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[[!tag standards]]

# FPR-to-GPR and GPR-to-FPR

TODO special constants instruction (e, tau/N, ln 2, sqrt 2, etc.) -- exclude any constants available through fmvis

**Draft Status** under development, for submission as an RFC

Links:

* <https://bugs.libre-soc.org/show_bug.cgi?id=650>
* <https://bugs.libre-soc.org/show_bug.cgi?id=230#c71>
* <https://bugs.libre-soc.org/show_bug.cgi?id=230#c74>
* <https://bugs.libre-soc.org/show_bug.cgi?id=230#c76>
* <https://bugs.libre-soc.org/show_bug.cgi?id=887> fmvis
* <https://bugs.libre-soc.org/show_bug.cgi?id=1015> int-fp RFC
* [[int_fp_mv/appendix]]
* [[sv/rfc/ls002]] - `fmvis` and `fishmv` External RFC Formal Submission
* [[sv/rfc/ls006]] - int-fp-mv External RFC Formal Submission

Trademarks:

* Rust is a Trademark of the Rust Foundation
* Java and Javascript are Trademarks of Oracle
* LLVM is a Trademark of the LLVM Foundation
* SPIR-V is a Trademark of the Khronos Group
* OpenCL is a Trademark of Apple, Inc.

Referring to these Trademarks within this document
is by necessity, in order to put the semantics of each language
into context, and is considered "fair use" under Trademark
Law.

Introduction:

High-performance CPU/GPU software needs to often convert between integers
and floating-point, therefore fast conversion/data-movement instructions
are needed.  Also given that initialisation of floats tends to take up
considerable space (even to just load 0.0) the inclusion of two compact
format float immediate instructions is up for consideration using 16-bit
immediates. BF16 is one of the formats: a second instruction allows a full
accuracy FP32 to be constructed.

Libre-SOC will be compliant with the
**Scalar Floating-Point Subset** (SFFS) i.e. is not implementing VMX/VSX,
and with its focus on modern 3D GPU hybrid workloads represents an
important new potential use-case for OpenPOWER.

Prior to the formation of the Compliancy Levels first introduced
in v3.0C and v3.1
the progressive historic development of the Scalar parts of the Power ISA assumed
that VSX would always be there to complement it. However With VMX/VSX 
**not available** in the newly-introduced SFFS Compliancy Level, the
existing non-VSX conversion/data-movement instructions require 
a Vector of load/store
instructions (slow and expensive) to transfer data between the FPRs and
the GPRs.  For a modern 3D GPU this kills any possibility of a
competitive edge.
Also, because SimpleV needs efficient scalar instructions in
order to generate efficient vector instructions, adding new instructions
for data-transfer/conversion between FPRs and GPRs multiplies the savings.

In addition, the vast majority of GPR <-> FPR data-transfers are as part
of a FP <-> Integer conversion sequence, therefore reducing the number
of instructions required is a priority.

Therefore, we are proposing adding:

* FPR load-immediate instructions, one equivalent to `BF16`, the
  other increasing accuracy to `FP32`
* FPR <-> GPR data-transfer instructions that just copy bits without conversion
* FPR <-> GPR combined data-transfer/conversion instructions that do
  Integer <-> FP conversions

If adding new Integer <-> FP conversion instructions, 
the opportunity may be taken to modernise the instructions and make them
well-suited for common/important conversion sequences:

* **standard IEEE754** - used by most languages and CPUs
* **standard OpenPOWER** - saturation with NaN
  converted to minimum valid integer
* **Java** - saturation with NaN converted to 0
* **JavaScript** - modulo wrapping with Inf/NaN converted to 0

The assembly listings in the [[int_fp_mv/appendix]] show how costly
some of these language-specific conversions are: Javascript, the
worst case, is 32 scalar instructions including seven branch instructions.

# Proposed New Scalar Instructions

All of the following instructions use the standard OpenPower conversion to/from 64-bit float format when reading/writing a 32-bit float from/to a FPR.  All integers however are sourced/stored in the *GPR*.

