import "github.com/cockroachdb/apd"
Package apd implements arbitrary-precision decimals.
apd implements much of the decimal specification from the General Decimal Arithmetic () description, which is refered to here as GDA. This is the same specification implemented by pythons decimal module () and GCCs decimal extension.
Panic-free operation. The math/big types don’t return errors, and instead panic under some conditions that are documented. This requires users to validate the inputs before using them. Meanwhile, we’d like our decimal operations to have more failure modes and more input requirements than the math/big types, so using that API would be difficult. apd instead returns errors when needed.
Support for standard functions. sqrt, ln, pow, etc.
Accurate and configurable precision. Operations will use enough internal precision to produce a correct result at the requested precision. Precision is set by a "context" structure that accompanies the function arguments, as discussed in the next section.
Good performance. Operations will either be fast enough or will produce an error if they will be slow. This prevents edge-case operations from consuming lots of CPU or memory.
Condition flags and traps. All operations will report whether their result is exact, is rounded, is over- or under-flowed, is subnormal (), or is some other condition. apd supports traps which will trigger an error on any of these conditions. This makes it possible to guarantee exactness in computations, if needed.
SQL scan and value methods are implemented. This allows the use of Decimals as placeholder parameters and row result Scan destinations.
apd has two main types. The first is Decimal which holds the values of decimals. It is simple and uses a big.Int with an exponent to describe values. Most operations on Decimals can’t produce errors as they work directly on the underlying big.Int. Notably, however, there are no arithmetic operations on Decimals.
The second main type is Context, which is where all arithmetic operations are defined. A Context describes the precision, range, and some other restrictions during operations. These operations can all produce failures, and so return errors.
Context operations, in addition to errors, return a Condition, which is a bitfield of flags that occurred during an operation. These include overflow, underflow, inexact, rounded, and others. The Traps field of a Context can be set which will produce an error if the corresponding flag occurs. An example of this is given below.
condition.go const.go context.go decimal.go decomposer.go doc.go error.go form_string.go format.go loop.go round.go table.go
const ( // MaxExponent is the highest exponent supported. Exponents near this range will // perform very slowly (many seconds per operation). MaxExponent = 100000 // MinExponent is the lowest exponent supported with the same limitations as // MaxExponent. MinExponent = -MaxExponent )
const ( // RoundDown rounds toward 0; truncate. RoundDown = "down" // RoundHalfUp rounds up if the digits are >= 0.5. RoundHalfUp = "half_up" // RoundHalfEven rounds up if the digits are > 0.5. If the digits are equal // to 0.5, it rounds up if the previous digit is odd, always producing an // even digit. RoundHalfEven = "half_even" // RoundCeiling towards +Inf: rounds up if digits are > 0 and the number // is positive. RoundCeiling = "ceiling" // RoundFloor towards -Inf: rounds up if digits are > 0 and the number // is negative. RoundFloor = "floor" // RoundHalfDown rounds up if the digits are > 0.5. RoundHalfDown = "half_down" // RoundUp rounds away from 0. RoundUp = "up" // Round05Up rounds zero or five away from 0; same as round-up, except that // rounding up only occurs if the digit to be rounded up is 0 or 5. Round05Up = "05up" )
const ( // DefaultTraps is the default trap set used by BaseContext. DefaultTraps = SystemOverflow | SystemUnderflow | Overflow | Underflow | Subnormal | DivisionUndefined | DivisionByZero | DivisionImpossible | InvalidOperation )
var BaseContext = Context{ Precision: 0, MaxExponent: MaxExponent, MinExponent: MinExponent, Traps: DefaultTraps, }
BaseContext is a useful default Context. Should not be mutated.
var ( // Roundings defines the set of Rounders used by Context. Users may add their // own, but modification of this map is not safe during any other parallel // Context operations. Roundings = map[string]Rounder{ RoundDown: roundDown, RoundHalfUp: roundHalfUp, RoundHalfEven: roundHalfEven, RoundCeiling: roundCeiling, RoundFloor: roundFloor, RoundHalfDown: roundHalfDown, RoundUp: roundUp, Round05Up: round05Up, } )
NewFromString creates a new decimal from s. It has no restrictions on exponents or precision.
NumDigits returns the number of decimal digits of b.
