a ò.;bV<ã@sîdZddlZddlZddlZddlZddlmmZ ddlm Z ddlmZm Z ddlmZddlmZmZmZmZddlmZddlmZdd lmZed ƒZejZe e d¡¡Zej Z!ej"Z#e e d¡¡Z$e$j Z%e$j"Z&d Z'dZ(dZ)dZ*dd„Z+dd„Z,dd„Z-dd„Z.dd„Z/dd„Z0dd„Z1dd „Z2d!d"„Z3d#d$„Z4d%d&„Z5d'd(„Z6dd*d+„Z7e6ej8e j9ƒe6ej:e j;ƒZƒZ?e6ej@e jAƒZBe6ejCe jDƒZEe6ejFe jGƒZHe7ejId,d-ƒZJe7ejKd.d/ƒZLe7ejMd0d1ƒZNe7ejOd2d3ƒZPe7ejQd4d5ƒZRe7ejSd6d7ƒZTe7ejUd8d9ƒZVe7ejWd:d;ƒZXe7ejYdd?ƒZ\e7ej]d@dAƒZ^e7ej_dBdCƒZ`e7ejadDdEƒZbe7ejcdFdGƒZde7ejedHdIƒZfe7ejgdJdKdLƒZhe7ejidMdNdLƒZje7ejkdOdPƒZle7ejmdQdRƒZne7ejodSdTdLƒZpe7ejqdUdVƒZreejsejtƒdWdX„ƒZueejsejvƒdYdZ„ƒZweejxejtƒd[d\„ƒZyeejxejvƒd]d^„ƒZzeej{ejtƒd_d`„ƒZ|eej{ejvƒdadb„ƒZ}eej~ejtejtƒdcdd„ƒZeej€ejtƒdedf„ƒZeej‚ejtejƒƒdgdh„ƒZ„eej…ej†ej†ƒdidj„ƒZ‡eej…ejˆejˆƒdkdl„ƒZ‰eej…ejtejtƒdmdn„ƒZŠeej‹ej†ej†ƒdodp„ƒZŒeej‹ejˆejˆƒdqdr„ƒZeej‹ejtejtƒdsdt„ƒZŽeejejtƒdudv„ƒZe5ejeƒeej‘ejtƒdwdx„ƒZ’e5ej‘e’ƒeej“ejtejtƒeej“ejtejvƒdydz„ƒƒZ”d{d|„Z•ee•ƒd}d~„ƒZ–dd€„Z—eej˜ejvejvƒe—ƒdS)‚zA Provide math calls that uses intrinsics or libc math functions. éN)ÚType)ÚRegistryÚimpl_ret_untracked)Útypeof)ÚtypesÚutilsÚconfigÚcgutils)Úoverload)Ú signature)Útrailing_zerosZmathimplÚfloat32Úfloat64iÿÿÿllÿÿÿÿlcCs| d||¡S)z< Return a condition testing whether *val* is a NaN. Zuno)Zfcmp_unordered©ÚbuilderÚval©rú5lib/python3.9/site-packages/numba/cpython/mathimpl.pyÚis_nan(srcCsTtj |jtdƒ¡}tj |jtdƒ¡}| tj||¡}| tj||¡}| ||¡S)zB Return a condition testing whether *val* is an infinite. z+infz-inf)ÚlcÚConstantÚrealÚtypeÚfloatZfcmpZFCMP_OEQÚor_)rrZpos_infZneg_infZisposinfZisneginfrrrÚis_inf.s rcCs| ||¡}| d||¡S)z? Return a condition testing whether *val* is a finite. Úord)ÚfsubZfcmp_ordered)rrZ val_minus_valrrrÚ is_finite8srcCs$|jt ¡ksJ‚| |t d¡¡S)z1 Bitcast a double into a 64-bit integer. é@)rrÚdoubleÚbitcastÚintrrrrÚf64_as_int64@sr#cCs$|jt d¡ksJ‚| |t ¡¡S)z1 Bitcast a 64-bit integer into a double. r)rrr"r!r rrrrÚint64_as_f64Gsr$cCs$|jt ¡ksJ‚| |t d¡¡S)z0 Bitcast a float into a 32-bit integer. é )rrrr!r"rrrrÚf32_as_int32Nsr&cCs$|jt d¡ksJ‚| |t ¡¡S)z0 Bitcast a 32-bit integer into a float. r%)rrr"r!rrrrrÚint32_as_f32Usr'cCs| tj |jd¡|¡S)zB Negate real number *val*, with proper handling of zeros. g€)rrrrrrrrrÚnegate_real\sr(cCs,|j}tj ||dd„|Dƒ¡}| ||¡S)z9 Call a LLVM intrinsic floating-point operation. cSsg|] }|j‘qSr)r)Ú.0ÚarrrÚ hóz%call_fp_intrinsic..)