From deac5976d743a49c24f821da5ded1aadc03a7b47 Mon Sep 17 00:00:00 2001 From: Stefan Israelsson Tampe Date: Mon, 9 Apr 2018 14:11:31 +0200 Subject: math functions added --- modules/language/python/module/math.scm | 191 ++++++++++++++++++++++++++++++++ 1 file changed, 191 insertions(+) create mode 100644 modules/language/python/module/math.scm (limited to 'modules') diff --git a/modules/language/python/module/math.scm b/modules/language/python/module/math.scm new file mode 100644 index 0000000..4ad8d2f --- /dev/null +++ b/modules/language/python/module/math.scm @@ -0,0 +1,191 @@ +(define-module (language python module math) + #:use-module (language python for) + #:use-module (language python try) + #:use-module (language python exceptions) + #:use-module (language python number) + #:use-module (system foreign) + #:use-module (rnrs bytevectors) + + #:export (ceil copysign fabs factorial floor fmod frexp fsum gcd isclose + isfinite isinf isnan modf trunc exp expm1 log log1p log2 log10 + pow sqrt acos asin atan cos sin tan atan2 hypot pi + degrees radians acosh asinh atanh cosh sinh tanh + erf erfc gamma lgamma e tau inf nan)) + +(define ceil + (lambda (x) + ((@ (guile) inexac->exact) + ((@ (guile) ceiling) + x)))) + +(define (copysign x y) + (let ((x ((@ (guile) abs) x))) + (if (< y 0) (- x) x))) + +(define (fabs x) ((@ (guile) abs) x)) + +(define (factorial x) + (if (not (and (number? x) (integer? x))) + (raise ValueError "Not an integer")) + (if (< x 0) + (raise ValueError "Negative integer")) + + (let lp ((x x)) + (if (= x 0) + 1 + (* x (lp (- x 1)))))) + +(define (floor x) + ((@ (guile) inexac->exact) + ((@ (guile) floor) + x))) + +(define (fmod x y) ((@ (guile) truncate-remainder) x y)) + +(define frexp + (let ((f (pointer->procedure double + (dynamic-func "frexp" (dynamic-link)) + (list double '*)))) + (lambda (x) + (let* ((v (make-bytevector 4)) + (vp (bytevector->pointer v))) + (list (f x) (bytevector-s32-ref v 0 (native-endianness))))))) + +(define (fsum it) + (for ((x : it)) ((s 0)) + (+ s x) + #:final s)) + + +(define gcd (@ (guile) gcd)) + +(define* (isclose a b #:key (rel_tol 1e-9) (abs_tol 0.0)) + (define e-abs (abs (- a b))) + (if (< e-abs (max (* rel_tol (max (abs a) (abs b))) abs_tol)) + #t + #f)) + +(define (isfinite x) + (if (or (inf? x) (nan? x)) + #f + #t)) + +(define isinf inf?) +(define isnan nan?) + +(define (ldexp x i) (* x ((@ (guile) expt) 2 i))) + +(define (modf x) + (let* ((x1 (floor x)) + (x2 (- x x1))) + (values x2 x1))) + +(define trunc py-trunc) + +;; Power and logarithms +(define exp (@ (guile) exp)) + +(define expm1 + (let ((f (pointer->procedure double + (dynamic-func "expm1" (dynamic-link)) + (list double)))) + (lambda (x) (f x)))) + +(define log (@ (guile) log)) + +(define log1p + (let ((f (pointer->procedure double + (dynamic-func "log1p" (dynamic-link)) + (list double)))) + + (lambda (x) (f x)))) + +(define log2 + (let ((f (pointer->procedure double + (dynamic-func "log2" (dynamic-link)) + (list double)))) + (lambda (x) (f x)))) + +(define log10 (@ (guile) log10)) + +(define pow expt) + +(define sqrt (@ (guile) sqrt)) + +;; Trigs +(define acos (@ (guile) acos)) +(define asin (@ (guile) asin)) +(define atan (@ (guile) atan)) +(define cos (@ (guile) cos)) +(define sin (@ (guile) sin)) +(define tan (@ (guile) tan)) + +(define atan2 + (let ((f (pointer->procedure double + (dynamic-func "atan2" (dynamic-link)) + (list double double)))) + (lambda (x y) (f x y)))) + +(define hypot + (let ((f (pointer->procedure double + (dynamic-func "hypot" (dynamic-link)) + (list double double)))) + + (lambda (x y) (f x y)))) + + +;; angular conversion +(define pi (* 4 (atan 1))) + +(define degrees + (let ((f (/ 360 (* 2 pi)))) + (lambda (x) (* f x)))) + +(define radians + (let ((f (/ (* 2 pi) 360))) + (lambda (x) (* f x)))) + +;; Hyperbolic funcitons +(define acosh (@ (guile) acosh)) +(define asinh (@ (guile) asinh)) +(define atanh (@ (guile) atanh)) +(define cosh (@ (guile) cosh)) +(define sinh (@ (guile) sinh)) +(define tanh (@ (guile) tanh)) + + +;; Special functions +(define erf + (let ((f (pointer->procedure double + (dynamic-func "erf" (dynamic-link)) + (list double)))) + (lambda (x) (f x)))) + +(define erfc + (let ((f (pointer->procedure double + (dynamic-func "erfc" (dynamic-link)) + (list double)))) + (lambda (x) (f x)))) + +(define gamma + (let ((f (pointer->procedure double + (dynamic-func "tgamma" (dynamic-link)) + (list double)))) + + (lambda (x) + (if (integer? x) + (factorial (- x 1)) + (f x))))) + +(define lgamma + (let ((f (pointer->procedure double + (dynamic-func "lgamma" (dynamic-link)) + (list double)))) + (lambda (x) + (f x)))) + +;; constants +(define e (exp 1)) +(define tau (* 2 pi)) +(define inf ((@ (guile) inf))) +(define nan ((@ (guile) nan))) -- cgit v1.2.3 From 19b1f73aa7eec9f0d8834889661b2e98ebc64041 Mon Sep 17 00:00:00 2001 From: Stefan Israelsson Tampe Date: Mon, 9 Apr 2018 14:50:28 +0200 Subject: complex math --- modules/language/python/module/cmath.scm | 63 ++++++++++++++++++++++++++++++++ 1 file changed, 63 insertions(+) create mode 100644 modules/language/python/module/cmath.scm (limited to 'modules') diff --git a/modules/language/python/module/cmath.scm b/modules/language/python/module/cmath.scm new file mode 100644 index 0000000..b02be2d --- /dev/null +++ b/modules/language/python/module/cmath.scm @@ -0,0 +1,63 @@ +(define-module (language python module cmath) + #:export (polar rect exp log log10 sqrt pi e tau inf nan infj nanj isclose + isnan isinf isfinite sin cos tan asin acos atan + sinh cosh tanh asinh acosh atanh)) + +(define (polar x) + (list (magnitude x) (angle x))) + +(define (rect r phi) + (make-polar r phi)) + +;; pow log + +(define exp (@ (guile) exp)) +(define log (@ (guile) log)) +(define log10 (@ (guile) log10)) +(define sqrt (@ (guile) sqrt)) + +;; trig +(define sin (@ (guile) sin)) +(define cos (@ (guile) cos)) +(define tan (@ (guile) tan)) +(define asin (@ (guile) asin)) +(define acos (@ (guile) acos)) +(define atan (@ (guile) atan)) + +;; hyp +(define sinh (@ (guile) sinh)) +(define cosh (@ (guile) cosh)) +(define tanh (@ (guile) tanh)) +(define asinh (@ (guile) asinh)) +(define acosh (@ (guile) acosh)) +(define atanh (@ (guile) atanh)) + +;; classification +(define isfinite1 (@ (language python module math) isfinite)) + +(define (isfinite x) + (and (isfinite1 (real-part x)) + (isfinite1 (imag-part x)))) + +(define (isinf x) + (or (inf? (real-part x)) + (inf? (imag-part x)))) + +(define (isnan x) + (or (nan? (real-part x)) + (nan? (imag-part x)))) + +(define* (isclose a b #:key (rel_tol 1e-9) (abs_tol 0.0)) + (define e-abs (magnitude (- a b))) + (if (< e-abs (max (* rel_tol (max (magnitude a) (magnitude b))) abs_tol)) + #t + #f)) + +(define pi (@ (language python module math) pi)) +(define e (@ (language python module math) e)) +(define tau (@ (language python module math) tau)) +(define inf (@ (language python module math) inf)) +(define nan (@ (language python module math) nan)) +(define infj (make-rectangular 0 inf)) +(define nanj (make-rectangular 0 nan)) + -- cgit v1.2.3 From 3cc8afbebe959aa7c43689258c160c8fe6e60574 Mon Sep 17 00:00:00 2001 From: Stefan Israelsson Tampe Date: Mon, 9 Apr 2018 14:59:32 +0200 Subject: real functions is real functions --- modules/language/python/module/math.scm | 39 +++++++++++++++++++-------------- 1 file changed, 22 insertions(+), 17 deletions(-) (limited to 'modules') diff --git a/modules/language/python/module/math.scm b/modules/language/python/module/math.scm index 4ad8d2f..ef137aa 100644 --- a/modules/language/python/module/math.scm +++ b/modules/language/python/module/math.scm @@ -12,6 +12,11 @@ degrees radians acosh asinh atanh cosh sinh tanh erf erfc gamma lgamma e tau inf nan)) +(define (real! s x) + (if (= (imag-part x) 0) + (real-part x) + (raise ValueError "real math fkn result in complex number" s))) + (define ceil (lambda (x) ((@ (guile) inexac->exact) @@ -83,7 +88,7 @@ (define trunc py-trunc) ;; Power and logarithms -(define exp (@ (guile) exp)) +(define (exp x) (real! 'exp ((@ (guile) exp)) x)) (define expm1 (let ((f (pointer->procedure double @@ -91,7 +96,7 @@ (list double)))) (lambda (x) (f x)))) -(define log (@ (guile) log)) +(define (log x) (real! 'log ((@ (guile) log)) x)) (define log1p (let ((f (pointer->procedure double @@ -106,19 +111,19 @@ (list double)))) (lambda (x) (f x)))) -(define log10 (@ (guile) log10)) +(define (log10 x) (real! 'log10 (@ (guile) log10))) -(define pow expt) +(define (pow x y) (real! 'pow ((@ (guile) expt) x y))) -(define sqrt (@ (guile) sqrt)) +(define (sqrt x) (real! 'sqrt (@ (guile) sqrt))) ;; Trigs -(define acos (@ (guile) acos)) -(define asin (@ (guile) asin)) -(define atan (@ (guile) atan)) -(define cos (@ (guile) cos)) -(define sin (@ (guile) sin)) -(define tan (@ (guile) tan)) +(define (acos x) (real! 'acos ((@ (guile) acos) x))) +(define (asin x) (real! 'asin ((@ (guile) asin) x))) +(define (atan x) (real! 'atan ((@ (guile) atan) x))) +(define (cos x) (real! 'cos ( (@ (guile) cos) x))) +(define (sin x) (real! 'sin ( (@ (guile) sin) x))) +(define (tan x) (real! 'tan ( (@ (guile) tan) x))) (define atan2 (let ((f (pointer->procedure double @@ -146,12 +151,12 @@ (lambda (x) (* f x)))) ;; Hyperbolic funcitons -(define acosh (@ (guile) acosh)) -(define asinh (@ (guile) asinh)) -(define atanh (@ (guile) atanh)) -(define cosh (@ (guile) cosh)) -(define sinh (@ (guile) sinh)) -(define tanh (@ (guile) tanh)) +(define (acosh x) (real! 'acosh ((@ (guile) acosh) x))) +(define (asinh x) (real! 'asinh ((@ (guile) asinh) x))) +(define (atanh x) (real! 'atanh ((@ (guile) atanh) x))) +(define (cosh x) (real! 'cosh ( (@ (guile) cosh) x))) +(define (sinh x) (real! 'sinh ( (@ (guile) sinh) x))) +(define (tanh x) (real! 'tanh ( (@ (guile) tanh) x))) ;; Special functions -- cgit v1.2.3 From acec233857e89fd5b64a8bf935ae87df40e3a11c Mon Sep 17 00:00:00 2001 From: Stefan Israelsson Tampe Date: Thu, 12 Apr 2018 16:04:20 +0200 Subject: decimal --- modules/language/python/module/decimal.scm | 5627 ++++++++++++++++++++++++++++ modules/language/python/module/python.scm | 77 +- 2 files changed, 5695 insertions(+), 9 deletions(-) create mode 100644 modules/language/python/module/decimal.scm (limited to 'modules') diff --git a/modules/language/python/module/decimal.scm b/modules/language/python/module/decimal.scm new file mode 100644 index 0000000..55a6675 --- /dev/null +++ b/modules/language/python/module/decimal.scm @@ -0,0 +1,5627 @@ +(define-module (language python module decimal) + #:use-module ((language python module collections) #:select (namedtuple)) + #:export ()) + +(define __name__ "decimal") +(define __xname__ __name__) +(define __version__ "1.70") +;; Highest version of the spec this complies with +;; See http://speleotrove.com/decimal/ + + +(define DecimalTuple (namedtuple "DecimalTuple" "sign digits exponent")) + +;; Rounding +(define ROUND_DOWN 'ROUND_DOWN) +(define ROUND_HALF_UP 'ROUND_HALF_UP) +(define ROUND_HALF_EVEN 'ROUND_HALF_EVEN) +(define ROUND_CEILING 'ROUND_CEILING) +(define ROUND_FLOOR 'ROUND_FLOOR) +(define ROUND_UP 'ROUND_UP) +(define ROUND_HALF_DOWN 'ROUND_HALF_DOWN) +(define ROUND_05UP 'ROUND_05UP) + +;; Compatibility with the C version +(define MAX_PREC 425000000) +(define MAX_EMAX 425000000) +(define MIN_EMIN -425000000) + +(if (= sys:maxsize (- (ash 1 63) 1)) + (begin + (set! MAX_PREC 999999999999999999) + (set! MAX_EMAX 999999999999999999) + (set! MIN_EMIN -999999999999999999))) + +(define MIN_ETINY (- MIN_EMIN (- MAX_PREC 1))) + +;; Context +(define (cx-prec x) (vector-ref x 0)) +(define (cx-emax x) (vector-ref x 1)) +(define (cx-raise x) (vector-ref x 2)) +(define (cx-error x) (vector-ref x 3)) +(define (cx-capitals x) (vector-ref x 4)) +(define (cx-rounding x) (vector-ref x 5)) +;; Errors + +(define-python-class DecimalException (ArithmeticError) + "Base exception class. + + Used exceptions derive from this. + If an exception derives from another exception besides this (such as + Underflow (Inexact, Rounded, Subnormal) that indicates that it is only + called if the others are present. This isn't actually used for + anything, though. + + handle -- Called when context._raise_error is called and the + trap_enabler is not set. First argument is self, second is the + context. More arguments can be given, those being after + the explanation in _raise_error (For example, + context._raise_error(NewError, '(-x)!', self._sign) would + call NewError().handle(context, self._sign).) + + To define a new exception, it should be sufficient to have it derive + from DecimalException. + " + + (define handle + (lambda (self context . args) + (values)))) + + +(define-python-class Clamped (DecimalException) + """Exponent of a 0 changed to fit bounds. + + This occurs and signals clamped if the exponent of a result has been + altered in order to fit the constraints of a specific concrete + representation. This may occur when the exponent of a zero result would + be outside the bounds of a representation, or when a large normal + number would have an encoded exponent that cannot be represented. In + this latter case, the exponent is reduced to fit and the corresponding + number of zero digits are appended to the coefficient ("fold-down"). + """) + +(define-python-class InvalidOperation (DecimalException) + "An invalid operation was performed. + + Various bad things cause this: + + Something creates a signaling NaN + -INF + INF + 0 * (+-)INF + (+-)INF / (+-)INF + x % 0 + (+-)INF % x + x._rescale( non-integer ) + sqrt(-x) , x > 0 + 0 ** 0 + x ** (non-integer) + x ** (+-)INF + An operand is invalid + + The result of the operation after these is a quiet positive NaN, + except when the cause is a signaling NaN, in which case the result is + also a quiet NaN, but with the original sign, and an optional + diagnostic information. + " + (define handle + (lambda (self context . args) + (if (bool args) + (let ((ans (_dec_from_triple + (ref (car args) '_sign) + (ref (car args) '_int) + "n" #t))) + ((ref ans '_fix_nan) context)) + _NaN)))) + +(define-python-class ConversionSyntax (InvalidOperation) + "Trying to convert badly formed string. + + This occurs and signals invalid-operation if a string is being + converted to a number and it does not conform to the numeric string + syntax. The result is [0,qNaN]. + " + (define handle + (lambda x _NaN))) + +(define-python-class DivisionByZero (DecimalException ZeroDivisionError) + "Division by 0. + + This occurs and signals division-by-zero if division of a finite number + by zero was attempted (during a divide-integer or divide operation, or a + power operation with negative right-hand operand), and the dividend was + not zero. + + The result of the operation is [sign,inf], where sign is the exclusive + or of the signs of the operands for divide, or is 1 for an odd power of + -0, for power. + " + + (define handle + (lambda (self context sign . args) + (pylist-ref _SignedInfinity sign)))) + +(define-python-class DivisionImpossible (InvalidOperation) + "Cannot perform the division adequately. + + This occurs and signals invalid-operation if the integer result of a + divide-integer or remainder operation had too many digits (would be + longer than precision). The result is [0,qNaN]. + " + + (define handle + (lambda x _NaN))) + +(define-python-class DivisionUndefined (InvalidOperation ZeroDivisionError) + "Undefined result of division. + + This occurs and signals invalid-operation if division by zero was + attempted (during a divide-integer, divide, or remainder operation), and + the dividend is also zero. The result is [0,qNaN]. + " + + (define handle + (lambda x _NaN))) + +(define-python-class Inexact (DecimalException) + "Had to round, losing information. + + This occurs and signals inexact whenever the result of an operation is + not exact (that is, it needed to be rounded and any discarded digits + were non-zero), or if an overflow or underflow condition occurs. The + result in all cases is unchanged. + + The inexact signal may be tested (or trapped) to determine if a given + operation (or sequence of operations) was inexact. + ") + +(define-python-class InvalidContext (InvalidOperation) + "Invalid context. Unknown rounding, for example. + + This occurs and signals invalid-operation if an invalid context was + detected during an operation. This can occur if contexts are not checked + on creation and either the precision exceeds the capability of the + underlying concrete representation or an unknown or unsupported rounding + was specified. These aspects of the context need only be checked when + the values are required to be used. The result is [0,qNaN]. + " + + (define handle + (lambda x _NaN))) + +(define-python-class Rounded (DecimalException) + "Number got rounded (not necessarily changed during rounding). + + This occurs and signals rounded whenever the result of an operation is + rounded (that is, some zero or non-zero digits were discarded from the + coefficient), or if an overflow or underflow condition occurs. The + result in all cases is unchanged. + + The rounded signal may be tested (or trapped) to determine if a given + operation (or sequence of operations) caused a loss of precision. + ") + +(define-python-class Subnormal (DecimalException) + "Exponent < Emin before rounding. + + This occurs and signals subnormal whenever the result of a conversion or + operation is subnormal (that is, its adjusted exponent is less than + Emin, before any rounding). The result in all cases is unchanged. + + The subnormal signal may be tested (or trapped) to determine if a given + or operation (or sequence of operations) yielded a subnormal result. + ") + +(define-python-class Overflow (Inexact Rounded) + "Numerical overflow. + + This occurs and signals overflow if the adjusted exponent of a result + (from a conversion or from an operation that is not an attempt to divide + by zero), after rounding, would be greater than the largest value that + can be handled by the implementation (the value Emax). + + The result depends on the rounding mode: + + For round-half-up and round-half-even (and for round-half-down and + round-up, if implemented), the result of the operation is [sign,inf], + where sign is the sign of the intermediate result. For round-down, the + result is the largest finite number that can be represented in the + current precision, with the sign of the intermediate result. For + round-ceiling, the result is the same as for round-down if the sign of + the intermediate result is 1, or is [0,inf] otherwise. For round-floor, + the result is the same as for round-down if the sign of the intermediate + result is 0, or is [1,inf] otherwise. In all cases, Inexact and Rounded + will also be raised. + " + + (define handle + (let ((l (list ROUND_HALF_UP ROUND_HALF_EVEN + ROUND_HALF_DOWN ROUND_U))) + (lambda (self context sign . args) + (let/ec ret + (if (memq (ref context 'rounding) l) + (ret (pylist-ref _SignedInfinity sign))) + + (if (= sign 0) + (if (eq? (ref context 'rounding) ROUND_CEILING) + (ret (pylist-ref _SignedInfinity sign)) + (ret (_dec_from_triple + sign + (* "9" (cx-prec context)) + (+ (- (cx-emax context) (cx-prec context)) 1))))) + + (if (= sign 1) + (if (eq? (ref context 'rounding) ROUND_FLOOR) + (ret (pylist-ref _SignedInfinity sign)) + (ret (_dec_from_triple + sign + (* "9" (cx-prec context)) + (+ (- (cx-emax context) (cx-prec context)) 1)))))))))) + + +(define-python-class Underflow (Inexact Rounded Subnormal) + "Numerical underflow with result rounded to 0. + + This occurs and signals underflow if a result is inexact and the + adjusted exponent of the result would be smaller (more negative) than + the smallest value that can be handled by the implementation (the value + Emin). That is, the result is both inexact and subnormal. + + The result after an underflow will be a subnormal number rounded, if + necessary, so that its exponent is not less than Etiny. This may result + in 0 with the sign of the intermediate result and an exponent of Etiny. + + In all cases, Inexact, Rounded, and Subnormal will also be raised. + ") + +(define-python-class FloatOperation (DecimalException TypeError) + """Enable stricter semantics for mixing floats and Decimals. + + If the signal is not trapped (default), mixing floats and Decimals is + permitted in the Decimal() constructor, context.create_decimal() and + all comparison operators. Both conversion and comparisons are exact. + Any occurrence of a mixed operation is silently recorded by setting + FloatOperation in the context flags. Explicit conversions with + Decimal.from_float() or context.create_decimal_from_float() do not + set the flag. + + Otherwise (the signal is trapped), only equality comparisons and explicit + conversions are silent. All other mixed operations raise FloatOperation. + """) + +;; List of public traps and flags +(define _signals + (vector Clamped DivisionByZero Inexact Overflow Rounded, + Underflow InvalidOperation Subnormal FloatOperation)) + +;; Map conditions (per the spec) to signals +(define _condition_map + `((,ConversionSyntax . ,InvalidOperation) + (,DivisionImpossible . ,InvalidOperation) + (,DivisionUndefined . ,InvalidOperation) + (,InvalidContext . ,InvalidOperation))) + +;; Valid rounding modes +(define _rounding_modes + (list ROUND_DOWN ROUND_HALF_UP ROUND_HALF_EVEN ROUND_CEILING, + ROUND_FLOOR ROUND_UP ROUND_HALF_DOWN ROUND_05UP)) + +;; ##### Context Functions ################################################## + +;; The getcontext() and setcontext() function manage access to a thread-local +;; current context. +(define *context* (make-fluid #f)) +(define (getcontext) + (fluid-ref *context*)) +(define (setcontext context) + (fluid-set! *context* context)) + +;; ##### Decimal class ####################################################### + +;; Do not subclass Decimal from numbers.Real and do not register it as such +;; (because Decimals are not interoperable with floats). See the notes in +;; numbers.py for more detail. + +(define _dec_from_triple + (lam (sign coefficient exponent (= special #f)) + "Create a decimal instance directly, without any validation, + normalization (e.g. removal of leading zeros) or argument + conversion. + + This function is for *internal use only*. + " + (Decimal sign coeficient exponent special))) + +(def _mk (self (= value "0") (= context None)) + "Create a decimal point instance. + + >>> Decimal('3.14') # string input + Decimal('3.14') + >>> Decimal((0, (3, 1, 4), -2)) # tuple (sign, digit_tuple, exponent) + Decimal('3.14') + >>> Decimal(314) # int + Decimal('314') + >>> Decimal(Decimal(314)) # another decimal instance + Decimal('314') + >>> Decimal(' 3.14 \\n') # leading and trailing whitespace okay + Decimal('3.14') + " + + ;; Note that the coefficient, self._int, is actually stored as + ;; a string rather than as a tuple of digits. This speeds up + ;; the "digits to integer" and "integer to digits" conversions + ;; that are used in almost every arithmetic operation on + ;; Decimals. This is an internal detail: the as_tuple function + ;; and the Decimal constructor still deal with tuples of + ;; digits. + + ;; From a string + ;; REs insist on real strings, so we can too. + (cond + ((isinstance value str) + (let ((m (parser (scm-str str)))) + (if (not m) + (let ((context (if (eq? context None) + (getcontext) + context))) + ((cx-raise context) + ConversionSyntax + (+ "Invalid literal for Decimal: " value)))) + + (let ((sign (get-parsed-sign m)) + (intpart (get-parsed-int m)) + (fracpart (get-parsed-frac m)) + (exp (get-parsed-exp m)) + (diag (get-parsed-diag m)) + (signal (get-parsed-sig m))) + + (set self 'sign sign) + + (if (not (eq? intpart None)) + (begin + (set self '_int (str (int (+ intpart fracpart)))) + (set self '_exp (- exp (len fracpart))) + (set self '_is_special False)) + (begin + (if (not (eq? diag None)) + (begin + ;; NaN + (set self '_int + (py-lstrip (str (int (if (bool diag) + diag + "0"))) + "0")) + (if signal + (set self '_exp "N") + (set self '_exp "n"))) + (begin + ;; infinity + (set self '_int "0") + (set self '_exp "F"))) + (set self '_is_special #t)))))) + + ;; From an integer + ((isinstance value int) + (if (>= value 0) + (set self '_sign 0) + (set self '_sign 1)) + (set self '_exp 0) + (set self '_int (str (abs value))) + (set self '_is_special #f)) + + ;; From another decimal + ((isinstance value Decimal) + (set self '_exp (ref value '_exp )) + (set self '_sign (ref value '_sign )) + (set self '_int (ref value '_int )) + (set self '_is_special (ref value '_is_special))) + + ;; From an internal working value + ((isinstance value _WorkRep) + (set self '_exp (int (ref value '_exp))) + (set self '_sign (ref value '_sign)) + (set self '_int (str (ref value 'int))) + (set self '_is_special #f)) + + ;; tuple/list conversion (possibly from as_tuple()) + ((isinstance value (list list tuple)) + (if (not (= (len value) 3)) + (raise (ValueError + (+ "Invalid tuple size in creation of Decimal " + "from list or tuple. The list or tuple " + "should have exactly three elements.")))) + ;; # process sign. The isinstance test rejects floats + (let ((v0 (pylist-ref value 0)) + (v1 (pylist-ref value 1)) + (v2 (pylist-ref value 2))) + (if (not (and (isinstance v0 int) + (or (= v0 0) (= v0 1)))) + (raise (ValueError + (+ "Invalid sign. The first value in the tuple " + "should be an integer; either 0 for a " + "positive number or 1 for a negative number.")))) + (set self '_sign v0) + (if (eq? v2 'F) + (begin + (set self '_int "0") + (set self '_exp v2) + (set self 'is_special #t)) + (let ((digits (py-list))) + ;; process and validate the digits in value[1] + (for ((digit : v1)) () + (if (and (isinstance digit int) + (<= 0 digit) + (<= digit 9)) + ;; skip leading zeros + (if (or (bool digits) (> digit 0)) + (pylist-append digits digit)) + (raise (ValueError + (+ "The second value in the tuple must " + "be composed of integers in the range " + "0 through 9."))))) + + (cond + ((or (eq? v2 'n) (eq? v2 'N)) + (begin + ;; NaN: digits form the diagnostic + (set self '_int (py-join "" (map str digits))) + (set self '_exp v2) + (set self '_is_special #t))) + ((isinstance v2 int) + ;; finite number: digits give the coefficient + (set self '_int (py-join "" (map str digits))) + (set self '_exp v2) + (set self '_is_special #f)) + (else + (raise (ValueError + (+ "The third value in the tuple must " + "be an integer, or one of the " + "strings 'F', 'n', 'N'."))))))))) + + ((isinstance value float) + (let ((context (if (eq? context None) + (getcontext) + context))) + ((cx-error context) + FloatOperation, + (+ "strict semantics for mixing floats and Decimals are " + "enabled")) + + (__init__ self ((ref Decimal 'from_float) value)))) + + (else + (raise (TypeError + (format #f "Cannot convert %r to Decimal" value)))))) + +(define-inlinable (divmod x y) + (values (quotient x y) (modulo x y))) + +(define-syntax twix + (syntax-rules (let) + ((_ a) a) + ((_ (let (a ...)) . l) + (a ... (twix - l))) + ((_ (a it code ...) . l) + (aif it a (begin code ...) (twix - l))))) + +(define-syntax-rule (norm-op op) + (begin + (set! op ((ref self '_convert_other) op)) + (if (eq? op NotImplemented) + other + #f))) + +(define-syntax-rule (get-context context code) + (let ((context (if (eq? context None) + (getcontext) + context))) + code)) + +(define-syntax-rule (un-special self context) + (if ((ref self '_is_special)) + (let ((ans ((ref self '_check_nans) #:context context))) + (if (bool ans) + (ret ans) + #f)) + #f)) + +(define-syntax-rule (bin-special o1 o2 context) + (if (or (ref o1 '_is_special) + (ref o2 '_is_special)) + (or (un-special o1 context) (un-special o2 context)))) + +(define-syntax-rule (add-special self other context) + (or (bin-special self other context) + (if ((ref self '_isinfinity)) + ;; If both INF, same sign => + ;; same as both, opposite => error. + (if (and (not (= (ref self '_sign) (ref other '_sign))) + ((ref other '_isinfinity))) + ((cx-error context) InvalidOperation "-INF + INF") + (Decimal self)) + (if ((ref other '_isinfinity)) + (ret (Decimal other)) ; Can't both be infinity here + #f)))) + +(define-syntax-rule (mul-special self other context) + (if (or (ref self '_is_special) (ref other '_is_special)) + (twix + ((bin-special self other context) it it) + + ((if ((ref self '_isinfinity)) + (if (not (bool other)) + ((cx-error context) InvalidOperation "(+-)INF * 0") + (pylist-ref _SignedInfinity resultsign)) + #f) it it) + + (if ((ref other '_isinfinity)) + (if (not (bool self)) + ((cx-error context) InvalidOperation "(+-)INF * 0") + (pylist-ref _SignedInfinity resultsign)) + #f)) + #f)) + + (define-syntax-rule (div-special self other context) + (if (or (ref self '_is_special) (ref other '_is_special)) + (twix + ((bin-special self other context) it it) + + ((and ((ref self '_isinfinity)) ((ref other '_isinfinity))) it + ((cx-error context) InvalidOperation "(+-)INF/(+-)INF")) + + (((ref self '_isinfinity)) it + (pylist-ref _SignedInfinity sign)) + + (((ref other '_isinfinity)) it + ((cx-error context) Clamped "Division by infinity") + (_dec_from_triple sign "0", (cx-etiny context)))))) + + +(define-python-class Decimal (object) + "Floating point class for decimal arithmetic." + + + ;; Generally, the value of the Decimal instance is given by + ;; (-1)**_sign * _int * 10**_exp + ;; Special values are signified by _is_special == True + + (define __init__ + (case-lambda + ((self sign coefficient exponent special) + (set self '_sign sign) + (set self '_int coefficient) + (set self '_exp exponent) + (set self '_is_special special)) + + ((self) + (_mk self)) + ((self a) + (_mk self a)) + ((self a b) + (_mk self a b)))) + + (define from_float + (classmethod + (lambda (cls f) + "Converts a float to a decimal number, exactly. + + Note that Decimal.from_float(0.1) is not the same as Decimal('0.1'). + Since 0.1 is not exactly representable in binary floating point, the + value is stored as the nearest representable value which is + 0x1.999999999999ap-4. The exact equivalent of the value in decimal + is 0.1000000000000000055511151231257827021181583404541015625. + + >>> Decimal.from_float(0.1) + Decimal('0.1000000000000000055511151231257827021181583404541015625') + >>> Decimal.from_float(float('nan')) + Decimal('NaN') + >>> Decimal.from_float(float('inf')) + Decimal('Infinity') + >>> Decimal.from_float(-float('inf')) + Decimal('-Infinity') + >>> Decimal.from_float(-0.0) + Decimal('-0') + + " + (cond + ((isinstance f int) ; handle integer inputs + (cls f)) + ((not (isinstance f float)) + (raise (TypeError "argument must be int or float."))) + ((or (inf? f) (nan? f)) + (cls (cond + ((nan? f) "") + ((eq? f (inf)) "") + (eq? f (- (inf))) ""))) + (else + (let* ((sign (if (>= f 0) 0 1)) + (me (frexp f)) + (m (car me)) + (e (cadr me)) + (res (_dec_from_triple sign, str(m) e))) + (if (eq? cls Decimal) + res + (cls res)))))))) + + (define _isnan + (lambda (self) + "Returns whether the number is not actually one. + + 0 if a number + 1 if NaN + 2 if sNaN + " + (if (ref self '_is_special) + (let ((exp (ref self '_exp))) + (cond + ((eq? exp 'n) 1) + ((eq? exp 'N) 2) + (else 0))) + 0))) + + (define _isinfinity + (lambda (self) + "Returns whether the number is infinite + + 0 if finite or not a number + 1 if +INF + -1 if -INF + " + (if (eq? (ref self '_exp) 'F) + (if (eq? (ref self '_sign) 1) + -1 + 1) + 0))) + + (define _check_nans + (lam (self (= other None) (= context None)) + "Returns whether the number is not actually one. + + if self, other are sNaN, signal + if self, other are NaN return nan + return 0 + + Done before operations. + " + + (let ((self_is_nan ((ref self '_isnan))) + (other_is_nan + (if (eq? other None) + #f + ((ref other '_isnan))))) + + (if (or self_is_nan other_is_nan) + (let ((context (if (eq? context None) + (getcontext) + context))) + (cond + ((eq? self_is_nan 2) + ((cx-error context) InvalidOperation "sNaN" self)) + ((eq? other_is_nan 2) + ((cx-error context) InvalidOperation "sNaN" other)) + (self_is_nan + ((ref self '_fix_nan) context)) + (else + ((ref other '_fix_nan) context)))) + 0)))) + + + (define _compare_check_nans + (lambda (self other context) + "Version of _check_nans used for the signaling comparisons + compare_signal, __le__, __lt__, __ge__, __gt__. + + Signal InvalidOperation if either self or other is a (quiet + or signaling) NaN. Signaling NaNs take precedence over quiet + NaNs. + + Return 0 if neither operand is a NaN. + + " + (let ((context (if (eq? context None) + (getcontext) + context))) + + (if (or (ref self '_is_special) + (ref other '_is_special)) + (cond + (((ref self 'is_snan)) + ((cx-error context) + InvalidOperation + "comparison involving sNaN" self)) + + (((ref other 'is_snan)) + ((cx-error context) + InvalidOperation + "comparison involving sNaN" other)) + + (((ref self 'is_qnan)) + ((cx-error context) + InvalidOperation + "comparison involving NaN" self)) + + (((ref other 'is_qnan)) + ((cx-error context) + InvalidOperation + "comparison involving NaN" other)) + + (else 0)) + 0)))) + + (define __bool__ + (lambda (self) + "Return True if self is nonzero; otherwise return False. + + NaNs and infinities are considered nonzero. + " + (or (ref self '_is_special) (not (equal (ref self '_int) "0"))))) + + (define _cmp + (lambda (self other) + "Compare the two non-NaN decimal instances self and other. + + Returns -1 if self < other, 0 if self == other and 1 + if self > other. This routine is for internal use only." + + (let ((self_sign (ref self '_sign)) + (other_sign (ref other '_sign))) + (cond + ((or (ref self '_is_special) (ref other '_is_special)) + (let ((self_inf ((ref self '_isinfinity))) + (other_inf ((ref other '_isinfinity)))) + (cond + ((eq? self_inf other_inf) 0) + ((< self_inf other_inf) -1) + (else 1))) + + ;; check for zeros; Decimal('0') == Decimal('-0') + ((not (bool self)) + (if (not (bool other)) + 0 + (let ((s (ref other '_sign))) + (if (= s 0) + -1 + 1)))) + ((not (bool other)) + (let ((s (ref self '_sign))) + (if (= s 0) + 1 + -1))) + + ((< other_sign self_sign) + -1) + ((< self_sign other_sign) + 1) + + (else + (let ((self_adjusted ((ref self 'adjusted))) + (other_adjusted ((ref other 'adjusted))) + (self_exp (ref self '_exp)) + (other_exp (ref other '_exp))) + (cond + ((= self_adjusted other_adjusted) + (let ((self_padded (+ (ref self '_int) + (* "0" (- self_exp other_exp)))) + (other_padded (+ (ref other '_int) + (* "0" (- other_exp self_exp))))) + (cond + ((equal? self_padded other_padded) + 0) + ((< self_padded other_padded) + (if (= self_sign 0) + -1 + 1)) + (else + (if (= self_sign 0) + 1 + -1))))) + ((> self_adjusted other_adjusted) + (if (= self_sign 0) + 1 + -1)) + (else + (if (= self_sign 0) + -1 + 1)))))))))) + + ;; Note: The Decimal standard doesn't cover rich comparisons for + ;; Decimals. In particular, the specification is silent on the + ;; subject of what should happen for a comparison involving a NaN. + ;; We take the following approach: + ;; + ;; == comparisons involving a quiet NaN always return False + ;; != comparisons involving a quiet NaN always return True + ;; == or != comparisons involving a signaling NaN signal + ;; InvalidOperation, and return False or True as above if the + ;; InvalidOperation is not trapped. + ;; <, >, <= and >= comparisons involving a (quiet or signaling) + ;; NaN signal InvalidOperation, and return False if the + ;; InvalidOperation is not trapped. + ;; + ;; This behavior is designed to conform as closely as possible to + ;; that specified by IEEE 754. + + (define __eq__ + (lam (self other (= context None)) + (let ((so (_convert_for_comparisonc self other #:equality_op #t)) + (self (car so)) + (other (cadr so))) + + (cond + ((eq? other NotImplemented) + other) + ((bool ((ref self '_check_nans) other context)) + #f) + (else (= ((ref self '_cmp) other) 0)))))) + + (define _xlt + (lambda (<) + (lam (self other (= context None)) + (let ((so (_convert_for_comparisonc self other #:equality_op #t)) + (self (car so)) + (other (cadr so))) + + (cond + ((eq? other NotImplemented) + other) + ((bool ((ref self '_compare_check_nans) other context)) + #f) + (else (< ((ref self '_cmp) other) 0))))))) + + (define __lt__ (_xlt < )) + (define __le__ (_xlt <=)) + (define __gt__ (_xlt > )) + (define __ge__ (_xlt >=)) + + (define compare + (lam (self other (= context None)) + "Compare self to other. Return a decimal value: + + a or b is a NaN ==> Decimal('NaN') + a < b ==> Decimal('-1') + a == b ==> Decimal('0') + a > b ==> Decimal('1') + " + (let ((other (_convert_other other #:raiseit #t))) + ;; Compare(NaN, NaN) = NaN + (if (or (ref self '_is_special) + (and (bool other) + (ref other '_is_special))) + (aif it ((ref self '_check_nans) other context) + it + (Decimal ((ref self '_cmp) other))))))) + + (define __hash__ + (lambda (self) + "x.__hash__() <==> hash(x)" + + ;; In order to make sure that the hash of a Decimal instance + ;; agrees with the hash of a numerically equal integer, float + ;; or Fraction, we follow the rules for numeric hashes outlined + ;; in the documentation. (See library docs, 'Built-in Types'). + (cond + ((ref self '_is_special) + (cond + (((ref self 'is_snan)) + (raise (TypeError "Cannot hash a signaling NaN value."))) + (((ref self 'is_snan)) + (hash (nan))) + ((= 1 (ref self '_sign)) + (hash (- (inf)))) + (else + (hash (inf))))) + + (else + (let* ((exp (ref self '_exp)) + (exp_hash + (if (>= exp 0) + (expt 10 exp _ pyhash-N) + (expt _PyHASH_10INV (- exp) pyhash-N))) + + (hash_ + (modulus (* (int (ref self '_int)) exp_hash) + pyhash-N)) + + (ans + (if (>= self 0) hash_ (- hash_)))) + (if (= ans -1) -2 ans)))))) + + (define as_tuple + (lambda (self) + "Represents the number as a triple tuple. + + To show the internals exactly as they are. + " + (DecimalTuple self._sign + (tuple (map int (ref self '_int))) + (ref self '_exp)))) + + (define as_integer_ratio + (lambda (self) + "Express a finite Decimal instance in the form n / d. + + Returns a pair (n, d) of integers. When called on an infinity + or NaN, raises OverflowError or ValueError respectively. + + >>> Decimal('3.14').as_integer_ratio() + (157, 50) + >>> Decimal('-123e5').as_integer_ratio() + (-12300000, 1) + >>> Decimal('0.00').as_integer_ratio() + (0, 1) + " + (if (ref self '_is_special) + (if ((ref self 'is_nan)) + (raise (ValueError + "cannot convert NaN to integer ratio")) + (raise (OverflowError + "cannot convert Infinity to integer ratio")))) + + (if (not (bool self)) + (values 0 1) + (let ((s (ref self '_sign)) + (n (int (ref self '_int))) + (e (ref self '_exp)) + (x + (* n (if (> exp 0) + (expt 10 exo) + (/ 1 (expt 10 (- expt))))))) + (values (numerator x) + (denomerator x)))))) + + (define __repr__ + (lambda (self) + "Represents the number as an instance of Decimal." + ;# Invariant: eval(repr(d)) == d + (format #f "Decimal('~a')" (str self)))) + + (define __str__ + (lam (self (= eng #f) (= context None)) + "Return string representation of the number in scientific notation. + + Captures all of the information in the underlying representation. + " + (let* ((sign (if (= (reg self '_sign) 0) "" "-")) + (exp (ref self '_exp)) + (i (ref self '_int)) + (leftdigits (+ exp (len i))) + (dotplace #f) + (intpart #f) + (fracpart #f) + (exppart #f)) + + (cond + ((ref self '_is_special) + (cond + ((eq? (ref self '_exp) 'F) + (+ sign "Infinity")) + ((eq? (ref self '_exp) 'n) + (+ sign "NaN" (ref self '_int))) + (else ; self._exp == 'N' + (+ sign "sNaN" (ref self '_int))))) + (else + ;; dotplace is number of digits of self._int to the left of the + ;; decimal point in the mantissa of the output string (that is, + ;; after adjusting the exponent) + (cond + ((and (<= exp 0) (> leftdigits -6)) + ;; no exponent required + (set! dotplace leftdigits)) + + ((not eng) + ;; usual scientific notation: 1 digit on left of the point + (set! dotplace 1)) + + ((equal? i "0") + ;; engineering notation, zero + (set! dotplace (- (modulo (+ leftdigits 1) 3) 1))) + (else + ;; engineering notation, nonzero + (set! dotplace (- (modulo (+ leftdigits 1) 3) 1)))) + + (cond + ((<= dotplace 0) + (set! intpart "0") + (set! fracpart (+ "." + (* "0" (- dotplace)) + i))) + ((>= dotplace (len i)) + (set! intpart (+ i (* "0" (- dotplace (len i))))) + (set! fracpart "")) + (else + (set! intpart (pylist-slice i None dotplace None)) + (set! fracpart (+ '.' (pylist-slice i dotplace None None))))) + + + (cond + ((= leftdigits dotplace) + (set! exp "")) + (else + (let ((context (if (eq? context None) + (getcontext) + context))) + (set! exp + (+ (pylist-ref (lise "e" "E") (cx-capitals context)) + (format #f "%@d" (- leftdigits dotplace))))))) + (+ sign intpart fracpart exp)))))) + + (define to_eng_string + (lam (self (= context None)) + "Convert to a string, using engineering notation if an exponent is needed. + Engineering notation has an exponent which is a multiple of 3. This + can leave up to 3 digits to the left of the decimal place and may + require the addition of either one or two trailing zeros. + " + ((ref self '__str__) #:eng #t #:contect context))) + + (define __neg__ + (lam (self (= contextNone)) + "Returns a copy with the sign switched. + + Rounds, if it has reason. + " + (twix + ((un-special self context) it it) + (let* ((context (if (eq? context None) + (getcontext) + context)) + (ans (if (and (not (bool self)) + (not (eq? (cx-rounding context) + ROUND_FLOOR))) + ;; -Decimal('0') is Decimal('0'), + ;; not Decimal('-0'), except + ;; in ROUND_FLOOR rounding mode. + ((ref self 'copy_abs)) + ((ref self 'copy_negate))))) + + ((ref ans '_fix) context))))) + + (define __pos__ + (lam (self (= context None)) + "Returns a copy, unless it is a sNaN. + + Rounds the number (if more than precision digits) + " + (twix + ((un-special self context) it it) + + (let* ((context (if (eq? context None) + (getcontext) + context)) + (ans (if (and (not (bool self)) + (not (eq? (cx-rounding context) + ROUND_FLOOR))) + ;; -Decimal('0') is Decimal('0'), + ;; not Decimal('-0'), except + ;; in ROUND_FLOOR rounding mode. + ((ref self 'copy_abs)) + (Decimal self)))) + + ((ref ans '_fix) context))))) + + (define __abs__ + (lam (self (= round #t) (= context None)) + "Returns the absolute value of self. + + If the keyword argument 'round' is false, do not round. The + expression self.