-# Ztrans - transcendental operations
+# Zftrans - transcendental operations
See:
* <http://bugs.libre-riscv.org/show_bug.cgi?id=127>
* <https://www.khronos.org/registry/spir-v/specs/unified1/OpenCL.ExtendedInstructionSet.100.html>
+* Discussion: <http://lists.libre-riscv.org/pipermail/libre-riscv-dev/2019-August/002342.html>
+* [[rv_major_opcode_1010011]] for opcode listing.
+* [[zfpacc_proposal]] for accuracy settings proposal
Extension subsets:
-* **Ztrans**: standard transcendentals (best suited to 3D)
-* **ZtransExt**: extra functions (useful, not generally needed for 3D)
-* **ZtransAdv**: much more complex to implement in hardware
+* **Zftrans**: standard transcendentals (best suited to 3D)
+* **ZftransExt**: extra functions (useful, not generally needed for 3D,
+ can be synthesised using Ztrans)
+* **Ztrigpi**: trig. xxx-pi sinpi cospi tanpi
+* **Ztrignpi**: trig non-xxx-pi sin cos tan
+* **Zarctrigpi**: arc-trig. a-xxx-pi: atan2pi asinpi acospi
+* **Zarctrignpi**: arc-trig. non-a-xxx-pi: atan2, asin, acos
+* **Zfhyp**: hyperbolic/inverse-hyperbolic. sinh, cosh, tanh, asinh,
+ acosh, atanh (can be synthesised - see below)
+* **ZftransAdv**: much more complex to implement in hardware
+* **Zfrsqrt**: Reciprocal square-root.
+
+Minimum recommended requirements for 3D: Zftrans, Ztrigpi, Zarctrigpi,
+Zarctrignpi
[[!toc levels=2]]
+# TODO:
+
+* Decision on accuracy, moved to [[zfpacc_proposal]]
+<http://lists.libre-riscv.org/pipermail/libre-riscv-dev/2019-August/002355.html>
+* Errors **MUST** be repeatable.
+* How about four Platform Specifications? 3DUNIX, UNIX, 3DEmbedded and Embedded?
+<http://lists.libre-riscv.org/pipermail/libre-riscv-dev/2019-August/002361.html>
+ Accuracy requirements for dual (triple) purpose implementations must
+ meet the higher standard.
+* Reciprocal Square-root is in its own separate extension (Zfrsqrt) as
+ it is desirable on its own by other implementors. This to be evaluated.
+
+# Proposed Opcodes vs Khronos OpenCL Opcodes <a name="khronos_equiv"></a>
+
+This list shows the (direct) equivalence between proposed opcodes and
+their Khronos OpenCL equivalents.
+
+See
+<https://www.khronos.org/registry/spir-v/specs/unified1/OpenCL.ExtendedInstructionSet.100.html>
+
+Special FP16 opcodes are *not* being proposed, except by indirect / inherent
+use of the "fmt" field that is already present in the RISC-V Specification.
+
+"Native" opcodes are *not* being proposed: implementors will be expected
+to use the (equivalent) proposed opcode covering the same function.
+
+"Fast" opcodes are *not* being proposed, because the Khronos Specification
+fast\_length, fast\_normalise and fast\_distance OpenCL opcodes require
+vectors (or can be done as scalar operations using other RISC-V instructions).
+
+The OpenCL FP32 opcodes are **direct** equivalents to the proposed opcodes.
+Deviation from conformance with the Khronos Specification - including the
+Khronos Specification accuracy requirements - is not an option.
