Note on considered alternative naming schemes: we decided to switch to using the reduced mnemonic naming scheme (over some people's objections) since it would be 5 instructions instead of dozens, though we did consider trying to match PowerISA's existing naming scheme for the instructions rather than only for the instruction aliases. https://bugs.libre-soc.org/show_bug.cgi?id=1015#c7

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
• appendix
• ls002.fmi - fmvis and fishmv External RFC Formal Submission
• ls006.fpintmv - 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:

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

The assembly listings in the 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 appendix

Float load immediate

These are like a variant of mtfpr 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 to instead write +0.0 if RA is register 0, at least allowing clearing FPRs.

fmvis fits with 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

fishmv FRS, D

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

Floating-point to Integer Conversion Overview

IEEE 754 does not specify what results are obtained when converting a NaN or out-of-range floating-point value to integer, so different programming languages and ISAs have made different choices. The different conversion modes supported by the cffpr instruction are as follows:

• P-Type:

  Used by most other PowerISA instructions, as well as commonly used floating-point to integer conversions on x86.

• S-Type:

  Used for several notable programming languages:
  • Java's conversion from float/double to long/int¹
  • Rust's as operator²
  • LLVM's llvm.fptosi.sat³ and llvm.fptoui.sat⁴ intrinsics
  • SPIR-V's OpenCL dialect's OpConvertFToU⁵ and OpConvertFToS⁶ instructions when decorated with the SaturatedConversion⁷ decorator.
  • Also WebAssembly's trunc_sat_u⁸ and trunc_sat_s⁹ instructions,

• E-Type:

  Used for ECMAScript's ToInt32 abstract operation¹⁰. Also implemented in ARMv8.3A as the FJCVTZS instruction¹¹.

Floating-point to Integer Conversion Semantics Summary

Let round be the result of bfp_ROUND_TO_INTEGER(rmode, input). Let w be the number of bits in the result's type. The result of Floating-point to Integer conversion is as follows:

+------+------+---------------------------------------------------------------+
|Type| Result | Category of rounding                                          |
|    | Sign   +----------+-----------+----------+-----------+---------+-------+
|    |        | NaN      | +Inf      | -Inf     | > Max     | < Min   | Else  |
|    |        |          |           |          | Possible  | Possible|       |
|    |        |          |           |          | Result    | Result  |       |
+----+--------+----------+-----------+----------+-----------+---------+-------+
|  P |Unsigned| 0        | 2^w - 1   | 0        | 2^w - 1   | 0       | round |
|    +--------+----------+-----------+----------+-----------+---------+-------+
|    | Signed | -2^(w-1) | 2^(w-1)-1 | -2^(w-1) | 2^(w-1)-1 | -2^(w-1)| round |
+----+--------+----------+-----------+----------+-----------+---------+-------+
|  S |Unsigned| 0        | 2^w - 1   | 0        | 2^w - 1   | 0       | round |
|    +--------+----------+-----------+----------+-----------+---------+-------+
|    | Signed | 0        | 2^(w-1)-1 | -2^(w-1) | 2^(w-1)-1 | -2^(w-1)| round |
+----+--------+----------+-----------+----------+-----------+---------+-------+
|  E | Either | 0                               | round & (2^w - 1)           |
+----+--------+---------------------------------+-----------------------------+

Immediate Tables

Tables that are used by mffpr[s][.]/mtfpr[s]/cffpr[o][.]/ctfpr[s][.]:

IT -- Integer Type

CVM -- Float to Integer Conversion Mode

\newpage{}

Move To/From Floating-Point Register Instructions

These instructions perform a copy from one register file to another, as if by using a GPR/FPR store, followed by a FPR/GPR load.

Move From Floating-Point Register

    mffpr RT, FRB
    mffpr. RT, FRB

    RT <- (FRB)

The contents of FPR[FRB] are placed into GPR[RT].

Special Registers altered:

    CR0     (if Rc=1)

Architecture Note:

mffpr is equivalent to the combination of stfd followed by ld.

