||z }| j ||| | | j ||| | | j || | | | j ||| | | j ||| | | j || | | | j || | | | j || | | | j | d | j |d d | j |d
d | j |ddd d | j |ddd d | j t |d | j t |dd | j t |dd | j t |ddd | j |t d t d d y )Nr r r r< x T j9W P)} "o `T"- l 8P9cC/[N
S9bXl 9@ {wM275k ) l Z'^%#> ; *Q!/ 61^f ^@ U@)rR gcdr r r rp )r` r[ r ycabs r testGcdzMathTests.testGcd s hh QA& QA& RQ' QA& QQ' QA& QQ' S" q) S" r* R + 9 8:;= ?
O 4V -AAAAA SAY * SAY * S!QZ + SQBZ + SQBZ + S!QZ + S!aR[! , S!aR[! , -
" S3' TC( S"c*A. S!R !, )S%0 )S%4 )S#t4 )S#q$7 [ -{2?Dr c ddl m} ddlm} t j
}t j t j t j d t j d t j d f}t t | dz D ]@ }| j ||d | t j t d |d | D B | j |d d
d | j |d d
d | j | |d |d
d | j | |d d |d
d |dd | j |t! d t! d t! d t! d t j d | j |dd d | j |d d | j | d | j dt j" d |d | j |ddd |ddd | j% t& 5 |d d d d | j% t& 5 |ddd d d d d t( j* j, d
z z }| j% t. t0 f 5 |d| d d d | j |t2 t2 | j |dt2 t2 | j |d t2 t2 | j |d t2 t2 | j |t4 t2 t2 | j |t2 t4 t2 | j |t6 t4 t2 | j |t4 t6 t2 | j |t2 t2 t2 | j |t2 t2 t2 | j |d t2 t2 | j9 t j: |t4 | j9 t j: |dt4 | j9 t j: |t4 d | j9 t j: |d t4 | j9 t j: |t4 t4 | j9 t j: |t4 t< d z }t d D ]D }| j9 t j> ||g|z |t j | z F t d D ]= } t@ d| z z }
| j t j
d |
z d|
z d
|
z ? y # 1 sw Y xY w# 1 sw Y xY w# 1 sw Y mxY w) Nr r Fractionr @g @r c 3 & K | ] }|d z yw)rH Nrj ).0rI s r <genexpr>z&MathTests.testHypot.<locals>.<genexpr> s 5qad 5s g (@r *@rQ rw
rU r r % %@r r r r r 皙?string皙@r r r r )!r r fractionsrd rR hypotr~ r} sqrtgammasinr r' assertAlmostEqualsumr r) r r r r> r#
max_10_expr r r r r r rS FLOAT_MAXisclose FLOAT_MIN) r` r rd rr r r# int_too_big_for_float fourthmaxr rD scales r testHypotzMathTests.testHypot s #&
vvtww #
3# Ns4y{# A " "tBQx # 5D!H 556
tS)40 r1 r* wr{GAJ7< xB /!R A8BPRCST tAwQa$q'BDIIaLQ
sC #. u t, #& MM#uT{ +
#sC #sC
y
) AJ
y
) & #x % & "s~~'@'@1'D E
M :
; , !* + ,
sS) q# , r3 - sC #. sC #. sC #. tS)3/ sD)3/ tS)3/ tcT*C0 rC4 #.
5:./
5C=12
5b>23
5S>23
5c?34
5:./ O r DA OODLL)Q )@)2TYYq\)A C
D D
9 DC s
*E TZZ%5 91U7 C DI & & , ,s$
X%< X2
X?%X/2X<?Y z7hypot() loses accuracy on machines with double roundingc t j }t j }t j d }dD ] \ }}t
j
| }t
j
| }| j |||| 5 t j | 5 t || dz || dz z j }d d d | j ||| d d d y # 1 sw Y -xY w# 1 sw Y xY w)N )prec) )z0x1.10e89518dca48p+29z0x1.1970f7565b7efp+30)z0x1.10106eb4b44a2p+29z0x1.ef0596cdc97f8p+29)z0x1.459c058e20bb7p+30z0x1.993ca009b9178p+29)z0x1.378371ae67c0cp+30z0x1.fbe6619854b4cp+29)z0x1.f4cd0574fb97ap+29z0x1.50fe31669340ep+30)z0x1.494b2cdd3d446p+29z0x1.212a5367b4c7cp+29)z0x1.f84e649f1e46dp+29z0x1.1fa56bef8eec4p+30)z0x1.2e817edd3d6fap+30z0x1.eb0814f1e9602p+29)z0x1.0d3a6e3d04245p+29z0x1.32a62fea52352p+30)z0x1.888e19611bfc5p+29z0x1.52b8e70b24353p+29)z0x1.538816d48a13fp+29z0x1.7967c5ca43e16p+29)z0x1.57b47b7234530p+29z0x1.74e2c7040e772p+29)z0x1.821b685e9b168p+30z0x1.677dc1c1e3dc6p+29)z0x1.9e8247f67097bp+29z0x1.24bd2dc4f4baep+29)z0x1.b73b59e0cb5f9p+29z0x1.da899ab784a97p+28)z0x1.94a8d2842a7cfp+30z0x1.326a51d4d8d8ap+30)z0x1.e930b9cd99035p+29z0x1.5a1030e18dff9p+30)z0x1.1592bbb0e4690p+29z0x1.a9c337b33fb9ap+29)z0x1.1243a50751fd4p+29z0x1.a5a10175622d9p+29)z0x1.57a8596e74722p+30z0x1.42d1af9d04da9p+30)z0x1.ee7dbd9565899p+29z0x1.7ab4d6fc6e4b4p+29)z0x1.5c6bfbec5c4dcp+30z0x1.02511184b4970p+30)z0x1.59dcebba995cap+30z0x1.50ca7e7c38854p+29)z0x1.768cdd94cf5aap+29z0x1.9cfdc5571d38ep+29)z0x1.dcf137d60262ep+29z0x1.1101621990b3ep+30)z0x1.3a2d006e288b0p+30z0x1.e9a240914326cp+29)z0x1.62a32f7f53c61p+29z0x1.47eb6cd72684fp+29)z0x1.d3bcb60748ef2p+29z0x1.3f13c4056312cp+30)z0x1.282bdb82f17f3p+30z0x1.640ba4c4eed3ap+30)z0x1.89d8c423ea0c6p+29z0x1.d35dcfe902bc3p+29)hxhyr r\ rH ) rR rr r r Contextr: r@ subTest localcontextrs r ) r` rr r high_precisionr r r r\ zs r testHypotAccuracyzMathTests.testHypotAccuracyB s
// c2$
* 1FBJ
b!A
b!A a1 5
1 )).9 F wqz1}wqz1} < B B DEAF q!a0
1
1O* 1PF F
1
1s$ >C;/C/!C;/C8 4C;;D c > ddl m} ddlm} t j
}t j }| j |dd d | j |dd d t d D ] }t d
D ]q }t d t | D }t d t | D }| j ||| |t d
t || D s | j |g dg d d | j |t g d t g d d | j |dd d | j |dd d | j | |d |d f |d |d f |d | j | |dd |dd f |dd |dd f |dd | j |dd |d | j |d d d | j |d d d | j d t j d |d d! | j d t j d |d!d | j |d"d# |d$d# G d% d&t } | j | | d d d | j t 5 |dd'( d d d | j t 5 |d d d d | j t 5 |dd'd) d d d | j t 5 |dd d d d | j t 5 |d*d d d d | j t" 5 |d+d, d d d | j t" 5 |dd- d d d | j t 5 |d.d/ d d d d0t$ j& j( d
z z }
| j t" t* f 5 |d|
fd1 d d d | j t" t* f 5 |d1d|
f d d d t d2 D ]Q }t- j, t- j, }}| j ||f|f t/ ||z
S t0 d3d4d d5t2 t4 g} t7 j8 | d67 D ] }t7 j8 | d67 D ] }t || D
cg c]
\ } }
| |
z
}} }
t; t= t j> | r | j ||| t2 et; t= t j@ | s| jC t j@ ||| tD d8z }t d D ] }|f|z }d!|z }| jC t jF ||| |t j | z | jC t jF ||| |t j | z t d D ]l }tH d|z z }d9|z d6|z f}d:}| j t j
|| d
|z | j t j
|| d
|z n y # 1 sw Y xY w# 1 sw Y xY w# 1 sw Y xY w# 1 sw Y xY w# 1 sw Y xY w# 1 sw Y xY w# 1 sw Y }xY w# 1 sw Y cxY w# 1 sw Y !xY w# 1 sw Y xY wc c}
} w );Nr rb rc )r r r )r r r r r rH r )r rH r rw c 3 H K | ] }t j d d ywrw Nr9 uniformrg ks r rh z%MathTests.testDist.<locals>.<genexpr> BA&..Q/B "c 3 H K | ] }t j d d ywr r r s r rh z%MathTests.testDist.<locals>.<genexpr> r r c 3 2 K | ] \ }}||z
d z yw)r Nrj )rg pxqxs r rh z%MathTests.testDist.<locals>.<genexpr> s F&"bb2g# - Fs )g ,@r )r r ri ) r )rH rj r r rH r rU )TTFTF)TFTTFr ) *@g )@
r rj r )r )r )r r r )r r r )r r r c e Zd Zy) MathTests.testDist.<locals>.TNrn rj r r Tr r r r )r rw rX pq)r< r r )rn ro rp )r rH r r )rw rX r< )r rw rX r< abcxyzr )rH r rk r rl r repeatr r )r r )%r r rq rd rR distrs r r tuplerv rw zipiterr r r r r> r# rx r r9 r& r r r itertoolsproductanymaprT rS r ry rz r{ )r` DFr rs r# rH r r r r| valuesr r diffsr} r rD r~ s r testDistzMathTests.testDist s (+yyyy
o/?@#F i4c: q A1X
BqBBBqBB&&AJ FC1I FFG
o/?@#F d? 3T:J5KLcR
k;7> gw/4 quadmadAbE];QrUC qRy!Ar( 3a2h"b 5JK2r $ > >@ c $
2 24
b" s+ MM#tGV 4 5
MM#tFG 4 5
) , ) ,
a lZ93?
