1. "F" Standard Extension for Single-Precision Floating-Point, Version 2.2
This chapter describes the standard instruction-set extension for single-precision floating-point, which is named "F" and adds single-precision floating-point computational instructions compliant with the IEEE 754-2008 arithmetic standard (ANSI/IEEE Std 754-2008, IEEE Standard for Floating-Point Arithmetic, 2008). The F extension depends on the "Zicsr" extension for control and status register access.
1.1. F Register State
The F extension adds 32 floating-point registers, f0-f31, each 32
bits wide, and a floating-point control and status register fcsr,
which contains the operating mode and exception status of the
floating-point unit. This additional state is shown in
Table 1. We use the term FLEN to describe the width of
the floating-point registers in the RISC-V ISA, and FLEN=32 for the F
single-precision floating-point extension. Most floating-point
instructions operate on values in the floating-point register file.
Floating-point load and store instructions transfer floating-point
values between registers and memory. Instructions to transfer values to and from the integer register file are also provided.
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We considered a unified register file for both integer and floating-point values as this simplifies software register allocation and calling conventions, and reduces total user state. However, a split organization increases the total number of registers accessible with a given instruction width, simplifies provision of enough regfile ports for wide superscalar issue, supports decoupled floating-point-unit architectures, and simplifies use of internal floating-point encoding techniques. Compiler support and calling conventions for split register file architectures are well understood, and using dirty bits on floating-point register file state can reduce context-switch overhead. |
FLEN-1 |
0 |
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f0 |
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f1 |
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f2 |
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f3 |
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f4 |
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f5 |
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f6 |
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f7 |
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f8 |
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f9 |
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f10 |
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f11 |
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f12 |
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f13 |
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f14 |
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f15 |
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f16 |
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f17 |
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f18 |
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f19 |
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f20 |
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f21 |
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f22 |
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f23 |
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f24 |
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f25 |
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f26 |
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f27 |
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f28 |
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f29 |
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f30 |
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f31 |
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FLEN |
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31 |
0 |
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fcsr |
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32 |
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1.2. Floating-Point Control and Status Register
The floating-point control and status register, fcsr, is a RISC-V
control and status register (CSR). It is a 32-bit read/write register
that selects the dynamic rounding mode for floating-point arithmetic
operations and holds the accrued exception flags, as shown in Floating-Point Control and Status Register.
Figure 1. Floating-point control and status register
The fcsr register can be read and written with the FRCSR and FSCSR
instructions, which are assembler pseudoinstructions built on the
underlying CSR access instructions. FRCSR reads fcsr by copying it
into integer register rd. FSCSR swaps the value in fcsr by copying
the original value into integer register rd, and then writing a new
value obtained from integer register rs1 into fcsr.
The fields within the fcsr can also be accessed individually through
different CSR addresses, and separate assembler pseudoinstructions are defined
for these accesses. The FRRM instruction reads the Rounding Mode field frm
(fcsr bits 7—5) and copies it into the least-significant three bits of
integer register rd, with zero in all other bits. FSRM swaps the value in
frm by copying the original value into integer register rd, and then
writing a new value obtained from the three least-significant bits of integer
register rs1 into frm. FRFLAGS and FSFLAGS are defined analogously for the
Accrued Exception Flags field fflags (fcsr bits 4—0).
Bits 31—8 of the fcsr are reserved for other standard extensions. If
these extensions are not present, implementations shall ignore writes to
these bits and supply a zero value when read. Standard software should
preserve the contents of these bits.
Floating-point operations use either a static rounding mode encoded in
the instruction, or a dynamic rounding mode held in frm. Rounding
modes are encoded as shown in Table 2. A value of 111 in the
instruction’s rm field selects the dynamic rounding mode held in
frm. The behavior of floating-point instructions that depend on
rounding mode when executed with a reserved rounding mode is reserved, including both static reserved rounding modes (101-110) and dynamic reserved rounding modes (101-111). Some instructions, including widening conversions, have the rm field but are nevertheless mathematically unaffected by the rounding mode; software should set their rm field to
RNE (000) but implementations must treat the rm field as usual (in
particular, with regard to decoding legal vs. reserved encodings).