+
+[[!table data="""
+Proposed opcode | OpenCL FP32 | OpenCL FP16 | OpenCL native | OpenCL fast |
+FSIN | sin | half\_sin | native\_sin | NONE |
+FCOS | cos | half\_cos | native\_cos | NONE |
+FTAN | tan | half\_tan | native\_tan | NONE |
+NONE (1) | sincos | NONE | NONE | NONE |
+FASIN | asin | NONE | NONE | NONE |
+FACOS | acos | NONE | NONE | NONE |
+FATAN | atan | NONE | NONE | NONE |
+FSINPI | sinpi | NONE | NONE | NONE |
+FCOSPI | cospi | NONE | NONE | NONE |
+FTANPI | tanpi | NONE | NONE | NONE |
+FASINPI | asinpi | NONE | NONE | NONE |
+FACOSPI | acospi | NONE | NONE | NONE |
+FATANPI | atanpi | NONE | NONE | NONE |
+FSINH | sinh | NONE | NONE | NONE |
+FCOSH | cosh | NONE | NONE | NONE |
+FTANH | tanh | NONE | NONE | NONE |
+FASINH | asinh | NONE | NONE | NONE |
+FACOSH | acosh | NONE | NONE | NONE |
+FATANH | atanh | NONE | NONE | NONE |
+FRSQRT | rsqrt | half\_rsqrt | native\_rsqrt | NONE |
+FCBRT | cbrt | NONE | NONE | NONE |
+FEXP2 | exp2 | half\_exp2 | native\_exp2 | NONE |
+FLOG2 | log2 | half\_log2 | native\_log2 | NONE |
+FEXPM1 | expm1 | NONE | NONE | NONE |
+FLOG1P | log1p | NONE | NONE | NONE |
+FEXP | exp | half\_exp | native\_exp | NONE |
+FLOG | log | half\_log | native\_log | NONE |
+FEXP10 | exp10 | half\_exp10 | native\_exp10 | NONE |
+FLOG10 | log10 | half\_log10 | native\_log10 | NONE |
+FATAN2 | atan2 | NONE | NONE | NONE |
+FATAN2PI | atan2pi | NONE | NONE | NONE |
+FPOW | pow | NONE | NONE | NONE |
+FROOT | rootn | NONE | NONE | NONE |
+FHYPOT | hypot | NONE | NONE | NONE |
+FRECIP | NONE | half\_recip | native\_recip | NONE |
+"""]]
+
+Note (1) FSINCOS is macro-op fused (see below).
+
# List of 2-arg opcodes
[[!table data="""
-opcode | Description | pseudo-code | Extension |
-FATAN2 | atan2 arc tangent | rd = atan2(rs2, rs1) | Ztrans |
-FATAN2PI | atan arc tangent / pi | rd = atan2(rs2, rs1) / pi | ZtransExt |
-FPOW | x power of y | rd = pow(rs1, rs2) | ZtransAdv |
-FROOT | x power 1/y | rd = pow(rs1, 1/rs2) | ZtransAdv |
+opcode | Description | pseudo-code | Extension |
+FATAN2 | atan2 arc tangent | rd = atan2(rs2, rs1) | Zarctrignpi |
+FATAN2PI | atan2 arc tangent / pi | rd = atan2(rs2, rs1) / pi | Zarctrigpi |
+FPOW | x power of y | rd = pow(rs1, rs2) | ZftransAdv |
+FROOT | x power 1/y | rd = pow(rs1, 1/rs2) | ZftransAdv |
+FHYPOT | hypotenuse | rd = sqrt(rs1^2 + rs2^2) | Zftrans |
+"""]]
+
+# List of 1-arg transcendental opcodes
+
+[[!table data="""
+opcode | Description | pseudo-code | Extension |
+FRSQRT | Reciprocal Square-root | rd = sqrt(rs1) | Zfrsqrt |
+FCBRT | Cube Root | rd = pow(rs1, 3) | Zftrans |
+FRECIP | Reciprocal | rd = 1.0 / rs1 | Zftrans |
+FEXP2 | power-of-2 | rd = pow(2, rs1) | Zftrans |
+FLOG2 | log2 | rd = log2(rs1) | Zftrans |
+FEXPM1 | exponential minus 1 | rd = pow(e, rs1) - 1.0 | Zftrans |
+FLOG1P | log plus 1 | rd = log(e, 1 + rs1) | Zftrans |
+FEXP | exponential | rd = pow(e, rs1) | ZftransExt |
+FLOG | natural log (base e) | rd = log(e, rs1) | ZftransExt |
+FEXP10 | power-of-10 | rd = pow(10, rs1) | ZftransExt |
+FLOG10 | log base 10 | rd = log10(rs1) | ZftransExt |
"""]]
-# List of 1-arg opcodes
+# List of 1-arg trigonometric opcodes
[[!table data="""
opcode | Description | pseudo-code | Extension |
-FCBRT | Cube Root | rd = pow(rs1, 3) | Ztrans |
-FEXP2 | power-of-2 | rd = pow(2, rs1) | Ztrans |
-FLOG2 | log2 | rd = log2(rs1) | Ztrans |