y
) + 9 * +
y
) O
y
) 2 Iy 1 2
y
) AJ
y
) 2 %y 1 2
z
* * y ) *
z
* * L ) *
y
) "s~~'@'@1'D E
M :
; 5 !*+V 4 5
M :
; 5 ! 23 4 5 r ;A==?FMMOqA T1$ -s1q5z : ;
tS$S9""6!4 <A &&va8
</21ay9VRb99s4::u-.$$T!QZ5TZZ/0OODJJtAqz$:;
< < O r PA q A
A OODLLaY1 5M N O OODLLaY1 5M N O P 9 7C s
*E5!E'"AA TYYq!_ag 6 TYYq!_ag 6 7a + + 2 2 2 2 * * * * 5 5 5 5 :s~ 5 \ \$ \1+
\>
] 9
]
]%
]2 ]? ^ ^
\!$\.1\;>] ]]"%]/2]<?^ ^c | j t 5 t j ddgg d d d d y # 1 sw Y y xY w)Nr rH )r r rw )r r rR r rd s r test_math_dist_leakz MathTests.test_math_dist_leak s7
z
* ) IIq!fi ( ) ) )s :Ac t t d t t dd z t dd D cg c] }t dd D ]
}d|z |z c}}z d d
z d d z gz }|D ] }| j |
5 t j | }| j t
| t | j ||z | | j ||dz |dz z d d d | j t 5 t j d d d d t j d }| j t
| t | j |d t j d }| j t
| t | j |d G d dt }t j |d }| j t
| t | j |d | j t 5 t j |d d d d ddt j d dd d g}|D ]P }| j |
5 | j t 5 t j | d d d d d d R y c c}}w # 1 sw Y XxY w# 1 sw Y xY w# 1 sw Y xY w# 1 sw Y @xY w# 1 sw Y xY w) Nr iX> i(F < r= i( rH r i' r i r] r r TFr c e Zd Zd Zd Zy)(MathTests.testIsqrt.<locals>.IntegerLikec || _ y r\ r] r_ s r ra z1MathTests.testIsqrt.<locals>.IntegerLike.__init__ s "
r c | j S r\ r] rd s r rs z2MathTests.testIsqrt.<locals>.IntegerLike.__index__ s zz!r Nrt rj r r IntegerLiker s
#
"r r i r
r re za stringz3.5y @g Y@r )listr r rR isqrtassertIsr rQ assertLessEqual
assertLessr r r objectr r r )r` r~ r# rD r^ rI r
bad_valuess r testIsqrtzMathTests.testIsqrt s
t 5 |45
6!&r3 HAsB HAq!taxHxH
I $wD!
" ! 4E E *
4JJu%
d1gs+$$QqS%0!ac{3
4
4 4
z
* JJrN
JJt
d1gs# A JJu
d1gs# A "& "
JJ{4( )
d1gs# B
z
* ( JJ{2 ' (
W__U 3T 4
&E E *
&&&y1 &JJu%&
&
& &W I
4
4 . ( (& &
&
&sN J4A%J:K K5K, K !K,:K KK K) %K,,K5 c 0 t j }| j |dd d | j |dd d | j |dd d | j |dd d | j |dd d | j |dd d | j |dd d | j |dd d | j |dd d
| j |d d d
| j |d d
d d}d}dD ] }||z }||z }||z |z }| j ||| | | j ||| | | j || | | | j ||| | | j ||| | | j || | | | j || | | | j || | | | j | d | j |d d | j |d d | j |dd d d | j |ddd d | j t |d | j t |dd | j t |dd | j t |ddd | j |t d t d d
y )Nr r r r< rM rN iY rO rP iH rR rS rT l ,`aUx-xB:Vn
Ldbl me%Y% l };T^ )rV l |/Kr2 rW i7 rY rZ )rR lcmr r r rp )r` r r r\ r] r^ r_ ds r test_lcmzMathTests.test_lcm, s hh QA& QA& RQ' QA& QQ' QA& QQ' S" s+ S" s+ R , 9 8: R T
! ( -AAAAAA A SAY * SAY * S!QZ + SQBZ + SQBZ + S!QZ + S!aR[! , S!aR[! , -
" S3' TC( S"c*E2 S!R !, )S%0 )S%4 )S#t4 )S#q$7 [ -{2?Er c | j t t j | j dt j dd d | j dt j dd d | j dt j dd d | j d t j dd d
| j t
t j d d | j t
t j d
d | j
t j d d d | j
t j d
d d | j
t j t d t | j
t j t d t | j t j t j t d dddddz fD ]j }| j
t j t | t | j
t j t | t | j
t j d | d | j
t j d
| d | j
t j d| d | j
t j d| d | j t j t j t | | j t
t j d | | j t
t j d
| | j
t j d| d | j
t j d| d | j
t j t | t | j
t j t | t | j t j t j t | m y )Nz
ldexp(0,1)r r z
ldexp(1,1)rH z ldexp(1,-1)r r z ldexp(-1,1)r r r r ir r i+i l d( Fx:^V r r ) r r rR r% r{ r r r r r rS r r` r s r testLdexpzMathTests.testLdexpX s )TZZ0
<Aa !4
<Aa !4
=$**Qr"2C8
=$**R"2B7 -RA -S'B B126 C2C8 C,c2 D$/6
4::c1#567 R0 <A TZZaR 0# 6 TZZqb 14 8 TZZQB / 4 TZZaR 0# 6 TZZQB / 4 TZZaR 0# 6 OODJJtzz#r': ; < mTZZQ ? mTZZa @ TZZA . 3 TZZQ / 5 TZZQ / 5 TZZa 0$ 7 OODJJtzz#q'9 : ; <r c t | j t t j | j dt j dt j
z d | j dt j d d | j dt j t j
d | j dt j dd d
| j d t j d d
z d d
| j dt j d d
z d d | j dt j d dz d | j t t j d | j t t j d dz | j t t j t | j t j t t | j t j t j t y )Nzlog(1/e)r r zlog(1)r zlog(e)z log(32,2)rU rH rw zlog(10**40, 10)r r zlog(10**40, 10**20)r z
log(10**1000)r gO+@r )
r r rR logr{ r~ r r r r r rS r rd s r testLogzMathTests.testLogx sc )TXX.