| Rounding Mode | Mnemonic | Meaning |
|---|---|---|
000 |
RNE |
Round to Nearest, ties to Even |
001 |
RTZ |
Round towards Zero |
010 |
RDN |
Round Down (towards \(-\infty\)) |
011 |
RUP |
Round Up (towards \(+\infty\)) |
100 |
RMM |
Round to Nearest, ties to Max Magnitude |
101 |
Reserved for future use. |
|
110 |
Reserved for future use. |
|
111 |
DYN |
In instruction’s rm field, selects dynamic rounding mode; In Rounding Mode register, reserved. |
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The C99 language standard effectively mandates the provision of a dynamic rounding mode register. In typical implementations, writes to the dynamic rounding mode CSR state will serialize the pipeline. Static rounding modes are used to implement specialized arithmetic operations that often have to switch frequently between different rounding modes. The ratified version of the F spec mandated that an illegal-instruction exception was raised when an instruction was executed with a reserved dynamic rounding mode. This has been weakened to reserved, which matches the behavior of static rounding-mode instructions. Raising an illegal-instruction exception is still valid behavior when encountering a reserved encoding, so implementations compatible with the ratified spec are compatible with the weakened spec. |
The accrued exception flags indicate the exception conditions that have arisen on any floating-point arithmetic instruction since the field was last reset by software, as shown in Table 3. The base RISC-V ISA does not support generating a trap on the setting of a floating-point exception flag.
| Flag Mnemonic | Flag Meaning |
|---|---|
NV |
Invalid Operation |
DZ |
Divide by Zero |
OF |
Overflow |
UF |
Underflow |
NX |
Inexact |
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As allowed by the standard, we do not support traps on floating-point exceptions in the F extension, but instead require explicit checks of the flags in software. We considered adding branches controlled directly by the contents of the floating-point accrued exception flags, but ultimately chose to omit these instructions to keep the ISA simple. |
1.3. NaN Generation and Propagation
Except when otherwise stated, if the result of a floating-point
operation is NaN, it is the canonical NaN. The canonical NaN has a
positive sign and all significand bits clear except the MSB, a.k.a. the
quiet bit. For single-precision floating-point, this corresponds to the pattern 0x7fc00000.
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We considered propagating NaN payloads, as is recommended by the standard, but this decision would have increased hardware cost. Moreover, since this feature is optional in the standard, it cannot be used in portable code. Implementors are free to provide a NaN payload propagation scheme as a nonstandard extension enabled by a nonstandard operating mode. However, the canonical NaN scheme described above must always be supported and should be the default mode. |
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We require implementations to return the standard-mandated default values in the case of exceptional conditions, without any further intervention on the part of user-level software (unlike the Alpha ISA floating-point trap barriers). We believe full hardware handling of exceptional cases will become more common, and so wish to avoid complicating the user-level ISA to optimize other approaches. Implementations can always trap to machine-mode software handlers to provide exceptional default values. |
1.4. Subnormal Arithmetic
Operations on subnormal numbers are handled in accordance with the IEEE 754-2008 standard.
In the parlance of the IEEE standard, tininess is detected after rounding.
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Detecting tininess after rounding results in fewer spurious underflow signals. |
1.5. Single-Precision Load and Store Instructions
Floating-point loads and stores use the same base+offset addressing mode as the integer base ISAs, with a base address in register rs1 and a 12-bit signed byte offset. The FLW instruction loads a single-precision floating-point value from memory into floating-point register rd. FSW stores a single-precision value from floating-point register rs2 to memory.
FLW and FSW are only guaranteed to execute atomically if the effective address is naturally aligned.
FLW and FSW do not modify the bits being transferred; in particular, the payloads of non-canonical NaNs are preserved.
As described in [ldst], the execution environment defines whether misaligned floating-point loads and stores are handled invisibly or raise a contained or fatal trap.
1.6. Single-Precision Floating-Point Computational Instructions
Floating-point arithmetic instructions with one or two source operands use the R-type format with the OP-FP major opcode. FADD.S and FMUL.S perform single-precision floating-point addition and multiplication respectively, between rs1 and rs2. FSUB.S performs the single-precision floating-point subtraction of rs2 from rs1. FDIV.S performs the single-precision floating-point division of rs1 by rs2. FSQRT.S computes the square root of rs1. In each case, the result is written to rd.
The 2-bit floating-point format field fmt is encoded as shown in Table 4. It is set to S (00) for all instructions in the F extension.
| fmt field | Mnemonic | Meaning |
|---|---|---|
00 |
S |
32-bit single-precision |
01 |
D |
64-bit double-precision |
10 |
H |
16-bit half-precision |
11 |
Q |
128-bit quad-precision |
All floating-point operations that perform rounding can select the rounding mode using the rm field with the encoding shown in Table 2.
Floating-point minimum-number and maximum-number instructions FMIN.S and FMAX.S write, respectively, the smaller or larger of rs1 and rs2 to rd. For the purposes of these instructions only, the value \(-0.0\) is considered to be less than the value \(+0.0\). If both inputs are NaNs, the result is the canonical NaN. If only one operand is a NaN, the result is the non-NaN operand. Signaling NaN inputs set the invalid operation exception flag, even when the result is not NaN.