__abs__(round=False) is equivalent to + self.copy_abs(). + " + (twix + ((not (bool round)) + ((ref self 'copy_abs))) + + ((un-special self context) it it) + + (if (= (ref self '_sign) 1) + ((ref self '__neg__) #:context context) + ((ref self '__pos__) #:context context))))) + + (define __add__ + (lam (self other (= context None)) + "Returns self + other. + + -INF + INF (or the reverse) cause InvalidOperation errors. + " + (twix + ((norm-op other) it it) + + (let (get-context context)) + + ((add-special o1 o2 context) it it) + + (let (let* ((negativezero 0) + (self_sign (ref self '_sign)) + (other_sign (ref other '_sign)) + (self_exp (ref self '_sign)) + (other_exp (ref other '_sign)) + (prec (cx-prec context)) + (exp (min self_exp other_exp)) + (sign #f) + (ans #f)) + + (if (and (eq? (cx-rounding context) ROUND_FLOOR) + (not (= self_sign other_sign))) + ;; If the answer is 0, the sign should be negative, + ;; in this case. + (set! negativezero 1)))) + + ((if (and (not (bool self)) (not (bool other))) + (begin + (set! sign (min self_sign other_sign)) + (if (= negativezero 1) + (set! sign 1)) + (set! ans (_dec_from_triple sign "0" exp)) + (set! ans ((ref ans '_fix) context)) + ans) + #f) it it) + + ((if (not (bool self)) + (begin + (set! exp (max exp (- other_exp prec 1))) + (set! ans ((ref other '_rescale) exp + (cx-rounding rounding))) + (set! ans ((ref ans '_fix) context)) + ans) + #f) it it) + + ((if (not (bool other)) + (begin + (set! exp (max exp (- self_exp prec 1))) + (set! ans ((ref self '_rescale) exp + (cx-rounding rounding))) + (set! ans ((ref ans '_fix) context)) + ans) + #f) it it) + + + (let (let* ((op1 (_WorkRep self)) + (op2 (_WorkRep other)) + (ab (_normalize op1 op2 prec)) + (op1 (car ab)) + (op2 (cadr ab)) + (result (_WorkRep))))) + + ((cond + ((not (= (ref op1 'sign) (ref op2 'sign))) + ;; Equal and opposite + (twix + ((= op1_i op2_i) it + (set! ans (_dec_from_triple negativezero "0" exp)) + (set! ans ((ref ans '_fix) context)) + ans) + + (begin + (if (< op1_i op2_i) + (let ((t op1)) + (set! op1 op2) + (set! op2 t))) + + (if (= (ref op1 'sign) 1) + (let ((t (ref op1 'sign))) + (set result 'sign 1) + (set op1 'sign (ref op2 'sign)) + (set op2 'sign t)) + (set result 'sign 0)) + #f))) + ((= (ref op1 'sign) 1) + (set result 'sign 1) + #f) + + (begin + (set result 'sign 0) + #f)) it it) + + (begin + (if (= (ref op2 'sign) 0) + (set result 'int (+ (ref op1 'int) (ref op2 'int))) + (set result 'int (- (ref op1 'int) (ref op2 'int)))) + + (set result 'exp (ref op1 'exp)) + (set! ans (Decimal result)) + ((ref ans '_fix) context))))) + + (define __radd__ __add__) + + (define __sub__ + (lam (self other (= context None)) + "Return self - other" + (twix + ((norm-op other) it it) + ((bin-special o1 o2 context) it it) + ((ref self '__add__) + ((ref other 'copy_negate)) #:context context)))) + + (define __rsub__ + (lam (self other (= context None)) + "Return other - self" + (twix + ((norm-op other) it it) + ((ref 'other '__sub__) self #:context context)))) + + (define __mul__ + (lam (self other (= context None)) + "Return self * other. + + (+-) INF * 0 (or its reverse) raise InvalidOperation. + " + (twix + ((norm-op other) it it) + (let (get-context context)) + + (let (let ((resultsign (logxor (ref self '_sign) + (ref other '_sign)))))) + + ((mul-special o1 o2 context) it it) + + (let (let ((resultexp (+ (ref self '_exp) (ref other '_exp)))))) + + ;; Special case for multiplying by zero + ((or (not (bool self)) (not (bool other))) + (let ((ans (_dec_from_triple resultsign "0" resultexp))) + ((ref and '_fix) context))) + + ;; Special case for multiplying by power of 10 + ((equal? (ref self '_int) "1") + (let ((ans (_dec_from_triple resultsign (ref other '_int) resultexp))) + ((ref and '_fix) context))) + + ((equal? (ref other '_int) "1") + (let ((ans (_dec_from_triple resultsign (ref self '_int) resultexp))) + ((ref and '_fix) context))) + + (let* ((op1 (_WorkRep self)) + (op2 (_WorkRep other)) + (ans (_dec_from_triple resultsign + (str (* (ref op1 ') (ref op2 'int))) + resultexp))) + ((ref and '_fix) context))))) + + (define __rmul__ __mul__) + + (define __truediv__ + (lam (self other (= context None)) + "Return self / other." + (twix + ((norm-op other) it it) + (let (get-context context)) + + (let (let ((sign (logxor (ref self '_sign) + (ref other '_sign)))))) + + ((div-special o1 o2 context) it it) + + ;; Special cases for zeroes + ((if (not (bool other)) + (if (not (bool self)) + ((cx-error context) DivisionUndefined "0 / 0") + ((cx-error context) DivisionByZero "x / 0" sign)) + #f) it it) + + (let ((exp #f) + (coeff #f) + (nself (len (ref self '_int))) + (nother (len (ref other '_int)))) + (if (not (bool self)) + (begin + (set! exp (- (ref self '_exp) (ref other '_exp))) + (set! coeff 0)) + ;; OK, so neither = 0, INF or NaN + (let ((shift (+ nother (- nself) prec 1)) + (op1 (_WorkRep self)) + (op2 (_WorkRep other))) + (set! exp (- (ref self '_exp) (ref other '_exp) shift)) + (call-with-values + (lambda () + (if (>= shift 0) + (divmod (* (ref op1 'int) (expt 10 shift)) + (ref op2 'int)) + (divmod (ref op1 'int) + (* (ref op2 'int) (expt 10 shift))))) + (lambda (coeff- remainder) + (set! coeff + (if (not (= remainder 0)) + ;; result is not exact adjust to ensure + ;; correct rounding + (if (= (modulus coeff- 5) 0) + (+ coeff- 1) + coeff) + (let (ideal_exp (- (ref self '_exp) + (ref other '_exp))) + (let lp ((coeff- coeff-) (exp- exp)) + (if (and (< exp- indeal_exp) + (= (modulo coeff 10) 0)) + (lp (/ coeff 10) (+ exp- 1)) + (begin + (set exp exp-) + coeff)))))))))) + + + (let ((ans (_dec_from_triple sign, (str coeff) exp))) + ((ref ans '_fix) context)))))) + + def _divide(self, other, context): + """Return (self // other, self % other), to context.prec precision. + + Assumes that neither self nor other is a NaN, that self is not + infinite and that other is nonzero. + """ + sign = self._sign ^ other._sign + if other._isinfinity(): + ideal_exp = self._exp + else: + ideal_exp = min(self._exp, other._exp) + + expdiff = self.adjusted() - other.adjusted() + if not self or other._isinfinity() or expdiff <= -2: + return (_dec_from_triple(sign, '0', 0), + self._rescale(ideal_exp, context.rounding)) + if expdiff <= context.prec: + op1 = _WorkRep(self) + op2 = _WorkRep(other) + if op1.exp >= op2.exp: + op1.int *= 10**(op1.exp - op2.exp) + else: + op2.int *= 10**(op2.exp - op1.exp) + q, r = divmod(op1.int, op2.int) + if q < 10**context.prec: + return (_dec_from_triple(sign, str(q), 0), + _dec_from_triple(self._sign, str(r), ideal_exp)) + + # Here the quotient is too large to be representable + ans = context._raise_error(DivisionImpossible, + 'quotient too large in //, % or divmod') + return ans, ans + + def __rtruediv__(self, other, context=None): + """Swaps self/other and returns __truediv__.""" + other = _convert_other(other) + if other is NotImplemented: + return other + return other.__truediv__(self, context=context) + + def __divmod__(self, other, context=None): + """ + Return (self // other, self % other) + """ + other = _convert_other(other) + if other is NotImplemented: + return other + + if context is None: + context = getcontext() + + ans = self._check_nans(other, context) + if ans: + return (ans, ans) + + sign = self._sign ^ other._sign + if self._isinfinity(): + if other._isinfinity(): + ans = context._raise_error(InvalidOperation, 'divmod(INF, INF)') + return ans, ans + else: + return (_SignedInfinity[sign], + context._raise_error(InvalidOperation, 'INF % x')) + + if not other: + if not self: + ans = context._raise_error(DivisionUndefined, 'divmod(0, 0)') + return ans, ans + else: + return (context._raise_error(DivisionByZero, 'x // 0', sign), + context._raise_error(InvalidOperation, 'x % 0')) + + quotient, remainder = self._divide(other, context) + remainder = remainder._fix(context) + return quotient, remainder + + def __rdivmod__(self, other, context=None): + """Swaps self/other and returns __divmod__.""" + other = _convert_other(other) + if other is NotImplemented: + return other + return other.__divmod__(self, context=context) + + def __mod__(self, other, context=None): + """ + self % other + """ + other = _convert_other(other) + if other is NotImplemented: + return other + + if context is None: + context = getcontext() + + ans = self._check_nans(other, context) + if ans: + return ans + + if self._isinfinity(): + return context._raise_error(InvalidOperation, 'INF % x') + elif not other: + if self: + return context._raise_error(InvalidOperation, 'x % 0') + else: + return context._raise_error(DivisionUndefined, '0 % 0') + + remainder = self._divide(other, context)[1] + remainder = remainder._fix(context) + return remainder + + def __rmod__(self, other, context=None): + """Swaps self/other and returns __mod__.""" + other = _convert_other(other) + if other is NotImplemented: + return other + return other.__mod__(self, context=context) + + def remainder_near(self, other, context=None): + """ + Remainder nearest to 0- abs(remainder-near) <= other/2 + """ + if context is None: + context = getcontext() + + other = _convert_other(other, raiseit=True) + + ans = self._check_nans(other, context) + if ans: + return ans + + # self == +/-infinity -> InvalidOperation + if self._isinfinity(): + return context._raise_error(InvalidOperation, + 'remainder_near(infinity, x)') + + # other == 0 -> either InvalidOperation or DivisionUndefined + if not other: + if self: + return context._raise_error(InvalidOperation, + 'remainder_near(x, 0)') + else: + return context._raise_error(DivisionUndefined, + 'remainder_near(0, 0)') + + # other = +/-infinity -> remainder = self + if other._isinfinity(): + ans = Decimal(self) + return ans._fix(context) + + # self = 0 -> remainder = self, with ideal exponent + ideal_exponent = min(self._exp, other._exp) + if not self: + ans = _dec_from_triple(self._sign, '0', ideal_exponent) + return ans._fix(context) + + # catch most cases of large or small quotient + expdiff = self.adjusted() - other.adjusted() + if expdiff >= context.prec + 1: + # expdiff >= prec+1 => abs(self/other) > 10**prec + return context._raise_error(DivisionImpossible) + if expdiff <= -2: + # expdiff <= -2 => abs(self/other) < 0.1 + ans = self._rescale(ideal_exponent, context.rounding) + return ans._fix(context) + + # adjust both arguments to have the same exponent, then divide + op1 = _WorkRep(self) + op2 = _WorkRep(other) + if op1.exp >= op2.exp: + op1.int *= 10**(op1.exp - op2.exp) + else: + op2.int *= 10**(op2.exp - op1.exp) + q, r = divmod(op1.int, op2.int) + # remainder is r*10**ideal_exponent; other is +/-op2.int * + # 10**ideal_exponent. Apply correction to ensure that + # abs(remainder) <= abs(other)/2 + if 2*r + (q&1) > op2.int: + r -= op2.int + q += 1 + + if q >= 10**context.prec: + return context._raise_error(DivisionImpossible) + + # result has same sign as self unless r is negative + sign = self._sign + if r < 0: + sign = 1-sign + r = -r + + ans = _dec_from_triple(sign, str(r), ideal_exponent) + return ans._fix(context) + + def __floordiv__(self, other, context=None): + """self // other""" + other = _convert_other(other) + if other is NotImplemented: + return other + + if context is None: + context = getcontext() + + ans = self._check_nans(other, context) + if ans: + return ans + + if self._isinfinity(): + if other._isinfinity(): + return context._raise_error(InvalidOperation, 'INF // INF') + else: + return _SignedInfinity[self._sign ^ other._sign] + + if not other: + if self: + return context._raise_error(DivisionByZero, 'x // 0', + self._sign ^ other._sign) + else: + return context._raise_error(DivisionUndefined, '0 // 0') + + return self._divide(other, context)[0] + + def __rfloordiv__(self, other, context=None): + """Swaps self/other and returns __floordiv__.""" + other = _convert_other(other) + if other is NotImplemented: + return other + return other.__floordiv__(self, context=context) + + def __float__(self): + """Float representation.""" + if self._isnan(): + if self.is_snan(): + raise ValueError("Cannot convert signaling NaN to float") + s = "-nan" if self._sign else "nan" + else: + s = str(self) + return float(s) + + def __int__(self): + """Converts self to an int, truncating if necessary.""" + if self._is_special: + if self._isnan(): + raise ValueError("Cannot convert NaN to integer") + elif self._isinfinity(): + raise OverflowError("Cannot convert infinity to integer") + s = (-1)**self._sign + if self._exp >= 0: + return s*int(self._int)*10**self._exp + else: + return s*int(self._int[:self._exp] or '0') + + __trunc__ = __int__ + + def real(self): + return self + real = property(real) + + def imag(self): + return Decimal(0) + imag = property(imag) + + def conjugate(self): + return self + + def __complex__(self): + return complex(float(self)) + + def _fix_nan(self, context): + """Decapitate the payload of a NaN to fit the context""" + payload = self._int + + # maximum length of payload is precision if clamp=0, + # precision-1 if clamp=1. + max_payload_len = context.prec - context.clamp + if len(payload) > max_payload_len: + payload = payload[len(payload)-max_payload_len:].lstrip('0') + return _dec_from_triple(self._sign, payload, self._exp, True) + return Decimal(self) + + def _fix(self, context): + """Round if it is necessary to keep self within prec precision. + + Rounds and fixes the exponent. Does not raise on a sNaN. + + Arguments: + self - Decimal instance + context - context used. + """ + + if self._is_special: + if self._isnan(): + # decapitate payload if necessary + return self._fix_nan(context) + else: + # self is +/-Infinity; return unaltered + return Decimal(self) + + # if self is zero then exponent should be between Etiny and + # Emax if clamp==0, and between Etiny and Etop if clamp==1. + Etiny = context.Etiny() + Etop = context.Etop() + if not self: + exp_max = [context.Emax, Etop][context.clamp] + new_exp = min(max(self._exp, Etiny), exp_max) + if new_exp != self._exp: + context._raise_error(Clamped) + return _dec_from_triple(self._sign, '0', new_exp) + else: + return Decimal(self) + + # exp_min is the smallest allowable exponent of the result, + # equal to max(self.adjusted()-context.prec+1, Etiny) + exp_min = len(self._int) + self._exp - context.prec + if exp_min > Etop: + # overflow: exp_min > Etop iff self.adjusted() > Emax + ans = context._raise_error(Overflow, 'above Emax', self._sign) + context._raise_error(Inexact) + context._raise_error(Rounded) + return ans + + self_is_subnormal = exp_min < Etiny + if self_is_subnormal: + exp_min = Etiny + + # round if self has too many digits + if self._exp < exp_min: + digits = len(self._int) + self._exp - exp_min + if digits < 0: + self = _dec_from_triple(self._sign, '1', exp_min-1) + digits = 0 + rounding_method = self._pick_rounding_function[context.rounding] + changed = rounding_method(self, digits) + coeff = self._int[:digits] or '0' + if changed > 0: + coeff = str(int(coeff)+1) + if len(coeff) > context.prec: + coeff = coeff[:-1] + exp_min += 1 + + # check whether the rounding pushed the exponent out of range + if exp_min > Etop: + ans = context._raise_error(Overflow, 'above Emax', self._sign) + else: + ans = _dec_from_triple(self._sign, coeff, exp_min) + + # raise the appropriate signals, taking care to respect + # the precedence described in the specification + if changed and self_is_subnormal: + context._raise_error(Underflow) + if self_is_subnormal: + context._raise_error(Subnormal) + if changed: + context._raise_error(Inexact) + context._raise_error(Rounded) + if not ans: + # raise Clamped on underflow to 0 + context._raise_error(Clamped) + return ans + + if self_is_subnormal: + context._raise_error(Subnormal) + + # fold down if clamp == 1 and self has too few digits + if context.clamp == 1 and self._exp > Etop: + context._raise_error(Clamped) + self_padded = self._int + '0'*(self._exp - Etop) + return _dec_from_triple(self._sign, self_padded, Etop) + + # here self was representable to begin with; return unchanged + return Decimal(self) + + # for each of the rounding functions below: + # self is a finite, nonzero Decimal + # prec is an integer satisfying 0 <= prec < len(self._int) + # + # each function returns either -1, 0, or 1, as follows: + # 1 indicates that self should be rounded up (away from zero) + # 0 indicates that self should be truncated, and that all the + # digits to be truncated are zeros (so the value is unchanged) + # -1 indicates that there are nonzero digits to be truncated + + def _round_down(self, prec): + """Also known as round-towards-0, truncate.""" + if _all_zeros(self._int, prec): + return 0 + else: + return -1 + + def _round_up(self, prec): + """Rounds away from 0.""" + return -self._round_down(prec) + + def _round_half_up(self, prec): + """Rounds 5 up (away from 0)""" + if self._int[prec] in '56789': + return 1 + elif _all_zeros(self._int, prec): + return 0 + else: + return -1 + + def _round_half_down(self, prec): + """Round 5 down""" + if _exact_half(self._int, prec): + return -1 + else: + return self._round_half_up(prec) + + def _round_half_even(self, prec): + """Round 5 to even, rest to nearest.""" + if _exact_half(self._int, prec) and \ + (prec == 0 or self._int[prec-1] in '02468'): + return -1 + else: + return self._round_half_up(prec) + + def _round_ceiling(self, prec): + """Rounds up (not away from 0 if negative.)""" + if self._sign: + return self._round_down(prec) + else: + return -self._round_down(prec) + + def _round_floor(self, prec): + """Rounds down (not towards 0 if negative)""" + if not self._sign: + return self._round_down(prec) + else: + return -self._round_down(prec) + + def _round_05up(self, prec): + """Round down unless digit prec-1 is 0 or 5.""" + if prec and self._int[prec-1] not in '05': + return self._round_down(prec) + else: + return -self._round_down(prec) + + _pick_rounding_function = dict( + ROUND_DOWN = _round_down, + ROUND_UP = _round_up, + ROUND_HALF_UP = _round_half_up, + ROUND_HALF_DOWN = _round_half_down, + ROUND_HALF_EVEN = _round_half_even, + ROUND_CEILING = _round_ceiling, + ROUND_FLOOR = _round_floor, + ROUND_05UP = _round_05up, + ) + + def __round__(self, n=None): + """Round self to the nearest integer, or to a given precision. + + If only one argument is supplied, round a finite Decimal + instance self to the nearest integer. If self is infinite or + a NaN then a Python exception is raised. If self is finite + and lies exactly halfway between two integers then it is + rounded to the integer with even last digit. + + >>> round(Decimal('123.456')) + 123 + >>> round(Decimal('-456.789')) + -457 + >>> round(Decimal('-3.0')) + -3 + >>> round(Decimal('2.5')) + 2 + >>> round(Decimal('3.5')) + 4 + >>> round(Decimal('Inf')) + Traceback (most recent call last): + ... + OverflowError: cannot round an infinity + >>> round(Decimal('NaN')) + Traceback (most recent call last): + ... + ValueError: cannot round a NaN + + If a second argument n is supplied, self is rounded to n + decimal places using the rounding mode for the current + context. + + For an integer n, round(self, -n) is exactly equivalent to + self.quantize(Decimal('1En')). + + >>> round(Decimal('123.456'), 0) + Decimal('123') + >>> round(Decimal('123.456'), 2) + Decimal('123.46') + >>> round(Decimal('123.456'), -2) + Decimal('1E+2') + >>> round(Decimal('-Infinity'), 37) + Decimal('NaN') + >>> round(Decimal('sNaN123'), 0) + Decimal('NaN123') + + """ + if n is not None: + # two-argument form: use the equivalent quantize call + if not isinstance(n, int): + raise TypeError('Second argument to round should be integral') + exp = _dec_from_triple(0, '1', -n) + return self.quantize(exp) + + # one-argument form + if self._is_special: + if self.is_nan(): + raise ValueError("cannot round a NaN") + else: + raise OverflowError("cannot round an infinity") + return int(self._rescale(0, ROUND_HALF_EVEN)) + + def __floor__(self): + """Return the floor of self, as an integer. + + For a finite Decimal instance self, return the greatest + integer n such that n <= self. If self is infinite or a NaN + then a Python exception is raised. + + """ + if self._is_special: + if self.is_nan(): + raise ValueError("cannot round a NaN") + else: + raise OverflowError("cannot round an infinity") + return int(self._rescale(0, ROUND_FLOOR)) + + def __ceil__(self): + """Return the ceiling of self, as an integer. + + For a finite Decimal instance self, return the least integer n + such that n >= self. If self is infinite or a NaN then a + Python exception is raised. + + """ + if self._is_special: + if self.is_nan(): + raise ValueError("cannot round a NaN") + else: + raise OverflowError("cannot round an infinity") + return int(self._rescale(0, ROUND_CEILING)) + + def fma(self, other, third, context=None): + """Fused multiply-add. + + Returns self*other+third with no rounding of the intermediate + product self*other. + + self and other are multiplied together, with no rounding of + the result. The third operand is then added to the result, + and a single final rounding is performed. + """ + + other = _convert_other(other, raiseit=True) + third = _convert_other(third, raiseit=True) + + # compute product; raise InvalidOperation if either operand is + # a signaling NaN or if the product is zero times infinity. + if self._is_special or other._is_special: + if context is None: + context = getcontext() + if self._exp == 'N': + return context._raise_error(InvalidOperation, 'sNaN', self) + if other._exp == 'N': + return context._raise_error(InvalidOperation, 'sNaN', other) + if self._exp == 'n': + product = self + elif other._exp == 'n': + product = other + elif self._exp == 'F': + if not other: + return context._raise_error(InvalidOperation, + 'INF * 0 in fma') + product = _SignedInfinity[self._sign ^ other._sign] + elif other._exp == 'F': + if not self: + return context._raise_error(InvalidOperation, + '0 * INF in fma') + product = _SignedInfinity[self._sign ^ other._sign] + else: + product = _dec_from_triple(self._sign ^ other._sign, + str(int(self._int) * int(other._int)), + self._exp + other._exp) + + return product.