Architecture Note:

mffpr is a separate instruction from mfvsrd because mfvsrd requires VSX which may not be available on simpler implementations. Additionally, SVP64 may treat VSX instructions differently than SFFS instructions in a future version of the architecture.

Move From Floating-Point Register Single

    mffprs RT, FRB
    mffprs. RT, FRB

    RT <- [0] * 32 || SINGLE((FRB))

The contents of FPR[FRB] are converted to BFP32 by using SINGLE, then zero-extended to 64-bits, and the result stored in GPR[RT].

Special Registers altered:

    CR0     (if Rc=1)

Architecture Note:

mffprs is equivalent to the combination of stfs followed by lwz.

\newpage{}

Move To Floating-Point Register

    mtfpr FRT, RB

    FRT <- (RB)

The contents of GPR[RB] are placed into FPR[FRT].

Special Registers altered:

    None

Architecture Note:

mtfpr is equivalent to the combination of std followed by lfd.

Architecture Note:

mtfpr is a separate instruction from mtvsrd because mtvsrd requires VSX which may not be available on simpler implementations. Additionally, SVP64 may treat VSX instructions differently than SFFS instructions in a future version of the architecture.

Move To Floating-Point Register Single

    mtfprs FRT, RB

    FRT <- DOUBLE((RB)[32:63])

The contents of bits 32:63 of GPR[RB] are converted to BFP64 by using DOUBLE, then the result is stored in GPR[RT].

Special Registers altered:

    None

Architecture Note:

mtfprs is equivalent to the combination of stw followed by lfs.

\newpage{}

Conversion To/From Floating-Point Register Instructions

Convert To Floating-Point Register

    ctfpr FRT, RB, IT
    ctfpr. FRT, RB, IT

    if IT[0] = 0 then  # 32-bit int -> 64-bit float
        # rounding never necessary, so don't touch FPSCR
        # based off xvcvsxwdp
        if IT = 0 then  # Signed 32-bit
            src <- bfp_CONVERT_FROM_SI32((RB)[32:63])
        else  # IT = 1 -- Unsigned 32-bit
            src <- bfp_CONVERT_FROM_UI32((RB)[32:63])
        FRT <- bfp64_CONVERT_FROM_BFP(src)
    else
        # rounding may be necessary. based off xscvuxdsp
        reset_xflags()
        switch(IT)
            case(0):  # Signed 32-bit
                src <- bfp_CONVERT_FROM_SI32((RB)[32:63])
            case(1):  # Unsigned 32-bit
                src <- bfp_CONVERT_FROM_UI32((RB)[32:63])
            case(2):  # Signed 64-bit
                src <- bfp_CONVERT_FROM_SI64((RB))
            default:  # Unsigned 64-bit
                src <- bfp_CONVERT_FROM_UI64((RB))
        rnd <- bfp_ROUND_TO_BFP64(0b0, FPSCR.RN, src)
        result <- bfp64_CONVERT_FROM_BFP(rnd)
        cls <- fprf_CLASS_BFP64(result)

        if xx_flag = 1 then SetFX(FPSCR.XX)

        FRT <- result
        FPSCR.FPRF <- cls
        FPSCR.FR <- inc_flag
        FPSCR.FI <- xx_flag

Convert from a unsigned/signed 32/64-bit integer in RB to a 64-bit float in FRT.

If converting from a unsigned/signed 32-bit integer to a 64-bit float, rounding is never necessary, so FPSCR is unmodified and exceptions are never raised. Otherwise, FPSCR is modified and exceptions are raised as usual.

Rc=1 tests FRT and sets CR1, exactly like all other Scalar Floating-Point operations.