Condition holds condition flags.
const ( // SystemOverflow is raised when an exponent is greater than MaxExponent. SystemOverflow Condition = 1 << iota // SystemUnderflow is raised when an exponent is less than MinExponent. SystemUnderflow // Overflow is raised when the exponent of a result is too large to be // represented. Overflow // Underflow is raised when a result is both subnormal and inexact. Underflow // Inexact is raised when a result is not exact (one or more non-zero // coefficient digits were discarded during rounding). Inexact // Subnormal is raised when a result is subnormal (its adjusted exponent is // less than Emin), before any rounding. Subnormal // Rounded is raised when a result has been rounded (that is, some zero or // non-zero coefficient digits were discarded). Rounded // DivisionUndefined is raised when both division operands are 0. DivisionUndefined // DivisionByZero is raised when a non-zero dividend is divided by zero. DivisionByZero // DivisionImpossible is raised when integer division cannot be exactly // represented with the given precision. DivisionImpossible // InvalidOperation is raised when a result would be undefined or impossible. InvalidOperation // Clamped is raised when the exponent of a result has been altered or // constrained in order to fit the constraints of the Decimal representation. Clamped )
Any returns true if any flag is true.
Clamped returns true if the Clamped flag is set.
DivisionByZero returns true if the DivisionByZero flag is set.
DivisionImpossible returns true if the DivisionImpossible flag is set.
DivisionUndefined returns true if the DivisionUndefined flag is set.
GoError converts r to an error based on the given traps and returns r. Traps are the conditions which will trigger an error result if the corresponding Flag condition occurred.
Inexact returns true if the Inexact flag is set.
InvalidOperation returns true if the InvalidOperation flag is set.
Overflow returns true if the Overflow flag is set.
Rounded returns true if the Rounded flag is set.
Subnormal returns true if the Subnormal flag is set.
SystemOverflow returns true if the SystemOverflow flag is set.
SystemUnderflow returns true if the SystemUnderflow flag is set.
Underflow returns true if the Underflow flag is set.
type Context struct { // Precision is the number of places to round during rounding; this is // effectively the total number of digits (before and after the decimal // point). Precision uint32 // MaxExponent specifies the largest effective exponent. The // effective exponent is the value of the Decimal in scientific notation. That // is, for 10e2, the effective exponent is 3 (1.0e3). Zero (0) is not a special // value; it does not disable this check. MaxExponent int32 // MinExponent is similar to MaxExponent, but for the smallest effective // exponent. MinExponent int32 // Traps are the conditions which will trigger an error result if the // corresponding Flag condition occurred. Traps Condition // Rounding specifies the Rounder to use during rounding. RoundHalfUp is used if // empty or not present in Roundings. Rounding string }
Context maintains options for Decimal operations. It can safely be used concurrently, but not modified concurrently. Arguments for any method can safely be used as both result and operand.
ExampleInexact demonstrates how to detect inexact operations.
Code:
d := apd.New(27, 0) three := apd.New(3, 0) c := apd.BaseContext.WithPrecision(5) for { res, err := c.Quo(d, d, three) fmt.Printf("d: %7s, inexact: %5v, err: %v\n", d, res.Inexact(), err) if err != nil { return } if res.Inexact() { return } }
Output:
d: 9, inexact: false, err: <nil> d: 3, inexact: false, err: <nil> d: 1, inexact: false, err: <nil> d: 0.33333, inexact: true, err: <nil>
ExampleOverflow demonstrates how to detect or error on overflow.
Code:
// Create a context that will overflow at 1e3. c := apd.Context{ MaxExponent: 2, Traps: apd.Overflow, } one := apd.New(1, 0) d := apd.New(997, 0) for { res, err := c.Add(d, d, one) fmt.Printf("d: %8s, overflow: %5v, err: %v\n", d, res.Overflow(), err) if err != nil { return } }
Output:
d: 998, overflow: false, err: <nil> d: 999, overflow: false, err: <nil> d: Infinity, overflow: true, err: overflow
Abs sets d to |x| (the absolute value of x).
Add sets d to the sum x+y.
Cbrt sets d to the cube root of x.
Ceil sets d to the smallest integer >= x.
Cmp compares x and y and sets d to:
-1 if x < y 0 if x == y +1 if x > y
This comparison respects the normal rules of special values (like NaN), and does not compare them.
Exp sets d = e**x.
Floor sets d to the largest integer <= x.
Ln sets d to the natural log of x.
Log10 sets d to the base 10 log of x.
Mul sets d to the product x*y.
Neg sets d to -x.