__add__(third, context) + + def _power_modulo(self, other, modulo, context=None): + """Three argument version of __pow__""" + + other = _convert_other(other) + if other is NotImplemented: + return other + modulo = _convert_other(modulo) + if modulo is NotImplemented: + return modulo + + if context is None: + context = getcontext() + + # deal with NaNs: if there are any sNaNs then first one wins, + # (i.e. behaviour for NaNs is identical to that of fma) + self_is_nan = self._isnan() + other_is_nan = other._isnan() + modulo_is_nan = modulo._isnan() + if self_is_nan or other_is_nan or modulo_is_nan: + if self_is_nan == 2: + return context._raise_error(InvalidOperation, 'sNaN', + self) + if other_is_nan == 2: + return context._raise_error(InvalidOperation, 'sNaN', + other) + if modulo_is_nan == 2: + return context._raise_error(InvalidOperation, 'sNaN', + modulo) + if self_is_nan: + return self._fix_nan(context) + if other_is_nan: + return other._fix_nan(context) + return modulo._fix_nan(context) + + # check inputs: we apply same restrictions as Python's pow() + if not (self._isinteger() and + other._isinteger() and + modulo._isinteger()): + return context._raise_error(InvalidOperation, + 'pow() 3rd argument not allowed ' + 'unless all arguments are integers') + if other < 0: + return context._raise_error(InvalidOperation, + 'pow() 2nd argument cannot be ' + 'negative when 3rd argument specified') + if not modulo: + return context._raise_error(InvalidOperation, + 'pow() 3rd argument cannot be 0') + + # additional restriction for decimal: the modulus must be less + # than 10**prec in absolute value + if modulo.adjusted() >= context.prec: + return context._raise_error(InvalidOperation, + 'insufficient precision: pow() 3rd ' + 'argument must not have more than ' + 'precision digits') + + # define 0**0 == NaN, for consistency with two-argument pow + # (even though it hurts!) + if not other and not self: + return context._raise_error(InvalidOperation, + 'at least one of pow() 1st argument ' + 'and 2nd argument must be nonzero ;' + '0**0 is not defined') + + # compute sign of result + if other._iseven(): + sign = 0 + else: + sign = self._sign + + # convert modulo to a Python integer, and self and other to + # Decimal integers (i.e. force their exponents to be >= 0) + modulo = abs(int(modulo)) + base = _WorkRep(self.to_integral_value()) + exponent = _WorkRep(other.to_integral_value()) + + # compute result using integer pow() + base = (base.int % modulo * pow(10, base.exp, modulo)) % modulo + for i in range(exponent.exp): + base = pow(base, 10, modulo) + base = pow(base, exponent.int, modulo) + + return _dec_from_triple(sign, str(base), 0) + + def _power_exact(self, other, p): + """Attempt to compute self**other exactly. + + Given Decimals self and other and an integer p, attempt to + compute an exact result for the power self**other, with p + digits of precision. Return None if self**other is not + exactly representable in p digits. + + Assumes that elimination of special cases has already been + performed: self and other must both be nonspecial; self must + be positive and not numerically equal to 1; other must be + nonzero. For efficiency, other._exp should not be too large, + so that 10**abs(other._exp) is a feasible calculation.""" + + # In the comments below, we write x for the value of self and y for the + # value of other. Write x = xc*10**xe and abs(y) = yc*10**ye, with xc + # and yc positive integers not divisible by 10. + + # The main purpose of this method is to identify the *failure* + # of x**y to be exactly representable with as little effort as + # possible. So we look for cheap and easy tests that + # eliminate the possibility of x**y being exact. Only if all + # these tests are passed do we go on to actually compute x**y. + + # Here's the main idea. Express y as a rational number m/n, with m and + # n relatively prime and n>0. Then for x**y to be exactly + # representable (at *any* precision), xc must be the nth power of a + # positive integer and xe must be divisible by n. If y is negative + # then additionally xc must be a power of either 2 or 5, hence a power + # of 2**n or 5**n. + # + # There's a limit to how small |y| can be: if y=m/n as above + # then: + # + # (1) if xc != 1 then for the result to be representable we + # need xc**(1/n) >= 2, and hence also xc**|y| >= 2. So + # if |y| <= 1/nbits(xc) then xc < 2**nbits(xc) <= + # 2**(1/|y|), hence xc**|y| < 2 and the result is not + # representable. + # + # (2) if xe != 0, |xe|*(1/n) >= 1, so |xe|*|y| >= 1. Hence if + # |y| < 1/|xe| then the result is not representable. + # + # Note that since x is not equal to 1, at least one of (1) and + # (2) must apply. Now |y| < 1/nbits(xc) iff |yc|*nbits(xc) < + # 10**-ye iff len(str(|yc|*nbits(xc)) <= -ye. + # + # There's also a limit to how large y can be, at least if it's + # positive: the normalized result will have coefficient xc**y, + # so if it's representable then xc**y < 10**p, and y < + # p/log10(xc). Hence if y*log10(xc) >= p then the result is + # not exactly representable. + + # if len(str(abs(yc*xe)) <= -ye then abs(yc*xe) < 10**-ye, + # so |y| < 1/xe and the result is not representable. + # Similarly, len(str(abs(yc)*xc_bits)) <= -ye implies |y| + # < 1/nbits(xc). + + x = _WorkRep(self) + xc, xe = x.int, x.exp + while xc % 10 == 0: + xc //= 10 + xe += 1 + + y = _WorkRep(other) + yc, ye = y.int, y.exp + while yc % 10 == 0: + yc //= 10 + ye += 1 + + # case where xc == 1: result is 10**(xe*y), with xe*y + # required to be an integer + if xc == 1: + xe *= yc + # result is now 10**(xe * 10**ye); xe * 10**ye must be integral + while xe % 10 == 0: + xe //= 10 + ye += 1 + if ye < 0: + return None + exponent = xe * 10**ye + if y.sign == 1: + exponent = -exponent + # if other is a nonnegative integer, use ideal exponent + if other._isinteger() and other._sign == 0: + ideal_exponent = self._exp*int(other) + zeros = min(exponent-ideal_exponent, p-1) + else: + zeros = 0 + return _dec_from_triple(0, '1' + '0'*zeros, exponent-zeros) + + # case where y is negative: xc must be either a power + # of 2 or a power of 5. + if y.sign == 1: + last_digit = xc % 10 + if last_digit in (2,4,6,8): + # quick test for power of 2 + if xc & -xc != xc: + return None + # now xc is a power of 2; e is its exponent + e = _nbits(xc)-1 + + # We now have: + # + # x = 2**e * 10**xe, e > 0, and y < 0. + # + # The exact result is: + # + # x**y = 5**(-e*y) * 10**(e*y + xe*y) + # + # provided that both e*y and xe*y are integers. Note that if + # 5**(-e*y) >= 10**p, then the result can't be expressed + # exactly with p digits of precision. + # + # Using the above, we can guard against large values of ye. + # 93/65 is an upper bound for log(10)/log(5), so if + # + # ye >= len(str(93*p//65)) + # + # then + # + # -e*y >= -y >= 10**ye > 93*p/65 > p*log(10)/log(5), + # + # so 5**(-e*y) >= 10**p, and the coefficient of the result + # can't be expressed in p digits. + + # emax >= largest e such that 5**e < 10**p. + emax = p*93//65 + if ye >= len(str(emax)): + return None + + # Find -e*y and -xe*y; both must be integers + e = _decimal_lshift_exact(e * yc, ye) + xe = _decimal_lshift_exact(xe * yc, ye) + if e is None or xe is None: + return None + + if e > emax: + return None + xc = 5**e + + elif last_digit == 5: + # e >= log_5(xc) if xc is a power of 5; we have + # equality all the way up to xc=5**2658 + e = _nbits(xc)*28//65 + xc, remainder = divmod(5**e, xc) + if remainder: + return None + while xc % 5 == 0: + xc //= 5 + e -= 1 + + # Guard against large values of ye, using the same logic as in + # the 'xc is a power of 2' branch. 10/3 is an upper bound for + # log(10)/log(2). + emax = p*10//3 + if ye >= len(str(emax)): + return None + + e = _decimal_lshift_exact(e * yc, ye) + xe = _decimal_lshift_exact(xe * yc, ye) + if e is None or xe is None: + return None + + if e > emax: + return None + xc = 2**e + else: + return None + + if xc >= 10**p: + return None + xe = -e-xe + return _dec_from_triple(0, str(xc), xe) + + # now y is positive; find m and n such that y = m/n + if ye >= 0: + m, n = yc*10**ye, 1 + else: + if xe != 0 and len(str(abs(yc*xe))) <= -ye: + return None + xc_bits = _nbits(xc) + if xc != 1 and len(str(abs(yc)*xc_bits)) <= -ye: + return None + m, n = yc, 10**(-ye) + while m % 2 == n % 2 == 0: + m //= 2 + n //= 2 + while m % 5 == n % 5 == 0: + m //= 5 + n //= 5 + + # compute nth root of xc*10**xe + if n > 1: + # if 1 < xc < 2**n then xc isn't an nth power + if xc != 1 and xc_bits <= n: + return None + + xe, rem = divmod(xe, n) + if rem != 0: + return None + + # compute nth root of xc using Newton's method + a = 1 << -(-_nbits(xc)//n) # initial estimate + while True: + q, r = divmod(xc, a**(n-1)) + if a <= q: + break + else: + a = (a*(n-1) + q)//n + if not (a == q and r == 0): + return None + xc = a + + # now xc*10**xe is the nth root of the original xc*10**xe + # compute mth power of xc*10**xe + + # if m > p*100//_log10_lb(xc) then m > p/log10(xc), hence xc**m > + # 10**p and the result is not representable. + if xc > 1 and m > p*100//_log10_lb(xc): + return None + xc = xc**m + xe *= m + if xc > 10**p: + return None + + # by this point the result *is* exactly representable + # adjust the exponent to get as close as possible to the ideal + # exponent, if necessary + str_xc = str(xc) + if other._isinteger() and other._sign == 0: + ideal_exponent = self._exp*int(other) + zeros = min(xe-ideal_exponent, p-len(str_xc)) + else: + zeros = 0 + return _dec_from_triple(0, str_xc+'0'*zeros, xe-zeros) + + def __pow__(self, other, modulo=None, context=None): + """Return self ** other [ % modulo]. + + With two arguments, compute self**other. + + With three arguments, compute (self**other) % modulo. For the + three argument form, the following restrictions on the + arguments hold: + + - all three arguments must be integral + - other must be nonnegative + - either self or other (or both) must be nonzero + - modulo must be nonzero and must have at most p digits, + where p is the context precision. + + If any of these restrictions is violated the InvalidOperation + flag is raised. + + The result of pow(self, other, modulo) is identical to the + result that would be obtained by computing (self**other) % + modulo with unbounded precision, but is computed more + efficiently. It is always exact. + """ + + if modulo is not None: + return self._power_modulo(other, modulo, context) + + other = _convert_other(other) + if other is NotImplemented: + return other + + if context is None: + context = getcontext() + + # either argument is a NaN => result is NaN + ans = self._check_nans(other, context) + if ans: + return ans + + # 0**0 = NaN (!), x**0 = 1 for nonzero x (including +/-Infinity) + if not other: + if not self: + return context._raise_error(InvalidOperation, '0 ** 0') + else: + return _One + + # result has sign 1 iff self._sign is 1 and other is an odd integer + result_sign = 0 + if self._sign == 1: + if other._isinteger(): + if not other._iseven(): + result_sign = 1 + else: + # -ve**noninteger = NaN + # (-0)**noninteger = 0**noninteger + if self: + return context._raise_error(InvalidOperation, + 'x ** y with x negative and y not an integer') + # negate self, without doing any unwanted rounding + self = self.copy_negate() + + # 0**(+ve or Inf)= 0; 0**(-ve or -Inf) = Infinity + if not self: + if other._sign == 0: + return _dec_from_triple(result_sign, '0', 0) + else: + return _SignedInfinity[result_sign] + + # Inf**(+ve or Inf) = Inf; Inf**(-ve or -Inf) = 0 + if self._isinfinity(): + if other._sign == 0: + return _SignedInfinity[result_sign] + else: + return _dec_from_triple(result_sign, '0', 0) + + # 1**other = 1, but the choice of exponent and the flags + # depend on the exponent of self, and on whether other is a + # positive integer, a negative integer, or neither + if self == _One: + if other._isinteger(): + # exp = max(self._exp*max(int(other), 0), + # 1-context.prec) but evaluating int(other) directly + # is dangerous until we know other is small (other + # could be 1e999999999) + if other._sign == 1: + multiplier = 0 + elif other > context.prec: + multiplier = context.prec + else: + multiplier = int(other) + + exp = self._exp * multiplier + if exp < 1-context.prec: + exp = 1-context.prec + context._raise_error(Rounded) + else: + context._raise_error(Inexact) + context._raise_error(Rounded) + exp = 1-context.prec + + return _dec_from_triple(result_sign, '1'+'0'*-exp, exp) + + # compute adjusted exponent of self + self_adj = self.adjusted() + + # self ** infinity is infinity if self > 1, 0 if self < 1 + # self ** -infinity is infinity if self < 1, 0 if self > 1 + if other._isinfinity(): + if (other._sign == 0) == (self_adj < 0): + return _dec_from_triple(result_sign, '0', 0) + else: + return _SignedInfinity[result_sign] + + # from here on, the result always goes through the call + # to _fix at the end of this function. + ans = None + exact = False + + # crude test to catch cases of extreme overflow/underflow. If + # log10(self)*other >= 10**bound and bound >= len(str(Emax)) + # then 10**bound >= 10**len(str(Emax)) >= Emax+1 and hence + # self**other >= 10**(Emax+1), so overflow occurs. The test + # for underflow is similar. + bound = self._log10_exp_bound() + other.adjusted() + if (self_adj >= 0) == (other._sign == 0): + # self > 1 and other +ve, or self < 1 and other -ve + # possibility of overflow + if bound >= len(str(context.Emax)): + ans = _dec_from_triple(result_sign, '1', context.Emax+1) + else: + # self > 1 and other -ve, or self < 1 and other +ve + # possibility of underflow to 0 + Etiny = context.Etiny() + if bound >= len(str(-Etiny)): + ans = _dec_from_triple(result_sign, '1', Etiny-1) + + # try for an exact result with precision +1 + if ans is None: + ans = self._power_exact(other, context.prec + 1) + if ans is not None: + if result_sign == 1: + ans = _dec_from_triple(1, ans._int, ans._exp) + exact = True + + # usual case: inexact result, x**y computed directly as exp(y*log(x)) + if ans is None: + p = context.prec + x = _WorkRep(self) + xc, xe = x.int, x.exp + y = _WorkRep(other) + yc, ye = y.int, y.exp + if y.sign == 1: + yc = -yc + + # compute correctly rounded result: start with precision +3, + # then increase precision until result is unambiguously roundable + extra = 3 + while True: + coeff, exp = _dpower(xc, xe, yc, ye, p+extra) + if coeff % (5*10**(len(str(coeff))-p-1)): + break + extra += 3 + + ans = _dec_from_triple(result_sign, str(coeff), exp) + + # unlike exp, ln and log10, the power function respects the + # rounding mode; no need to switch to ROUND_HALF_EVEN here + + # There's a difficulty here when 'other' is not an integer and + # the result is exact. In this case, the specification + # requires that the Inexact flag be raised (in spite of + # exactness), but since the result is exact _fix won't do this + # for us. (Correspondingly, the Underflow signal should also + # be raised for subnormal results.) We can't directly raise + # these signals either before or after calling _fix, since + # that would violate the precedence for signals. So we wrap + # the ._fix call in a temporary context, and reraise + # afterwards. + if exact and not other._isinteger(): + # pad with zeros up to length context.prec+1 if necessary; this + # ensures that the Rounded signal will be raised. + if len(ans._int) <= context.prec: + expdiff = context.prec + 1 - len(ans._int) + ans = _dec_from_triple(ans._sign, ans._int+'0'*expdiff, + ans._exp-expdiff) + + # create a copy of the current context, with cleared flags/traps + newcontext = context.copy() + newcontext.clear_flags() + for exception in _signals: + newcontext.traps[exception] = 0 + + # round in the new context + ans = ans._fix(newcontext) + + # raise Inexact, and if necessary, Underflow + newcontext._raise_error(Inexact) + if newcontext.flags[Subnormal]: + newcontext._raise_error(Underflow) + + # propagate signals to the original context; _fix could + # have raised any of Overflow, Underflow, Subnormal, + # Inexact, Rounded, Clamped. Overflow needs the correct + # arguments. Note that the order of the exceptions is + # important here. + if newcontext.flags[Overflow]: + context._raise_error(Overflow, 'above Emax', ans._sign) + for exception in Underflow, Subnormal, Inexact, Rounded, Clamped: + if newcontext.flags[exception]: + context._raise_error(exception) + + else: + ans = ans._fix(context) + + return ans + + def __rpow__(self, other, context=None): + """Swaps self/other and returns __pow__.""" + other = _convert_other(other) + if other is NotImplemented: + return other + return other.__pow__(self, context=context) + + def normalize(self, context=None): + """Normalize- strip trailing 0s, change anything equal to 0 to 0e0""" + + if context is None: + context = getcontext() + + if self._is_special: + ans = self._check_nans(context=context) + if ans: + return ans + + dup = self._fix(context) + if dup._isinfinity(): + return dup + + if not dup: + return _dec_from_triple(dup._sign, '0', 0) + exp_max = [context.Emax, context.Etop()][context.clamp] + end = len(dup._int) + exp = dup._exp + while dup._int[end-1] == '0' and exp < exp_max: + exp += 1 + end -= 1 + return _dec_from_triple(dup._sign, dup._int[:end], exp) + + def quantize(self, exp, rounding=None, context=None): + """Quantize self so its exponent is the same as that of exp. + + Similar to self._rescale(exp._exp) but with error checking. + """ + exp = _convert_other(exp, raiseit=True) + + if context is None: + context = getcontext() + if rounding is None: + rounding = context.rounding + + if self._is_special or exp._is_special: + ans = self._check_nans(exp, context) + if ans: + return ans + + if exp._isinfinity() or self._isinfinity(): + if exp._isinfinity() and self._isinfinity(): + return Decimal(self) # if both are inf, it is OK + return context._raise_error(InvalidOperation, + 'quantize with one INF') + + # exp._exp should be between Etiny and Emax + if not (context.Etiny() <= exp._exp <= context.Emax): + return context._raise_error(InvalidOperation, + 'target exponent out of bounds in quantize') + + if not self: + ans = _dec_from_triple(self._sign, '0', exp._exp) + return ans._fix(context) + + self_adjusted = self.adjusted() + if self_adjusted > context.Emax: + return context._raise_error(InvalidOperation, + 'exponent of quantize result too large for current context') + if self_adjusted - exp._exp + 1 > context.prec: + return context._raise_error(InvalidOperation, + 'quantize result has too many digits for current context') + + ans = self._rescale(exp._exp, rounding) + if ans.adjusted() > context.Emax: + return context._raise_error(InvalidOperation, + 'exponent of quantize result too large for current context') + if len(ans._int) > context.prec: + return context._raise_error(InvalidOperation, + 'quantize result has too many digits for current context') + + # raise appropriate flags + if ans and ans.adjusted() < context.Emin: + context._raise_error(Subnormal) + if ans._exp > self._exp: + if ans != self: + context._raise_error(Inexact) + context._raise_error(Rounded) + + # call to fix takes care of any necessary folddown, and + # signals Clamped if necessary + ans = ans._fix(context) + return ans + + def same_quantum(self, other, context=None): + """Return True if self and other have the same exponent; otherwise + return False. + + If either operand is a special value, the following rules are used: + * return True if both operands are infinities + * return True if both operands are NaNs + * otherwise, return False. + """ + other = _convert_other(other, raiseit=True) + if self._is_special or other._is_special: + return (self.is_nan() and other.is_nan() or + self.is_infinite() and other.is_infinite()) + return self._exp == other._exp + + def _rescale(self, exp, rounding): + """Rescale self so that the exponent is exp, either by padding with zeros + or by truncating digits, using the given rounding mode. + + Specials are returned without change. This operation is + quiet: it raises no flags, and uses no information from the + context. + + exp = exp to scale to (an integer) + rounding = rounding mode + """ + if self._is_special: + return Decimal(self) + if not self: + return _dec_from_triple(self._sign, '0', exp) + + if self._exp >= exp: + # pad answer with zeros if necessary + return _dec_from_triple(self._sign, + self._int + '0'*(self._exp - exp), exp) + + # too many digits; round and lose data. If self.adjusted() < + # exp-1, replace self by 10**(exp-1) before rounding + digits = len(self._int) + self._exp - exp + if digits < 0: + self = _dec_from_triple(self._sign, '1', exp-1) + digits = 0 + this_function = self._pick_rounding_function[rounding] + changed = this_function(self, digits) + coeff = self._int[:digits] or '0' + if changed == 1: + coeff = str(int(coeff)+1) + return _dec_from_triple(self._sign, coeff, exp) + + def _round(self, places, rounding): + """Round a nonzero, nonspecial Decimal to a fixed number of + significant figures, using the given rounding mode. + + Infinities, NaNs and zeros are returned unaltered. + + This operation is quiet: it raises no flags, and uses no + information from the context. + + """ + if places <= 0: + raise ValueError("argument should be at least 1 in _round") + if self._is_special or not self: + return Decimal(self) + ans = self._rescale(self.adjusted()+1-places, rounding) + # it can happen that the rescale alters the adjusted exponent; + # for example when rounding 99.97 to 3 significant figures. + # When this happens we end up with an extra 0 at the end of + # the number; a second rescale fixes this. + if ans.adjusted() != self.adjusted(): + ans = ans._rescale(ans.adjusted()+1-places, rounding) + return ans + + def to_integral_exact(self, rounding=None, context=None): + """Rounds to a nearby integer. + + If no rounding mode is specified, take the rounding mode from + the context. This method raises the Rounded and Inexact flags + when appropriate. + + See also: to_integral_value, which does exactly the same as + this method except that it doesn't raise Inexact or Rounded. + """ + if self._is_special: + ans = self._check_nans(context=context) + if ans: + return ans + return Decimal(self) + if self._exp >= 0: + return Decimal(self) + if not self: + return _dec_from_triple(self._sign, '0', 0) + if context is None: + context = getcontext() + if rounding is None: + rounding = context.rounding + ans = self._rescale(0, rounding) + if ans != self: + context._raise_error(Inexact) + context._raise_error(Rounded) + return ans + + def to_integral_value(self, rounding=None, context=None): + """Rounds to the nearest integer, without raising inexact, rounded.""" + if context is None: + context = getcontext() + if rounding is None: + rounding = context.rounding + if self._is_special: + ans = self._check_nans(context=context) + if ans: + return ans + return Decimal(self) + if self._exp >= 0: + return Decimal(self) + else: + return self._rescale(0, rounding) + + # the method name changed, but we provide also the old one, for compatibility + to_integral = to_integral_value + + def sqrt(self, context=None): + """Return the square root of self.""" + if context is None: + context = getcontext() + + if self._is_special: + ans = self._check_nans(context=context) + if ans: + return ans + + if self._isinfinity() and self._sign == 0: + return Decimal(self) + + if not self: + # exponent = self._exp // 2. sqrt(-0) = -0 + ans = _dec_from_triple(self._sign, '0', self._exp // 2) + return ans._fix(context) + + if self._sign == 1: + return context._raise_error(InvalidOperation, 'sqrt(-x), x > 0') + + # At this point self represents a positive number. Let p be + # the desired precision and express self in the form c*100**e + # with c a positive real number and e an integer, c and e + # being chosen so that 100**(p-1) <= c < 100**p. Then the + # (exact) square root of self is sqrt(c)*10**e, and 10**(p-1) + # <= sqrt(c) < 10**p, so the closest representable Decimal at + # precision p is n*10**e where n = round_half_even(sqrt(c)), + # the closest integer to sqrt(c) with the even integer chosen + # in the case of a tie. + # + # To ensure correct rounding in all cases, we use the + # following trick: we compute the square root to an extra + # place (precision p+1 instead of precision p), rounding down. + # Then, if the result is inexact and its last digit is 0 or 5, + # we increase the last digit to 1 or 6 respectively; if it's + # exact we leave the last digit alone. Now the final round to + # p places (or fewer in the case of underflow) will round + # correctly and raise the appropriate flags. + + # use an extra digit of precision + prec = context.prec+1 + + # write argument in the form c*100**e where e = self._exp//2 + # is the 'ideal' exponent, to be used if the square root is + # exactly representable. l is the number of 'digits' of c in + # base 100, so that 100**(l-1) <= c < 100**l. + op = _WorkRep(self) + e = op.exp >> 1 + if op.exp & 1: + c = op.int * 10 + l = (len(self._int) >> 1) + 1 + else: + c = op.int + l = len(self._int)+1 >> 1 + + # rescale so that c has exactly prec base 100 'digits' + shift = prec-l + if shift >= 0: + c *= 100**shift + exact = True + else: + c, remainder = divmod(c, 100**-shift) + exact = not remainder + e -= shift + + # find n = floor(sqrt(c)) using Newton's method + n = 10**prec + while True: + q = c//n + if n <= q: + break + else: + n = n + q >> 1 + exact = exact and n*n == c + + if exact: + # result is exact; rescale to use ideal exponent e + if shift >= 0: + # assert n % 10**shift == 0 + n //= 10**shift + else: + n *= 10**-shift + e += shift + else: + # result is not exact; fix last digit as described above + if n % 5 == 0: + n += 1 + + ans = _dec_from_triple(0, str(n), e) + + # round, and fit to current context + context = context._shallow_copy() + rounding = context._set_rounding(ROUND_HALF_EVEN) + ans = ans._fix(context) + context.rounding = rounding + + return ans + + def max(self, other, context=None): + """Returns the larger value. + + Like max(self, other) except if one is not a number, returns + NaN (and signals if one is sNaN). Also rounds. + """ + other = _convert_other(other, raiseit=True) + + if context is None: + context = getcontext() + + if self._is_special or other._is_special: + # If one operand is a quiet NaN and the other is number, then the + # number is always returned + sn = self._isnan() + on = other._isnan() + if sn or on: + if on == 1 and sn == 0: + return self._fix(context) + if sn == 1 and on == 0: + return other._fix(context) + return self._check_nans(other, context) + + c = self._cmp(other) + if c == 0: + # If both operands are finite and equal in numerical value + # then an ordering is applied: + # + # If the signs differ then max returns the operand with the + # positive sign and min returns the operand with the negative sign + # + # If the signs are the same then the exponent is used to select + # the result. This is exactly the ordering used in compare_total. + c = self.compare_total(other) + + if c == -1: + ans = other + else: + ans = self + + return ans._fix(context) + + def min(self, other, context=None): + """Returns the smaller value. + + Like min(self, other) except if one is not a number, returns + NaN (and signals if one is sNaN). Also rounds. + """ + other = _convert_other(other, raiseit=True) + + if context is None: + context = getcontext() + + if self._is_special or other._is_special: + # If one operand is a quiet NaN and the other is number, then the + # number is always returned + sn = self._isnan() + on = other._isnan() + if sn or on: + if on == 1 and sn == 0: + return self._fix(context) + if sn == 1 and on == 0: + return other._fix(context) + return self._check_nans(other, context) + + c = self._cmp(other) + if c == 0: + c = self.compare_total(other) + + if c == -1: + ans = self + else: + ans = other + + return ans._fix(context) + + def _isinteger(self): + """Returns whether self is an integer""" + if self._is_special: + return False + if self._exp >= 0: + return True + rest = self._int[self._exp:] + return rest == '0'*len(rest) + + def _iseven(self): + """Returns True if self is even. Assumes self is an integer.""" + if not self or self._exp > 0: + return True + return self._int[-1+self._exp] in '02468' + + def adjusted(self): + """Return the adjusted exponent of self""" + try: + return self._exp + len(self._int) - 1 + # If NaN or Infinity, self._exp is string + except TypeError: + return 0 + + def canonical(self): + """Returns the same Decimal object. + + As we do not have different encodings for the same number, the + received object already is in its canonical form. + """ + return self + + def compare_signal(self, other, context=None): + """Compares self to the other operand numerically. + + It's pretty much like compare(), but all NaNs signal, with signaling + NaNs taking precedence over quiet NaNs. + """ + other = _convert_other(other, raiseit = True) + ans = self._compare_check_nans(other, context) + if ans: + return ans + return self.compare(other, context=context) + + def compare_total(self, other, context=None): + """Compares self to other using the abstract representations. + + This is not like the standard compare, which use their numerical + value. Note that a total ordering is defined for all possible abstract + representations. + """ + other = _convert_other(other, raiseit=True) + + # if one is negative and the other is positive, it's easy + if self._sign and not other._sign: + return _NegativeOne + if not self._sign and other._sign: + return _One + sign = self._sign + + # let's handle both NaN types + self_nan = self._isnan() + other_nan = other._isnan() + if self_nan or other_nan: + if self_nan == other_nan: + # compare payloads as though they're integers + self_key = len(self._int), self._int + other_key = len(other._int), other._int + if self_key < other_key: + if sign: + return _One + else: + return _NegativeOne + if self_key > other_key: + if sign: + return _NegativeOne + else: + return _One + return _Zero + + if sign: + if self_nan == 1: + return _NegativeOne + if other_nan == 1: + return _One + if self_nan == 2: + return _NegativeOne + if other_nan == 2: + return _One + else: + if self_nan == 1: + return _One + if other_nan == 1: + return _NegativeOne + if self_nan == 2: + return _One + if other_nan == 2: + return _NegativeOne + + if self < other: + return _NegativeOne + if self > other: + return _One + + if self._exp < other._exp: + if sign: + return _One + else: + return _NegativeOne + if self._exp > other._exp: + if sign: + return _NegativeOne + else: + return _One + return _Zero + + + def compare_total_mag(self, other, context=None): + """Compares self to other using abstract repr., ignoring sign. + + Like compare_total, but with operand's sign ignored and assumed to be 0. + """ + other = _convert_other(other, raiseit=True) + + s = self.copy_abs() + o = other.copy_abs() + return s.compare_total(o) + + def copy_abs(self): + """Returns a copy with the sign set to 0. """ + return _dec_from_triple(0, self._int, self._exp, self._is_special) + + def copy_negate(self): + """Returns a copy with the sign inverted.""" + if self._sign: + return _dec_from_triple(0, self._int, self._exp, self._is_special) + else: + return _dec_from_triple(1, self._int, self._exp, self._is_special) + + def copy_sign(self, other, context=None): + """Returns self with the sign of other.""" + other = _convert_other(other, raiseit=True) + return _dec_from_triple(other._sign, self._int, + self._exp, self._is_special) + + def exp(self, context=None): + """Returns e ** self.""" + + if context is None: + context = getcontext() + + # exp(NaN) = NaN + ans = self._check_nans(context=context) + if ans: + return ans + + # exp(-Infinity) = 0 + if self._isinfinity() == -1: + return _Zero + + # exp(0) = 1 + if not self: + return _One + + # exp(Infinity) = Infinity + if self._isinfinity() == 1: + return Decimal(self) + + # the result is now guaranteed to be inexact (the true + # mathematical result is transcendental). There's no need to + # raise Rounded and Inexact here---they'll always be raised as + # a result of the call to _fix. + p = context.prec + adj = self.adjusted() + + # we only need to do any computation for quite a small range + # of adjusted exponents---for example, -29 <= adj <= 10 for + # the default context. For smaller exponent the result is + # indistinguishable from 1 at the given precision, while for + # larger exponent the result either overflows or underflows. + if self._sign == 0 and adj > len(str((context.Emax+1)*3)): + # overflow + ans = _dec_from_triple(0, '1', context.Emax+1) + elif self._sign == 1 and adj > len(str((-context.Etiny()+1)*3)): + # underflow to 0 + ans = _dec_from_triple(0, '1', context.Etiny()-1) + elif self._sign == 0 and adj < -p: + # p+1 digits; final round will raise correct flags + ans = _dec_from_triple(0, '1' + '0'*(p-1) + '1', -p) + elif self._sign == 1 and adj < -p-1: + # p+1 digits; final round will raise correct flags + ans = _dec_from_triple(0, '9'*(p+1), -p-1) + # general case + else: + op = _WorkRep(self) + c, e = op.int, op.exp + if op.sign == 1: + c = -c + + # compute correctly rounded result: increase precision by + # 3 digits at a time until we get an unambiguously + # roundable result + extra = 3 + while True: + coeff, exp = _dexp(c, e, p+extra) + if coeff % (5*10**(len(str(coeff))-p-1)): + break + extra += 3 + + ans = _dec_from_triple(0, str(coeff), exp) + + # at this stage, ans should round correctly with *any* + # rounding mode, not just with ROUND_HALF_EVEN + context = context._shallow_copy() + rounding = context._set_rounding(ROUND_HALF_EVEN) + ans = ans._fix(context) + context.rounding = rounding + + return ans + + def is_canonical(self): + """Return True if self is canonical; otherwise return False. + + Currently, the encoding of a Decimal instance is always + canonical, so this method returns True for any Decimal. + """ + return True + + def is_finite(self): + """Return True if self is finite; otherwise return False. + + A Decimal instance is considered finite if it is neither + infinite nor a NaN. + """ + return not self._is_special + + def is_infinite(self): + """Return True if self is infinite; otherwise return False.""" + return self._exp == 'F' + + def is_nan(self): + """Return True if self is a qNaN or sNaN; otherwise return False.""" + return self._exp in ('n', 'N') + + def is_normal(self, context=None): + """Return True if self is a normal number; otherwise return False.""" + if self._is_special or not self: + return False + if context is None: + context = getcontext() + return context.Emin <= self.adjusted() + + def is_qnan(self): + """Return True if self is a quiet NaN; otherwise return False.""" + return self._exp == 'n' + + def is_signed(self): + """Return True if self is negative; otherwise return False.""" + return self._sign == 1 + + def is_snan(self): + """Return True if self is a signaling NaN; otherwise return False.""" + return self._exp == 'N' + + def is_subnormal(self, context=None): + """Return True if self is subnormal; otherwise return False.""" + if self._is_special or not self: + return False + if context is None: + context = getcontext() + return self.adjusted() < context.Emin + + def is_zero(self): + """Return True if self is a zero; otherwise return False.""" + return not self._is_special and self._int == '0' + + def _ln_exp_bound(self): + """Compute a lower bound for the adjusted exponent of self.ln(). + In other words, compute r such that self.ln() >= 10**r. Assumes + that self is finite and positive and that self != 1. + """ + + # for 0.1 <= x <= 10 we use the inequalities 1-1/x <= ln(x) <= x-1 + adj = self._exp + len(self._int) - 1 + if adj >= 1: + # argument >= 10; we use 23/10 = 2.3 as a lower bound for ln(10) + return len(str(adj*23//10)) - 1 + if adj <= -2: + # argument <= 0.1 + return len(str((-1-adj)*23//10)) - 1 + op = _WorkRep(self) + c, e = op.int, op.exp + if adj == 0: + # 1 < self < 10 + num = str(c-10**-e) + den = str(c) + return len(num) - len(den) - (num < den) + # adj == -1, 0.1 <= self < 1 + return e + len(str(10**-e - c)) - 1 + + + def ln(self, context=None): + """Returns the natural (base e) logarithm of self.""" + + if context is None: + context = getcontext() + + # ln(NaN) = NaN + ans = self._check_nans(context=context) + if ans: + return ans + + # ln(0.0) == -Infinity + if not self: + return _NegativeInfinity + + # ln(Infinity) = Infinity + if self._isinfinity() == 1: + return _Infinity + + # ln(1.0) == 0.0 + if self == _One: + return _Zero + + # ln(negative) raises InvalidOperation + if self._sign == 1: + return context._raise_error(InvalidOperation, + 'ln of a negative value') + + # result is irrational, so necessarily inexact + op = _WorkRep(self) + c, e = op.int, op.exp + p = context.prec + + # correctly rounded result: repeatedly increase precision by 3 + # until we get an unambiguously roundable result + places = p - self._ln_exp_bound() + 2 # at least p+3 places + while True: + coeff = _dlog(c, e, places) + # assert len(str(abs(coeff)))-p >= 1 + if coeff % (5*10**(len(str(abs(coeff)))-p-1)): + break + places += 3 + ans = _dec_from_triple(int(coeff<0), str(abs(coeff)), -places) + + context = context._shallow_copy() + rounding = context._set_rounding(ROUND_HALF_EVEN) + ans = ans._fix(context) + context.rounding = rounding + return ans + + def _log10_exp_bound(self): + """Compute a lower bound for the adjusted exponent of self.log10(). + In other words, find r such that self.log10() >= 10**r. + Assumes that self is finite and positive and that self != 1. + """ + + # For x >= 10 or x < 0.1 we only need a bound on the integer + # part of log10(self), and this comes directly from the + # exponent of x. For 0.1 <= x <= 10 we use the inequalities + # 1-1/x <= log(x) <= x-1. If x > 1 we have |log10(x)| > + # (1-1/x)/2.31 > 0. If x < 1 then |log10(x)| > (1-x)/2.31 > 0 + + adj = self._exp + len(self._int) - 1 + if adj >= 1: + # self >= 10 + return len(str(adj))-1 + if adj <= -2: + # self < 0.1 + return len(str(-1-adj))-1 + op = _WorkRep(self) + c, e = op.int, op.exp + if adj == 0: + # 1 < self < 10 + num = str(c-10**-e) + den = str(231*c) + return len(num) - len(den) - (num < den) + 2 + # adj == -1, 0.1 <= self < 1 + num = str(10**-e-c) + return len(num) + e - (num < "231") - 1 + + def log10(self, context=None): + """Returns the base 10 logarithm of self.""" + + if context is None: + context = getcontext() + + # log10(NaN) = NaN + ans = self._check_nans(context=context) + if ans: + return ans + + # log10(0.0) == -Infinity + if not self: + return _NegativeInfinity + + # log10(Infinity) = Infinity + if self._isinfinity() == 1: + return _Infinity + + # log10(negative or -Infinity) raises InvalidOperation + if self._sign == 1: + return context._raise_error(InvalidOperation, + 'log10 of a negative value') + + # log10(10**n) = n + if self._int[0] == '1' and self._int[1:] == '0'*(len(self._int) - 1): + # answer may need rounding + ans = Decimal(self._exp + len(self._int) - 1) + else: + # result is irrational, so necessarily inexact + op = _WorkRep(self) + c, e = op.int, op.exp + p = context.prec + + # correctly rounded result: repeatedly increase precision + # until result is unambiguously roundable + places = p-self._log10_exp_bound()+2 + while True: + coeff = _dlog10(c, e, places) + # assert len(str(abs(coeff)))-p >= 1 + if coeff % (5*10**(len(str(abs(coeff)))-p-1)): + break + places += 3 + ans = _dec_from_triple(int(coeff<0), str(abs(coeff)), -places) + + context = context._shallow_copy() + rounding = context._set_rounding(ROUND_HALF_EVEN) + ans = ans._fix(context) + context.rounding = rounding + return ans + + def logb(self, context=None): + """ Returns the exponent of the magnitude of self's MSD. + + The result is the integer which is the exponent of the magnitude + of the most significant digit of self (as though it were truncated + to a single digit while maintaining the value of that digit and + without limiting the resulting exponent). + """ + # logb(NaN) = NaN + ans = self._check_nans(context=context) + if ans: + return ans + + if context is None: + context = getcontext() + + # logb(+/-Inf) = +Inf + if self._isinfinity(): + return _Infinity + + # logb(0) = -Inf, DivisionByZero + if not self: + return context._raise_error(DivisionByZero, 'logb(0)', 1) + + # otherwise, simply return the adjusted exponent of self, as a + # Decimal. Note that no attempt is made to fit the result + # into the current context. + ans = Decimal(self.adjusted()) + return ans._fix(context) + + def _islogical(self): + """Return True if self is a logical operand. + + For being logical, it must be a finite number with a sign of 0, + an exponent of 0, and a coefficient whose digits must all be + either 0 or 1. + """ + if self._sign != 0 or self._exp != 0: + return False + for dig in self._int: + if dig not in '01': + return False + return True + + def _fill_logical(self, context, opa, opb): + dif = context.prec - len(opa) + if dif > 0: + opa = '0'*dif + opa + elif dif < 0: + opa = opa[-context.prec:] + dif = context.prec - len(opb) + if dif > 0: + opb = '0'*dif + opb + elif dif < 0: + opb = opb[-context.prec:] + return opa, opb + + def logical_and(self, other, context=None): + """Applies an 'and' operation between self and other's digits.""" + if context is None: + context = getcontext() + + other = _convert_other(other, raiseit=True) + + if not self._islogical() or not other._islogical(): + return context._raise_error(InvalidOperation) + + # fill to context.prec + (opa, opb) = self._fill_logical(context, self._int, other._int) + + # make the operation, and clean starting zeroes + result = "".join([str(int(a)&int(b)) for a,b in zip(opa,opb)]) + return _dec_from_triple(0, result.lstrip('0') or '0', 0) + + def logical_invert(self, context=None): + """Invert all its digits.""" + if context is None: + context = getcontext() + return self.logical_xor(_dec_from_triple(0,'1'*context.prec,0), + context) + + def logical_or(self, other, context=None): + """Applies an 'or' operation between self and other's digits.""" + if context is None: + context = getcontext() + + other = _convert_other(other, raiseit=True) + + if not self._islogical() or not other._islogical(): + return context._raise_error(InvalidOperation) + + # fill to context.prec + (opa, opb) = self._fill_logical(context, self._int, other._int) + + # make the operation, and clean starting zeroes + result = "".join([str(int(a)|int(b)) for a,b in zip(opa,opb)]) + return _dec_from_triple(0, result.lstrip('0') or '0', 0) + + def logical_xor(self, other, context=None): + """Applies an 'xor' operation between self and other's digits.""" + if context is None: + context = getcontext() + + other = _convert_other(other, raiseit=True) + + if not self._islogical() or not other._islogical(): + return context._raise_error(InvalidOperation) + + # fill to context.prec + (opa, opb) = self._fill_logical(context, self._int, other._int) + + # make the operation, and clean starting zeroes + result = "".join([str(int(a)^int(b)) for a,b in zip(opa,opb)]) + return _dec_from_triple(0, result.lstrip('0') or '0', 0) + + def max_mag(self, other, context=None): + """Compares the values numerically with their sign ignored.""" + other = _convert_other(other, raiseit=True) + + if context is None: + context = getcontext() + + if self._is_special or other._is_special: + # If one operand is a quiet NaN and the other is number, then the + # number is always returned + sn = self._isnan() + on = other._isnan() + if sn or on: + if on == 1 and sn == 0: + return self._fix(context) + if sn == 1 and on == 0: + return other._fix(context) + return self._check_nans(other, context) + + c = self.copy_abs()._cmp(other.copy_abs()) + if c == 0: + c = self.compare_total(other) + + if c == -1: + ans = other + else: + ans = self + + return ans._fix(context) + + def min_mag(self, other, context=None): + """Compares the values numerically with their sign ignored.""" + other = _convert_other(other, raiseit=True) + + if context is None: + context = getcontext() + + if self._is_special or other._is_special: + # If one operand is a quiet NaN and the other is number, then the + # number is always returned + sn = self._isnan() + on = other._isnan() + if sn or on: + if on == 1 and sn == 0: + return self._fix(context) + if sn == 1 and on == 0: + return other._fix(context) + return self._check_nans(other, context) + + c = self.copy_abs()._cmp(other.copy_abs()) + if c == 0: + c = self.compare_total(other) + + if c == -1: + ans = self + else: + ans = other + + return ans._fix(context) + + def next_minus(self, context=None): + """Returns the largest representable number smaller than itself.""" + if context is None: + context = getcontext() + + ans = self._check_nans(context=context) + if ans: + return ans + + if self._isinfinity() == -1: + return _NegativeInfinity + if self._isinfinity() == 1: + return _dec_from_triple(0, '9'*context.prec, context.Etop()) + + context = context.copy() + context._set_rounding(ROUND_FLOOR) + context._ignore_all_flags() + new_self = self._fix(context) + if new_self != self: + return new_self + return self.__sub__(_dec_from_triple(0, '1', context.Etiny()-1), + context) + + def next_plus(self, context=None): + """Returns the smallest representable number larger than itself.""" + if context is None: + context = getcontext() + + ans = self._check_nans(context=context) + if ans: + return ans + + if self._isinfinity() == 1: + return _Infinity + if self._isinfinity() == -1: + return _dec_from_triple(1, '9'*context.prec, context.Etop()) + + context = context.copy() + context._set_rounding(ROUND_CEILING) + context._ignore_all_flags() + new_self = self._fix(context) + if new_self != self: + return new_self + return self.