:txx$&& 126
8TXXa[!,
8TXXdff -q1
;A2
$dhhr2vr&:B?
($((2r66*BAF
?DHHRX$6% ' *dhh5 *dhhT : *dhh5 # ,
488C=12r c | j t t j dddz ddz fD ]C }| j t j | t j t | E | j t t j d | j t j t t y )NrH Z i, r ) r r rR log1prv r: r r r r s r testLog1pzMathTests.testLog1p s )TZZ0QUAsF# HA " "4::a=$**U1X2F G H *djj"5 C #.r c , | j t t j | j t j d d | j t j d d | j t j d d | j t j ddz d | j t j dd z d
| j t j dd z d | j t
t j d
| j t
t j t | j t j t j t y )Nr r rH r r r i g @ g @i g @@r )
r r rR log2r r r r rS r rd s r testLog2zMathTests.testLog2 s )TYY/
1 s+ 1 s+ 1 s+
1d7+V4 1d7+V4 1d7+V4 *dii6 *dii6
499S>23r r c t dd D cg c]+ }t j t j d| - }}t dd D cg c]
}t | }}| j || y c c}w c c}w )Nr6 r r )r rR r r% r: r )r` r rG r( s r
testLog2ExactzMathTests.testLog2Exact si
:?ud9KLA$))DJJsA ./LL&+E4&89E!H99 * M9s 0A6A;c @ | j t t j | j dt j d d | j dt j d d | j dt j d d | j d t j dd
z d | j t
t j d | j t
t j dd
z | j t
t j t | j t j t t | j t j t j t y )
Nz
log10(0.1)皙?r zlog10(1)r r z log10(10)r zlog10(10**1000)r g @@r )
r r rR log10r{ r r r r r r rS r rd s r testLog10zMathTests.testLog10 s )TZZ0
<C "5
:tzz!}a0
;
22
$djjT&:FC *djj$7 *djj2t8)< *djj$7 # ,
4::c?34r c t j }t j }t j
}| j
|t g d d d | j
|ddgddg d | j
|g g d dd
|d d |d
d f |d |d fdd |d d fd |d d fd |d ffD ] }||f||d d d ffD ]~ \ }}| j || 5 t d t ||d D } ||| }| j
|| | j
t | t | d d d | j t | | j t |g | j t |g g g | j t |d dg | j t |dgd | j t |ddgdg | j t |dgddg d } | j t 5 |t! d | d d d d | j t 5 | | d t! d d d d G d d }
| j t 5 |d |
dgg d d d d | j t 5 |g dd |
dg d d d | j t 5 |dd gd dg d d d | j t 5 |d dgdd g d d d | j
|d t j" gd d g t j" | j
|d t j" gt j" d g t j" | j
|d t j" gt j" t j" g t j" | j
|d t j" gd d g t j" | j% t j& |d t j" gt j" t j" g | j% t j& |d t j( gd d g | j% t j& |d t j" gt j( d g | j% t j& |d t j" gd t j( g d } | j
|| d! y # 1 sw Y xY w# 1 sw Y dxY w# 1 sw Y ;xY w# 1 sw Y
xY w# 1 sw Y xY w# 1 sw Y xY w# 1 sw Y xY w)"N)r r r r r @re g @g 0@r )r g r rw r )r r r r c 3 , K | ] \ }}||z y wr\ rj )rg p_iq_is r rh z(MathTests.testSumProd.<locals>.<genexpr> s "Tc39"Ts Tstrictr r r c 3 > K t | D ] }| t wr\ )r RuntimeError)r r# s r raise_afterz*MathTests.testSumProd.<locals>.raise_after s$ 1X
s c e Zd Zd Zd Zy)*MathTests.testSumProd.<locals>.BadMultiplyc t r\ r r` others r __mul__z2MathTests.testSumProd.<locals>.BadMultiply.__mul__ ""r c t r\ r r s r __rmul__z3MathTests.testSumProd.<locals>.BadMultiply.__rmul__ r r N)rg rh ri r r rj r r BadMultiplyr s
#
#r r r g333333$@g3333334@gL>@gL4@))r r r )r r )rR sumprodr r rq rd r r r rw r r r r r r r r r rS r ) r` r r rd rJ r r r( rG r r r s r testSumProdzMathTests.testSumProd s ,,// %%
l!3Y?E #sc3Z8$? R !,
a^Xa^ ,
S\73< (
(1a. !
!Q
CA Q!QttW .
C1\\A\+ C ""TSAd=S"T TH $Q]F$$Xv6$$T(^T&\B C C
C C$
)W- )Wb1 )Wb"b9 )WdRD9 )WrdD9
*gBx"> *gtb"X>
|
, / E"I{1~ . /
|
, / KNE"I . / # #
|
, 8 R +Y 7 8
|
, 8 IKM2 6 7 8
y
) ) UAJB ( )
y
) ) QGeQZ ( )
$!1D$<@$((K $!1DHHd3CDdhhO $!1DHHdhh3GH$((S $ !2T4LADHH9M
7D$((+;txxi=R#STU
7D$((+;dD\#JKL
7D$((+;dhh=M#NOP
7D$((+;dDHH=M#NOP O $ -qC C, / / / / 8 8 8 8 ) ) ) )sU 7A V'V" V/ V<W ?W*W#V "V,/V9<W WW #W-zBsumprod() accuracy not guaranteed on machines with double roundingc t j }| j |dgdz dgdz d | j |dgdz ddgdz d | j |g ddgd z d
y ) Nr r r r r TF)r g\nTr g\nr r )rR r r )r` r s r test_sumprod_accuracyz MathTests.test_sumprod_accuracy st
,, #aSV4c: #dE]R-?@#F !<seAgFLr cpuc P t j }t j }t j
}t j } G fddt G fddt }d }d }ddd d
d d d
ddz d d f
ddddz z dddz z dddz z dddd d dd z f d d d!t d" t d" t d# d$d%d& |d' d(f d)d* |d+ |d, |d'd- |d.d/ d0d1d2 d f
|d3 |d4 |d5 |d6 |d7 |d7 |d# d8d9f d:dddz z d dd;d<d=d>fd?d@dAdBdCdDdEd dF fg }|D ]U } t dG D ]E }
|| |
H D ]6 } || |
H D ]' } | | f}
| j ||g|
||g|
|
) 8 G W y )INc 0 e Zd Z fdZ fdZeZeZd Zy)*MathTests.test_sumprod_stress.<locals>.Intc > t | t | z S r\ rQ r` r Ints r __add__z2MathTests.test_sumprod_stress.<locals>.Int.__add__ 3t9s5z122r c > t | t | z S r\ r r s r r z2MathTests.test_sumprod_stress.<locals>.Int.__mul__ r r c dt | dS )NzInt()r rd s r __repr__z3MathTests.test_sumprod_stress.<locals>.Int.__repr__ c$i[**r Nrg rh ri r r __radd__r r
r s r r r
3
3 H H
+r r c 0 e Zd Z fdZ fdZeZeZd Zy)*MathTests.test_sumprod_stress.<locals>.Fltc > t | t | z S r\ r r s r r z2MathTests.test_sumprod_stress.<locals>.Flt.__add__# r r c > t | t | z S r\ r r s r r z2MathTests.test_sumprod_stress.<locals>.Flt.__mul__% r r c dt | dS )NzFlt(r r rd s r r
z3MathTests.test_sumprod_stress.<locals>.Flt.__repr__) r r Nr r s r Fltr " r r r c F d}t | |d D ]
\ }}|||z z
} |S )zThis defines the target behavior including expections and special values.
However, it is subject to rounding errors, so float inputs should be exactly
representable with only a few bits.
r Tr )r )r r r r r s r baseline_sumprodz7MathTests.test_sumprod_stress.<locals>.baseline_sumprod, s8
E 1T 2
#Ss"
#Lr c | | }dt | t | fS # t t f$ r t $ r}t | ddfcY d}~S d}~ww xY w)zHMake comparing functions easier. Returns error status, type, and result.NNone)AssertionError NameError Exceptionr repr)funcr r r~ s r runz*MathTests.test_sumprod_stress.<locals>.run6 sZ
- t
f tF|3 3 #I.