Integer operands and results being in the GPR is the key differentiator between the proposed instructions
(the entire rationale) compared to existing Scalar Power ISA.
In all existing Power ISA Scalar conversion instructions, all
operands are FPRs, even if the format of the source or destination
data is actually a scalar integer.

*(The existing Scalar instructions being FP-FP only is based on an assumption
that VSX will be implemented, and VSX is not part of the SFFS Compliancy
Level. An earlier version of the Power ISA used to have similar
FPR<->GPR instructions to these:
they were deprecated due to this incorrect assumption that VSX would
always be present).*

Note that source and destination widths can be overridden by SimpleV
SVP64, and that SVP64 also has Saturation Modes *in addition*
to those independently described here. SVP64 Overrides and Saturation
work on *both* Fixed *and* Floating Point operands and results.
 The interactions with SVP64
are explained in the  [[int_fp_mv/appendix]]

# Float load immediate  <a name="fmvis"></a>

These are like a variant of `fmvfg` and `oris`, combined.
Power ISA currently requires a large
number of instructions to get Floating Point constants into registers.
`fmvis` on its own is equivalent to BF16 to FP32/64 conversion,
but if followed up by `fishmv` an additional 16 bits of accuracy in the
mantissa may be achieved.

These instructions **always** save
resources compared to FP-load for exactly the same reason
that `li` saves resources: an L1-Data-Cache and memory read
is avoided.

*IBM may consider it worthwhile to extend these two instructions to
v3.1 Prefixed (`pfmvis` and `pfishmv`: 8RR, imm0 extended).
If so it is recommended that
`pfmvis` load a full FP32 immediate and `pfishmv` supplies the three high
missing exponent bits (numbered 8 to 10) and the lower additional
29 mantissa bits (23 to 51) needed to construct a full FP64 immediate.
Strictly speaking the sequence `fmvis fishmv pfishmv` achieves the
same effect in the same number of bytes as `pfmvis pfishmv`,
making `pfmvis` redundant.*

Just as Floating-point Load does not set FP Flags neither does fmvis or fishmv.
As fishmv is specifically intended to work in conjunction with fmvis
to provide additional accuracy, all bits other than those which
would have been set by a prior fmvis instruction are deliberately ignored.
(If these instructions involved reading from registers rather than immediates
it would be a different story).

## Load BF16 Immediate

`fmvis FRS, D`

Reinterprets `D << 16` as a 32-bit float, which is then converted to a
64-bit float and written to `FRS`.  This is equivalent to reinterpreting
`D` as a `BF16` and converting to 64-bit float.
There is no need for an Rc=1 variant because this is an immediate loading
instruction.

Example:

```
# clearing a FPR
fmvis f4, 0 # writes +0.0 to f4
# loading handy constants
fmvis f4, 0x8000 # writes -0.0 to f4
fmvis f4, 0x3F80 # writes +1.0 to f4
fmvis f4, 0xBF80 # writes -1.0 to f4
fmvis f4, 0xBFC0 # writes -1.5 to f4
fmvis f4, 0x7FC0 # writes +qNaN to f4
fmvis f4, 0x7F80 # writes +Infinity to f4
fmvis f4, 0xFF80 # writes -Infinity to f4
fmvis f4, 0x3FFF # writes +1.9921875 to f4

# clearing 128 FPRs with 2 SVP64 instructions
# by issuing 32 vec4 (subvector length 4) ops
setvli VL=MVL=32
sv.fmvis/vec4 f0, 0 # writes +0.0 to f0-f127
```
Important: If the float load immediate instruction(s) are left out,
change all [GPR to FPR conversion instructions](#GPR-to-FPR-conversions)
to instead write `+0.0` if `RA` is register `0`, at least
allowing clearing FPRs.