__add__(_dec_from_triple(0, '1', context.Etiny()-1), + context) + + def next_toward(self, other, context=None): + """Returns the number closest to self, in the direction towards other. + + The result is the closest representable number to self + (excluding self) that is in the direction towards other, + unless both have the same value. If the two operands are + numerically equal, then the result is a copy of self with the + sign set to be the same as the sign of other. + """ + other = _convert_other(other, raiseit=True) + + if context is None: + context = getcontext() + + ans = self._check_nans(other, context) + if ans: + return ans + + comparison = self._cmp(other) + if comparison == 0: + return self.copy_sign(other) + + if comparison == -1: + ans = self.next_plus(context) + else: # comparison == 1 + ans = self.next_minus(context) + + # decide which flags to raise using value of ans + if ans._isinfinity(): + context._raise_error(Overflow, + 'Infinite result from next_toward', + ans._sign) + context._raise_error(Inexact) + context._raise_error(Rounded) + elif ans.adjusted() < context.Emin: + context._raise_error(Underflow) + context._raise_error(Subnormal) + context._raise_error(Inexact) + context._raise_error(Rounded) + # if precision == 1 then we don't raise Clamped for a + # result 0E-Etiny. + if not ans: + context._raise_error(Clamped) + + return ans + + def number_class(self, context=None): + """Returns an indication of the class of self. + + The class is one of the following strings: + sNaN + NaN + -Infinity + -Normal + -Subnormal + -Zero + +Zero + +Subnormal + +Normal + +Infinity + """ + if self.is_snan(): + return "sNaN" + if self.is_qnan(): + return "NaN" + inf = self._isinfinity() + if inf == 1: + return "+Infinity" + if inf == -1: + return "-Infinity" + if self.is_zero(): + if self._sign: + return "-Zero" + else: + return "+Zero" + if context is None: + context = getcontext() + if self.is_subnormal(context=context): + if self._sign: + return "-Subnormal" + else: + return "+Subnormal" + # just a normal, regular, boring number, :) + if self._sign: + return "-Normal" + else: + return "+Normal" + + def radix(self): + """Just returns 10, as this is Decimal, :)""" + return Decimal(10) + + def rotate(self, other, context=None): + """Returns a rotated copy of self, value-of-other times.""" + if context is None: + context = getcontext() + + other = _convert_other(other, raiseit=True) + + ans = self._check_nans(other, context) + if ans: + return ans + + if other._exp != 0: + return context._raise_error(InvalidOperation) + if not (-context.prec <= int(other) <= context.prec): + return context._raise_error(InvalidOperation) + + if self._isinfinity(): + return Decimal(self) + + # get values, pad if necessary + torot = int(other) + rotdig = self._int + topad = context.prec - len(rotdig) + if topad > 0: + rotdig = '0'*topad + rotdig + elif topad < 0: + rotdig = rotdig[-topad:] + + # let's rotate! + rotated = rotdig[torot:] + rotdig[:torot] + return _dec_from_triple(self._sign, + rotated.lstrip('0') or '0', self._exp) + + def scaleb(self, other, context=None): + """Returns self operand after adding the second value to its exp.""" + if context is None: + context = getcontext() + + other = _convert_other(other, raiseit=True) + + ans = self._check_nans(other, context) + if ans: + return ans + + if other._exp != 0: + return context._raise_error(InvalidOperation) + liminf = -2 * (context.Emax + context.prec) + limsup = 2 * (context.Emax + context.prec) + if not (liminf <= int(other) <= limsup): + return context._raise_error(InvalidOperation) + + if self._isinfinity(): + return Decimal(self) + + d = _dec_from_triple(self._sign, self._int, self._exp + int(other)) + d = d._fix(context) + return d + + def shift(self, other, context=None): + """Returns a shifted copy of self, value-of-other times.""" + if context is None: + context = getcontext() + + other = _convert_other(other, raiseit=True) + + ans = self._check_nans(other, context) + if ans: + return ans + + if other._exp != 0: + return context._raise_error(InvalidOperation) + if not (-context.prec <= int(other) <= context.prec): + return context._raise_error(InvalidOperation) + + if self._isinfinity(): + return Decimal(self) + + # get values, pad if necessary + torot = int(other) + rotdig = self._int + topad = context.prec - len(rotdig) + if topad > 0: + rotdig = '0'*topad + rotdig + elif topad < 0: + rotdig = rotdig[-topad:] + + # let's shift! + if torot < 0: + shifted = rotdig[:torot] + else: + shifted = rotdig + '0'*torot + shifted = shifted[-context.prec:] + + return _dec_from_triple(self._sign, + shifted.lstrip('0') or '0', self._exp) + + # Support for pickling, copy, and deepcopy + def __reduce__(self): + return (self.__class__, (str(self),)) + + def __copy__(self): + if type(self) is Decimal: + return self # I'm immutable; therefore I am my own clone + return self.__class__(str(self)) + + def __deepcopy__(self, memo): + if type(self) is Decimal: + return self # My components are also immutable + return self.__class__(str(self)) + + # PEP 3101 support. the _localeconv keyword argument should be + # considered private: it's provided for ease of testing only. + def __format__(self, specifier, context=None, _localeconv=None): + """Format a Decimal instance according to the given specifier. + + The specifier should be a standard format specifier, with the + form described in PEP 3101. Formatting types 'e', 'E', 'f', + 'F', 'g', 'G', 'n' and '%' are supported. If the formatting + type is omitted it defaults to 'g' or 'G', depending on the + value of context.capitals. + """ + + # Note: PEP 3101 says that if the type is not present then + # there should be at least one digit after the decimal point. + # We take the liberty of ignoring this requirement for + # Decimal---it's presumably there to make sure that + # format(float, '') behaves similarly to str(float). + if context is None: + context = getcontext() + + spec = _parse_format_specifier(specifier, _localeconv=_localeconv) + + # special values don't care about the type or precision + if self._is_special: + sign = _format_sign(self._sign, spec) + body = str(self.copy_abs()) + if spec['type'] == '%': + body += '%' + return _format_align(sign, body, spec) + + # a type of None defaults to 'g' or 'G', depending on context + if spec['type'] is None: + spec['type'] = ['g', 'G'][context.capitals] + + # if type is '%', adjust exponent of self accordingly + if spec['type'] == '%': + self = _dec_from_triple(self._sign, self._int, self._exp+2) + + # round if necessary, taking rounding mode from the context + rounding = context.rounding + precision = spec['precision'] + if precision is not None: + if spec['type'] in 'eE': + self = self._round(precision+1, rounding) + elif spec['type'] in 'fF%': + self = self._rescale(-precision, rounding) + elif spec['type'] in 'gG' and len(self._int) > precision: + self = self._round(precision, rounding) + # special case: zeros with a positive exponent can't be + # represented in fixed point; rescale them to 0e0. + if not self and self._exp > 0 and spec['type'] in 'fF%': + self = self._rescale(0, rounding) + + # figure out placement of the decimal point + leftdigits = self._exp + len(self._int) + if spec['type'] in 'eE': + if not self and precision is not None: + dotplace = 1 - precision + else: + dotplace = 1 + elif spec['type'] in 'fF%': + dotplace = leftdigits + elif spec['type'] in 'gG': + if self._exp <= 0 and leftdigits > -6: + dotplace = leftdigits + else: + dotplace = 1 + + # find digits before and after decimal point, and get exponent + if dotplace < 0: + intpart = '0' + fracpart = '0'*(-dotplace) + self._int + elif dotplace > len(self._int): + intpart = self._int + '0'*(dotplace-len(self._int)) + fracpart = '' + else: + intpart = self._int[:dotplace] or '0' + fracpart = self._int[dotplace:] + exp = leftdigits-dotplace + + # done with the decimal-specific stuff; hand over the rest + # of the formatting to the _format_number function + return _format_number(self._sign, intpart, fracpart, exp, spec) + +def _dec_from_triple(sign, coefficient, exponent, special=False): + """Create a decimal instance directly, without any validation, + normalization (e.g. removal of leading zeros) or argument + conversion. + + This function is for *internal use only*. + """ + + self = object.__new__(Decimal) + self._sign = sign + self._int = coefficient + self._exp = exponent + self._is_special = special + + return self + +# Register Decimal as a kind of Number (an abstract base class). +# However, do not register it as Real (because Decimals are not +# interoperable with floats). +_numbers.Number.register(Decimal) + + +##### Context class ####################################################### + +class _ContextManager(object): + """Context manager class to support localcontext(). + + Sets a copy of the supplied context in __enter__() and restores + the previous decimal context in __exit__() + """ + def __init__(self, new_context): + self.new_context = new_context.copy() + def __enter__(self): + self.saved_context = getcontext() + setcontext(self.new_context) + return self.new_context + def __exit__(self, t, v, tb): + setcontext(self.saved_context) + +class Context(object): + """Contains the context for a Decimal instance. + + Contains: + prec - precision (for use in rounding, division, square roots..) + rounding - rounding type (how you round) + traps - If traps[exception] = 1, then the exception is + raised when it is caused. Otherwise, a value is + substituted in. + flags - When an exception is caused, flags[exception] is set. + (Whether or not the trap_enabler is set) + Should be reset by user of Decimal instance. + Emin - Minimum exponent + Emax - Maximum exponent + capitals - If 1, 1*10^1 is printed as 1E+1. + If 0, printed as 1e1 + clamp - If 1, change exponents if too high (Default 0) + """ + + def __init__(self, prec=None, rounding=None, Emin=None, Emax=None, + capitals=None, clamp=None, flags=None, traps=None, + _ignored_flags=None): + # Set defaults; for everything except flags and _ignored_flags, + # inherit from DefaultContext. + try: + dc = DefaultContext + except NameError: + pass + + self.prec = prec if prec is not None else dc.prec + self.rounding = rounding if rounding is not None else dc.rounding + self.Emin = Emin if Emin is not None else dc.Emin + self.Emax = Emax if Emax is not None else dc.Emax + self.capitals = capitals if capitals is not None else dc.capitals + self.clamp = clamp if clamp is not None else dc.clamp + + if _ignored_flags is None: + self._ignored_flags = [] + else: + self._ignored_flags = _ignored_flags + + if traps is None: + self.traps = dc.traps.copy() + elif not isinstance(traps, dict): + self.traps = dict((s, int(s in traps)) for s in _signals + traps) + else: + self.traps = traps + + if flags is None: + self.flags = dict.fromkeys(_signals, 0) + elif not isinstance(flags, dict): + self.flags = dict((s, int(s in flags)) for s in _signals + flags) + else: + self.flags = flags + + def _set_integer_check(self, name, value, vmin, vmax): + if not isinstance(value, int): + raise TypeError("%s must be an integer" % name) + if vmin == '-inf': + if value > vmax: + raise ValueError("%s must be in [%s, %d]. got: %s" % (name, vmin, vmax, value)) + elif vmax == 'inf': + if value < vmin: + raise ValueError("%s must be in [%d, %s]. got: %s" % (name, vmin, vmax, value)) + else: + if value < vmin or value > vmax: + raise ValueError("%s must be in [%d, %d]. got %s" % (name, vmin, vmax, value)) + return object.__setattr__(self, name, value) + + def _set_signal_dict(self, name, d): + if not isinstance(d, dict): + raise TypeError("%s must be a signal dict" % d) + for key in d: + if not key in _signals: + raise KeyError("%s is not a valid signal dict" % d) + for key in _signals: + if not key in d: + raise KeyError("%s is not a valid signal dict" % d) + return object.__setattr__(self, name, d) + + def __setattr__(self, name, value): + if name == 'prec': + return self._set_integer_check(name, value, 1, 'inf') + elif name == 'Emin': + return self._set_integer_check(name, value, '-inf', 0) + elif name == 'Emax': + return self._set_integer_check(name, value, 0, 'inf') + elif name == 'capitals': + return self._set_integer_check(name, value, 0, 1) + elif name == 'clamp': + return self._set_integer_check(name, value, 0, 1) + elif name == 'rounding': + if not value in _rounding_modes: + # raise TypeError even for strings to have consistency + # among various implementations. + raise TypeError("%s: invalid rounding mode" % value) + return object.__setattr__(self, name, value) + elif name == 'flags' or name == 'traps': + return self._set_signal_dict(name, value) + elif name == '_ignored_flags': + return object.__setattr__(self, name, value) + else: + raise AttributeError( + "'decimal.Context' object has no attribute '%s'" % name) + + def __delattr__(self, name): + raise AttributeError("%s cannot be deleted" % name) + + # Support for pickling, copy, and deepcopy + def __reduce__(self): + flags = [sig for sig, v in self.flags.items() if v] + traps = [sig for sig, v in self.traps.items() if v] + return (self.__class__, + (self.prec, self.rounding, self.Emin, self.Emax, + self.capitals, self.clamp, flags, traps)) + + def __repr__(self): + """Show the current context.""" + s = [] + s.append('Context(prec=%(prec)d, rounding=%(rounding)s, ' + 'Emin=%(Emin)d, Emax=%(Emax)d, capitals=%(capitals)d, ' + 'clamp=%(clamp)d' + % vars(self)) + names = [f.__name__ for f, v in self.flags.items() if v] + s.append('flags=[' + ', '.join(names) + ']') + names = [t.__name__ for t, v in self.traps.items() if v] + s.append('traps=[' + ', '.join(names) + ']') + return ', '.join(s) + ')' + + def clear_flags(self): + """Reset all flags to zero""" + for flag in self.flags: + self.flags[flag] = 0 + + def clear_traps(self): + """Reset all traps to zero""" + for flag in self.traps: + self.traps[flag] = 0 + + def _shallow_copy(self): + """Returns a shallow copy from self.""" + nc = Context(self.prec, self.rounding, self.Emin, self.Emax, + self.capitals, self.clamp, self.flags, self.traps, + self._ignored_flags) + return nc + + def copy(self): + """Returns a deep copy from self.""" + nc = Context(self.prec, self.rounding, self.Emin, self.Emax, + self.capitals, self.clamp, + self.flags.copy(), self.traps.copy(), + self._ignored_flags) + return nc + __copy__ = copy + + def _raise_error(self, condition, explanation = None, *args): + """Handles an error + + If the flag is in _ignored_flags, returns the default response. + Otherwise, it sets the flag, then, if the corresponding + trap_enabler is set, it reraises the exception. Otherwise, it returns + the default value after setting the flag. + """ + error = _condition_map.get(condition, condition) + if error in self._ignored_flags: + # Don't touch the flag + return error().handle(self, *args) + + self.flags[error] = 1 + if not self.traps[error]: + # The errors define how to handle themselves. + return condition().handle(self, *args) + + # Errors should only be risked on copies of the context + # self._ignored_flags = [] + raise error(explanation) + + def _ignore_all_flags(self): + """Ignore all flags, if they are raised""" + return self._ignore_flags(*_signals) + + def _ignore_flags(self, *flags): + """Ignore the flags, if they are raised""" + # Do not mutate-- This way, copies of a context leave the original + # alone. + self._ignored_flags = (self._ignored_flags + list(flags)) + return list(flags) + + def _regard_flags(self, *flags): + """Stop ignoring the flags, if they are raised""" + if flags and isinstance(flags[0], (tuple,list)): + flags = flags[0] + for flag in flags: + self._ignored_flags.remove(flag) + + # We inherit object.__hash__, so we must deny this explicitly + __hash__ = None + + def Etiny(self): + """Returns Etiny (= Emin - prec + 1)""" + return int(self.Emin - self.prec + 1) + + def Etop(self): + """Returns maximum exponent (= Emax - prec + 1)""" + return int(self.Emax - self.prec + 1) + + def _set_rounding(self, type): + """Sets the rounding type. + + Sets the rounding type, and returns the current (previous) + rounding type. Often used like: + + context = context.copy() + # so you don't change the calling context + # if an error occurs in the middle. + rounding = context._set_rounding(ROUND_UP) + val = self.__sub__(other, context=context) + context._set_rounding(rounding) + + This will make it round up for that operation. + """ + rounding = self.rounding + self.rounding = type + return rounding + + def create_decimal(self, num='0'): + """Creates a new Decimal instance but using self as context. + + This method implements the to-number operation of the + IBM Decimal specification.""" + + if isinstance(num, str) and (num != num.strip() or '_' in num): + return self._raise_error(ConversionSyntax, + "trailing or leading whitespace and " + "underscores are not permitted.") + + d = Decimal(num, context=self) + if d._isnan() and len(d._int) > self.prec - self.clamp: + return self._raise_error(ConversionSyntax, + "diagnostic info too long in NaN") + return d._fix(self) + + def create_decimal_from_float(self, f): + """Creates a new Decimal instance from a float but rounding using self + as the context. + + >>> context = Context(prec=5, rounding=ROUND_DOWN) + >>> context.create_decimal_from_float(3.1415926535897932) + Decimal('3.1415') + >>> context = Context(prec=5, traps=[Inexact]) + >>> context.create_decimal_from_float(3.1415926535897932) + Traceback (most recent call last): + ... + decimal.Inexact: None + + """ + d = Decimal.from_float(f) # An exact conversion + return d._fix(self) # Apply the context rounding + + # Methods + def abs(self, a): + """Returns the absolute value of the operand. + + If the operand is negative, the result is the same as using the minus + operation on the operand. Otherwise, the result is the same as using + the plus operation on the operand. + + >>> ExtendedContext.abs(Decimal('2.1')) + Decimal('2.1') + >>> ExtendedContext.abs(Decimal('-100')) + Decimal('100') + >>> ExtendedContext.abs(Decimal('101.5')) + Decimal('101.5') + >>> ExtendedContext.abs(Decimal('-101.5')) + Decimal('101.5') + >>> ExtendedContext.abs(-1) + Decimal('1') + """ + a = _convert_other(a, raiseit=True) + return a.__abs__(context=self) + + def add(self, a, b): + """Return the sum of the two operands. + + >>> ExtendedContext.add(Decimal('12'), Decimal('7.00')) + Decimal('19.00') + >>> ExtendedContext.add(Decimal('1E+2'), Decimal('1.01E+4')) + Decimal('1.02E+4') + >>> ExtendedContext.add(1, Decimal(2)) + Decimal('3') + >>> ExtendedContext.add(Decimal(8), 5) + Decimal('13') + >>> ExtendedContext.add(5, 5) + Decimal('10') + """ + a = _convert_other(a, raiseit=True) + r = a.__add__(b, context=self) + if r is NotImplemented: + raise TypeError("Unable to convert %s to Decimal" % b) + else: + return r + + def _apply(self, a): + return str(a._fix(self)) + + def canonical(self, a): + """Returns the same Decimal object. + + As we do not have different encodings for the same number, the + received object already is in its canonical form. + + >>> ExtendedContext.canonical(Decimal('2.50')) + Decimal('2.50') + """ + if not isinstance(a, Decimal): + raise TypeError("canonical requires a Decimal as an argument.") + return a.canonical() + + def compare(self, a, b): + """Compares values numerically. + + If the signs of the operands differ, a value representing each operand + ('-1' if the operand is less than zero, '0' if the operand is zero or + negative zero, or '1' if the operand is greater than zero) is used in + place of that operand for the comparison instead of the actual + operand. + + The comparison is then effected by subtracting the second operand from + the first and then returning a value according to the result of the + subtraction: '-1' if the result is less than zero, '0' if the result is + zero or negative zero, or '1' if the result is greater than zero. + + >>> ExtendedContext.compare(Decimal('2.1'), Decimal('3')) + Decimal('-1') + >>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.1')) + Decimal('0') + >>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.10')) + Decimal('0') + >>> ExtendedContext.compare(Decimal('3'), Decimal('2.1')) + Decimal('1') + >>> ExtendedContext.compare(Decimal('2.1'), Decimal('-3')) + Decimal('1') + >>> ExtendedContext.compare(Decimal('-3'), Decimal('2.1')) + Decimal('-1') + >>> ExtendedContext.compare(1, 2) + Decimal('-1') + >>> ExtendedContext.compare(Decimal(1), 2) + Decimal('-1') + >>> ExtendedContext.compare(1, Decimal(2)) + Decimal('-1') + """ + a = _convert_other(a, raiseit=True) + return a.compare(b, context=self) + + def compare_signal(self, a, b): + """Compares the values of the two operands numerically. + + It's pretty much like compare(), but all NaNs signal, with signaling + NaNs taking precedence over quiet NaNs. + + >>> c = ExtendedContext + >>> c.compare_signal(Decimal('2.1'), Decimal('3')) + Decimal('-1') + >>> c.compare_signal(Decimal('2.1'), Decimal('2.1')) + Decimal('0') + >>> c.flags[InvalidOperation] = 0 + >>> print(c.flags[InvalidOperation]) + 0 + >>> c.compare_signal(Decimal('NaN'), Decimal('2.1')) + Decimal('NaN') + >>> print(c.flags[InvalidOperation]) + 1 + >>> c.flags[InvalidOperation] = 0 + >>> print(c.flags[InvalidOperation]) + 0 + >>> c.compare_signal(Decimal('sNaN'), Decimal('2.1')) + Decimal('NaN') + >>> print(c.flags[InvalidOperation]) + 1 + >>> c.compare_signal(-1, 2) + Decimal('-1') + >>> c.compare_signal(Decimal(-1), 2) + Decimal('-1') + >>> c.compare_signal(-1, Decimal(2)) + Decimal('-1') + """ + a = _convert_other(a, raiseit=True) + return a.compare_signal(b, context=self) + + def compare_total(self, a, b): + """Compares two operands using their abstract representation. + + This is not like the standard compare, which use their numerical + value. Note that a total ordering is defined for all possible abstract + representations. + + >>> ExtendedContext.compare_total(Decimal('12.73'), Decimal('127.9')) + Decimal('-1') + >>> ExtendedContext.compare_total(Decimal('-127'), Decimal('12')) + Decimal('-1') + >>> ExtendedContext.compare_total(Decimal('12.30'), Decimal('12.3')) + Decimal('-1') + >>> ExtendedContext.compare_total(Decimal('12.30'), Decimal('12.30')) + Decimal('0') + >>> ExtendedContext.compare_total(Decimal('12.3'), Decimal('12.300')) + Decimal('1') + >>> ExtendedContext.compare_total(Decimal('12.3'), Decimal('NaN')) + Decimal('-1') + >>> ExtendedContext.compare_total(1, 2) + Decimal('-1') + >>> ExtendedContext.compare_total(Decimal(1), 2) + Decimal('-1') + >>> ExtendedContext.compare_total(1, Decimal(2)) + Decimal('-1') + """ + a = _convert_other(a, raiseit=True) + return a.compare_total(b) + + def compare_total_mag(self, a, b): + """Compares two operands using their abstract representation ignoring sign. + + Like compare_total, but with operand's sign ignored and assumed to be 0. + """ + a = _convert_other(a, raiseit=True) + return a.compare_total_mag(b) + + def copy_abs(self, a): + """Returns a copy of the operand with the sign set to 0. + + >>> ExtendedContext.copy_abs(Decimal('2.1')) + Decimal('2.1') + >>> ExtendedContext.copy_abs(Decimal('-100')) + Decimal('100') + >>> ExtendedContext.copy_abs(-1) + Decimal('1') + """ + a = _convert_other(a, raiseit=True) + return a.copy_abs() + + def copy_decimal(self, a): + """Returns a copy of the decimal object. + + >>> ExtendedContext.copy_decimal(Decimal('2.1')) + Decimal('2.1') + >>> ExtendedContext.copy_decimal(Decimal('-1.00')) + Decimal('-1.00') + >>> ExtendedContext.copy_decimal(1) + Decimal('1') + """ + a = _convert_other(a, raiseit=True) + return Decimal(a) + + def copy_negate(self, a): + """Returns a copy of the operand with the sign inverted. + + >>> ExtendedContext.copy_negate(Decimal('101.5')) + Decimal('-101.5') + >>> ExtendedContext.copy_negate(Decimal('-101.5')) + Decimal('101.5') + >>> ExtendedContext.copy_negate(1) + Decimal('-1') + """ + a = _convert_other(a, raiseit=True) + return a.copy_negate() + + def copy_sign(self, a, b): + """Copies the second operand's sign to the first one. + + In detail, it returns a copy of the first operand with the sign + equal to the sign of the second operand. + + >>> ExtendedContext.copy_sign(Decimal( '1.50'), Decimal('7.33')) + Decimal('1.50') + >>> ExtendedContext.copy_sign(Decimal('-1.50'), Decimal('7.33')) + Decimal('1.50') + >>> ExtendedContext.copy_sign(Decimal( '1.50'), Decimal('-7.33')) + Decimal('-1.50') + >>> ExtendedContext.copy_sign(Decimal('-1.50'), Decimal('-7.33')) + Decimal('-1.50') + >>> ExtendedContext.copy_sign(1, -2) + Decimal('-1') + >>> ExtendedContext.copy_sign(Decimal(1), -2) + Decimal('-1') + >>> ExtendedContext.copy_sign(1, Decimal(-2)) + Decimal('-1') + """ + a = _convert_other(a, raiseit=True) + return a.copy_sign(b) + + def divide(self, a, b): + """Decimal division in a specified context. + + >>> ExtendedContext.divide(Decimal('1'), Decimal('3')) + Decimal('0.333333333') + >>> ExtendedContext.divide(Decimal('2'), Decimal('3')) + Decimal('0.666666667') + >>> ExtendedContext.divide(Decimal('5'), Decimal('2')) + Decimal('2.5') + >>> ExtendedContext.divide(Decimal('1'), Decimal('10')) + Decimal('0.1') + >>> ExtendedContext.divide(Decimal('12'), Decimal('12')) + Decimal('1') + >>> ExtendedContext.divide(Decimal('8.00'), Decimal('2')) + Decimal('4.00') + >>> ExtendedContext.divide(Decimal('2.400'), Decimal('2.0')) + Decimal('1.20') + >>> ExtendedContext.divide(Decimal('1000'), Decimal('100')) + Decimal('10') + >>> ExtendedContext.divide(Decimal('1000'), Decimal('1')) + Decimal('1000') + >>> ExtendedContext.divide(Decimal('2.40E+6'), Decimal('2')) + Decimal('1.20E+6') + >>> ExtendedContext.divide(5, 5) + Decimal('1') + >>> ExtendedContext.divide(Decimal(5), 5) + Decimal('1') + >>> ExtendedContext.divide(5, Decimal(5)) + Decimal('1') + """ + a = _convert_other(a, raiseit=True) + r = a.