NewFromString creates a new decimal from s. The returned Decimal has its exponents restricted by the context and its value rounded if it contains more digits than the context's precision.
Pow sets d = x**y.
Quantize adjusts and rounds x as necessary so it is represented with exponent exp and stores the result in d.
Code:
input, _, _ := apd.NewFromString("123.45") output := new(apd.Decimal) c := apd.BaseContext.WithPrecision(10) for i := int32(-3); i <= 3; i++ { res, _ := c.Quantize(output, input, i) fmt.Printf("%2v: %s", i, output) if res != 0 { fmt.Printf(" (%s)", res) } fmt.Println() }
Output:
-3: 123.450 -2: 123.45 -1: 123.5 (inexact, rounded) 0: 123 (inexact, rounded) 1: 1.2E+2 (inexact, rounded) 2: 1E+2 (inexact, rounded) 3: 0E+3 (inexact, rounded)
Quo sets d to the quotient x/y for y != 0. c.Precision must be > 0. If an exact division is required, use a context with high precision and verify it was exact by checking the Inexact flag on the return Condition.
QuoInteger sets d to the integer part of the quotient x/y. If the result cannot fit in d.Precision digits, an error is returned.
Reduce sets d to x with all trailing zeros removed and returns the number of zeros removed.
Rem sets d to the remainder part of the quotient x/y. If the integer part cannot fit in d.Precision digits, an error is returned.
Round sets d to rounded x, rounded to the precision specified by c. If c has zero precision, no rounding will occur. If c has no Rounding specified, RoundHalfUp is used.
RoundToIntegralExact sets d to integral value of x.
ExampleRoundToIntegralExact demonstrates how to use RoundToIntegralExact to check if a number is an integer or not. Note the variations between integer (which allows zeros after the decimal point) and strict (which does not). See the documentation on Inexact and Rounded.
Code:
inputs := []string{ "123.4", "123.0", "123", "12E1", "120E-1", "120E-2", } for _, input := range inputs { d, _, _ := apd.NewFromString(input) res, _ := apd.BaseContext.RoundToIntegralExact(d, d) integer := !res.Inexact() strict := !res.Rounded() fmt.Printf("input: % 6s, output: %3s, integer: %5t, strict: %5t, res:", input, d, integer, strict) if res != 0 { fmt.Printf(" %s", res) } fmt.Println() }
Output:
input: 123.4, output: 123, integer: false, strict: false, res: inexact, rounded input: 123.0, output: 123, integer: true, strict: false, res: rounded input: 123, output: 123, integer: true, strict: true, res: input: 12E1, output: 120, integer: true, strict: true, res: input: 120E-1, output: 12, integer: true, strict: false, res: rounded input: 120E-2, output: 1, integer: false, strict: false, res: inexact, rounded
RoundToIntegralValue sets d to integral value of x. Inexact and Rounded flags are ignored and removed.
SetString sets d to s and returns d. The returned Decimal has its exponents restricted by the context and its value rounded if it contains more digits than the context's precision.
Sqrt sets d to the square root of x. Sqrt uses the Babylonian method for computing the square root, which uses O(log p) steps for p digits of precision.
Sub sets d to the difference x-y.
WithPrecision returns a copy of c but with the specified precision.
Decimal is an arbitrary-precision decimal. Its value is:
Negative × Coeff × 10**Exponent
Coeff must be positive. If it is negative results may be incorrect and apd may panic.
New creates a new decimal with the given coefficient and exponent.
NewWithBigInt creates a new decimal with the given coefficient and exponent.
Abs sets d to |x| and returns d.
Append appends to buf the string form of the decimal number d, as generated by d.Text, and returns the extended buffer.
Cmp compares d and x and returns:
-1 if d < x 0 if d == x +1 if d > x undefined if d or x are NaN
CmpTotal compares d and x using their abstract representation rather than their numerical value. A total ordering is defined for all possible abstract representations, as described below. If the first operand is lower in the total order than the second operand then the result is -1, if the operands have the same abstract representation then the result is 0, and if the first operand is higher in the total order than the second operand then the result is 1.
Numbers (representations which are not NaNs) are ordered such that a larger numerical value is higher in the ordering. If two representations have the same numerical value then the exponent is taken into account; larger (more positive) exponents are higher in the ordering.
For example, the following values are ordered from lowest to highest. Note the difference in ordering between 1.2300 and 1.23.