`fmvis` fits with DX-Form:

|  0-5   | 6-10 | 11-15 | 16-25 | 26-30 | 31  | Form    |
|--------|------|-------|-------|-------|-----|---------|
|  Major | FRS  | d1    | d0    | XO    | d2  | DX-Form |

Pseudocode:

    bf16 = d0 || d1 || d2 # create BF16 immediate
    fp32 = bf16 || [0]*16 # convert BF16 to FP32
    FRS = DOUBLE(fp32)    # convert FP32 to FP64

Special registers altered:

    None

## Float Immediate Second-Half MV <a name="fishmv"></a>

`fishmv FRS, D`

DX-Form:

|  0-5   | 6-10 | 11-15 | 16-25 | 26-30 | 31  | Form    |
|--------|------|-------|-------|-------|-----|---------|
|  Major | FRS  | d1    | d0    | XO    | d2  | DX-Form |

Strategically similar to how `oris` is used to construct
32-bit Integers, an additional 16-bits of immediate is
inserted into `FRS` to extend its accuracy to
a full FP32 (stored as usual in FP64 Format within the FPR).
If a prior `fmvis` instruction had been used to
set the upper 16-bits of an FP32 value, `fishmv` contains the
lower 16-bits.

The key difference between using `li` and `oris` to construct 32-bit
GPR Immediates and `fishmv` is that the `fmvis` will have converted
the `BF16` immediate to FP64 (Double) format.
This is taken into consideration
as can be seen in the pseudocode below.

Pseudocode:

    fp32 <- SINGLE((FRS))            # convert to FP32
    fp32[16:31] <- d0 || d1 || d2    # replace LSB half
    FRS <- DOUBLE(fp32)              # convert back to FP64

Special registers altered:

    None

**This instruction performs a Read-Modify-Write.** *FRS is read, the additional
16 bit immediate inserted, and the result also written to FRS*

Example:

```
# these two combined instructions write 0x3f808000
# into f4 as an FP32 to be converted to an FP64.
# actual contents in f4 after conversion: 0x3ff0_1000_0000_0000
# first the upper bits, happens to be +1.0
fmvis f4, 0x3F80 # writes +1.0 to f4
# now write the lower 16 bits of an FP32
fishmv f4, 0x8000 # writes +1.00390625 to f4
```

# Moves & Generalized Bit Reverses

These instructions perform a generalized bit reverse on the underlying bits in
FPRs, optionally moving between FPR/GPR register files. These instructions are
designed to replace using a store/load pair to `memcpy`/transmute the bitwise
representation of floating-point values, with optional endian swaps.

# FPR to FPR Generalized Bit Reverse
* `fgrevi FRT, FRA, SH` XS-form
* `fgrevi. FRT, FRA, SH` XS-form
* `fgrevisd FRT, FRA, SH` XS-form
* `fgrevisd. FRT, FRA, SH` XS-form
* `fgrevids FRT, FRA, SH` XS-form
* `fgrevids. FRT, FRA, SH` XS-form
* `fgrevis FRT, FRA, SH` XS-form
* `fgrevis. FRT, FRA, SH` XS-form

Jacob: maybe leave out sd/ds forms?

read a 32/64-bit float from `FRA`, do a generalized bit reverse on the
zero-extended bitwise representation, then write the result as a 32/64-bit
float to `FRT`.
This can be used to do any combination of endian swaps, which are useful
for emulating a big-endian `memcpy`/transmute e.g. from `f32x2` to `f64` or
from the MSB half of `f64` to `f32` or similar.

Pseudo-code:

```
v <- (FRA)
if insn in ["fgrevisd", "fgrevisd.", "fgrevis", "fgrevis."] then
    v <- [0] * 32 || SINGLE(v)
v <- GREV64(v, SH)
if insn in ["fgrevids", "fgrevids.", "fgrevis", "fgrevis."] then
    FRT <- DOUBLE(v[32:63])
else
    FRT <- v
```

All instructions, including `*s` forms, are explicitly XS-form and have 6-bit
SH immediates, this allows having `f32` values in the MSB 32-bits of the
input/result.

Rc=1 tests FRT and sets CR1, following usual fp Rc=1 semantics.