Special Registers altered:

    CR1               (if Rc=1)
    FPRF FR FI FX XX  (if IT[0]=1)

Assembly Aliases

\newpage{}

Convert To Floating-Point Register Single

    ctfprs FRT, RB, IT
    ctfprs. FRT, RB, IT

    # rounding may be necessary. based off xscvuxdsp
    reset_xflags()
    switch(IT)
        case(0):  # Signed 32-bit
            src <- bfp_CONVERT_FROM_SI32((RB)[32:63])
        case(1):  # Unsigned 32-bit
            src <- bfp_CONVERT_FROM_UI32((RB)[32:63])
        case(2):  # Signed 64-bit
            src <- bfp_CONVERT_FROM_SI64((RB))
        default:  # Unsigned 64-bit
            src <- bfp_CONVERT_FROM_UI64((RB))
    rnd <- bfp_ROUND_TO_BFP32(FPSCR.RN, src)
    result32 <- bfp32_CONVERT_FROM_BFP(rnd)
    cls <- fprf_CLASS_BFP32(result32)
    result <- DOUBLE(result32)

    if xx_flag = 1 then SetFX(FPSCR.XX)

    FRT <- result
    FPSCR.FPRF <- cls
    FPSCR.FR <- inc_flag
    FPSCR.FI <- xx_flag

Convert from a unsigned/signed 32/64-bit integer in RB to a 32-bit float in FRT, following the usual 32-bit float in 64-bit float format. FPSCR is modified and exceptions are raised as usual.

Rc=1 tests FRT and sets CR1, exactly like all other Scalar Floating-Point operations.

Special Registers altered:

    CR1     (if Rc=1)
    FPRF FR FI FX XX

Assembly Aliases

\newpage{}

Convert From Floating-Point Register

    cffpr RT, FRB, CVM, IT
    cffpr. RT, FRB, CVM, IT
    cffpro RT, FRB, CVM, IT
    cffpro. RT, FRB, CVM, IT

    # based on xscvdpuxws
    reset_xflags()
    src <- bfp_CONVERT_FROM_BFP64((FRB))

    switch(IT)
        case(0):  # Signed 32-bit
            range_min <- bfp_CONVERT_FROM_SI32(0x8000_0000)
            range_max <- bfp_CONVERT_FROM_SI32(0x7FFF_FFFF)
            js_mask <- 0x0000_0000_FFFF_FFFF
        case(1):  # Unsigned 32-bit
            range_min <- bfp_CONVERT_FROM_UI32(0)
            range_max <- bfp_CONVERT_FROM_UI32(0xFFFF_FFFF)
            js_mask <- 0x0000_0000_FFFF_FFFF
        case(2):  # Signed 64-bit
            range_min <- bfp_CONVERT_FROM_SI64(-0x8000_0000_0000_0000)
            range_max <- bfp_CONVERT_FROM_SI64(0x7FFF_FFFF_FFFF_FFFF)
            js_mask <- 0xFFFF_FFFF_FFFF_FFFF
        default:  # Unsigned 64-bit
            range_min <- bfp_CONVERT_FROM_UI64(0)
            range_max <- bfp_CONVERT_FROM_UI64(0xFFFF_FFFF_FFFF_FFFF)
            js_mask <- 0xFFFF_FFFF_FFFF_FFFF

    if (CVM[2] = 1) | (FPSCR.RN = 0b01) then
        rnd <- bfp_ROUND_TO_INTEGER_TRUNC(src)
    else if FPSCR.RN = 0b00 then
        rnd <- bfp_ROUND_TO_INTEGER_NEAR_EVEN(src)
    else if FPSCR.RN = 0b10 then
        rnd <- bfp_ROUND_TO_INTEGER_CEIL(src)
    else if FPSCR.RN = 0b11 then
        rnd <- bfp_ROUND_TO_INTEGER_FLOOR(src)