ÚmodulerZFunctionZ intrinsicÚcall)rÚnameÚargsÚmodZintrrrrÚcall_fp_intrinsiccsr2cs‡fdd„}|S)zŒ Return an implementation factory to convert the single integral input argument to a float64, then defer to the *wrapped_impl*. c sT|\}|jd}| |||tj¡}ttjtjƒ}ˆ||||fƒ}| ||tj|j¡S)Nr)r0ÚcastrrrÚreturn_type) ÚcontextrÚsigr0rÚ input_typeZfpvalZ inner_sigÚres©Úwrapped_implrrÚimplementerqs z2_unary_int_input_wrapper_impl..implementerr)r:r;rr9rÚ_unary_int_input_wrapper_impllsr<cCst|ƒ}t|tjƒ|ƒdS©N)r<ÚlowerrÚInteger)ÚfnÚ float_implÚimplrrrÚunary_math_int_impl{srCcs&t|tjƒ‡fdd„ƒ}t||ƒ|S)zO Implement the math function *fn* using the LLVM intrinsic *intrcode*. cst|ˆ|ƒ}t|||j|ƒSr=)r2rr4©r5rr6r0r8©ÚintrcoderrrAƒsz#unary_math_intr..float_impl)r>rÚFloatrC)r@rFrArrErÚunary_math_intrs rHFcs:|r tjnd}‡‡fdd„}t|tjƒ|ƒt||ƒ|S)a! Register implementations of Python function *fn* using the external function named *f32extern* and *f64extern* (for float32 and float64 inputs, respectively). If *int_restype* is true, then the function's return value should be integral, otherwise floating-point. Ncs„|\}|j}|jd}| |¡}tjˆtjˆi|}t ||g¡} tj |j| |d} | | |f¡}| ||||j¡}t |||j|ƒS)z9 Implement *fn* for a types.Float input. r©r/)r-r0Úget_value_typerr rrÚfunctionr Úinsert_pure_functionr.r3r4r)r5rr6r0rr1r7ÚltyÚ func_nameÚfntyr@r8©Ú f32externÚ f64externrrrA•s þýz%unary_math_extern..float_impl)rÚint64r>rGrC)r@rQrRZint_restypeZ f_restyperArrPrÚunary_math_extern‹s rTZlog1pfÚlog1pZexpm1fÚexpm1ZerffÚerfZerfcfÚerfcZtanfÚtanZasinfÚasinZacosfÚacosZatanfÚatanZasinhfÚasinhZacoshfÚacoshZatanhfÚatanhZsinhfÚsinhZcoshfÚcoshZtanhfÚtanhZlog2fÚlog2ZceilfÚceilTZfloorfÚfloorZnumba_gammafZnumba_gammaZsqrtfÚsqrtZtruncfÚtruncZlgammafÚlgammacCs |\}t||ƒ}t|||j|ƒSr=)rrr4©r5rr6r0rr8rrrÚisnan_float_implÕs rjcCstj}t|||j|ƒSr=©r Z false_bitrr4rDrrrÚisnan_int_implÛsrlcCs |\}t||ƒ}t|||j|ƒSr=)rrr4rirrrÚisinf_float_implás rmcCstj}t|||j|ƒSr=rkrDrrrÚisinf_int_implçsrncCs |\}t||ƒ}t|||j|ƒSr=)rrr4rirrrÚisfinite_float_implís rocCstj}t|||j|ƒSr=)r Ztrue_bitrr4rDrrrÚisfinite_int_implôsrpcCsN|dj}|j}t |tj |||f¡d|j¡}| ||¡}t |||j |ƒS)Nrzllvm.copysign.%s)rr-r Úget_or_insert_functionrrrKZintrinsic_namer.rr4)r5rr6r0rMr1r@r8rrrÚcopysign_float_implús ÿrrcCs¤|\}| |jd¡}| |jd¡}tj||dd}t ||t |¡f¡}dddœt|ƒ} t |j || ¡} | | ||f¡}t ||| |¡f¡}t|||j|ƒS)NréÚexprIZnumba_frexpfZnumba_frexp©rr )Ú get_data_typer0r4r Zalloca_oncerrKZpointerÚstrrqr-r.Zmake_anonymous_structÚloadr)r5rr6r0rÚflttyÚinttyZexpptrrOÚfnamer@r8rrrÚ frexp_implsþýr|cCsn|\}}t|j|jƒ\}}t |||f¡}dddœt|ƒ} tj|j|| d} | | ||f¡}t |||j|ƒS)NZnumba_ldexpfZnumba_ldexprurI)Úmaprvr0rrKrwr rLr-r.rr4)r5rr6r0rrtryrzrOr{r@r8rrrÚ ldexp_implsþýr~cCsL|\}}| |t ¡¡}| |t ¡¡}ttjtjtjƒ}t|||||fƒSr=)Úsitofprr rrrÚatan2_float_impl©r5rr6r0ÚyÚxÚfsigrrrÚatan2_s64_impl)s r…cCsL|\}}| |t ¡¡}| |t ¡¡}ttjtjtjƒ}t|||||fƒSr=)Zuitofprr