-FEXPM1 | exponent minus 1 | rd = pow(e, rs1) - 1.0 | Ztrans |
-FLOG1P | log plus 1 | rd = log(e, 1 + rs1) | Ztrans |
-FEXP | exponent | rd = pow(e, rs1) | ZtransExt |
-FLOG | natural log (base e) | rd = log(e, rs1) | ZtransExt |
-FEXP10 | power-of-10 | rd = pow(10, rs1) | ZtransExt |
-FLOG10 | log base 10 | rd = log10(rs1) | ZtransExt |
-FSIN | sin (radians) | | Ztrans |
-FCOS | cos (radians) | | Ztrans |
-FTAN | tan (radians) | | Ztrans |
-FASIN | arcsin (radians) | rd = asin(rs1) | Ztrans |
-FACOS | arccos (radians) | rd = acos(rs1) | Ztrans |
-FATAN | arctan (radians) | rd = atan(rs1) | Ztrans |
-FSINPI | sin times pi | rd = sin(pi * rs1) | ZtransExt |
-FCOSPI | cos times pi | rd = cos(pi * rs1) | ZtransExt |
-FTANPI | tan times pi | rd = tan(pi * rs1) | ZtransExt |
-FSINH | hyperbolic sin (radians) | | ZtransExt |
-FCOSH | hyperbolic cos (radians) | | ZtransExt |
-FTANH | hyperbolic tan (radians) | | ZtransExt |
-FASINH | inverse hyperbolic sin | | ZtransExt |
-FACOSH | inverse hyperbolic cos | | ZtransExt |
-FATANH | inverse hyperbolic tan | | ZtransExt |
+FSIN | sin (radians) | rd = sin(rs1) | Ztrignpi |
+FCOS | cos (radians) | rd = cos(rs1) | Ztrignpi |
+FTAN | tan (radians) | rd = tan(rs1) | Ztrignpi |
+FASIN | arcsin (radians) | rd = asin(rs1) | Zarctrignpi |
+FACOS | arccos (radians) | rd = acos(rs1) | Zarctrignpi |
+FATAN | arctan (radians) | rd = atan(rs1) | Zarctrignpi |
+FSINPI | sin times pi | rd = sin(pi * rs1) | Ztrigpi |
+FCOSPI | cos times pi | rd = cos(pi * rs1) | Ztrigpi |
+FTANPI | tan times pi | rd = tan(pi * rs1) | Ztrigpi |
+FASINPI | arcsin / pi | rd = asin(rs1) / pi | Zarctrigpi |
+FACOSPI | arccos / pi | rd = acos(rs1) / pi | Zarctrigpi |
+FATANPI | arctan / pi | rd = atan(rs1) / pi | Zarctrigpi |
+FSINH | hyperbolic sin (radians) | rd = sinh(rs1) | Zfhyp |
+FCOSH | hyperbolic cos (radians) | rd = cosh(rs1) | Zfhyp |
+FTANH | hyperbolic tan (radians) | rd = tanh(rs1) | Zfhyp |
+FASINH | inverse hyperbolic sin | rd = asinh(rs1) | Zfhyp |
+FACOSH | inverse hyperbolic cos | rd = acosh(rs1) | Zfhyp |
+FATANH | inverse hyperbolic tan | rd = atanh(rs1) | Zfhyp |
"""]]
-# Pseudo-code ops
+# Synthesis, Pseudo-code ops and macro-ops
+
+The pseudo-ops are best left up to the compiler rather than being actual
+pseudo-ops, by allocating one scalar FP register for use as a constant
+(loop invariant) set to "1.0" at the beginning of a function or other
+suitable code block.
+
+* FSINCOS - fused macro-op between FSIN and FCOS (issued in that order).
+* FSINCOSPI - fused macro-op between FSINPI and FCOSPI (issued in that order).
+
+FATANPI example pseudo-code:
+
+ lui t0, 0x3F800 // upper bits of f32 1.0
+ fmv.x.s ft0, t0
+ fatan2pi.s rd, rs1, ft0
+
+Hyperbolic function example (obviates need for Zfhyp except for
+high-performance or correctly-rounding):
+
+ ASINH( x ) = ln( x + SQRT(x**2+1))
+
+# Reciprocal
+
+Used to be an alias. Some imolementors may wish to implement divide as y times recip(x)
+
+# To evaluate: should LOG be replaced with LOG1P (and EXP with EXPM1)?
+
+RISC principle says "exclude LOG because it's covered by LOGP1 plus an ADD".
+Research needed to ensure that implementors are not compromised by such
+a decision
+<http://lists.libre-riscv.org/pipermail/libre-riscv-dev/2019-August/002358.html>
+
+> > correctly-rounded LOG will return different results than LOGP1 and ADD.
