%YAML 1.2
---
scalar_functions:
  -
    name: "ceil"
    description: >
      Rounding to the ceiling of the value `x`.
    impls:
      - args:
          - value: fp32
            name: "x"
        return: fp32
      - args:
          - value: fp64
            name: "x"
        return: fp64
  -
    name: "floor"
    description: >
      Rounding to the floor of the value `x`.
    impls:
      - args:
          - value: fp32
            name: "x"
        return: fp32
      - args:
          - value: fp64
            name: "x"
        return: fp64
  -
    name: "round"
    description: >
      Rounding the value `x` to `s` decimal places.
    impls:
      - args:
          - value: i8
            name: "x"
            description: >
              Numerical expression to be rounded.
          - value: i32
            name: "s"
            description: >
              Number of decimal places to be rounded to.

              When `s` is a positive number, nothing will happen
              since `x` is an integer value.

              When `s` is a negative number, the rounding is
              performed to the nearest multiple of `10^(-s)`.
        options:
          rounding:
            description: >
              When a boundary is computed to lie somewhere between two values,
              and this value cannot be exactly represented, this specifies how
              to round it.

                - TIE_TO_EVEN: round to nearest value; if exactly halfway, tie
                  to the even option.
                - TIE_AWAY_FROM_ZERO: round to nearest value; if exactly
                  halfway, tie away from zero.
                - TRUNCATE: always round toward zero.
                - CEILING: always round toward positive infinity.
                - FLOOR: always round toward negative infinity.
                - AWAY_FROM_ZERO: round negative values with FLOOR rule, round positive values with CEILING rule
                - TIE_DOWN: round ties with FLOOR rule
                - TIE_UP: round ties with CEILING rule
                - TIE_TOWARDS_ZERO: round ties with TRUNCATE rule
                - TIE_TO_ODD: round to nearest value; if exactly halfway, tie
                  to the odd option.
            values: [ TIE_TO_EVEN, TIE_AWAY_FROM_ZERO, TRUNCATE, CEILING, FLOOR,
              AWAY_FROM_ZERO, TIE_DOWN, TIE_UP, TIE_TOWARDS_ZERO, TIE_TO_ODD ]
        nullability: DECLARED_OUTPUT
        return: i8?
      - args:
          - value: i16
            name: "x"
            description: >
              Numerical expression to be rounded.
          - value: i32
            name: "s"
            description: >
              Number of decimal places to be rounded to.

              When `s` is a positive number, nothing will happen
              since `x` is an integer value.

              When `s` is a negative number, the rounding is
              performed to the nearest multiple of `10^(-s)`.
        options:
          rounding:
            description: >
              When a boundary is computed to lie somewhere between two values,
              and this value cannot be exactly represented, this specifies how
              to round it.

                - TIE_TO_EVEN: round to nearest value; if exactly halfway, tie
                  to the even option.
                - TIE_AWAY_FROM_ZERO: round to nearest value; if exactly
                  halfway, tie away from zero.
                - TRUNCATE: always round toward zero.
                - CEILING: always round toward positive infinity.
                - FLOOR: always round toward negative infinity.
                - AWAY_FROM_ZERO: round negative values with FLOOR rule, round positive values with CEILING rule
                - TIE_DOWN: round ties with FLOOR rule
                - TIE_UP: round ties with CEILING rule
                - TIE_TOWARDS_ZERO: round ties with TRUNCATE rule
                - TIE_TO_ODD: round to nearest value; if exactly halfway, tie
                  to the odd option.
            values: [ TIE_TO_EVEN, TIE_AWAY_FROM_ZERO, TRUNCATE, CEILING, FLOOR,
              AWAY_FROM_ZERO, TIE_DOWN, TIE_UP, TIE_TOWARDS_ZERO, TIE_TO_ODD ]
        nullability: DECLARED_OUTPUT
        return: i16?
      - args:
          - value: i32
            name: "x"
            description: >
              Numerical expression to be rounded.
          - value: i32
            name: "s"
            description: >
              Number of decimal places to be rounded to.

              When `s` is a positive number, nothing will happen
              since `x` is an integer value.

              When `s` is a negative number, the rounding is
              performed to the nearest multiple of `10^(-s)`.
        options:
          rounding:
            description: >
              When a boundary is computed to lie somewhere between two values,
              and this value cannot be exactly represented, this specifies how
              to round it.

                - TIE_TO_EVEN: round to nearest value; if exactly halfway, tie
                  to the even option.
                - TIE_AWAY_FROM_ZERO: round to nearest value; if exactly
                  halfway, tie away from zero.
                - TRUNCATE: always round toward zero.
                - CEILING: always round toward positive infinity.
                - FLOOR: always round toward negative infinity.
                - AWAY_FROM_ZERO: round negative values with FLOOR rule, round positive values with CEILING rule
                - TIE_DOWN: round ties with FLOOR rule
                - TIE_UP: round ties with CEILING rule
                - TIE_TOWARDS_ZERO: round ties with TRUNCATE rule
                - TIE_TO_ODD: round to nearest value; if exactly halfway, tie
                  to the odd option.
            values: [ TIE_TO_EVEN, TIE_AWAY_FROM_ZERO, TRUNCATE, CEILING, FLOOR,
              AWAY_FROM_ZERO, TIE_DOWN, TIE_UP, TIE_TOWARDS_ZERO, TIE_TO_ODD ]
        nullability: DECLARED_OUTPUT
        return: i32?
      - args:
          - value: i64
            name: "x"
            description: >
              Numerical expression to be rounded.
          - value: i32
            name: "s"
            description: >
              Number of decimal places to be rounded to.