# GPR to FPR moves & Generalized Bit Reverses

* `fgrevfgi FRT, RA, SH` XS-form
* `fgrevfgi. FRT, RA, SH` XS-form
* `fgrevfgis FRT, RA, SH` XS-form
* `fgrevfgis. FRT, RA, SH` XS-form

read from a GPR and do a generalized bit reverse (grev) on
the bits, writing the resulting bits as a 32/64-bit float to a FPR.
This can be used to do a bitwise copy from a GPR to a FPR.
This can also be used to do any combination of endian swaps, which are useful
for emulating a big-endian `memcpy`/transmute e.g. from `u32x2` to `f64` or
from `i8x4` to `f32` or similar.

Pseudo-code:

```
v <- GREV64((RA), SH)
if insn = "fgrevfgis" or insn = "fgrevfgis." then
    FRT <- DOUBLE(v[32:63])
else
    FRT <- v
```

Rc=1 tests FRT and sets CR1, following usual fp Rc=1 semantics.

Note `fgrevfgis` is explicitly XS-form and has a 6-bit SH immediate, this
allows taking the `f32` value from the MSB 32-bits of the input GPR.

# FPR to GPR Moves & Generalized Bit Reverses

* `fgrevtgi RT, FRA, SH` XS-form
* `fgrevtgi. RT, FRA, SH` XS-form
* `fgrevtgis RT, FRA, SH` XS-form
* `fgrevtgis. RT, FRA, SH` XS-form

read a 32/64-bit float from a FPR and do a generalized bit reverse (grev) on
the zero-extended bitwise bits, writing the result to a GPR. This can be used
to do a bitwise copy from a FPR to a GPR. This can also be used to do any
combination of endian swaps, which are useful for emulating a big-endian
`memcpy`/transmute, e.g. from `f64` to `u32x2` or from `f32` to `i8x4` or
similar.

Pseudo-code:

```
v <- (FRA)
if insn = "fgrevtgis" or insn = "fgrevtgis." then
    v <- [0] * 32 || SINGLE(v)
RT <- GREV64(v, SH)
```

Rc=1 tests RT and sets CR0, exactly like all other Scalar Fixed-Point
operations.

Note `fgrevtgis` is explicitly XS-form and has a 6-bit SH immediate, this
allows putting the `f32` value into the MSB 32-bits of the result.

* `fmvtg RT, FRA` (alias of `fgrevtgi RT, FRA, 0`)
* `fmvtg. RT, FRA` (alias of `fgrevtgi. RT, FRA, 0`)

move a 64-bit float from a FPR to a GPR, just copying bits directly.
As a direct bitcopy, no exceptions occur and no status flags are set.

Rc=1 tests RT and sets CR0, exactly like all other Scalar Fixed-Point
operations.

* `fmvtgs RT, FRA` (alias of `fgrevtgis RT, FRA, 0`)
* `fmvtgs. RT, FRA` (alias of `fgrevtgis. RT, FRA, 0`)

move a 32-bit float from a FPR to a GPR, just copying bits. Converts the
64-bit float in `FRA` to a 32-bit float, using the same method as `stfs`,
then writes the 32-bit float to `RT`, setting the high 32-bits to zeros.
Effectively, `fmvtgs` is a macro-fusion of `stfs` and `lwz` and therefore
does not behave like `frsp` and does not set any fp exception flags.

Since RT is a GPR, Rc=1 follows standard *integer* behaviour, i.e.
tests RT and sets CR0.

# GPR to FPR moves & Generalized Bit Reverses

* `fgrevfgi FRT, RA, SH` XS-form
* `fgrevfgi. FRT, RA, SH` XS-form
* `fgrevfgis FRT, RA, SH` XS-form
* `fgrevfgis. FRT, RA, SH` XS-form

read from a GPR and do a generalized bit reverse (grev) on
the bits, writing the resulting bits as a 32/64-bit float to a FPR.
This can be used to do a bitwise copy from a GPR to a FPR.
This can also be used to do any combination of endian swaps, which are useful
for emulating a big-endian `memcpy`/transmute e.g. from `u32x2` to `f64` or
from `i8x4` to `f32` or similar.

Pseudo-code:

```
v <- GREV64((RA), SH)
if insn = "fgrevfgis" or insn = "fgrevfgis." then
    FRT <- DOUBLE(v[32:63])
else
    FRT <- v
```

Rc=1 tests FRT and sets CR1, following usual fp Rc=1 semantics.