-Awf,,
-s A
A A Ar r i l l r r rH P r r< ) @g g @ &@g y@g ? ?r g 3r r r i i:, r$ r g 8r i g @r r r NaNr r y @ @rj r r g z10.5z-2.25r i y @ ?a iz6.125z12.375z-2.75r InfrQ g +@g pl g pg `g )g <g r' g r% g g g `7@TFrw r r ) rR r r r r r rq rd rQ r: r r )r` r r r rd r r r" poolspoolsizeargs1args2r r s @r test_sumprod_stressz MathTests.test_sumprod_stress s
,,##// %% +# + +% + 4 VUE5%BSV L M
1c6\2ag:r!T'z8UNQ3
8
3eElU5\M5<4R#
'
E76?GG,<hr1o#r"M2sCF
D
W
wx 0''2BGAJ '%. '%."d
L
Bq$wJ1iZ
A
E6643q6 B
" D a
$T$ 7 E!(d!; %u~ (( 0 84 8 /$ /
r c R
dd l ddlm ddlm ddlm} ddlmm m
ddl m
m
m ddlm} |dd fd
fd d
f d
fd
fd d}dd | fdt# | D }| j% |d y )Nr rc )starmap)
namedtuple)r r r )choicesr r; )median
DotExample)r r\ target_sumprod conditionc
t | }t | }t j t ||d S )NTr )r rw mulr )r r\ vec1vec2rd operatorr5 s r DotExactzDMathTests.test_sumprod_extended_precision_accuracy.<locals>.DotExactl s: x#Dx#Dwx||StD-IJK Kr c z d t t | t t | z t | | z S )Nr )r r& )r r\ rA s r ConditionzEMathTests.test_sumprod_extended_precision_accuracy.<locals>.Conditionq s1 #c1+s3{;;c(1a.>QQ Qr c ` || z
|dz
z }t | D cg c]
}| ||z z c}S c c}w Nr )r )lohir widthr# s r linspacezDMathTests.test_sumprod_extended_precision_accuracy.<locals>.linspacet s4 "WQ'E,1!H5qBN5 55s +c | dz }dg| z }dg| z } | }
t t |dz | }t |dz dz |d< d|d< |D cg c] } dd | z c}|d | |D cg c] } dd | z c}|d | t t t |dz d| |z
}t || D ]H } dd |||z
z ||< dd |||z
z || z
|| z ||< J t t || } | t | \ }} || ||
|| S c c}w c c}w )
a Algorithm 6.1 (GenDot) works as follows. The condition number (5.7) of
the dot product xT y is proportional to the degree of cancellation. In
order to achieve a prescribed cancellation, we generate the first half of
the vectors x and y randomly within a large exponent range. This range is
chosen according to the anticipated condition number. The second half of x
and y is then constructed choosing xi randomly with decreasing exponent,
and calculating yi such that some cancellation occurs. Finally, we permute
the vectors x, y randomly and calculate the achieved condition number.
rH r )r r r r r r N)r rQ r r roundr )r r] n2r r\ r_ r~ r r# pairsrC rA r9 r7 r rI r r; r s r GenDotzBMathTests.test_sumprod_extended_precision_accuracy.<locals>.GenDotx s aB A AQA c!A#h2.Aq1u:>AaDAbE<=>qgdC(472>AcrF<=>qgdC(472>AcrF S1cAbD 9:;A2q\
V tS)D1r6O;! c*T!AF)_<x1~MQRSTQUU!
V
QOE EN;DAq aHQNIaOD D ?>s E:E c p |\ }}}} t | | gz t | dgz } ||z S rE )r ) resexr r\ r: r; r rA r s r
RelativeErrorzIMathTests.test_sumprod_extended_precision_accuracy.<locals>.RelativeError sD .0 +Aq.)aSD6)47aS=9AN*+ +r c b d| } | |j |j } || S )Nr )r r\ )dotfuncr] r rQ rP rN rR s r TrialzAMathTests.test_sumprod_extended_precision_accuracy.<locals>.Trial s/ A B"$$%C b) )r r r gꌠ9Y>)Fc 3 N K | ] } t j y wr\ )rR r )rg r# rU r] r s r rh zEMathTests.test_sumprod_extended_precision_accuracy.<locals>.<genexpr> s NAeDLL!Q 7 Ns "%r5 )r@ rq rd r r5 collectionsr6 rR r r r r9 r7 r r;
statisticsr8 r r )r` r6 r8 times relative_errrC rA r9 rd rN rR rU r] r7 r r rI r r r@ r; r5 r s @@@@@@@@@@@@@@@@@@r (test_sumprod_extended_precision_accuracyz2MathTests.test_sumprod_extended_precision_accuracy\ s &%*))44% .WX
L
R 6$ E $ EL ,
*
Nu NN e,r c V j t t j fd} |dt j d d |dt j d d j t j t
dt
f j t j t d t f t j t } j t j |d
j t j |d y ) Nc ||c\ }}\ }}t ||z
t kD st ||z
rj | d|d| y y r r )rz r r( v1v2e1e2r` s r testmodfz$MathTests.testModf.<locals>.testmodf sN !' HRhr22b5zC 3r"u: 3 4 $.r z modf(1.5)r )r r z
modf(-1.5)r )r r r r r r )
r r rR modfr r r r r rS )r` rb modf_nans ` r testModfzMathTests.testModf s )TYY/ 4 diinj9 tyy = 3 #s4 4 4,799S>
8A;/0
8A;/0r c t% | j t t j | j dt j dd d | j dt j dd d | j dt j dd d | j dt j dd d | j t j t d t | j t j t d t | j t j dt d
| j t j dt d
| j t j t j t d | j t j t j dt | j t j t j dt | j t j dt d | j t j d t d | j t j d d d | j t j d d
d | j t j d d d | j t j d d d
| j t j d d d
| j t t j d d | j t t j d d | j t t j d d | j t j d t t | j t j t j d t | j t j t t t | j t j t d t | j t j t d
t | j t j t d t | j t j t d d
| j t j t d d
| j t j t d d | j t j t d d | j t j t d d | j t j t t d | j t j t j t t | j t j dt d | j t j dd d | j t j dd
d | j t j dd d | j t j dd d
| j t j dd d
| j t t j dd | j t t j dd | j t t j dd | j t j dt t | j t j t j dt | j t j t t t | j t j t d t | j t j t d
t | j t j t d t | j t j t d d
| j t j t d d
| j t j t d d | j t j t d d | j t j t d d | j t j t t d | j t j t j t t | j t j dt d
| j t j dd d | j t t j dd
| j t j dd d
| j t j dd d
| j t j dd d
| j t j dd d
| j t t j dd | j t j dd d | j t j dt d
| j t j t j dt | j t j d
t d
| j t j d
d d
| j t j d
d
d
| j t j d
d d
| j t j d
d d
| j t j d
d d
| j t j d
d d
| j t j d
d d
| j t j d
d d
| j t j d
t d
| j t j d
t d
| j t j d
d d
| j t j dd d
| j t j t d d
| j t j d
d d
| j t j dd d
| j t j t d d
| j t t j dd
| j t t j dd | j t j dt d | j t j dt d | j t j dt t | j t j dt t | j t j dt t | j t j dt t | j t j d t d | j t j d t d | j t j dt t | j t j dt t | j t j dt d | j t j dt d | j t j dt d | j t j dt d | j t j d t t | j t j d t t | j d t j dd d | j d t j dd d! | j d"t j dd
d | j d#t j dd d
| j d$t j dd d
| j d%t j dd d& | j d't j dd d( | j d)t j dd d* | j t t j dd& | j t t j dd y )+Nzpow(0,1)r r zpow(1,0)zpow(2,1)rH z pow(2,-1)r r r r r r r r g r r r g .ggffffff?rn ?r ggggffffffz (-2.)**3.g z (-2.)**2.r z (-2.)**1.z (-2.)**0.z
(-2.)**-0.z
(-2.)**-1.r z
(-2.)**-2.r& z
(-2.)**-3.g ) r r rR powr{ r r r r rS r r rd s r testPowzMathTests.testPow s )TXX.