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Note that in version 2.2 of the F extension, the FMIN.S and FMAX.S instructions were amended to implement the proposed IEEE 754-201x minimumNumber and maximumNumber operations, rather than the IEEE 754-2008 minNum and maxNum operations. These operations differ in their handling of signaling NaNs. |
Floating-point fused multiply-add instructions require a new standard instruction format. R4-type instructions specify three source registers (rs1, rs2, and rs3) and a destination register (rd). This format is only used by the floating-point fused multiply-add instructions.
FMADD.S multiplies the values in rs1 and rs2, adds the value in rs3, and writes the final result to rd. FMADD.S computes (rs1\(\times\)rs2)\(\+\)rs3.
FMSUB.S multiplies the values in rs1 and rs2, subtracts the value in rs3, and writes the final result to rd. FMSUB.S computes (rs1\(\times\)rs2)\(\-\)rs3.
FNMSUB.S multiplies the values in rs1 and rs2, negates the product, adds the value in rs3, and writes the final result to rd. FNMSUB.S computes -(rs1\(\times\)rs2)\(\+\)rs3.
FNMADD.S multiplies the values in rs1 and rs2, negates the product, subtracts the value in rs3, and writes the final result to rd. FNMADD.S computes -(rs1\(\times\)rs2)\(\-\)rs3.
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The FNMSUB and FNMADD instructions are counterintuitively named, owing to the naming of the corresponding instructions in MIPS-IV. The MIPS instructions were defined to negate the sum, rather than negating the product as the RISC-V instructions do, so the naming scheme was more rational at the time. The two definitions differ with respect to signed-zero results. The RISC-V definition matches the behavior of the x86 and ARM fused multiply-add instructions, but unfortunately the RISC-V FNMSUB and FNMADD instruction names are swapped compared to x86 and ARM. |
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The fused multiply-add (FMA) instructions consume a large part of the 32-bit instruction encoding space. Some alternatives considered were to restrict FMA to only use dynamic rounding modes, but static rounding modes are useful in code that exploits the lack of product rounding. Another alternative would have been to use rd to provide rs3, but this would require additional move instructions in some common sequences. The current design still leaves a large portion of the 32-bit encoding space open while avoiding having FMA be non-orthogonal. |
The fused multiply-add instructions must set the invalid operation exception flag when the multiplicands are \(\infty\) and zero, even when the addend is a quiet NaN.
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The IEEE 754-2008 standard permits, but does not require, raising the invalid exception for the operation \(\infty\times 0\ +\)qNaN. |
1.7. Single-Precision Floating-Point Conversion and Move Instructions
Floating-point-to-integer and integer-to-floating-point conversion instructions are encoded in the OP-FP major opcode space. FCVT.W.S or FCVT.L.S converts a floating-point number in floating-point register rs1 to a signed 32-bit or 64-bit integer, respectively, in integer register rd. FCVT.S.W or FCVT.S.L converts a 32-bit or 64-bit signed integer, respectively, in integer register rs1 into a floating-point number in floating-point register rd. FCVT.WU.S, FCVT.LU.S, FCVT.S.WU, and FCVT.S.LU variants convert to or from unsigned integer values. For XLEN\(>32\), FCVT.W[U].S sign-extends the 32-bit result to the destination register width. FCVT.L[U].S and FCVT.S.L[U] are RV64-only instructions. If the rounded result is not representable in the destination format, it is clipped to the nearest value and the invalid flag is set. Table 5 gives the range of valid inputs for FCVT.int.S and the behavior for invalid inputs.
All floating-point to integer and integer to floating-point conversion
instructions round according to the rm field. A floating-point
register can be initialized to floating-point positive zero using
FCVT.S.W rd, x0, which will never set any exception flags.
| FCVT.W.S | FCVT.WU.S | FCVT.L.S | FCVT.LU.S | |
|---|---|---|---|---|
Minimum valid input (after rounding) |
\(-2^{31}\) |
0 |
\(-2^{63}\) |
0 |
Maximum valid input (after rounding) |
\(2^{31}-1\) |
\(2^{32}-1\) |
\(2^{63}-1\) |
\(2^{64}-1\) |
Output for out-of-range negative input |
\(-2^{31}\) |
0 |
\(-2^{63}\) |
0 |
Output for \(-\infty\) |
\(-2^{31}\) |
0 |
\(-2^{63}\) |
0 |
Output for out-of-range positive input |
\(2^{31}-1\) |
\(2^{32}-1\) |
\(2^{63}-1\) |
\(2^{64}-1\) |
Output for \(+\infty\) or NaN |
\(2^{31}-1\) |
\(2^{32}-1\) |
\(2^{63}-1\) |
\(2^{64}-1\) |
All floating-point conversion instructions set the Inexact exception flag if the rounded result differs from the operand value and the Invalid exception flag is not set.