rrrr€rrrrÚatan2_u64_impl1s r†cCs|t|ƒdksJ‚|j}|jd}| |¡}tjdtjdi|}t |||f¡}t j |j||d} | | |¡} t|||j | ƒS)NérZatan2fÚatan2rI)Úlenr-r0rJrr rrrKr rLr.rr4)r5rr6r0r1ZtyrMrNrOr@r8rrrr€9s þýr€cCs\|\}}| |t ¡¡}| |t ¡¡}ttjtjtjƒ}t|||||fƒ}t|||j|ƒSr=© rrr rrrÚhypot_float_implrr4©r5rr6r0rƒr‚r„r8rrrÚhypot_s64_implLsrcCs\|\}}| |t ¡¡}| |t ¡¡}ttjtjtjƒ}t|||||fƒ}t|||j|ƒSr=rŠrŒrrrÚhypot_u64_implVsrŽcsÆ|j\}}||kr |jks&nJ‚|\}}tjtjdkr@dndtjtjdkrTdndi|}t ||¡‰tjdkrštj dkrš|t dƒƒ‰‡‡fdd „} n‡fd d „} | || ||¡} t|||j| ƒS)NZwin32Z_hypotfZhypotfZ_hypotÚhypotr%Úinfcs"t |¡st |¡rˆSˆ||ƒSr=)ÚmathÚisinf©rƒr‚©rÚ plat_hypotrrÚ hypot_implqsz$hypot_float_impl..hypot_implcs ˆ||ƒSr=rr“)r•rrr–vs) r0r4rr ÚsysÚplatformrZExternalFunctionrZMACHINE_BITSrÚcompile_internalr)r5rr6r0ÚxtyÚytyrƒr‚r{r–r8rr”rr‹`s þýr‹cCs6|\}| |jtjd¡}| ||¡}t|||j|ƒS©Né´©Zget_constantr4r‘ZpiZfmulr©r5rr6r0rƒZcoefr8rrrÚradians_float_implsr cCs6|\}| |jdtj¡}| ||¡}t|||j|ƒSrœržrŸrrrÚdegrees_float_implŠsr¡cCs| tj|¡}|||ƒSr=)Zget_functionÚoperatorÚpow)r5rr6r0rBrrrÚpow_impl•sr¤cCsdS)z8Convert integer to unsigned integer of equivalent width.Nr©ÚTrrrÚ _unsignedžsr§cs>|tjvrdd„S|tjvr:ttd |j¡ƒ‰‡fdd„SdS)NcSs|Sr=rr¥rrrÚ¥r,z _unsigned_impl..zuint{}csˆ|ƒSr=rr¥©ZnewTrrr¨¨r,)rZunsigned_domainZ signed_domainÚgetattrÚformatZbitwidthr¥rr©rÚ_unsigned_impl¢s r¬c CsV|j\}}||kr |jks&nJ‚|\}}dd„}| ||||¡} t|||j| ƒS)Nc Ss²t|ƒ}|dkrt|ƒS|dkr(t|ƒSt|ƒ}t|ƒ}t||ƒ}ttt ||¡ƒƒ}ttt ||¡ƒƒ}||krž||kr„||}}||8}t |t|ƒ¡}qjt ||ƒ|¡}|S)zO Stein's algorithm, heavily cribbed from Julia implementation. r)rÚabsrÚminr§ÚnpZright_shiftZ left_shift) r*Úbr¦ZzaZzbÚkÚuÚvÚrrrrÚgcd°s zgcd_impl..gcd)r0r4r™r) r5rr6r0ršr›rƒr‚rµr8rrrÚgcd_impl«s r¶)F)™Ú__doc__r‘r¢r—Znumpyr¯Zllvmlite.llvmpy.coreZllvmpyZcorerrZnumba.core.imputilsrrZnumbarZ numba.corerrrr Znumba.core.extendingr Znumba.core.typingrZnumba.cpython.unsafe.numbersrÚregistryr>ZfinfoZdtypeZ _NP_FLT_FINFOÚmaxZFLT_MAXZtinyZFLT_MINZ _NP_DBL_FINFOZDBL_MAXZDBL_MINZFLOAT_ABS_MASKZFLOAT_SIGN_MASKZDOUBLE_ABS_MASKZDOUBLE_SIGN_MASKrrrr#r$r&r'r(r2r<rCrHrTZfabsZ INTR_FABSrtZINTR_EXPZexp_implÚlogZINTR_LOGZlog_implZlog10Z INTR_LOG10Z log10_implZsinZINTR_SINZsin_implZcosZINTR_COSZcos_implrUZ log1p_implrVZ expm1_implrWZerf_implrXZ erfc_implrYZtan_implrZZ asin_implr[Z acos_implr\Z atan_implr]Z asinh_implr^Z acosh_implr_Z atanh_implr`Z sinh_implraZ cosh_implrbZ tanh_implrcZ log2_implrdZ ceil_implreZ floor_implZgammaZ gamma_implrfZ sqrt_implrgZ trunc_implrhZlgamma_implZisnanrGrjr?rlr’rmrnZisfiniterorpZcopysignrrZfrexpr|ZldexpZintcr~rˆrSr…Zuint64r†r€rrrŽr‹Zradiansr Zdegreesr¡r£r¤r§r¬r¶rµrrrrÚsØ $