Note `fgrevfgis` is explicitly XS-form and has a 6-bit SH immediate, this
allows taking the `f32` value from the MSB 32-bits of the input GPR.

* `fmvfg FRT, RA` (alias of `fgrevfgi FRT, RA, 0`)
* `fmvfg. FRT, RA` (alias of `fgrevfgi. FRT, RA, 0`)

move a 64-bit float from a GPR to a FPR, just copying bits. No exceptions
are raised, no flags are altered of any kind.

Rc=1 tests FRT and sets CR1, following usual fp Rc=1 semantics.

* `fmvfgs FRT, RA` (alias of `fgrevfgis FRT, RA, 0`)
* `fmvfgs. FRT, RA` (alias of `fgrevfgis. FRT, RA, 0`)

move a 32-bit float from a GPR to a FPR, just copying bits. Converts the
32-bit float in `RA` to a 64-bit float, using the same method as `lfs`,
then writes the 64-bit float to `FRT`. Effectively, `fmvfgs` is a
macro-fusion of `stw` and `lfs` and therefore no fp exception flags are set.

Rc=1 tests FRT and sets CR1, following usual fp Rc=1 semantics.

# Conversions

Unlike the move instructions
these instructions perform conversions between Integer and
Floating Point. Truncation can therefore occur, as well
as exceptions.

Mode values:

| Mode | `rounding_mode` | Semantics                        |
|------|-----------------|----------------------------------|
| 000  | from `FPSCR`    | [OpenPower semantics]            |
| 001  | Truncate        | [OpenPower semantics]            |
| 010  | from `FPSCR`    | [Java semantics]                 |
| 011  | Truncate        | [Java semantics]                 |
| 100  | from `FPSCR`    | [JavaScript semantics]           |
| 101  | Truncate        | [JavaScript semantics]           |
| rest | --              | illegal instruction trap for now |

[OpenPower semantics]: #fp-to-int-openpower-conversion-semantics
[Java semantics]: #fp-to-int-java-conversion-semantics
[JavaScript semantics]: #fp-to-int-javascript-conversion-semantics

## GPR to FPR conversions

**Format**

|  0-5   | 6-10 | 11-15  | 16-25 | 26-30 | 31 | Form |
|--------|------|--------|-------|-------|----|------|
|  Major | FRT  | //Mode | RA    | XO    | Rc |X-Form|

All of the following GPR to FPR conversions use the rounding mode from `FPSCR`.

* `fcvtfgw FRT, RA`
  Convert from 32-bit signed integer in the GPR `RA` to 64-bit float in 
  `FRT`.
* `fcvtfgws FRT, RA`
  Convert from 32-bit signed integer in the GPR `RA` to 32-bit float in 
  `FRT`.
* `fcvtfguw FRT, RA`
  Convert from 32-bit unsigned integer in the GPR `RA` to 64-bit float in 
  `FRT`.
* `fcvtfguws FRT, RA`
  Convert from 32-bit unsigned integer in the GPR `RA` to 32-bit float in 
  `FRT`.
* `fcvtfgd FRT, RA`
  Convert from 64-bit signed integer in the GPR `RA` to 64-bit float in 
  `FRT`.
* `fcvtfgds FRT, RA`
  Convert from 64-bit signed integer in the GPR `RA` to 32-bit float in 
  `FRT`.
* `fcvtfgud FRT, RA`
  Convert from 64-bit unsigned integer in the GPR `RA` to 64-bit float in 
  `FRT`.
* `fcvtfguds FRT, RA`
  Convert from 64-bit unsigned integer in the GPR `RA` to 32-bit float in 
  `FRT`.

## FPR to GPR (Integer) conversions

<div id="fpr-to-gpr-conversion-mode"></div>

Different programming languages turn out to have completely different
semantics for FP to Integer conversion.  Below is an overview
of the different variants, listing the languages and hardware that
implements each variant.