    switch(CVM)
        case(0, 1):  # P-Type
            if IsNaN(rnd) then
                result <- si64_CONVERT_FROM_BFP(range_min)
            else if bfp_COMPARE_GT(rnd, range_max) then
                result <- ui64_CONVERT_FROM_BFP(range_max)
            else if bfp_COMPARE_LT(rnd, range_min) then
                result <- si64_CONVERT_FROM_BFP(range_min)
            else if IT[1] = 1 then  # Unsigned 32/64-bit
                result <- ui64_CONVERT_FROM_BFP(rnd)
            else  # Signed 32/64-bit
                result <- si64_CONVERT_FROM_BFP(rnd)
        case(2, 3):  # S-Type
            if IsNaN(rnd) then
                result <- [0] * 64
            else if bfp_COMPARE_GT(rnd, range_max) then
                result <- ui64_CONVERT_FROM_BFP(range_max)
            else if bfp_COMPARE_LT(rnd, range_min) then
                result <- si64_CONVERT_FROM_BFP(range_min)
            else if IT[1] = 1 then  # Unsigned 32/64-bit
                result <- ui64_CONVERT_FROM_BFP(rnd)
            else  # Signed 32/64-bit
                result <- si64_CONVERT_FROM_BFP(rnd)
        default:  # E-Type
            # CVM = 6, 7 are illegal instructions
            # using a 128-bit intermediate works here because the largest type
            # this instruction can convert from has 53 significand bits, and
            # the largest type this instruction can convert to has 64 bits,
            # and the sum of those is strictly less than the 128 bits of the
            # intermediate result.
            limit <- bfp_CONVERT_FROM_UI128([1] * 128)
            if IsInf(rnd) | IsNaN(rnd) then
                result <- [0] * 64
            else if bfp_COMPARE_GT(bfp_ABSOLUTE(rnd), limit) then
                result <- [0] * 64
            else
                result128 <- si128_CONVERT_FROM_BFP(rnd)
                result <- result128[64:127] & js_mask

    switch(IT)
        case(0):  # Signed 32-bit
            result <- EXTS64(result[32:63])
            result_bfp <- bfp_CONVERT_FROM_SI32(result[32:63])
        case(1):  # Unsigned 32-bit
            result <- EXTZ64(result[32:63])
            result_bfp <- bfp_CONVERT_FROM_UI32(result[32:63])
        case(2):  # Signed 64-bit
            result_bfp <- bfp_CONVERT_FROM_SI64(result)
        default:  # Unsigned 64-bit
            result_bfp <- bfp_CONVERT_FROM_UI64(result)

    overflow <- 0  # signals SO only when OE = 1
    if IsNaN(src) | ¬bfp_COMPARE_EQ(rnd, result_bfp) then
        overflow <- 1  # signals SO only when OE = 1
        vxcvi_flag <- 1
        xx_flag <- 0
        inc_flag <- 0
    else
        xx_flag <- ¬bfp_COMPARE_EQ(src, result_bfp)
        inc_flag <- bfp_COMPARE_GT(bfp_ABSOLUTE(result_bfp), bfp_ABSOLUTE(src))

    if vxsnan_flag = 1 then SetFX(FPSCR.VXSNAN)
    if vxcvi_flag = 1 then SetFX(FPSCR.VXCVI)
    if xx_flag = 1 then SetFX(FPSCR.XX)

    vx_flag <- vxsnan_flag | vxcvi_flag
    vex_flag <- FPSCR.VE & vx_flag
    if vex_flag = 0 then
        RT <- result
        FPSCR.FPRF <- undefined
        FPSCR.FR <- inc_flag
        FPSCR.FI <- xx_flag
    else
        FPSCR.FR <- 0
        FPSCR.FI <- 0

Convert from 64-bit float in FRB to a unsigned/signed 32/64-bit integer in RT, with the conversion overflow/rounding semantics following the chosen CVM value. FPSCR is modified and exceptions are raised as usual.

This instruction has 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. When RT is not written (vex_flag = 1), all CR0 bits except SO are undefined.

Special Registers altered:

    CR0              (if Rc=1)
    XER SO, OV, OV32 (if OE=1)
    FPRF=0bUUUUU FR FI FX XX VXSNAN VXCV

Assembly Aliases