:txx!}a0
:txx!}a0
:txx!}a0
;24 #q)3/ $*D1 $((1c*R0 $((1d+b1
488C#345
488As#345
488As#345 !S)1-
"c*B/ "b)2. "c*B/ "b)2. "b)2. "c*B/ *dhhC8 *dhhD9 *dhhC8 "d+S1
488B#456
#s+S1 #r*C0 #s+S1 #r*C0 #r*B/ #s+R0 #s+R0 #t,b1 #s+R0 #t,b1
488C#567
#s+R0 #r*C0 #s+R0 #r*B/ #r*B/ #s+R0 *dhhS9 *dhhT: *dhhS9 #t,c2
488C#567
$,c2 $+T2 $,c2 $+S1 $+R0 $,b1 $,b1 $-r2 $,c2 $-r2
488D##678
#s+R0 #r*C0 *dhhS9 #r*B/ #r*B/ #s+R0 #s+R0 *dhhT: #s+S1 #t,b1
488C#567
"c*B/ "b)2. "c*B/ "b)2. "b)2. "c*B/ "c*B/ "d+R0 "c*B/ "d+R0 "c*B/
#r*B/ $+R0 #r*B/ #s+R0 $,b1 #s+R0
*dhhS9 *dhhd;
#t,b1 #t,b1 #t,c2 #t,c2 $-s3 $-s3 $-r2 $-r2
#s+S1 #s+S1 #s+R0 #s+R0 $,b1 $,b1 $,c2 $,c2
;s 3T:
;s 3S9
;s 3T:
;s 3S9
<$!5s;
<$!5t<
<$!5t<
<$!5v> *dhhd; *dhhc:r c | j t t j | j dt j d t j
| j dt j d t j
dz | j dt j d t j
dz | j d t j d
d
y ) Nz radians(180) z radians(90)r rH z radians(-45)ir z
radians(0)r )r r rR radiansr{ r} rd s r testRadianszMathTests.testRadians\ s )T\\2
>4<<#4dgg>
=$,,r"2DGGAI>
>4<<#4twwhqjA
< a !4r c ddl m fd}g d}|D ] } j | 5 |j \ }}}t j | }t j | }t j | } |||| t
j || }
j |
j | j d d d t j d } t dd D ]d } | dk( r | | z }t d D ]I }
|
| z }t
j || }
||||
t
j | | }
|| ||
K f t d
d d d
t t fD ]T } j t
j t | j t
j |t V dD ]V } j t
j |t | j t
j |t | X t d
d d
dt fD ] } j t 5 t
j t | d d d j t 5 t
j t | d d d j t 5 t
j |d
d d d j t 5 t
j |d d d d y # 1 sw Y xY w# 1 sw Y xY w# 1 sw Y xY w# 1 sw Y exY w# 1 sw Y xY w)Nr rc c B | | | }}}j t | t |dz ||z
|z }j |t | t | t |dz k( r"j |dz t |dz yy)z
Check that r matches remainder(x, y) according to the IEEE 754
specification. Assumes that x, y and r are finite and y is nonzero.
rH N)r r& r rQ ) r r\ rfxfyfrr rd r` s r
validate_specz.MathTests.testRemainder.<locals>.validate_specg s
"!hqk8A;BB R#bd) 4bBA QA '2w#bd)# 1c!A#h/ $r )0z -4.0 1 -0.0z -3.8 1 0.8z -3.0 1 -0.0z -2.8 1 -0.8z -2.0 1 -0.0z -1.8 1 0.8z -1.0 1 -0.0z -0.8 1 -0.8z -0.0 1 -0.0z 0.0 1 0.0z 0.8 1 0.8z 1.0 1 0.0z 1.8 1 -0.8z 2.0 1 0.0z 2.8 1 0.8z 3.0 1 0.0z 3.8 1 -0.8z 4.0 1 0.0z&0x0.0p+0 0x1.921fb54442d18p+2 0x0.0p+0z?0x1.921fb54442d18p+0 0x1.921fb54442d18p+2 0x1.921fb54442d18p+0z?0x1.921fb54442d17p+1 0x1.921fb54442d18p+2 0x1.921fb54442d17p+1z?0x1.921fb54442d18p+1 0x1.921fb54442d18p+2 0x1.921fb54442d18p+1z?0x1.921fb54442d19p+1 0x1.921fb54442d18p+2 -0x1.921fb54442d17p+1z?0x1.921fb54442d17p+2 0x1.921fb54442d18p+2 -0x0.0000000000001p+2z00x1.921fb54442d18p+2 0x1.921fb54442d18p+2 0x0p0z?0x1.921fb54442d19p+2 0x1.921fb54442d18p+2 0x0.0000000000001p+2z?0x1.2d97c7f3321d1p+3 0x1.921fb54442d18p+2 0x1.921fb54442d14p+1z?0x1.2d97c7f3321d2p+3 0x1.921fb54442d18p+2 -0x1.921fb54442d18p+1z?0x1.2d97c7f3321d3p+3 0x1.921fb54442d18p+2 -0x1.921fb54442d14p+1z?0x1.921fb54442d17p+3 0x1.921fb54442d18p+2 -0x0.0000000000001p+3z00x1.921fb54442d18p+3 0x1.921fb54442d18p+2 0x0p0z?0x1.921fb54442d19p+3 0x1.921fb54442d18p+2 0x0.0000000000001p+3z?0x1.f6a7a2955385dp+3 0x1.921fb54442d18p+2 0x1.921fb54442d14p+1z?0x1.f6a7a2955385ep+3 0x1.921fb54442d18p+2 0x1.921fb54442d18p+1z?0x1.f6a7a2955385fp+3 0x1.921fb54442d18p+2 -0x1.921fb54442d14p+1z?0x1.1475cc9eedf00p+5 0x1.921fb54442d18p+2 0x1.921fb54442d10p+1z?0x1.1475cc9eedf01p+5 0x1.921fb54442d18p+2 -0x1.921fb54442d10p+1z 1 0.c 0.4z -1 0.c -0.4z 1 -0.c 0.4z -1 -0.c -0.4z 1.4 0.c -0.4z-1.4 0.c 0.4z 1.4 -0.c -0.4z-1.4 -0.c 0.4z$0x1.dp+1023 0x1.4p+1023 0x0.9p+1023z$0x1.ep+1023 0x1.4p+1023 -0x0.ap+1023z$0x1.fp+1023 0x1.4p+1023 -0x0.9p+1023)casez1p-1074ir r r r r r )r r r r r )rq rd r r9 r: r@ rR remainderr hexr r r r assertIsNaNr r )r` rt testcasesru x_hexy_hex expected_hexr r\ r( rG tinyr mr^ rd s ` @r
testRemainderzMathTests.testRemainderc s &
0 9
v
?D 4 (
?-1ZZ\*ulMM%(MM%( == 6 aH- 1- x||~>
?
?
? }}Y'sB -AAvDA3Z
-H 1- aF+ A. qb!V,
- - 3c4s; 9E T^^C 7 8 T^^E3 7 8 9
, AE T^^E3 7 ? T^^E4 8% @ A D$S#6 ,E"":.
+sE*
+"":.
,tU+
,"":.
+uc*
+"":.
,ud+
,
, ,O
?
?P
+
+
,
,
+
+
,
,s< B"L
L L,=L81ML L) ,L5 8M M c | j t t j | j dt j d d | j dt j t j
dz d | j dt j t j
dz d | j
t j t j t | j
t j t j t | j
t j t j t y # t $ rU | j t t j t | j t t j t Y w xY w)Nzsin(0)r z sin(pi/2)rH r z
sin(-pi/2)r ) r r rR ru r{ r} r rS r r r r rd s r testSinzMathTests.testSin s
)TXX.
