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IEEE 754-2008 supports four rounding modes, which determine the answer given by a floating-point computation when the exact result lies between two floating-point numbers but is not a floating-point number itself:

`to-nearest`

Round to the nearest floating-point number. If there are two equidistant ones, choose the one whose least significant digit is even. Also known as “round-to-nearest/ties-to-even”.

`toward-zero`

Round to the floating-point number closest to zero.

`downward`

Round to the greatest floating-point number below.

`upward`

Round to the least floating-point number above.

**Warning:** Not all procedures in MIT/GNU Scheme respect the
rounding mode.
Only the basic arithmetic operations — *+*, *-*, ***,
*/*, and sqrt — will reliably respect it.
The main purpose of changing the rounding mode is to diagnose
numerical instability by injecting small perturbations throughout the
computation.

**Bug:** It would be nice if we had “round-to-odd”, where any
inexact result is rounded to the nearest *odd* floating-point
number, for implementing “doubled”-precision algorithms.
But we don’t.
Sorry.

- procedure:
**flo:default-rounding-mode** Returns a symbol for the default rounding mode, which is always

`to-nearest`

.

- procedure:
**flo:rounding-modes** Returns a list of the supported rounding modes as symbols.

- procedure:
**flo:rounding-mode** - procedure:
**flo:set-rounding-mode!***mode* Gets or sets the current rounding mode as a symbol, entering a per-thread environment.

- procedure:
**flo:with-rounding-mode***mode thunk* Call

`thunk`in a per-thread environment with the rounding mode set to`mode`. On return, the floating-point environment, including rounding mode, is restored to what it was before.Non-local exit from and re-entrance to

`thunk`behaves as if the call is surrounded by`flo:preserving-environment`

(see Floating-Point Environment).

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