+> > Likewise for EXP and EXPM1
+
+> ok, they stay in as real opcodes, then.
+
+# ATAN / ATAN2 commentary
+
+Discussion starts here:
+<http://lists.libre-riscv.org/pipermail/libre-riscv-dev/2019-August/002470.html>
+
+from Mitch Alsup:
+
+would like to point out that the general implementations of ATAN2 do a
+bunch of special case checks and then simply call ATAN.
+
+ double ATAN2( double y, double x )
+ { // IEEE 754-2008 quality ATAN2
+
+ // deal with NANs
+ if( ISNAN( x ) ) return x;
+ if( ISNAN( y ) ) return y;
+
+ // deal with infinities
+ if( x == +∞ && |y|== +∞ ) return copysign( π/4, y );
+ if( x == +∞ ) return copysign( 0.0, y );
+ if( x == -∞ && |y|== +∞ ) return copysign( 3π/4, y );
+ if( x == -∞ ) return copysign( π, y );
+ if( |y|== +∞ ) return copysign( π/2, y );
+
+ // deal with signed zeros
+ if( x == 0.0 && y != 0.0 ) return copysign( π/2, y );
+ if( x >=+0.0 && y == 0.0 ) return copysign( 0.0, y );
+ if( x <=-0.0 && y == 0.0 ) return copysign( π, y );
+
+ // calculate ATAN2 textbook style
+ if( x > 0.0 ) return ATAN( |y / x| );
+ if( x < 0.0 ) return π - ATAN( |y / x| );
+ }
+
+
+Yet the proposed encoding makes ATAN2 the primitive and has ATAN invent
+a constant and then call/use ATAN2.
+
+When one considers an implementation of ATAN, one must consider several
+ranges of evaluation::
+
+ x [ -∞, -1.0]:: ATAN( x ) = -π/2 + ATAN( 1/x );
+ x (-1.0, +1.0]:: ATAN( x ) = + ATAN( x );
+ x [ 1.0, +∞]:: ATAN( x ) = +π/2 - ATAN( 1/x );
+
+I should point out that the add/sub of π/2 can not lose significance
+since the result of ATAN(1/x) is bounded 0..π/2
+
+The bottom line is that I think you are choosing to make too many of
+these into OpCodes, making the hardware function/calculation unit (and
+sequencer) more complicated that necessary.
+
+--------------------------------------------------------
+
+I might suggest that if there were a way for a calculation to be performed
+and the result of that calculation
+
+chained to a subsequent calculation such that the precision of the
+result-becomes-operand is wider than
+
+what will fit in a register, then you can dramatically reduce the count
+of instructions in this category while retaining
+
+acceptable accuracy:
+
+ z = x / y
+
+can be calculated as::
+
+ z = x * (1/y)
+
+Where 1/y has about 26-to-32 bits of fraction. No, it's not IEEE 754-2008
+accurate, but GPUs want speed and
+
+1/y is fully pipelined (F32) while x/y cannot be (at reasonable area). It
+is also not "that inaccurate" displaying 0.625-to-0.52 ULP.
+
+Given that one has the ability to carry (and process) more fraction bits,
+one can then do high precision multiplies of π or other transcendental
+radixes.
+
+And GPUs have been doing this almost since the dawn of 3D.
-* FRCP rd, rs1 - pseudo-code alias for rd = 1.0 / rs1
-* SINCOS - fused macro-op between FSIN and FCOS (issued in that order).
-* SINCOSPI - fused macro-op between FSINPI and FCOSPI (issued in that order).
+ // calculate ATAN2 high performance style
+ // Note: at this point x != y
+ //
+ if( x > 0.0 )
+ {
+ if( y < 0.0 && |y| < |x| ) return - π/2 - ATAN( x / y );
+ if( y < 0.0 && |y| > |x| ) return + ATAN( y / x );
+ if( y > 0.0 && |y| < |x| ) return + ATAN( y / x );
+ if( y > 0.0 && |y| > |x| ) return + π/2 - ATAN( x / y );
+ }
+ if( x < 0.0 )
+ {
+ if( y < 0.0 && |y| < |x| ) return + π/2 + ATAN( x / y );
+ if( y < 0.0 && |y| > |x| ) return + π - ATAN( y / x );
+ if( y > 0.0 && |y| < |x| ) return + π - ATAN( y / x );
+ if( y > 0.0 && |y| > |x| ) return +3π/2 + ATAN( x / y );
+ }
+This way the adds and subtracts from the constant are not in a precision
+precarious position.