-NaN -NaNSignaling -Infinity -127 -1.00 -1 -0.000 -0 0 1.2300 1.23 1E+9 Infinity NaNSignaling NaN
Compose sets the internal decimal value from parts. If the value cannot be represented then an error should be returned.
func (d *Decimal) Decompose(buf []byte) (form byte, negative bool, coefficient []byte, exponent int32)
Decompose returns the internal decimal state into parts. If the provided buf has sufficient capacity, buf may be returned as the coefficient with the value set and length set as appropriate.
Float64 returns the float64 representation of x. This conversion may lose data (see strconv.ParseFloat for caveats).
Format implements fmt.Formatter. It accepts many of the regular formats for floating-point numbers ('e', 'E', 'f', 'F', 'g', 'G') as well as 's' and 'v', which are handled like 'G'. Format also supports the output field width, as well as the format flags '+' and ' ' for sign control, '0' for space or zero padding, and '-' for left or right justification. It does not support precision. See the fmt package for details.
Int64 returns the int64 representation of x. If x cannot be represented in an int64, an error is returned.
IsZero returns true if d == 0 or -0.
MarshalText implements the encoding.TextMarshaler interface.
Modf sets integ to the integral part of d and frac to the fractional part such that d = integ+frac. If d is negative, both integ or frac will be either 0 or negative. integ.Exponent will be >= 0; frac.Exponent will be <= 0. Either argument can be nil, preventing it from being set.
Neg sets d to -x and returns d.
NumDigits returns the number of decimal digits of d.Coeff.
Reduce sets d to x with all trailing zeros removed and returns d and the number of zeros removed.
Scan implements the database/sql.Scanner interface. It supports string, []byte, int64, float64.
Set sets d's fields to the values of x and returns d.
SetFinite sets d to x with exponent e and returns d.
SetFloat64 sets d's Coefficient and Exponent to x and returns d. d will hold the exact value of f.
SetInt64 sets d to x and returns d.
SetString sets d to s and returns d. It has no restrictions on exponents or precision.
Sign returns, if d is Finite:
-1 if d < 0 0 if d == 0 or -0 +1 if d > 0
Otherwise (if d is Infinite or NaN):
-1 if d.Negative == true +1 if d.Negative == false
String formats x like x.Text('G'). It matches the to-scientific-string conversion of the GDA spec.
Text converts the floating-point number x to a string according to the given format. The format is one of:
'e' -d.dddde±dd, decimal exponent, exponent digits 'E' -d.ddddE±dd, decimal exponent, exponent digits 'f' -ddddd.dddd, no exponent 'g' like 'e' for large exponents, like 'f' otherwise 'G' like 'E' for large exponents, like 'f' otherwise
If format is a different character, Text returns a "%" followed by the unrecognized.Format character. The 'f' format has the possibility of displaying precision that is not present in the Decimal when it appends zeros (the 'g' format avoids the use of 'f' in this case). All other formats always show the exact precision of the Decimal.
UnmarshalText implements the encoding.TextUnmarshaler interface.
Value implements the database/sql/driver.Valuer interface. It converts d to a string.
type ErrDecimal struct { Ctx *Context // Flags are the accumulated flags from operations. Flags Condition // contains filtered or unexported fields }
ErrDecimal performs operations on decimals and collects errors during operations. If an error is already set, the operation is skipped. Designed to be used for many operations in a row, with a single error check at the end.
Code:
c := apd.BaseContext.WithPrecision(5) ed := apd.MakeErrDecimal(c) d := apd.New(10, 0) fmt.Printf("%s, err: %v\n", d, ed.Err()) ed.Add(d, d, apd.New(2, 1)) // add 20 fmt.Printf("%s, err: %v\n", d, ed.Err()) ed.Quo(d, d, apd.New(0, 0)) // divide by zero fmt.Printf("%s, err: %v\n", d, ed.Err()) ed.Sub(d, d, apd.New(1, 0)) // attempt to subtract 1 // The subtraction doesn't occur and doesn't change the error. fmt.Printf("%s, err: %v\n", d, ed.Err())
Output:
10, err: <nil> 30, err: <nil> Infinity, err: division by zero Infinity, err: division by zero
func MakeErrDecimal(c *Context) ErrDecimal
MakeErrDecimal creates a ErrDecimal with given context.
func (e *ErrDecimal) Abs(d, x *Decimal) *Decimal
Abs performs e.Ctx.Abs(d, x) and returns d.