              When `s` is a positive number, nothing will happen
              since `x` is an integer value.

              When `s` is a negative number, the rounding is
              performed to the nearest multiple of `10^(-s)`.
        options:
          rounding:
            description: >
              When a boundary is computed to lie somewhere between two values,
              and this value cannot be exactly represented, this specifies how
              to round it.

                - TIE_TO_EVEN: round to nearest value; if exactly halfway, tie
                  to the even option.
                - TIE_AWAY_FROM_ZERO: round to nearest value; if exactly
                  halfway, tie away from zero.
                - TRUNCATE: always round toward zero.
                - CEILING: always round toward positive infinity.
                - FLOOR: always round toward negative infinity.
                - AWAY_FROM_ZERO: round negative values with FLOOR rule, round positive values with CEILING rule
                - TIE_DOWN: round ties with FLOOR rule
                - TIE_UP: round ties with CEILING rule
                - TIE_TOWARDS_ZERO: round ties with TRUNCATE rule
                - TIE_TO_ODD: round to nearest value; if exactly halfway, tie
                  to the odd option.
            values: [ TIE_TO_EVEN, TIE_AWAY_FROM_ZERO, TRUNCATE, CEILING, FLOOR,
              AWAY_FROM_ZERO, TIE_DOWN, TIE_UP, TIE_TOWARDS_ZERO, TIE_TO_ODD ]
        nullability: DECLARED_OUTPUT
        return: i64?
      - args:
          - value: fp32
            name: "x"
            description: >
              Numerical expression to be rounded.
          - value: i32
            name: "s"
            description: >
              Number of decimal places to be rounded to.

              When `s` is a positive number, the rounding
              is performed to a `s` number of decimal places.

              When `s` is a negative number, the rounding is
              performed to the left side of the decimal point
              as specified by `s`.
        options:
          rounding:
            description: >
              When a boundary is computed to lie somewhere between two values,
              and this value cannot be exactly represented, this specifies how
              to round it.

                - TIE_TO_EVEN: round to nearest value; if exactly halfway, tie
                  to the even option.
                - TIE_AWAY_FROM_ZERO: round to nearest value; if exactly
                  halfway, tie away from zero.
                - TRUNCATE: always round toward zero.
                - CEILING: always round toward positive infinity.
                - FLOOR: always round toward negative infinity.
                - AWAY_FROM_ZERO: round negative values with FLOOR rule, round positive values with CEILING rule
                - TIE_DOWN: round ties with FLOOR rule
                - TIE_UP: round ties with CEILING rule
                - TIE_TOWARDS_ZERO: round ties with TRUNCATE rule
                - TIE_TO_ODD: round to nearest value; if exactly halfway, tie
                  to the odd option.
            values: [ TIE_TO_EVEN, TIE_AWAY_FROM_ZERO, TRUNCATE, CEILING, FLOOR,
              AWAY_FROM_ZERO, TIE_DOWN, TIE_UP, TIE_TOWARDS_ZERO, TIE_TO_ODD ]
        nullability: DECLARED_OUTPUT
        return: fp32?
      - args:
          - value: fp64
            name: "x"
            description: >
              Numerical expression to be rounded.
          - value: i32
            name: "s"
            description: >
              Number of decimal places to be rounded to.

              When `s` is a positive number, the rounding
              is performed to a `s` number of decimal places.

              When `s` is a negative number, the rounding is
              performed to the left side of the decimal point
              as specified by `s`.
        options:
          rounding:
            description: >
              When a boundary is computed to lie somewhere between two values,
              and this value cannot be exactly represented, this specifies how
              to round it.

                - TIE_TO_EVEN: round to nearest value; if exactly halfway, tie
                  to the even option.
                - TIE_AWAY_FROM_ZERO: round to nearest value; if exactly
                  halfway, tie away from zero.
                - TRUNCATE: always round toward zero.
                - CEILING: always round toward positive infinity.
                - FLOOR: always round toward negative infinity.
                - AWAY_FROM_ZERO: round negative values with FLOOR rule, round positive values with CEILING rule
                - TIE_DOWN: round ties with FLOOR rule
                - TIE_UP: round ties with CEILING rule
                - TIE_TOWARDS_ZERO: round ties with TRUNCATE rule
                - TIE_TO_ODD: round to nearest value; if exactly halfway, tie
                  to the odd option.
            values: [ TIE_TO_EVEN, TIE_AWAY_FROM_ZERO, TRUNCATE, CEILING, FLOOR,
              AWAY_FROM_ZERO, TIE_DOWN, TIE_UP, TIE_TOWARDS_ZERO, TIE_TO_ODD ]
        nullability: DECLARED_OUTPUT
        return: fp64?