**Standard IEEE754 conversion**

This conversion is outlined in the IEEE754 specification.  It is used
by nearly all programming languages and CPUs.  In the case of OpenPOWER,
the rounding mode is read from FPSCR

**Standard OpenPower conversion**

This conversion, instead of exact IEEE754 Compliance, performs
"saturation with NaN converted to minimum valid integer". This
is also exactly the same as the x86 ISA conversion semantics.
OpenPOWER however has instructions for both:

* rounding mode read from FPSCR
* rounding mode always set to truncate

**Java conversion**

For the sake of simplicity, the FP -> Integer conversion semantics generalized from those used by Java's semantics (and Rust's `as` operator) will be referred to as
[Java conversion semantics](#fp-to-int-java-conversion-semantics).

Those same semantics are used in some way by all of the following languages (not necessarily for the default conversion method):

* Java's
  [FP -> Integer conversion](https://docs.oracle.com/javase/specs/jls/se16/html/jls-5.html#jls-5.1.3)
* Rust's FP -> Integer conversion using the
  [`as` operator](https://doc.rust-lang.org/reference/expressions/operator-expr.html#semantics)
* LLVM's
  [`llvm.fptosi.sat`](https://llvm.org/docs/LangRef.html#llvm-fptosi-sat-intrinsic) and
  [`llvm.fptoui.sat`](https://llvm.org/docs/LangRef.html#llvm-fptoui-sat-intrinsic) intrinsics
* SPIR-V's OpenCL dialect's
  [`OpConvertFToU`](https://www.khronos.org/registry/spir-v/specs/unified1/SPIRV.html#OpConvertFToU) and
  [`OpConvertFToS`](https://www.khronos.org/registry/spir-v/specs/unified1/SPIRV.html#OpConvertFToS)
  instructions when decorated with
  [the `SaturatedConversion` decorator](https://www.khronos.org/registry/spir-v/specs/unified1/SPIRV.html#_a_id_decoration_a_decoration).
* WebAssembly has also introduced
 [trunc_sat_u](ttps://webassembly.github.io/spec/core/exec/numerics.html#op-trunc-sat-u) and
 [trunc_sat_s](https://webassembly.github.io/spec/core/exec/numerics.html#op-trunc-sat-s)

**JavaScript conversion**

For the sake of simplicity, the FP -> Integer conversion semantics generalized from those used by JavaScripts's `ToInt32` abstract operation will be referred to as [JavaScript conversion semantics](#fp-to-int-javascript-conversion-semantics).

This instruction is present in ARM assembler as FJCVTZS
<https://developer.arm.com/documentation/dui0801/g/hko1477562192868>

**Format**

|  0-5   | 6-10 | 11-15  | 16-25 | 26-30 | 31 | Form |
|--------|------|--------|-------|-------|----|------|
|  Major | RT   | //Mode | FRA   | XO    | Rc |X-Form|

**Rc=1 and OE=1**

All of these insructions have an Rc=1 mode which sets CR0
in the normal way for any instructions producing a GPR result.
Additionally, when OE=1, if the numerical value of the FP number
is not 100% accurately preserved (due to truncation or saturation
and including when the FP number was NaN) then this is considered
to be an integer Overflow condition, and CR0.SO, XER.SO and XER.OV
are all set as normal for any GPR instructions that overflow.