func (e *ErrDecimal) Add(d, x, y *Decimal) *Decimal
Add performs e.Ctx.Add(d, x, y) and returns d.
func (e *ErrDecimal) Ceil(d, x *Decimal) *Decimal
Ceil performs e.Ctx.Ceil(d, x) and returns d.
func (e *ErrDecimal) Err() error
Err returns the first error encountered or the context's trap error if present.
func (e *ErrDecimal) Exp(d, x *Decimal) *Decimal
Exp performs e.Ctx.Exp(d, x) and returns d.
func (e *ErrDecimal) Floor(d, x *Decimal) *Decimal
Floor performs e.Ctx.Floor(d, x) and returns d.
func (e *ErrDecimal) Int64(d *Decimal) int64
Int64 returns 0 if err is set. Otherwise returns d.Int64().
func (e *ErrDecimal) Ln(d, x *Decimal) *Decimal
Ln performs e.Ctx.Ln(d, x) and returns d.
func (e *ErrDecimal) Log10(d, x *Decimal) *Decimal
Log10 performs d.Log10(x) and returns d.
func (e *ErrDecimal) Mul(d, x, y *Decimal) *Decimal
Mul performs e.Ctx.Mul(d, x, y) and returns d.
func (e *ErrDecimal) Neg(d, x *Decimal) *Decimal
Neg performs e.Ctx.Neg(d, x) and returns d.
func (e *ErrDecimal) Pow(d, x, y *Decimal) *Decimal
Pow performs e.Ctx.Pow(d, x, y) and returns d.
func (e *ErrDecimal) Quantize(d, v *Decimal, exp int32) *Decimal
Quantize performs e.Ctx.Quantize(d, v, exp) and returns d.
func (e *ErrDecimal) Quo(d, x, y *Decimal) *Decimal
Quo performs e.Ctx.Quo(d, x, y) and returns d.
func (e *ErrDecimal) QuoInteger(d, x, y *Decimal) *Decimal
QuoInteger performs e.Ctx.QuoInteger(d, x, y) and returns d.
func (e *ErrDecimal) Reduce(d, x *Decimal) (int, *Decimal)
Reduce performs e.Ctx.Reduce(d, x) and returns the number of zeros removed and d.
func (e *ErrDecimal) Rem(d, x, y *Decimal) *Decimal
Rem performs e.Ctx.Rem(d, x, y) and returns d.
func (e *ErrDecimal) Round(d, x *Decimal) *Decimal
Round performs e.Ctx.Round(d, x) and returns d.
func (e *ErrDecimal) RoundToIntegralExact(d, x *Decimal) *Decimal
RoundToIntegralExact performs e.Ctx.RoundToIntegralExact(d, x) and returns d.
func (e *ErrDecimal) RoundToIntegralValue(d, x *Decimal) *Decimal
RoundToIntegralValue performs e.Ctx.RoundToIntegralValue(d, x) and returns d.
func (e *ErrDecimal) Sqrt(d, x *Decimal) *Decimal
Sqrt performs e.Ctx.Sqrt(d, x) and returns d.
func (e *ErrDecimal) Sub(d, x, y *Decimal) *Decimal
Sub performs e.Ctx.Sub(d, x, y) and returns d.
Form specifies the form of a Decimal.
const ( // Finite is the finite form. Finite Form = iota // Infinite is the infinite form. Infinite // NaNSignaling is the signaling NaN form. It will always raise the // InvalidOperation condition during an operation. NaNSignaling // NaN is the NaN form. NaN )
NullDecimal represents a string that may be null. NullDecimal implements the database/sql.Scanner interface so it can be used as a scan destination:
var d NullDecimal err := db.QueryRow("SELECT num FROM foo WHERE id=?", id).Scan(&d) ... if d.Valid { // use d.Decimal } else { // NULL value }
func (nd *NullDecimal) Scan(value interface{}) error
Scan implements the database/sql.Scanner interface.
func (nd NullDecimal) Value() (driver.Value, error)
Value implements the database/sql/driver.Valuer interface.
Rounder defines a function that returns true if 1 should be added to the absolute value of a number being rounded. result is the result to which the 1 would be added. neg is true if the number is negative. half is -1 if the discarded digits are < 0.5, 0 if = 0.5, or 1 if > 0.5.
Round sets d to rounded x.
Package apd imports 7 packages (graph) and is imported by 53 packages. Updated 2019-05-05. Refresh now. Tools for package owners.