8TXXa[!,
; 3Q7
<477(1*!5r: : OODJJtxx} 5 6 OODJJtxx~ 6 7
488C=12 : j$((C 8 j$((D 9 :s ;A6E- -AG
G c | j t t j | j dt j d d | j dt j d dz t j
d dz z
d | j dt j d t j d z d | j
t j t t | j
t j t t | j t j t j t y )Nzsinh(0)r zsinh(1)**2-cosh(1)**2r rH r zsinh(1)+sinh(-1)) r r rR sinhr{ r r r r r rS r rd s r testSinhzMathTests.testSinh s )TYY/
9diilA.
*DIIaL!ODIIaL!O,KRP
%tyy|DIIbM'A1E 3 - 4 $/
499S>23r c | j t t j | j dt j d d | j dt j d d | j dt j d d | j dt j d d | j d
t j d d | j d
t j d d | j dt j d d | j t j t t | j t t j d | j t t j t | j t j t j t y )Nzsqrt(0)r r z sqrt(2.5)r gS[:XL?z
sqrt(0.25)r& r z sqrt(25.25)g @9@g)#L@zsqrt(1)r zsqrt(4)r rH r ) r r rR rs r{ r r r r r rS r rd s r testSqrtzMathTests.testSqrt s" )TYY/
9diilA.
9diinc2
; #0BC
<4 #6
=$))E"24EF
9diilA.
9diilA. 3 - *dii4 *dii6
499S>23r c | j t t j | j dt j d d | j dt j t j
dz d | j dt j t j
dz d | j
t j t j t | j
t j t j t | j
t j t j t y # | j t t j t | j t t j t Y xY w)Nztan(0)r z tan(pi/4)r r z
tan(-pi/4)r ) r r rR tanr{ r} r rS r r r r rd s r testTanzMathTests.testTan s )TXX.
8TXXa[!,
; 3Q7
<477(1*!5r: : OODJJtxx} 5 6 OODJJtxx~ 6 7
488C=12 : j$((C 8 j$((D 9s ;A6E- -AGc X | j t t j | j dt j d d | j dt j d t j d z dt j
d | j dt j t d | j dt j t d | j t j t j t y ) Nztanh(0)r ztanh(1)+tanh(-1)r r r z tanh(inf)z
tanh(-inf)) r r rR tanhr{ r r r r rS r rd s r testTanhzMathTests.testTanh s )TYY/
9diilA.
%tyy|DIIbM'A1 88A; (
; #2
<4 "5
499S>23r c | j t j d d | j t j dt j d t j dd y )Nr r )r rR r r rd s r testTanhSignzMathTests.testTanhSign sM
3 - r499S>: r3/ 1r c N | j t j d d | j t j d d | j t t j d t | j t t j d t | j t j d d | j t j d d | j t j d d | j t j d d | j t j d d | j t j d d
G d d } G d
dt
} G d d }| j t j | d | j t j | d | j
t t j | j
t t j dd | j
t t j t d | j
t t j | y )Nr r r r g?gg !r g-?Yic e Zd Zd Zy)'MathTests.test_trunc.<locals>.TestTruncc yN rj rd s r __trunc__z1MathTests.test_trunc.<locals>.TestTrunc.__trunc__2 r r Nrg rh ri r rj r r TestTruncr 1 r r r c e Zd Zd Zy)(MathTests.test_trunc.<locals>.FloatTruncc yr rj rd s r r z2MathTests.test_trunc.<locals>.FloatTrunc.__trunc__5 r r Nr rj r r
FloatTruncr 4 r r r c e Zd Zy))MathTests.test_trunc.<locals>.TestNoTruncNrn rj r r TestNoTruncr 7 r r r r rH g 7@) r rR truncr rQ r: r r rZ )r` r r r s r
test_trunczMathTests.test_trunc% s A * B , djjm,c2 djjo.4 C !, D)2. H-q1 I.3 I.3 H-t4
IK0"5 JL126 )TZZ0 )TZZA6 )TZZ4 A )TZZ ?r c 2 | j t j d | j t j d | j t j d | j t j d | j t j t d | j t j t d | j t j t d y )Nr r r r r r r )r rR isfinite assertFalser: rd s r testIsfinitezMathTests.testIsfiniteB s
c*+
d+,
c*+
d+, uU|45 uU|45 uV}56r c | j t j t d | j t j t d | j t j t d dz | j t j t d | j t j d | j t j d y )Nr z-nanr r r )r rR rS r: r rd s r testIsnanzMathTests.testIsnanK s
5<01
5=12
5<"#456 E%L12 B ( B (r c 2 | j t j t d | j t j t d | j t j d | j t j d | j t j t d | j t j d | j t j d y )Nr r g g r r r )r rR rT r: r rd s r testIsinfzMathTests.testIsinfS s
5<01
5=12
5)*
6*+ E%L12 B ( B (r c | j t j t j | j t j
dt j d y )Nr )r rR rS r r r rd s r test_nan_constantzMathTests.test_nan_constant\ s:
488,- r4884b9r c N | j t j t j | j t j d | j t j t
d | j t j t
d y )Nr r r )r rR rT r
assertGreaterr r: rd s r test_inf_constantzMathTests.test_inf_constanta sa
488,- 488S) 5<0 $((E&M2r zrequires verbose modec d t j d }dk7 r| j d t j d }| j d t j d }| j d y # | j d Y zxY w# t $ r Y Kw xY w# t
$ r Y y w xY w) Ni 6ez6underflowing exp() should not have raised an exceptionr z)underflowing exp() should have returned 0i ʚ;z.overflowing exp() didn't trigger OverflowErrorr z sqrt(-1) didn't raise ValueError)rR rD ry r rs r r` r s r test_exceptionszMathTests.test_exceptionsl s (%A
6 IIA B H$A
IIF G : $A
II8 95 (
II '
( s. A< B B# <B B B # B/.B/c dh}d }t j dk( r@t j d } t t t
|j
d }d}g }t t D ] \ }}}} }
} } | dk7 s| dk7 r|dv r|
|dk r||v r't t | }
d | v sd
| v rd }
nd | v rd
}
|
| }d\ }}t |
||| }|g|j |||| }|j | |r$| j! ddj# | z y y # t $ r Y w xY w# t $ r d }Y t $ r d
}Y w xY w)Ntan0064darwinr .{}: {}({!r}): {}r )rectpolar)r rw invaliddivide-by-zeror overflowr rw r z Failures in test_testfile:
)r> platformmac_verr r rQ r9 r rN test_filegetattrrR r rX r' rA ry join)r`
SKIP_ON_TIGER osx_version version_txtrV failuresr@ rA araiereirE r! r r* r+ rU msgs r
test_testfilezMathTests.test_testfile s #
<<8 #"**,Q/K
#C[->->s-C$D E &-;I-F " ! )BBBESyB#I&&&;+@ & 4$DE!%5%>!u$$
) b & GW"2vw@G//"b"g6C OOC E" !H II6 kk(+,
- U
6
&%
)(
)s) (D! 5D0! D-,D-0 E
=
E
E
c d}g }t t D ] \ }}}}}t t | }d|v sd|v rd}nd|v rd} || } d\ }
} |dk( rd }
n$|d
k( rd } n |d k( r|d
k\ r|dk rd}
n
|dk rd}
nd}
t
|| |
| } | u|j |||| }
|j |
|r$| j ddj | z y y # t $ r d} Y t
$ r d} Y w xY w)Nr r r r r r r rt r lgammagV瞯<erfcr r r $@r r z Failures in test_mtestfile:
r ) rF math_testcasesr rR r r rX r' rA ry r )r` rV r r@ rA rB r( rE r! r) r* r+ rU r s r test_mtestfilezMathTests.test_mtestfile sE %,;N,K 8 ! (BC54$DE!%5%>'u$*
&3i & GW W} x
v #* 9 G4Z !G "G"8S'7CG//"b#w7C OOC q8 !t II7 kk(+,
- a
#"
&%
&s C C1$
C10C1c t j }| j |g d | j |g d d | j |t t dd d | j |t t t dd d | j |t dd d d | j |g d d
| j |g d d | j |g d
d | j |g d d | j |g d d | j |g d t
d | j t | | j t |d | j t |g d | j t |g dd | j t |ddgd t d t d g}| j t ||t d | j t |dgdgdgg | j t |ddig | j t |ddigdz ddi | j t |dgdgdggg | j |ddgd d | j |ddgddg g d | j |g ddi ddi | j t 5 |dd gd d d d | j |g d d | j |g d d | j |g d! d d2d"}t dd# }| j || || t d$d% }| j || || t d&d' }| j || d t dd' D cg c]
}t
| }}| j || || t d&d% D cg c]
}t
| }}| j || || t d&d' D cg c]
}t
| }}| j || | j |dddt
d( ddg | j |dd t
d( ddg | j |dt
d( d dg | j |dt
d) t
