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DD_QD (MuPAT) >> DD_QD (MuPAT) > Overloads

# Overloads

Available overloads for DD and QD real numbers

### For DD numbers (16 bytes)

All these features are illustrated in the example of the dd() page.

DD = array. dd = scalar. SQ = SQuare matrix. col = column vector.

Supported functions:

eye(DD), zeros(DD), ones(DD), rand(DD)

abs(DD), ceil(DD), floor(DD)

min(DD), min(DD,'r'|1|'c'|2'), max(DD), max(DD,'r'|1|'c'|2')

cos(dd), sin(dd), tan(dd)

`exp(dd), lu(SQ), norm(col), qr(DD), sqrt(dd)`

### For QD numbers (32 bytes)

All these features are illustrated in the example of the qd() page.

QD = array. qd = scalar. SQ = SQuare matrix. col = column vector.

Supported functions:

eye(QD), zeros(QD), ones(QD), rand(QD)

abs(QD), ceil(QD), floor(QD)

min(QD), min(QD,'r'|1|'c'|2'), max(QD), max(QD,'r'|1|'c'|2')

cos(qd), sin(qd), tan(qd)

`exp(qd), lu(SQ), norm(col), qr(QD), sqrt(qd)`

### Supported operators:

All these features are illustrated in the example of the dd() and qd() pages.

d = scalar decimal number (8 bytes). D = array of decimal numbers (8 bytes).

- Display of numbers :

  Scalar numbers are displayed with all their digits, without respect to format().

  Otherwise, arrays are displayed as raw tlist.

- Transposition : DD', QD'.

  Only real extended numbers are supported.

- Addition A + B :

  A \ B | d | D | dd | DD | qd | QD
  --- | --- | --- | --- | --- | --- | ---
  d | . | . | + | + | + | +
  D | . | . | + | + | + | +
  dd | + | + | + | + | + | +
  DD | + | + | + | + | + | +
  qd | + | + | + | + | + | +
  QD | + | + | + | + | + | +

- Opposition : -DD, -QD

- Substraction A - B :

  A \ B | d | D | dd | DD | qd | QD
  --- | --- | --- | --- | --- | --- | ---
  d | . | . | - | - | - | -
  D | . | . | - | - | - | -
  dd | - | - | - | - | - | -
  DD | - | - | - | - | - | -
  qd | - | - | - | - | - | -
  QD | - | - | - | - | - | -

- Multiplication A * B : A and B must have compatible sizes

  A \ B | d | D | dd | DD | qd | QD
  --- | --- | --- | --- | --- | --- | ---
  d | . | . | * | * | * | *
  D | . | . | * | * | * | *
  dd | * | * | * | * | * | *
  DD | * | * | * | * | * | *
  qd | * | * | * | * | * | *
  QD | * | * | * | * | * | *

- Elementwise multiplication A .* B : not supported.

- Division A / b : b must be scalar.

  A / b | d | D | dd | DD | qd | QD
  --- | --- | --- | --- | --- | --- | ---
  d | . | . | / |  | / |
  D | . | . | / |  | / |
  dd | / |  | / |  | / |
  DD | / |  | / |  | / |
  qd | / |  | / |  | / |
  QD | / |  | / |  | / |

- Comparisons : Both operands a and b must be scalar.

  All comparisons a<b, a<=b, a==b, a~=b, a>=b, a>b are supported.

  a / b | d | D | dd | DD | qd | QD
  --- | --- | --- | --- | --- | --- | ---
  d | . | . | c |  | c |
  D | . | . |  |  |  |
  dd | c |  | c |  | c |
  DD |  |  |  |  |  |
  qd | c |  | c |  | c |
  QD |  |  |  |  |  |

- Extraction

- Insertion

- Concatenations, size()

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