Immediate Tables

Tables that are used by fmvtg[s][.]/fmvfg[s][.]/fcvt[s]tg[o][.]/fcvtfg[s][.]:

IT -- Integer Type

CVM -- Float to Integer Conversion Mode

Moves

These instructions perform a straight unaltered bit-level copy from one Register File to another.

Floating Move To GPR

    fmvtg RT, FRB
    fmvtg. RT, FRB

    RT <- (FRB)

Move a 64-bit float from a FPR to a GPR, just copying bits of the IEEE 754 representation directly. This is equivalent to stfd followed by ld. As fmvtg is just copying bits, FPSCR is not affected in any way.

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

Special Registers altered:

    CR0     (if Rc=1)

Floating Move To GPR Single

    fmvtgs RT, FRB
    fmvtgs. RT, FRB

    RT <- [0] * 32 || SINGLE((FRB))  # SINGLE since that's what stfs uses

Move a BFP32 from a FPR to a GPR, by using SINGLE to extract the standard BFP32 form from FRB and zero-extending the result to 64-bits and storing to RT. This is equivalent to stfs followed by lwz. As fmvtgs is just copying the BFP32 form, FPSCR is not affected in any way.

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

Special Registers altered:

    CR0     (if Rc=1)

\newpage{}

Double-Precision Floating Move From GPR

    fmvfg FRT, RB
    fmvfg. FRT, RB

    FRT <- (RB)

move a 64-bit float from a GPR to a FPR, just copying bits of the IEEE 754 representation directly. This is equivalent to std followed by lfd. As fmvfg is just copying bits, FPSCR is not affected in any way.

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

Special Registers altered:

    CR1     (if Rc=1)

Floating Move From GPR Single

    fmvfgs FRT, RB
    fmvfgs. FRT, RB

    FRT <- DOUBLE((RB)[32:63])  # DOUBLE since that's what lfs uses

Move a BFP32 from a GPR to a FPR, by using DOUBLE on the least significant 32-bits of RB to do the standard BFP32 in BFP64 trick and store the result in FRT. This is equivalent to stw followed by lfs. As fmvfgs is just copying the BFP32 form, FPSCR is not affected in any way.

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

Special Registers altered:

    CR1     (if Rc=1)

\newpage{}

Conversions

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

Double-Precision Floating Convert From Integer In GPR

    fcvtfg FRT, RB, IT
    fcvtfg. 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{}

Floating Convert From Integer In GPR Single

    fcvtfgs FRT, RB, IT
    fcvtfgs. 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{}

Floating-point to Integer Conversion Overview

IEEE 754 doesn't 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. Below is an overview of the different variants, listing the languages and hardware that implements each variant.

For convenience, those different conversion semantics will be given names based on which common ISA or programming language uses them, since there may not be an established name for them:

Standard OpenPower conversion

This conversion 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/Saturating 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/Saturating 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 (only for long/int results)
• Rust's FP -> Integer conversion using the as operator
• LLVM's llvm.fptosi.sat and llvm.fptoui.sat intrinsics
• SPIR-V's OpenCL dialect's OpConvertFToU and OpConvertFToS instructions when decorated with the SaturatedConversion decorator.
• WebAssembly has also introduced trunc_sat_u and 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.

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

Rc=1 and OE=1

All of these instructions 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.

\newpage{}

FP to Integer Conversion Simplified Pseudo-code

Key for pseudo-code:

OpenPower conversion semantics (section A.2 page 1009 (page 1035) of Power ISA v3.1B):

    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)

Java/Saturating conversion semantics (only for long/int results) (with adjustment to add non-truncate rounding modes):

    def fp_to_int_java_saturating<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)

Section 7.1 of the ECMAScript / JavaScript conversion semantics (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

\newpage{}

Double-Precision Floating Convert To Integer In GPR

    fcvttg RT, FRB, CVM, IT
    fcvttg. RT, FRB, CVM, IT
    fcvttgo RT, FRB, CVM, IT
    fcvttgo. 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):  # OpenPower semantics
            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):  # Java/Saturating semantics
            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:  # JavaScript semantics
            # 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.

These instructions 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. 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

\newpage{}

Floating Convert Single To Integer In GPR

    fcvtstg RT, FRB, CVM, IT
    fcvtstg. RT, FRB, CVM, IT
    fcvtstgo RT, FRB, CVM, IT
    fcvtstgo. RT, FRB, CVM, IT

    # based on xscvdpuxws
    reset_xflags()
    src <- bfp_CONVERT_FROM_BFP32(SINGLE((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):  # OpenPower semantics
            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):  # Java/Saturating semantics
            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:  # JavaScript semantics
            # 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 32-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, following the usual 32-bit float in 64-bit float format. FPSCR is modified and exceptions are raised as usual.

These instructions 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. 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