__truediv__(b, context=self) + if r is NotImplemented: + raise TypeError("Unable to convert %s to Decimal" % b) + else: + return r + + def divide_int(self, a, b): + """Divides two numbers and returns the integer part of the result. + + >>> ExtendedContext.divide_int(Decimal('2'), Decimal('3')) + Decimal('0') + >>> ExtendedContext.divide_int(Decimal('10'), Decimal('3')) + Decimal('3') + >>> ExtendedContext.divide_int(Decimal('1'), Decimal('0.3')) + Decimal('3') + >>> ExtendedContext.divide_int(10, 3) + Decimal('3') + >>> ExtendedContext.divide_int(Decimal(10), 3) + Decimal('3') + >>> ExtendedContext.divide_int(10, Decimal(3)) + Decimal('3') + """ + a = _convert_other(a, raiseit=True) + r = a.__floordiv__(b, context=self) + if r is NotImplemented: + raise TypeError("Unable to convert %s to Decimal" % b) + else: + return r + + def divmod(self, a, b): + """Return (a // b, a % b). + + >>> ExtendedContext.divmod(Decimal(8), Decimal(3)) + (Decimal('2'), Decimal('2')) + >>> ExtendedContext.divmod(Decimal(8), Decimal(4)) + (Decimal('2'), Decimal('0')) + >>> ExtendedContext.divmod(8, 4) + (Decimal('2'), Decimal('0')) + >>> ExtendedContext.divmod(Decimal(8), 4) + (Decimal('2'), Decimal('0')) + >>> ExtendedContext.divmod(8, Decimal(4)) + (Decimal('2'), Decimal('0')) + """ + a = _convert_other(a, raiseit=True) + r = a.__divmod__(b, context=self) + if r is NotImplemented: + raise TypeError("Unable to convert %s to Decimal" % b) + else: + return r + + def exp(self, a): + """Returns e ** a. + + >>> c = ExtendedContext.copy() + >>> c.Emin = -999 + >>> c.Emax = 999 + >>> c.exp(Decimal('-Infinity')) + Decimal('0') + >>> c.exp(Decimal('-1')) + Decimal('0.367879441') + >>> c.exp(Decimal('0')) + Decimal('1') + >>> c.exp(Decimal('1')) + Decimal('2.71828183') + >>> c.exp(Decimal('0.693147181')) + Decimal('2.00000000') + >>> c.exp(Decimal('+Infinity')) + Decimal('Infinity') + >>> c.exp(10) + Decimal('22026.4658') + """ + a =_convert_other(a, raiseit=True) + return a.exp(context=self) + + def fma(self, a, b, c): + """Returns a multiplied by b, plus c. + + The first two operands are multiplied together, using multiply, + the third operand is then added to the result of that + multiplication, using add, all with only one final rounding. + + >>> ExtendedContext.fma(Decimal('3'), Decimal('5'), Decimal('7')) + Decimal('22') + >>> ExtendedContext.fma(Decimal('3'), Decimal('-5'), Decimal('7')) + Decimal('-8') + >>> ExtendedContext.fma(Decimal('888565290'), Decimal('1557.96930'), Decimal('-86087.7578')) + Decimal('1.38435736E+12') + >>> ExtendedContext.fma(1, 3, 4) + Decimal('7') + >>> ExtendedContext.fma(1, Decimal(3), 4) + Decimal('7') + >>> ExtendedContext.fma(1, 3, Decimal(4)) + Decimal('7') + """ + a = _convert_other(a, raiseit=True) + return a.fma(b, c, context=self) + + def is_canonical(self, a): + """Return True if the operand is canonical; otherwise return False. + + Currently, the encoding of a Decimal instance is always + canonical, so this method returns True for any Decimal. + + >>> ExtendedContext.is_canonical(Decimal('2.50')) + True + """ + if not isinstance(a, Decimal): + raise TypeError("is_canonical requires a Decimal as an argument.") + return a.is_canonical() + + def is_finite(self, a): + """Return True if the operand is finite; otherwise return False. + + A Decimal instance is considered finite if it is neither + infinite nor a NaN. + + >>> ExtendedContext.is_finite(Decimal('2.50')) + True + >>> ExtendedContext.is_finite(Decimal('-0.3')) + True + >>> ExtendedContext.is_finite(Decimal('0')) + True + >>> ExtendedContext.is_finite(Decimal('Inf')) + False + >>> ExtendedContext.is_finite(Decimal('NaN')) + False + >>> ExtendedContext.is_finite(1) + True + """ + a = _convert_other(a, raiseit=True) + return a.is_finite() + + def is_infinite(self, a): + """Return True if the operand is infinite; otherwise return False. + + >>> ExtendedContext.is_infinite(Decimal('2.50')) + False + >>> ExtendedContext.is_infinite(Decimal('-Inf')) + True + >>> ExtendedContext.is_infinite(Decimal('NaN')) + False + >>> ExtendedContext.is_infinite(1) + False + """ + a = _convert_other(a, raiseit=True) + return a.is_infinite() + + def is_nan(self, a): + """Return True if the operand is a qNaN or sNaN; + otherwise return False. + + >>> ExtendedContext.is_nan(Decimal('2.50')) + False + >>> ExtendedContext.is_nan(Decimal('NaN')) + True + >>> ExtendedContext.is_nan(Decimal('-sNaN')) + True + >>> ExtendedContext.is_nan(1) + False + """ + a = _convert_other(a, raiseit=True) + return a.is_nan() + + def is_normal(self, a): + """Return True if the operand is a normal number; + otherwise return False. + + >>> c = ExtendedContext.copy() + >>> c.Emin = -999 + >>> c.Emax = 999 + >>> c.is_normal(Decimal('2.50')) + True + >>> c.is_normal(Decimal('0.1E-999')) + False + >>> c.is_normal(Decimal('0.00')) + False + >>> c.is_normal(Decimal('-Inf')) + False + >>> c.is_normal(Decimal('NaN')) + False + >>> c.is_normal(1) + True + """ + a = _convert_other(a, raiseit=True) + return a.is_normal(context=self) + + def is_qnan(self, a): + """Return True if the operand is a quiet NaN; otherwise return False. + + >>> ExtendedContext.is_qnan(Decimal('2.50')) + False + >>> ExtendedContext.is_qnan(Decimal('NaN')) + True + >>> ExtendedContext.is_qnan(Decimal('sNaN')) + False + >>> ExtendedContext.is_qnan(1) + False + """ + a = _convert_other(a, raiseit=True) + return a.is_qnan() + + def is_signed(self, a): + """Return True if the operand is negative; otherwise return False. + + >>> ExtendedContext.is_signed(Decimal('2.50')) + False + >>> ExtendedContext.is_signed(Decimal('-12')) + True + >>> ExtendedContext.is_signed(Decimal('-0')) + True + >>> ExtendedContext.is_signed(8) + False + >>> ExtendedContext.is_signed(-8) + True + """ + a = _convert_other(a, raiseit=True) + return a.is_signed() + + def is_snan(self, a): + """Return True if the operand is a signaling NaN; + otherwise return False. + + >>> ExtendedContext.is_snan(Decimal('2.50')) + False + >>> ExtendedContext.is_snan(Decimal('NaN')) + False + >>> ExtendedContext.is_snan(Decimal('sNaN')) + True + >>> ExtendedContext.is_snan(1) + False + """ + a = _convert_other(a, raiseit=True) + return a.is_snan() + + def is_subnormal(self, a): + """Return True if the operand is subnormal; otherwise return False. + + >>> c = ExtendedContext.copy() + >>> c.Emin = -999 + >>> c.Emax = 999 + >>> c.is_subnormal(Decimal('2.50')) + False + >>> c.is_subnormal(Decimal('0.1E-999')) + True + >>> c.is_subnormal(Decimal('0.00')) + False + >>> c.is_subnormal(Decimal('-Inf')) + False + >>> c.is_subnormal(Decimal('NaN')) + False + >>> c.is_subnormal(1) + False + """ + a = _convert_other(a, raiseit=True) + return a.is_subnormal(context=self) + + def is_zero(self, a): + """Return True if the operand is a zero; otherwise return False. + + >>> ExtendedContext.is_zero(Decimal('0')) + True + >>> ExtendedContext.is_zero(Decimal('2.50')) + False + >>> ExtendedContext.is_zero(Decimal('-0E+2')) + True + >>> ExtendedContext.is_zero(1) + False + >>> ExtendedContext.is_zero(0) + True + """ + a = _convert_other(a, raiseit=True) + return a.is_zero() + + def ln(self, a): + """Returns the natural (base e) logarithm of the operand. + + >>> c = ExtendedContext.copy() + >>> c.Emin = -999 + >>> c.Emax = 999 + >>> c.ln(Decimal('0')) + Decimal('-Infinity') + >>> c.ln(Decimal('1.000')) + Decimal('0') + >>> c.ln(Decimal('2.71828183')) + Decimal('1.00000000') + >>> c.ln(Decimal('10')) + Decimal('2.30258509') + >>> c.ln(Decimal('+Infinity')) + Decimal('Infinity') + >>> c.ln(1) + Decimal('0') + """ + a = _convert_other(a, raiseit=True) + return a.ln(context=self) + + def log10(self, a): + """Returns the base 10 logarithm of the operand. + + >>> c = ExtendedContext.copy() + >>> c.Emin = -999 + >>> c.Emax = 999 + >>> c.log10(Decimal('0')) + Decimal('-Infinity') + >>> c.log10(Decimal('0.001')) + Decimal('-3') + >>> c.log10(Decimal('1.000')) + Decimal('0') + >>> c.log10(Decimal('2')) + Decimal('0.301029996') + >>> c.log10(Decimal('10')) + Decimal('1') + >>> c.log10(Decimal('70')) + Decimal('1.84509804') + >>> c.log10(Decimal('+Infinity')) + Decimal('Infinity') + >>> c.log10(0) + Decimal('-Infinity') + >>> c.log10(1) + Decimal('0') + """ + a = _convert_other(a, raiseit=True) + return a.log10(context=self) + + def logb(self, a): + """ Returns the exponent of the magnitude of the operand's MSD. + + The result is the integer which is the exponent of the magnitude + of the most significant digit of the operand (as though the + operand were truncated to a single digit while maintaining the + value of that digit and without limiting the resulting exponent). + + >>> ExtendedContext.logb(Decimal('250')) + Decimal('2') + >>> ExtendedContext.logb(Decimal('2.50')) + Decimal('0') + >>> ExtendedContext.logb(Decimal('0.03')) + Decimal('-2') + >>> ExtendedContext.logb(Decimal('0')) + Decimal('-Infinity') + >>> ExtendedContext.logb(1) + Decimal('0') + >>> ExtendedContext.logb(10) + Decimal('1') + >>> ExtendedContext.logb(100) + Decimal('2') + """ + a = _convert_other(a, raiseit=True) + return a.logb(context=self) + + def logical_and(self, a, b): + """Applies the logical operation 'and' between each operand's digits. + + The operands must be both logical numbers. + + >>> ExtendedContext.logical_and(Decimal('0'), Decimal('0')) + Decimal('0') + >>> ExtendedContext.logical_and(Decimal('0'), Decimal('1')) + Decimal('0') + >>> ExtendedContext.logical_and(Decimal('1'), Decimal('0')) + Decimal('0') + >>> ExtendedContext.logical_and(Decimal('1'), Decimal('1')) + Decimal('1') + >>> ExtendedContext.logical_and(Decimal('1100'), Decimal('1010')) + Decimal('1000') + >>> ExtendedContext.logical_and(Decimal('1111'), Decimal('10')) + Decimal('10') + >>> ExtendedContext.logical_and(110, 1101) + Decimal('100') + >>> ExtendedContext.logical_and(Decimal(110), 1101) + Decimal('100') + >>> ExtendedContext.logical_and(110, Decimal(1101)) + Decimal('100') + """ + a = _convert_other(a, raiseit=True) + return a.logical_and(b, context=self) + + def logical_invert(self, a): + """Invert all the digits in the operand. + + The operand must be a logical number. + + >>> ExtendedContext.logical_invert(Decimal('0')) + Decimal('111111111') + >>> ExtendedContext.logical_invert(Decimal('1')) + Decimal('111111110') + >>> ExtendedContext.logical_invert(Decimal('111111111')) + Decimal('0') + >>> ExtendedContext.logical_invert(Decimal('101010101')) + Decimal('10101010') + >>> ExtendedContext.logical_invert(1101) + Decimal('111110010') + """ + a = _convert_other(a, raiseit=True) + return a.logical_invert(context=self) + + def logical_or(self, a, b): + """Applies the logical operation 'or' between each operand's digits. + + The operands must be both logical numbers. + + >>> ExtendedContext.logical_or(Decimal('0'), Decimal('0')) + Decimal('0') + >>> ExtendedContext.logical_or(Decimal('0'), Decimal('1')) + Decimal('1') + >>> ExtendedContext.logical_or(Decimal('1'), Decimal('0')) + Decimal('1') + >>> ExtendedContext.logical_or(Decimal('1'), Decimal('1')) + Decimal('1') + >>> ExtendedContext.logical_or(Decimal('1100'), Decimal('1010')) + Decimal('1110') + >>> ExtendedContext.logical_or(Decimal('1110'), Decimal('10')) + Decimal('1110') + >>> ExtendedContext.logical_or(110, 1101) + Decimal('1111') + >>> ExtendedContext.logical_or(Decimal(110), 1101) + Decimal('1111') + >>> ExtendedContext.logical_or(110, Decimal(1101)) + Decimal('1111') + """ + a = _convert_other(a, raiseit=True) + return a.logical_or(b, context=self) + + def logical_xor(self, a, b): + """Applies the logical operation 'xor' between each operand's digits. + + The operands must be both logical numbers. + + >>> ExtendedContext.logical_xor(Decimal('0'), Decimal('0')) + Decimal('0') + >>> ExtendedContext.logical_xor(Decimal('0'), Decimal('1')) + Decimal('1') + >>> ExtendedContext.logical_xor(Decimal('1'), Decimal('0')) + Decimal('1') + >>> ExtendedContext.logical_xor(Decimal('1'), Decimal('1')) + Decimal('0') + >>> ExtendedContext.logical_xor(Decimal('1100'), Decimal('1010')) + Decimal('110') + >>> ExtendedContext.logical_xor(Decimal('1111'), Decimal('10')) + Decimal('1101') + >>> ExtendedContext.logical_xor(110, 1101) + Decimal('1011') + >>> ExtendedContext.logical_xor(Decimal(110), 1101) + Decimal('1011') + >>> ExtendedContext.logical_xor(110, Decimal(1101)) + Decimal('1011') + """ + a = _convert_other(a, raiseit=True) + return a.logical_xor(b, context=self) + + def max(self, a, b): + """max compares two values numerically and returns the maximum. + + If either operand is a NaN then the general rules apply. + Otherwise, the operands are compared as though by the compare + operation. If they are numerically equal then the left-hand operand + is chosen as the result. Otherwise the maximum (closer to positive + infinity) of the two operands is chosen as the result. + + >>> ExtendedContext.max(Decimal('3'), Decimal('2')) + Decimal('3') + >>> ExtendedContext.max(Decimal('-10'), Decimal('3')) + Decimal('3') + >>> ExtendedContext.max(Decimal('1.0'), Decimal('1')) + Decimal('1') + >>> ExtendedContext.max(Decimal('7'), Decimal('NaN')) + Decimal('7') + >>> ExtendedContext.max(1, 2) + Decimal('2') + >>> ExtendedContext.max(Decimal(1), 2) + Decimal('2') + >>> ExtendedContext.max(1, Decimal(2)) + Decimal('2') + """ + a = _convert_other(a, raiseit=True) + return a.max(b, context=self) + + def max_mag(self, a, b): + """Compares the values numerically with their sign ignored. + + >>> ExtendedContext.max_mag(Decimal('7'), Decimal('NaN')) + Decimal('7') + >>> ExtendedContext.max_mag(Decimal('7'), Decimal('-10')) + Decimal('-10') + >>> ExtendedContext.max_mag(1, -2) + Decimal('-2') + >>> ExtendedContext.max_mag(Decimal(1), -2) + Decimal('-2') + >>> ExtendedContext.max_mag(1, Decimal(-2)) + Decimal('-2') + """ + a = _convert_other(a, raiseit=True) + return a.max_mag(b, context=self) + + def min(self, a, b): + """min compares two values numerically and returns the minimum. + + If either operand is a NaN then the general rules apply. + Otherwise, the operands are compared as though by the compare + operation. If they are numerically equal then the left-hand operand + is chosen as the result. Otherwise the minimum (closer to negative + infinity) of the two operands is chosen as the result. + + >>> ExtendedContext.min(Decimal('3'), Decimal('2')) + Decimal('2') + >>> ExtendedContext.min(Decimal('-10'), Decimal('3')) + Decimal('-10') + >>> ExtendedContext.min(Decimal('1.0'), Decimal('1')) + Decimal('1.0') + >>> ExtendedContext.min(Decimal('7'), Decimal('NaN')) + Decimal('7') + >>> ExtendedContext.min(1, 2) + Decimal('1') + >>> ExtendedContext.min(Decimal(1), 2) + Decimal('1') + >>> ExtendedContext.min(1, Decimal(29)) + Decimal('1') + """ + a = _convert_other(a, raiseit=True) + return a.min(b, context=self) + + def min_mag(self, a, b): + """Compares the values numerically with their sign ignored. + + >>> ExtendedContext.min_mag(Decimal('3'), Decimal('-2')) + Decimal('-2') + >>> ExtendedContext.min_mag(Decimal('-3'), Decimal('NaN')) + Decimal('-3') + >>> ExtendedContext.min_mag(1, -2) + Decimal('1') + >>> ExtendedContext.min_mag(Decimal(1), -2) + Decimal('1') + >>> ExtendedContext.min_mag(1, Decimal(-2)) + Decimal('1') + """ + a = _convert_other(a, raiseit=True) + return a.min_mag(b, context=self) + + def minus(self, a): + """Minus corresponds to unary prefix minus in Python. + + The operation is evaluated using the same rules as subtract; the + operation minus(a) is calculated as subtract('0', a) where the '0' + has the same exponent as the operand. + + >>> ExtendedContext.minus(Decimal('1.3')) + Decimal('-1.3') + >>> ExtendedContext.minus(Decimal('-1.3')) + Decimal('1.3') + >>> ExtendedContext.minus(1) + Decimal('-1') + """ + a = _convert_other(a, raiseit=True) + return a.__neg__(context=self) + + def multiply(self, a, b): + """multiply multiplies two operands. + + If either operand is a special value then the general rules apply. + Otherwise, the operands are multiplied together + ('long multiplication'), resulting in a number which may be as long as + the sum of the lengths of the two operands. + + >>> ExtendedContext.multiply(Decimal('1.20'), Decimal('3')) + Decimal('3.60') + >>> ExtendedContext.multiply(Decimal('7'), Decimal('3')) + Decimal('21') + >>> ExtendedContext.multiply(Decimal('0.9'), Decimal('0.8')) + Decimal('0.72') + >>> ExtendedContext.multiply(Decimal('0.9'), Decimal('-0')) + Decimal('-0.0') + >>> ExtendedContext.multiply(Decimal('654321'), Decimal('654321')) + Decimal('4.28135971E+11') + >>> ExtendedContext.multiply(7, 7) + Decimal('49') + >>> ExtendedContext.multiply(Decimal(7), 7) + Decimal('49') + >>> ExtendedContext.multiply(7, Decimal(7)) + Decimal('49') + """ + a = _convert_other(a, raiseit=True) + r = a.