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8.16.0.4
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4 Decimal Numbers🔗ℹ

 (require scramble/decimal) package: scramble-lib

Added in version 0.4 of package scramble-lib.

struct

(struct decimal (unscaled scale))

  unscaled : exact-integer?
  scale : exact-integer?
Represents an exact decimal number as an integer and a scale. The number represented is (/ unscaled (expt 10 scale)); for example, (decimal 12345 3) represents the number 12.345.

The scale value is also called precision throughout this document. When non-negative, it corresponds to the number of places after the decimal point. When negative, it indicates the number of places before the decimal point that are insignificant.

procedure

(real->decimal x precision) → decimal?

  x : rational?
  precision : exact-integer?
Converts x to a decimal with the given precision. If x cannot be represented exactly with the given precision, it is rounded. If x is a special real, such as +inf.0 or +nan.0, an exception is raised.

> (real->decimal 1/8 4)

#<decimal:0.1250>

> (real->decimal 1/3 3)

#<decimal:0.333>

procedure

(string->decimal s) → (or/c decimal? #f)

  s : string?
Returns the decimal number represented by s, or #f if s does not contain a decimal number. The acceptable formats are #rx"-?[0-9]*[.][0-9]+" and #rx"-?[0-9]+#*[.]?". The resulting decimal’s scale is determined either by the number of digits after the decimal point or the number of # markers before the decimal point; the latter indicate negative scale.

> (string->decimal "123.45")

#<decimal:123.45>

> (string->decimal ".98")

#<decimal:0.98>

> (string->decimal "-22.44")

#<decimal:-22.44>

> (string->decimal "123##")

#<decimal:123##>

> (string->decimal "-.")

#f

procedure

(decimal->string dec) → string?

  dec : decimal?
Converts the decimal dec into a string. If dec has negative scale, the insignificant digits are indicated with #.

> (decimal->string (decimal 12345 2))

"123.45"

> (decimal->string (decimal 25 -3))

"25###"

procedure

(decimal->exact dec) → (and/c rational? exact?)

  dec : (or/c decimal? rational?)

procedure

(decimal->inexact dec) → (and/c real? inexact?)

  dec : (or/c decimal? real?)
Converts the given decimal into an ordinary exact or inexact number, respectively. For convenience, both functions also accept ordinary real numbers.

Examples:
> (decimal->exact (string->decimal "123.45"))

2469/20

> (decimal->exact (string->decimal "987"))

987

> (decimal->exact 1/4)

1/4

> (decimal->inexact (string->decimal "123.45"))

123.45

> (decimal->inexact +inf.0)

+inf.0

procedure

(decimal-adjust dec precision) → decimal?

  dec : decimal?
  precision : exact-integer?
Returns a new decimal with the given precision as close as possible to dec. If the given precision is less than the precision (scale) of dec, the decimal is rounded.

Examples:
> (decimal-adjust (string->decimal "123.456") 5)

#<decimal:123.45600>

> (decimal-adjust (string->decimal "123.456") 1)

#<decimal:123.5>

> (decimal-adjust (string->decimal "12.5") 0)

#<decimal:12>

> (decimal-adjust (string->decimal "13.5") 0)

#<decimal:14>

> (decimal-adjust (string->decimal "123456") -2)

#<decimal:1235##>

procedure

(decimal+ v ...) → (or/c decimal? real?)

  v : (or/c decimal? real?)

procedure

(decimal- v ...+) → (or/c decimal? real?)

  v : (or/c decimal? real?)

procedure

(decimal* v ...) → (or/c decimal? real?)

  v : (or/c decimal? real?)
Returns the sum, difference, or product, respectively, of the given decimals.

The precision of an operation involving two decimals is the max of the operand precisions for addition and subtraction, and the sum of the precisions for multiplications. The precision of an operation involving a decimal and an ordinary real number is the precision of the decimal. Operations are performed left to right.

Warning: Arithmetic on mixtures of reals and decimals is neither associative nor generally commutative, due to the precision rules above. For example:

> (decimal+ (string->decimal "1.00") pi (string->decimal "0.0001"))

#<decimal:4.1401>

> (decimal+ (string->decimal "0.0001") pi (string->decimal "1.00"))

#<decimal:4.1417>

procedure

(decimal-cmp v1 v2) → (or/c '< '= '> #f)

  v1 : (or/c decimal? real?)
  v2 : (or/c decimal? real?)
Compares the numeric values of the given decimals and/or reals.

Examples:
> (decimal-cmp (string->decimal "2.0") (string->decimal "2.000"))

'=

> (decimal-cmp (string->decimal "1.000") 1)

'=

> (decimal-cmp (string->decimal "123.45") 100)

'>

> (decimal-cmp (string->decimal "999") +inf.0)

'<

procedure

(decimal<? v ...+) → boolean?

  v : (or/c decimal? real?)

procedure

(decimal<=? v ...+) → boolean?

  v : (or/c decimal? real?)

procedure

(decimal=? v ...+) → boolean?

  v : (or/c decimal? real?)

procedure

(decimal>? v ...+) → boolean?

  v : (or/c decimal? real?)

procedure

(decimal>=? v ...+) → boolean?

  v : (or/c decimal? real?)
Compares the chain of the numeric values of the given decimals and/or reals.

procedure

(decimal-min v ...+) → (or/c decimal? real?)

  v : (or/c decimal? real?)

procedure

(decimal-max v ...+) → (or/c decimal? real?)

  v : (or/c decimal? real?)
Returns the minimum or maximum, respectively, of the given decimals and/or reals.

procedure

(decimal-abs dec) → decimal?

  dec : decimal?
Returns the absolute value of the given decimal.

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