d( dg | j |dt
d* t
d( dg | j |dt
d( t
d) dg | j |dt
d( t
d* dg | j |dddt
d) d+d,g t
d* | j |dddt
d* d+d,g t
d) | j |ddd t
d) d+d,g | j |ddd t
d* d+d,g | j |dddt
d) d+d dg | j |dddt
d* d+d dg | j t |g d- t | j t |g d. t | j t |t dd# t | j t |t dd# d/ t | j t |dt j d0 dd,dd1g t j y # 1 sw Y xY wc c}w c c}w c c}w )3Nr rw )r rH r i r i _7 )r rH r r rw rO )r r r r r rY )r rH r r r )r r r r rw )r r r r r )r r r r r r )r^ r_ r] a cr br ab abababababab) r rH r rH r rH r rH r rH r rH r )r r rH r r )r r rH r )r rH r r c | D ] }||z } |S r\ rj )r* r elems r _naive_prodz(MathTests.test_prod.<locals>._naive_prod2 s
Lr i' ir ir r r r r r )r rH r r rw rX )r r r r rw rX r r rX )r )rR prodr r r r r: r r bytearrayrx r rQ r r )r` r r r r* r s r test_prodzMathTests.test_prod s yy b1% b*A. d51: ./6 d4a
#3 45t< eArl"5w? o.4 78%@ 12E: 34e<
12E: 56e E )T* )T2. )T?; )T?"E )TD$<sCD/9T?3 )T63 H )TQC!qc?; )TQqE73 )TQqE719QqEB )TQC!qc?"E
q!fD1>B q!fQF35YZ bA/!A7
y
) "b1
l+Q/ l+Q/ l+Q/ E? h X)>?$ h X)>?% h + ',Atn5E!H55 h X)>?&+E2&67E!H77 h X)>?&+E4&89E!H99 h (
q!Qe a ;<= q!U5\1a 89: q%,1 567 q%,e Q ?@A q%-u a @AB q%,e Q ?@A q%,f
a @AB q!Qe R :;U6]K q!Qf
b ;<eElK q1U5\2q 9:; q1U6]B :;< q!Qe b!Q ?@A q!Qf
r1a @AB
d#5 67= d#7 895A d5E? 34c: d5E?# >?G dAws';Q1a#H IJ *m . 679s ^01^=1_1_0^:c t j }t j }t d D ]` }|dk rt |dz n|dk r t d n
t d D ]- }| j ||| || |||z
z / b t dd D ]I }t d| D ]8 }| j ||| ||dz
|dz
|z ||dz
| z : K t dd D ]S }| j ||d d | j ||d | | j ||| || U t d D ]? }| j || || | j ||d || A | j t |dd | j t |dt j d | j t |dd
| j t |d d | j t |t j d d | j t |d d | j t | | j t |ddd
| j t | | j t |dd | j t |ddz d | j t |dd | j t |dddz | j |dd d | j |dddz d ddz }| j ||d d | j ||d | | j ||d ||dz
z t j d r| j t ||| dD ]D \ }}| j ||| d | j t ||| t F | j |t! d t! d d | j |t# d t# d d t d
D ]r }| j t |t! d t! | t | j t |t# d t# | t t y )Nr r r r= r r r r r 1r 10r r rH r Tcpython)TT)TF)FFrw )rR permr r r r r r r r r check_impl_detailr r r rQ rm rp )r` r r r r s r testPermzMathTests.testPermd s8 yyNN s CA&'#geAElC59USUY
C a!*1 1q51A!AC
C C q# VA1a[
V aT!a%Q-?!-Cd1q5RSn-TU
V V
q# 7A T!QZ + T!QZ + T!QZ1 6 7 r :A T!Wil 3 T!T]IaL 9 :
)T2s3 )T2ws/CD )T2s3 )T43 )T7??4+@!D )T43 )T* )T2q!4 )T*
*dB2 *dQWHa8 *dAr2 *dA4x8
aQ' aD)1-
tG aQ' aQ' aQ!A#Y/ $ $T 2 mT1a 8? 1DAq T!QZ + MM$tAqz*C 0 1
k!nk!n=rB k!nk!n=rBq KA MM$tKNKN CDc J MM$tKNKN CDc J Kr c
t j }t j }t d D ]i }|dk rt |dz n|dk r t d n
t d D ]6 }| j ||| || || |||z
z z 8 k t dd D ]F }t d| D ]5 }| j ||| ||dz
|dz
||dz
| z 7 H t d D ]4 }| j ||d d | j ||| d 6 t dd D ]7 }| j ||d | | j |||dz
| 9 t d D ]8 }t |dz D ]% }| j ||| ||||z
' : | j t |dd | j t |dt j d | j t |dd
| j t |d d | j t |t j d d | j t |d d | j t |d | j t |ddd
| j t | | j t |dd | j t |ddz d | j t |dd | j t |dddz | j |dd d | j |dddz d ddz }| j ||d d | j ||d | | j ||d ||dz
z dz | j ||| d | j |||dz
| | j |||dz
||dz
z dz t j d r| j t |||dz dD ]D \ }}| j ||| d | j t ||| t F | j |t! d t! d d | j |t# d t# d d t d
D ]r }| j t |t! d t! | t | j t |t# d t# | t t y )Nr r r r= r r r rH r r r r r r r Tr r rw )rR combr r r r r r r r r r r r r rQ rm rp )r` r r r r s r testCombzMathTests.testComb s yyNN s :A&'#geAElC59USUY
: aYq\!! yQ'77.9 :
: : q# RA1a[
R aT!a%Q-?$q1ua.-PQ
R R
s ,A T!QZ + T!QZ + , q# 0A T!QZ + T!QU^Q / 0
s =A16]
= aT!QU^<
= =
)T2s3 )T2ws/CD )T2s3 )T43 )T7??4+@!D )T43 )T2. )T2q!4 )T*
*dB2 *dQWHa8 *dAr2 *dA4x8
aQ' aD)1-
tG aQ' aQ' aQ!A#Y!^4 aQ' a1 q) a1 qAaCyA~6 $ $T 2 mT1ad ;? 1DAq T!QZ + MM$tAqz*C 0 1
k!nk!n=rB k!nk!n=rBq KA MM$tKNKN CDc J MM$tKNKN CDc J Kr c | j t j dt d | j t j dt d | j t j dd d | j t j dd d | j t j d t t j d
| j t j d t t j d | j t j d t d
t j d
| j t j d t d
t j d | j t j d t d
t j d | j t j d t d
t j d t
d d D ]z }| j t j dd|
d | j t j dd|
d | j t j dd|
d | t j j t j j z }| j t j dt | | j t j dt | | j t j dt | | j t j dt | | j t j |d d | j t j | d d | j t j |d d | j t j | d d t j j }| j t j t d | | j t j t d | | j t j |t t | j t j | t t | j t j t d | j t j d t | j t j t t | j d t j d t d
| j t 5 t j d t d
d d d y # 1 sw Y y xY w)Ng 0Cg/Cg 0Cg Cr gCg gr z0x1.fffffffffffffp-1z0x1.0000000000001p+0r )stepsr z0x1.ffffffffffffdp-1z0x1.0000000000003p+0rw r r r r )r rR nextafterr r: r@ r assertEqualSignr> r# minepsilonr& rx r r r )r` r smallest_subnormallargest_normals r test_nextafterzMathTests.test_nextafter s-
(:SDA+ - (:C@+ - (=sC. 0 (>D/ 1
cT2 '=> @ S1 '=> @ cT; '=> @ S: '=> @ cT; '=> @ S: '=> @ 1a[ PE T^^CE BC H d%!H$ O d%!H$ O P !^^ / /#..2H2H H c24FG c24FG sd36H5HI sd36H5HI T^^,> EtL T^^-?,? FM T^^,> EtL T^^-?,? FM ++ S1>B c2^OD <cB #>E
S12 S12 S12 dnnS#Q ?@
z
* / NN32 . / / /s . WW c D | j t j d t j j
| j t j d d | j t j d d | j t j d d | j t j d t j j t j j
z | j t j t t t j t t z
| j t j t t | j t j t j ddddt fD ]V }| j | 5 | j t j | t j | d d d X y # 1 sw Y cxY w) Nr l l r l g @r rm )
r rR r r> r# r r ry r r rx r r r s r test_ulpzMathTests.test_ulp& sp # (>(>? '*C0 '*C0 '*F3
# ++cnn.D.DD F ),"T^^It%DD F
# , $((+, sGWc2 <A "
< 1" txx{;
<
< <
<
<s :HH c , G d d }t j t j t j fD ]L } | }| j t
5 |d| d d d | j
t |dd N y # 1 sw Y (xY w)Nc e Zd Zd Zy)$MathTests.test_issue39871.<locals>.Fc d| _ ddz y )NTr r ) convertedrd s r re z.MathTests.test_issue39871.<locals>.F.__float__A s !%!r N)rg rh ri re rj r r r r @ s
r r z not a numberr F)rR r r rv r r r r )r` r r! r\ s r test_issue39871zMathTests.test_issue39871= s} JJ
t~~= =DA""9-
(^Q'
(
WQ U ; < =
(
(s
B
B c p t j | s!| j dj | y y )NzExpected a NaN, got {!r}.)rR rS ry r' r_ s r rx zMathTests.assertIsNaNO s+ zz% II188? @ !r c | j || | j t j d| t j d| y)zSimilar to assertEqual(), but compare also the sign with copysign().