__mul__(b, context=self) + if r is NotImplemented: + raise TypeError("Unable to convert %s to Decimal" % b) + else: + return r + + def next_minus(self, a): + """Returns the largest representable number smaller than a. + + >>> c = ExtendedContext.copy() + >>> c.Emin = -999 + >>> c.Emax = 999 + >>> ExtendedContext.next_minus(Decimal('1')) + Decimal('0.999999999') + >>> c.next_minus(Decimal('1E-1007')) + Decimal('0E-1007') + >>> ExtendedContext.next_minus(Decimal('-1.00000003')) + Decimal('-1.00000004') + >>> c.next_minus(Decimal('Infinity')) + Decimal('9.99999999E+999') + >>> c.next_minus(1) + Decimal('0.999999999') + """ + a = _convert_other(a, raiseit=True) + return a.next_minus(context=self) + + def next_plus(self, a): + """Returns the smallest representable number larger than a. + + >>> c = ExtendedContext.copy() + >>> c.Emin = -999 + >>> c.Emax = 999 + >>> ExtendedContext.next_plus(Decimal('1')) + Decimal('1.00000001') + >>> c.next_plus(Decimal('-1E-1007')) + Decimal('-0E-1007') + >>> ExtendedContext.next_plus(Decimal('-1.00000003')) + Decimal('-1.00000002') + >>> c.next_plus(Decimal('-Infinity')) + Decimal('-9.99999999E+999') + >>> c.next_plus(1) + Decimal('1.00000001') + """ + a = _convert_other(a, raiseit=True) + return a.next_plus(context=self) + + def next_toward(self, a, b): + """Returns the number closest to a, in direction towards b. + + The result is the closest representable number from the first + operand (but not the first operand) that is in the direction + towards the second operand, unless the operands have the same + value. + + >>> c = ExtendedContext.copy() + >>> c.Emin = -999 + >>> c.Emax = 999 + >>> c.next_toward(Decimal('1'), Decimal('2')) + Decimal('1.00000001') + >>> c.next_toward(Decimal('-1E-1007'), Decimal('1')) + Decimal('-0E-1007') + >>> c.next_toward(Decimal('-1.00000003'), Decimal('0')) + Decimal('-1.00000002') + >>> c.next_toward(Decimal('1'), Decimal('0')) + Decimal('0.999999999') + >>> c.next_toward(Decimal('1E-1007'), Decimal('-100')) + Decimal('0E-1007') + >>> c.next_toward(Decimal('-1.00000003'), Decimal('-10')) + Decimal('-1.00000004') + >>> c.next_toward(Decimal('0.00'), Decimal('-0.0000')) + Decimal('-0.00') + >>> c.next_toward(0, 1) + Decimal('1E-1007') + >>> c.next_toward(Decimal(0), 1) + Decimal('1E-1007') + >>> c.next_toward(0, Decimal(1)) + Decimal('1E-1007') + """ + a = _convert_other(a, raiseit=True) + return a.next_toward(b, context=self) + + def normalize(self, a): + """normalize reduces an operand to its simplest form. + + Essentially a plus operation with all trailing zeros removed from the + result. + + >>> ExtendedContext.normalize(Decimal('2.1')) + Decimal('2.1') + >>> ExtendedContext.normalize(Decimal('-2.0')) + Decimal('-2') + >>> ExtendedContext.normalize(Decimal('1.200')) + Decimal('1.2') + >>> ExtendedContext.normalize(Decimal('-120')) + Decimal('-1.2E+2') + >>> ExtendedContext.normalize(Decimal('120.00')) + Decimal('1.2E+2') + >>> ExtendedContext.normalize(Decimal('0.00')) + Decimal('0') + >>> ExtendedContext.normalize(6) + Decimal('6') + """ + a = _convert_other(a, raiseit=True) + return a.normalize(context=self) + + def number_class(self, a): + """Returns an indication of the class of the operand. + + The class is one of the following strings: + -sNaN + -NaN + -Infinity + -Normal + -Subnormal + -Zero + +Zero + +Subnormal + +Normal + +Infinity + + >>> c = ExtendedContext.copy() + >>> c.Emin = -999 + >>> c.Emax = 999 + >>> c.number_class(Decimal('Infinity')) + '+Infinity' + >>> c.number_class(Decimal('1E-10')) + '+Normal' + >>> c.number_class(Decimal('2.50')) + '+Normal' + >>> c.number_class(Decimal('0.1E-999')) + '+Subnormal' + >>> c.number_class(Decimal('0')) + '+Zero' + >>> c.number_class(Decimal('-0')) + '-Zero' + >>> c.number_class(Decimal('-0.1E-999')) + '-Subnormal' + >>> c.number_class(Decimal('-1E-10')) + '-Normal' + >>> c.number_class(Decimal('-2.50')) + '-Normal' + >>> c.number_class(Decimal('-Infinity')) + '-Infinity' + >>> c.number_class(Decimal('NaN')) + 'NaN' + >>> c.number_class(Decimal('-NaN')) + 'NaN' + >>> c.number_class(Decimal('sNaN')) + 'sNaN' + >>> c.number_class(123) + '+Normal' + """ + a = _convert_other(a, raiseit=True) + return a.number_class(context=self) + + def plus(self, a): + """Plus corresponds to unary prefix plus in Python. + + The operation is evaluated using the same rules as add; the + operation plus(a) is calculated as add('0', a) where the '0' + has the same exponent as the operand. + + >>> ExtendedContext.plus(Decimal('1.3')) + Decimal('1.3') + >>> ExtendedContext.plus(Decimal('-1.3')) + Decimal('-1.3') + >>> ExtendedContext.plus(-1) + Decimal('-1') + """ + a = _convert_other(a, raiseit=True) + return a.__pos__(context=self) + + def power(self, a, b, modulo=None): + """Raises a to the power of b, to modulo if given. + + With two arguments, compute a**b. If a is negative then b + must be integral. The result will be inexact unless b is + integral and the result is finite and can be expressed exactly + in 'precision' digits. + + With three arguments, compute (a**b) % modulo. For the + three argument form, the following restrictions on the + arguments hold: + + - all three arguments must be integral + - b must be nonnegative + - at least one of a or b must be nonzero + - modulo must be nonzero and have at most 'precision' digits + + The result of pow(a, b, modulo) is identical to the result + that would be obtained by computing (a**b) % modulo with + unbounded precision, but is computed more efficiently. It is + always exact. + + >>> c = ExtendedContext.copy() + >>> c.Emin = -999 + >>> c.Emax = 999 + >>> c.power(Decimal('2'), Decimal('3')) + Decimal('8') + >>> c.power(Decimal('-2'), Decimal('3')) + Decimal('-8') + >>> c.power(Decimal('2'), Decimal('-3')) + Decimal('0.125') + >>> c.power(Decimal('1.7'), Decimal('8')) + Decimal('69.7575744') + >>> c.power(Decimal('10'), Decimal('0.301029996')) + Decimal('2.00000000') + >>> c.power(Decimal('Infinity'), Decimal('-1')) + Decimal('0') + >>> c.power(Decimal('Infinity'), Decimal('0')) + Decimal('1') + >>> c.power(Decimal('Infinity'), Decimal('1')) + Decimal('Infinity') + >>> c.power(Decimal('-Infinity'), Decimal('-1')) + Decimal('-0') + >>> c.power(Decimal('-Infinity'), Decimal('0')) + Decimal('1') + >>> c.power(Decimal('-Infinity'), Decimal('1')) + Decimal('-Infinity') + >>> c.power(Decimal('-Infinity'), Decimal('2')) + Decimal('Infinity') + >>> c.power(Decimal('0'), Decimal('0')) + Decimal('NaN') + + >>> c.power(Decimal('3'), Decimal('7'), Decimal('16')) + Decimal('11') + >>> c.power(Decimal('-3'), Decimal('7'), Decimal('16')) + Decimal('-11') + >>> c.power(Decimal('-3'), Decimal('8'), Decimal('16')) + Decimal('1') + >>> c.power(Decimal('3'), Decimal('7'), Decimal('-16')) + Decimal('11') + >>> c.power(Decimal('23E12345'), Decimal('67E189'), Decimal('123456789')) + Decimal('11729830') + >>> c.power(Decimal('-0'), Decimal('17'), Decimal('1729')) + Decimal('-0') + >>> c.power(Decimal('-23'), Decimal('0'), Decimal('65537')) + Decimal('1') + >>> ExtendedContext.power(7, 7) + Decimal('823543') + >>> ExtendedContext.power(Decimal(7), 7) + Decimal('823543') + >>> ExtendedContext.power(7, Decimal(7), 2) + Decimal('1') + """ + a = _convert_other(a, raiseit=True) + r = a.__pow__(b, modulo, context=self) + if r is NotImplemented: + raise TypeError("Unable to convert %s to Decimal" % b) + else: + return r + + def quantize(self, a, b): + """Returns a value equal to 'a' (rounded), having the exponent of 'b'. + + The coefficient of the result is derived from that of the left-hand + operand. It may be rounded using the current rounding setting (if the + exponent is being increased), multiplied by a positive power of ten (if + the exponent is being decreased), or is unchanged (if the exponent is + already equal to that of the right-hand operand). + + Unlike other operations, if the length of the coefficient after the + quantize operation would be greater than precision then an Invalid + operation condition is raised. This guarantees that, unless there is + an error condition, the exponent of the result of a quantize is always + equal to that of the right-hand operand. + + Also unlike other operations, quantize will never raise Underflow, even + if the result is subnormal and inexact. + + >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.001')) + Decimal('2.170') + >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.01')) + Decimal('2.17') + >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.1')) + Decimal('2.2') + >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+0')) + Decimal('2') + >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+1')) + Decimal('0E+1') + >>> ExtendedContext.quantize(Decimal('-Inf'), Decimal('Infinity')) + Decimal('-Infinity') + >>> ExtendedContext.quantize(Decimal('2'), Decimal('Infinity')) + Decimal('NaN') + >>> ExtendedContext.quantize(Decimal('-0.1'), Decimal('1')) + Decimal('-0') + >>> ExtendedContext.quantize(Decimal('-0'), Decimal('1e+5')) + Decimal('-0E+5') + >>> ExtendedContext.quantize(Decimal('+35236450.6'), Decimal('1e-2')) + Decimal('NaN') + >>> ExtendedContext.quantize(Decimal('-35236450.6'), Decimal('1e-2')) + Decimal('NaN') + >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-1')) + Decimal('217.0') + >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-0')) + Decimal('217') + >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+1')) + Decimal('2.2E+2') + >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+2')) + Decimal('2E+2') + >>> ExtendedContext.quantize(1, 2) + Decimal('1') + >>> ExtendedContext.quantize(Decimal(1), 2) + Decimal('1') + >>> ExtendedContext.quantize(1, Decimal(2)) + Decimal('1') + """ + a = _convert_other(a, raiseit=True) + return a.quantize(b, context=self) + + def radix(self): + """Just returns 10, as this is Decimal, :) + + >>> ExtendedContext.radix() + Decimal('10') + """ + return Decimal(10) + + def remainder(self, a, b): + """Returns the remainder from integer division. + + The result is the residue of the dividend after the operation of + calculating integer division as described for divide-integer, rounded + to precision digits if necessary. The sign of the result, if + non-zero, is the same as that of the original dividend. + + This operation will fail under the same conditions as integer division + (that is, if integer division on the same two operands would fail, the + remainder cannot be calculated). + + >>> ExtendedContext.remainder(Decimal('2.1'), Decimal('3')) + Decimal('2.1') + >>> ExtendedContext.remainder(Decimal('10'), Decimal('3')) + Decimal('1') + >>> ExtendedContext.remainder(Decimal('-10'), Decimal('3')) + Decimal('-1') + >>> ExtendedContext.remainder(Decimal('10.2'), Decimal('1')) + Decimal('0.2') + >>> ExtendedContext.remainder(Decimal('10'), Decimal('0.3')) + Decimal('0.1') + >>> ExtendedContext.remainder(Decimal('3.6'), Decimal('1.3')) + Decimal('1.0') + >>> ExtendedContext.remainder(22, 6) + Decimal('4') + >>> ExtendedContext.remainder(Decimal(22), 6) + Decimal('4') + >>> ExtendedContext.remainder(22, Decimal(6)) + Decimal('4') + """ + a = _convert_other(a, raiseit=True) + r = a.__mod__(b, context=self) + if r is NotImplemented: + raise TypeError("Unable to convert %s to Decimal" % b) + else: + return r + + def remainder_near(self, a, b): + """Returns to be "a - b * n", where n is the integer nearest the exact + value of "x / b" (if two integers are equally near then the even one + is chosen). If the result is equal to 0 then its sign will be the + sign of a. + + This operation will fail under the same conditions as integer division + (that is, if integer division on the same two operands would fail, the + remainder cannot be calculated). + + >>> ExtendedContext.remainder_near(Decimal('2.1'), Decimal('3')) + Decimal('-0.9') + >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('6')) + Decimal('-2') + >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('3')) + Decimal('1') + >>> ExtendedContext.remainder_near(Decimal('-10'), Decimal('3')) + Decimal('-1') + >>> ExtendedContext.remainder_near(Decimal('10.2'), Decimal('1')) + Decimal('0.2') + >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('0.3')) + Decimal('0.1') + >>> ExtendedContext.remainder_near(Decimal('3.6'), Decimal('1.3')) + Decimal('-0.3') + >>> ExtendedContext.remainder_near(3, 11) + Decimal('3') + >>> ExtendedContext.remainder_near(Decimal(3), 11) + Decimal('3') + >>> ExtendedContext.remainder_near(3, Decimal(11)) + Decimal('3') + """ + a = _convert_other(a, raiseit=True) + return a.remainder_near(b, context=self) + + def rotate(self, a, b): + """Returns a rotated copy of a, b times. + + The coefficient of the result is a rotated copy of the digits in + the coefficient of the first operand. The number of places of + rotation is taken from the absolute value of the second operand, + with the rotation being to the left if the second operand is + positive or to the right otherwise. + + >>> ExtendedContext.rotate(Decimal('34'), Decimal('8')) + Decimal('400000003') + >>> ExtendedContext.rotate(Decimal('12'), Decimal('9')) + Decimal('12') + >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('-2')) + Decimal('891234567') + >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('0')) + Decimal('123456789') + >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('+2')) + Decimal('345678912') + >>> ExtendedContext.rotate(1333333, 1) + Decimal('13333330') + >>> ExtendedContext.rotate(Decimal(1333333), 1) + Decimal('13333330') + >>> ExtendedContext.rotate(1333333, Decimal(1)) + Decimal('13333330') + """ + a = _convert_other(a, raiseit=True) + return a.rotate(b, context=self) + + def same_quantum(self, a, b): + """Returns True if the two operands have the same exponent. + + The result is never affected by either the sign or the coefficient of + either operand. + + >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.001')) + False + >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.01')) + True + >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('1')) + False + >>> ExtendedContext.same_quantum(Decimal('Inf'), Decimal('-Inf')) + True + >>> ExtendedContext.same_quantum(10000, -1) + True + >>> ExtendedContext.same_quantum(Decimal(10000), -1) + True + >>> ExtendedContext.same_quantum(10000, Decimal(-1)) + True + """ + a = _convert_other(a, raiseit=True) + return a.same_quantum(b) + + def scaleb (self, a, b): + """Returns the first operand after adding the second value its exp. + + >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('-2')) + Decimal('0.0750') + >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('0')) + Decimal('7.50') + >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('3')) + Decimal('7.50E+3') + >>> ExtendedContext.scaleb(1, 4) + Decimal('1E+4') + >>> ExtendedContext.scaleb(Decimal(1), 4) + Decimal('1E+4') + >>> ExtendedContext.scaleb(1, Decimal(4)) + Decimal('1E+4') + """ + a = _convert_other(a, raiseit=True) + return a.scaleb(b, context=self) + + def shift(self, a, b): + """Returns a shifted copy of a, b times. + + The coefficient of the result is a shifted copy of the digits + in the coefficient of the first operand. The number of places + to shift is taken from the absolute value of the second operand, + with the shift being to the left if the second operand is + positive or to the right otherwise. Digits shifted into the + coefficient are zeros. + + >>> ExtendedContext.shift(Decimal('34'), Decimal('8')) + Decimal('400000000') + >>> ExtendedContext.shift(Decimal('12'), Decimal('9')) + Decimal('0') + >>> ExtendedContext.shift(Decimal('123456789'), Decimal('-2')) + Decimal('1234567') + >>> ExtendedContext.shift(Decimal('123456789'), Decimal('0')) + Decimal('123456789') + >>> ExtendedContext.shift(Decimal('123456789'), Decimal('+2')) + Decimal('345678900') + >>> ExtendedContext.shift(88888888, 2) + Decimal('888888800') + >>> ExtendedContext.shift(Decimal(88888888), 2) + Decimal('888888800') + >>> ExtendedContext.shift(88888888, Decimal(2)) + Decimal('888888800') + """ + a = _convert_other(a, raiseit=True) + return a.shift(b, context=self) + + def sqrt(self, a): + """Square root of a non-negative number to context precision. + + If the result must be inexact, it is rounded using the round-half-even + algorithm. + + >>> ExtendedContext.sqrt(Decimal('0')) + Decimal('0') + >>> ExtendedContext.sqrt(Decimal('-0')) + Decimal('-0') + >>> ExtendedContext.sqrt(Decimal('0.39')) + Decimal('0.624499800') + >>> ExtendedContext.sqrt(Decimal('100')) + Decimal('10') + >>> ExtendedContext.sqrt(Decimal('1')) + Decimal('1') + >>> ExtendedContext.sqrt(Decimal('1.0')) + Decimal('1.0') + >>> ExtendedContext.sqrt(Decimal('1.00')) + Decimal('1.0') + >>> ExtendedContext.sqrt(Decimal('7')) + Decimal('2.64575131') + >>> ExtendedContext.sqrt(Decimal('10')) + Decimal('3.16227766') + >>> ExtendedContext.sqrt(2) + Decimal('1.41421356') + >>> ExtendedContext.prec + 9 + """ + a = _convert_other(a, raiseit=True) + return a.sqrt(context=self) + + def subtract(self, a, b): + """Return the difference between the two operands. + + >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.07')) + Decimal('0.23') + >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.30')) + Decimal('0.00') + >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('2.07')) + Decimal('-0.77') + >>> ExtendedContext.subtract(8, 5) + Decimal('3') + >>> ExtendedContext.subtract(Decimal(8), 5) + Decimal('3') + >>> ExtendedContext.subtract(8, Decimal(5)) + Decimal('3') + """ + a = _convert_other(a, raiseit=True) + r = a.__sub__(b, context=self) + if r is NotImplemented: + raise TypeError("Unable to convert %s to Decimal" % b) + else: + return r + + def to_eng_string(self, a): + """Convert to a string, using engineering notation if an exponent is needed. + + Engineering notation has an exponent which is a multiple of 3. This + can leave up to 3 digits to the left of the decimal place and may + require the addition of either one or two trailing zeros. + + The operation is not affected by the context. + + >>> ExtendedContext.to_eng_string(Decimal('123E+1')) + '1.23E+3' + >>> ExtendedContext.to_eng_string(Decimal('123E+3')) + '123E+3' + >>> ExtendedContext.to_eng_string(Decimal('123E-10')) + '12.3E-9' + >>> ExtendedContext.to_eng_string(Decimal('-123E-12')) + '-123E-12' + >>> ExtendedContext.to_eng_string(Decimal('7E-7')) + '700E-9' + >>> ExtendedContext.to_eng_string(Decimal('7E+1')) + '70' + >>> ExtendedContext.to_eng_string(Decimal('0E+1')) + '0.00E+3' + + """ + a = _convert_other(a, raiseit=True) + return a.to_eng_string(context=self) + + def to_sci_string(self, a): + """Converts a number to a string, using scientific notation. + + The operation is not affected by the context. + """ + a = _convert_other(a, raiseit=True) + return a.__str__(context=self) + + def to_integral_exact(self, a): + """Rounds to an integer. + + When the operand has a negative exponent, the result is the same + as using the quantize() operation using the given operand as the + left-hand-operand, 1E+0 as the right-hand-operand, and the precision + of the operand as the precision setting; Inexact and Rounded flags + are allowed in this operation. The rounding mode is taken from the + context. + + >>> ExtendedContext.to_integral_exact(Decimal('2.1')) + Decimal('2') + >>> ExtendedContext.to_integral_exact(Decimal('100')) + Decimal('100') + >>> ExtendedContext.to_integral_exact(Decimal('100.0')) + Decimal('100') + >>> ExtendedContext.to_integral_exact(Decimal('101.5')) + Decimal('102') + >>> ExtendedContext.to_integral_exact(Decimal('-101.5')) + Decimal('-102') + >>> ExtendedContext.to_integral_exact(Decimal('10E+5')) + Decimal('1.0E+6') + >>> ExtendedContext.to_integral_exact(Decimal('7.89E+77')) + Decimal('7.89E+77') + >>> ExtendedContext.to_integral_exact(Decimal('-Inf')) + Decimal('-Infinity') + """ + a = _convert_other(a, raiseit=True) + return a.to_integral_exact(context=self) + + def to_integral_value(self, a): + """Rounds to an integer. + + When the operand has a negative exponent, the result is the same + as using the quantize() operation using the given operand as the + left-hand-operand, 1E+0 as the right-hand-operand, and the precision + of the operand as the precision setting, except that no flags will + be set. The rounding mode is taken from the context. + + >>> ExtendedContext.to_integral_value(Decimal('2.1')) + Decimal('2') + >>> ExtendedContext.to_integral_value(Decimal('100')) + Decimal('100') + >>> ExtendedContext.to_integral_value(Decimal('100.0')) + Decimal('100') + >>> ExtendedContext.to_integral_value(Decimal('101.5')) + Decimal('102') + >>> ExtendedContext.to_integral_value(Decimal('-101.5')) + Decimal('-102') + >>> ExtendedContext.to_integral_value(Decimal('10E+5')) + Decimal('1.0E+6') + >>> ExtendedContext.to_integral_value(Decimal('7.89E+77')) + Decimal('7.89E+77') + >>> ExtendedContext.to_integral_value(Decimal('-Inf')) + Decimal('-Infinity') + """ + a = _convert_other(a, raiseit=True) + return a.to_integral_value(context=self) + + # the method name changed, but we provide also the old one, for compatibility + to_integral = to_integral_value + +class _WorkRep(object): + __slots__ = ('sign','int','exp') + # sign: 0 or 1 + # int: int + # exp: None, int, or string + + def __init__(self, value=None): + if value is None: + self.sign = None + self.int = 0 + self.exp = None + elif isinstance(value, Decimal): + self.sign = value._sign + self.int = int(value._int) + self.exp = value._exp + else: + # assert isinstance(value, tuple) + self.sign = value[0] + self.int = value[1] + self.exp = value[2] + + def __repr__(self): + return "(%r, %r, %r)" % (self.sign, self.int, self.exp) + + __str__ = __repr__ + + + +def _normalize(op1, op2, prec = 0): + """Normalizes op1, op2 to have the same exp and length of coefficient. + + Done during addition. + """ + if op1.exp < op2.exp: + tmp = op2 + other = op1 + else: + tmp = op1 + other = op2 + + # Let exp = min(tmp.exp - 1, tmp.adjusted() - precision - 1). + # Then adding 10**exp to tmp has the same effect (after rounding) + # as adding any positive quantity smaller than 10**exp; similarly + # for subtraction. So if other is smaller than 10**exp we replace + # it with 10**exp. This avoids tmp.exp - other.exp getting too large. + tmp_len = len(str(tmp.int)) + other_len = len(str(other.int)) + exp = tmp.exp + min(-1, tmp_len - prec - 2) + if other_len + other.exp - 1 < exp: + other.int = 1 + other.exp = exp + + tmp.int *= 10 ** (tmp.exp - other.exp) + tmp.exp = other.exp + return op1, op2 + + diff --git a/modules/language/python/module/python.scm b/modules/language/python/module/python.scm index 30434af..f433360 100644 --- a/modules/language/python/module/python.scm +++ b/modules/language/python/module/python.scm @@ -130,15 +130,74 @@ #t (is-a? (ref sub '__goops__) (ref cls '__goops__))))) -(define-method (isinstance x y) #f) +(define-method (isinstance x y) + (if (null? y) + #f + (if (pair? y) + (or (isinstance x (car y)) + (isinstance x (cdr y))) + (is-a? x y)))) + +(define-method (isinstance (i ) y) + (if (issubclass y int) + #t + (if (pair? y) + (or (isinstance i (car y)) + (isinstance i (cdr y))) + (is-a? i y)))) + +(define-method (isinstance (i ) y) + (if (issubclass y float) + #t + (if (pair? y) + (or (isinstance i (car y)) + (isinstance i (cdr y))) + (is-a? i y)))) + +(define-method (isinstance (i ) y) + (if (issubclass y tuple) + #t + (if (pair? y) + (or (isinstance i (car y)) + (isinstance i (cdr y))) + (is-a? i y)))) + +(define-method (isinstance (i ) y) + (if (issubclass y str) + #t + (if (pair? y) + (or (isinstance i (car y)) + (isinstance i (cdr y))) + (is-a? i y)))) + +(define-method (isinstance (i ) y) + (if (issubclass y bytes) + #t + (if (pair? y) + (or (isinstance i (car y)) + (isinstance i (cdr y))) + (is-a? i y)))) + + +(define-method (isinstance o (cl

)) + (cond + ((eq? cl py-list) + (is-a? o )) + (else #f))) + (define-method (isinstance (o

) (cl

)) - (aif it (ref cl '__instancecheck__) - (it o) - (if (pair? cl) - (or - (isinstance o (car cl)) - (isinstance o (cdr cl))) - (is-a? o (ref cl '__goops__))))) + (cond + ((ref cl '__instancecheck__) => + (lambda (it) + (it o))) + ((pair? cl) + (or + (isinstance o (car cl)) + (isinstance o (cdr cl)))) + (else + (is-a? o (ref cl '__goops__))))) + + (define iter (case-lambda @@ -181,7 +240,7 @@ (define (id x) (object-address x)) (define (input str) - (format #t str) + ((@ (guile) format) #t str) (readline)) (define (idx x) x) -- cgit v1.2.3