**Instructions**

* `fcvttgw RT, FRA, Mode`
  Convert from 64-bit float to 32-bit signed integer, writing the result
  to the GPR `RT`. Converts using [mode `Mode`]. Similar to `fctiw` or `fctiwz`
* `fcvttguw RT, FRA, Mode`
  Convert from 64-bit float to 32-bit unsigned integer, writing the result
  to the GPR `RT`. Converts using [mode `Mode`]. Similar to `fctiwu` or `fctiwuz`
* `fcvttgd RT, FRA, Mode`
  Convert from 64-bit float to 64-bit signed integer, writing the result
  to the GPR `RT`. Converts using [mode `Mode`]. Similar to `fctid` or `fctidz`
* `fcvttgud RT, FRA, Mode`
  Convert from 64-bit float to 64-bit unsigned integer, writing the result
  to the GPR `RT`. Converts using [mode `Mode`]. Similar to `fctidu` or `fctiduz`
* `fcvtstgw RT, FRA, Mode`
  Convert from 32-bit float to 32-bit signed integer, writing the result
  to the GPR `RT`. Converts using [mode `Mode`]
* `fcvtstguw RT, FRA, Mode`
  Convert from 32-bit float to 32-bit unsigned integer, writing the result
  to the GPR `RT`. Converts using [mode `Mode`]
* `fcvtstgd RT, FRA, Mode`
  Convert from 32-bit float to 64-bit signed integer, writing the result
  to the GPR `RT`. Converts using [mode `Mode`]
* `fcvtstgud RT, FRA, Mode`
  Convert from 32-bit float to 64-bit unsigned integer, writing the result
  to the GPR `RT`. Converts using [mode `Mode`]

[mode `Mode`]: #fpr-to-gpr-conversion-mode

## FP to Integer Conversion Pseudo-code

Key for pseudo-code:

| term                      | result type | definition                                                                                         |
|---------------------------|-------------|----------------------------------------------------------------------------------------------------|
| `fp`                      | --          | `f32` or `f64` (or other types from SimpleV)                                                       |
| `int`                     | --          | `u32`/`u64`/`i32`/`i64` (or other types from SimpleV)                                              |
| `uint`                    | --          | the unsigned integer of the same bit-width as `int`                                                |
| `int::BITS`               | `int`       | the bit-width of `int`                                                                             |
| `uint::MIN_VALUE`         | `uint`      | the minimum value `uint` can store: `0`                   |
| `uint::MAX_VALUE`          | `uint`       | the maximum value `uint` can store: `2^int::BITS - 1`  |
| `int::MIN_VALUE`          | `int`       | the minimum value `int` can store : `-2^(int::BITS-1)`              |
| `int::MAX_VALUE`          | `int`       | the maximum value `int` can store :  `2^(int::BITS-1) - 1`  |
| `int::VALUE_COUNT`        | Integer     | the number of different values `int` can store (`2^int::BITS`). too big to fit in `int`.           |
| `rint(fp, rounding_mode)` | `fp`        | rounds the floating-point value `fp` to an integer according to rounding mode `rounding_mode`      |

<div id="fp-to-int-openpower-conversion-semantics"></div>
OpenPower conversion semantics (section A.2 page 999 (page 1023) of OpenPower ISA v3.1):

```
def fp_to_int_open_power<fp, int>(v: fp) -> int:
    if v is NaN:
        return int::MIN_VALUE
    if v >= int::MAX_VALUE:
        return int::MAX_VALUE
    if v <= int::MIN_VALUE:
        return int::MIN_VALUE
    return (int)rint(v, rounding_mode)
```

<div id="fp-to-int-java-conversion-semantics"></div>
[Java conversion semantics](https://docs.oracle.com/javase/specs/jls/se16/html/jls-5.html#jls-5.1.3)
/
[Rust semantics](https://doc.rust-lang.org/reference/expressions/operator-expr.html#semantics)
(with adjustment to add non-truncate rounding modes):

```
def fp_to_int_java<fp, int>(v: fp) -> int:
    if v is NaN:
        return 0
    if v >= int::MAX_VALUE:
        return int::MAX_VALUE
    if v <= int::MIN_VALUE:
        return int::MIN_VALUE
    return (int)rint(v, rounding_mode)
```

<div id="fp-to-int-javascript-conversion-semantics"></div>
Section 7.1 of the ECMAScript / JavaScript
[conversion semantics](https://262.ecma-international.org/11.0/#sec-toint32) (with adjustment to add non-truncate rounding modes):

```
def fp_to_int_java_script<fp, int>(v: fp) -> int:
    if v is NaN or infinite:
        return 0
    v = rint(v, rounding_mode)  # assume no loss of precision in result
    v = v mod int::VALUE_COUNT  # 2^32 for i32, 2^64 for i64, result is non-negative
    bits = (uint)v
    return (int)bits
```