Function useful to compare signed zeros.
r N)r rR r )r` r r\ s r r zMathTests.assertEqualSignS s:
A sA.
c10EFr Nr )Urg rh ri r{ r r r r r r r r r r r r r unittestskipIfr> r machiner r r r r r r r cpython_onlyr r r r! HAVE_DOUBLE_ROUNDINGrK r` r r r r r r r r r r requires_mac_verr r r r requires_resourcer3 r[ re ri rm r r r r r r r r r r r r r
skipUnlessr r r r r r r r r r rx r rj r r rv rv s 6. 45 454 5;:z4 6B : :B 3 X__S\\W,W1A1A1A1CGW1W[]4]45< =/ @:
< < 7>4,8$ X__)MO\:O \:|(ETIDV X__)NP:1P :1xo7b)
3&j*FX <@3 / 4 4" W b!$+ % +
5N.b X__)]_ M _ M W u%H &HT X__)]_ W u%Q- & _
Q-f1&G;j5 ~, ~,@ 34 4 34 1 1 @:7)):
3 X"9: : ; :> 6- 6-p @- @-DZ*x>K@DKL 8/ 8/v < <,=$AGr rv c ~ e Zd Zej Zd Zd Zd Zd Zd Z d Z
d Z d Z d Z
d
Zd Zd Zd
Zd Zd Zy) IsCloseTestsc ` | j | j ||g|i ||d|d y )N and z should be close!r )r rz r` r^ r_ r kwargss r
assertIsClosezIsCloseTests.assertIsClose_ s5 Q;D;F;<=q A Cr c ` | j | j ||g|i ||d|d y )Nr
z should not be close!r )r rz r s r assertIsNotClosez IsCloseTests.assertIsNotClosec s7 a<T<V<ABA F Hr c F |D ] \ }} | j ||g|i | y r\ )r r` examplesr r
r^ r_ s r assertAllClosezIsCloseTests.assertAllCloseg s1 6DAq D q! 5d 5f 5 6r c F |D ] \ }} | j ||g|i | y r\ )r r s r assertAllNotClosez IsCloseTests.assertAllNotClosek s1 9DAq !D ! !!Q 8 8 8 9r c | j t 5 | j ddd d d d | j t 5 | j dddd d d d y # 1 sw Y =xY w# 1 sw Y y xY w)Nr g0.+rel_tolr2 g _©r r+ )r r r rd s r test_negative_tolerancesz%IsCloseTests.test_negative_toleranceso s~
z
* 6 q!W 5 6
z
* D q!VU C D D 6 6 D Ds A'A3'A03A<c 4 g d}| j |dd y )N))r r )N@ir );r )i90 g @)r r )NF r r r r )r` identical_exampless r test_identicalzIsCloseTests.test_identicalv s" 0
.SIr c X g d}| j |d | j |d y )N))g חAg חA)g:0yEgnyE)g ѭ?gfNӭ?:0yE>r & .>r r )r` eight_decimal_places_exampless r test_eight_decimal_placesz&IsCloseTests.test_eight_decimal_places s5 )C%
94H <d Kr c X g d}| j |d | j |d y )N))r% r )g& .r )gu?j/ʠr rg r r$ r )r r )r` near_zero_exampless r test_near_zerozIsCloseTests.test_near_zero s4 .
13 ? .=r c | j t t | j t t d | j t t | j t t d y )Nr r )r r r rd s r test_identical_infinitez$IsCloseTests.test_identical_infinite sL 3$ 3S1 4& 4s3r c t t ft dfdt ft t ft t ft t ft dfdt ft dfdt fg
}| j |d y )Nr2 r gg?r )r r r r )r` not_close_exampless r test_inf_ninf_nanz IsCloseTests.test_inf_ninf_nan sg "Cj "Fm %sm "Cj "Cj "Dk "Cj "Cj "El $cl ,
1;L Mr c ` g d}| j |d g d}| j |d y )N))r r )333333 r2 )Y nr3 r r ))r g ?)g?r )gZbtigTbtir& )r` zero_tolerance_close_examples!zero_tolerance_not_close_exampless r test_zero_tolerancez IsCloseTests.test_zero_tolerance s? )=%
93G-N)
@# Nr c . | j ddgd y )N)r r )r r r r r rd s r test_asymmetryzIsCloseTests.test_asymmetry s Wg .<r c X ddg}| j |d | j |d y )N) )i[i[r$ r r% r& )r` integer_exampless r
test_integerszIsCloseTests.test_integers s: 2 2 4
,d; / >r c ddl m} |d |d f |d |d f |d |d f |d |d
fg}| j |d | j |d
y )Nr rb z
1.00000001z1.0z1.00000001e-20z1.0e-20z1.00000001e-100z1.0e-100z
1.00000001e20z1.0e20r$ r r% )r r r r )r` r decimal_exampless r
test_decimalszIsCloseTests.test_decimals s # $\ 2GEN C $%5 6 8J K $%6 79L M $_ 5wx7H I K
,d; / >r c ddl m} |dd dz |d f |d |d f |dd |dd fg}| j |d | j |d
y ) Nr rc r r; r: l (qe r r$ r r% )rq rd r r )r` rd fraction_exampless r test_fractionszIsCloseTests.test_fractions sz & a
#a
'! 5
i
(9"5 6
i
((1f*= > @
-t< 0$ ?r N)rg rh ri rR rz r r r r r r" r( r+ r- r0 r6 r8 r= r@ rC rj r r r r \ s^ llGCH69DJL>4
N
O=? ? @r r c @ ddl m} |j |d |S )Nr ) DocFileSuitez ieee754.txt)doctestrE addTest)loadertestspatternrE s r
load_testsrK s $ MM,}-. Lr r )9 test.supportr r testr r rq r r rR osr r9 r r> r r: r r r r# r& ry r r{ r r\ r rg argvfile__file__pathdirnamecurdirtest_dirr r r r r r r$ r/ rF rN rX rZ rQ rm r rp TestCaserv r rK mainrj r r <module>rX s 4
El El V} NN NN 1A) z 88A;D D
77??4 -BII h(<= GGLL#8 9
L5 H ,B$:40+Z # & k!G!! k!G\Cx@8$$ x@v
zHMMO r