Floating-point to floating-point sign-injection instructions, FSGNJ.S, FSGNJN.S, and FSGNJX.S, produce a result that takes all bits except the sign bit from rs1. For FSGNJ, the result’s sign bit is rs2's sign bit; for FSGNJN, the result’s sign bit is the opposite of rs2's sign bit; and for FSGNJX, the sign bit is the XOR of the sign bits of rs1 and rs2. Sign-injection instructions do not set floating-point exception flags, nor do they canonicalize NaNs. Note, FSGNJ.S rx, ry, ry moves ry to rx (assembler pseudoinstruction FMV.S rx, ry); FSGNJN.S rx, ry, ry moves the negation of ry to rx (assembler pseudoinstruction FNEG.S rx, ry); and FSGNJX.S rx, ry, ry moves the absolute value of ry to rx (assembler pseudoinstruction FABS.S rx, ry).
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The sign-injection instructions provide floating-point MV, ABS, and NEG, as well as supporting a few other operations, including the IEEE copySign operation and sign manipulation in transcendental math function libraries. Although MV, ABS, and NEG only need a single register operand, whereas FSGNJ instructions need two, it is unlikely most microarchitectures would add optimizations to benefit from the reduced number of register reads for these relatively infrequent instructions. Even in this case, a microarchitecture can simply detect when both source registers are the same for FSGNJ instructions and only read a single copy. |
Instructions are provided to move bit patterns between the floating-point and integer registers. FMV.X.W moves the single-precision value in floating-point register rs1 represented in IEEE 754-2008 encoding to the lower 32 bits of integer register rd. The bits are not modified in the transfer, and in particular, the payloads of non-canonical NaNs are preserved. For RV64, the higher 32 bits of the destination register are filled with copies of the floating-point number’s sign bit.
FMV.W.X moves the single-precision value encoded in IEEE 754-2008 standard encoding from the lower 32 bits of integer register rs1 to the floating-point register rd. The bits are not modified in the transfer, and in particular, the payloads of non-canonical NaNs are preserved.
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The FMV.W.X and FMV.X.W instructions were previously called FMV.S.X and FMV.X.S. The use of W is more consistent with their semantics as an instruction that moves 32 bits without interpreting them. This became clearer after defining NaN-boxing. To avoid disturbing existing code, both the W and S versions will be supported by tools. |
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The base floating-point ISA was defined so as to allow implementations to employ an internal recoding of the floating-point format in registers to simplify handling of subnormal values and possibly to reduce functional unit latency. To this end, the F extension avoids representing integer values in the floating-point registers by defining conversion and comparison operations that read and write the integer register file directly. This also removes many of the common cases where explicit moves between integer and floating-point registers are required, reducing instruction count and critical paths for common mixed-format code sequences. |
1.8. Single-Precision Floating-Point Compare Instructions
Floating-point compare instructions (FEQ.S, FLT.S, FLE.S) perform the specified comparison between floating-point registers (\(\mbox{\em rs1} = \mbox{\em rs2}\), \(\mbox{\em rs1} < \mbox{\em rs2}\), \(\mbox{\em rs1} \leq \mbox{\em rs2}\)) writing 1 to the integer register rd if the condition holds, and 0 otherwise.
FLT.S and FLE.S perform what the IEEE 754-2008 standard refers to as signaling comparisons: that is, they set the invalid operation exception flag if either input is NaN. FEQ.S performs a quiet comparison: it only sets the invalid operation exception flag if either input is a signaling NaN. For all three instructions, the result is 0 if either operand is NaN.
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The F extension provides a \(\leq\) comparison, whereas the base ISAs provide a \(\geq\) branch comparison. Because \(\leq\) can be synthesized from \(\geq\) and vice-versa, there is no performance implication to this inconsistency, but it is nevertheless an unfortunate incongruity in the ISA. |
1.9. Single-Precision Floating-Point Classify Instruction
The FCLASS.S instruction examines the value in floating-point register rs1 and writes to integer register rd a 10-bit mask that indicates the class of the floating-point number. The format of the mask is described in Table 6. The corresponding bit in rd will be set if the property is true and clear otherwise. All other bits in rd are cleared. Note that exactly one bit in rd will be set. FCLASS.S does not set the floating-point exception flags.
| rd bit | Meaning |
|---|---|
0 |
rs1 is \(-\infty\). |
1 |
rs1 is a negative normal number. |
2 |
rs1 is a negative subnormal number. |
3 |
rs1 is \(-0\). |
4 |
rs1 is \(+0\). |
5 |
rs1 is a positive subnormal number. |
6 |
rs1 is a positive normal number. |
7 |
rs1 is \(+\infty\). |
8 |
rs1 is a signaling NaN. |
9 |
rs1 is a quiet NaN. |