# [llvm-dev] RFC: A proposal for vectorizing loops with calls to math functions using SVML

Masten, Matt via llvm-dev llvm-dev at lists.llvm.org
Thu Mar 31 17:20:51 PDT 2016

```RFC: A proposal for vectorizing loops with calls to math functions using SVML (short
vector math library).

=========
Overview
=========

Very simply, SVML (Intel short vector math library) functions are vector variants of
scalar math functions that take vector arguments, apply an operation to each
element, and store the result in a vector register. These vector variants can be
generated by the compiler, based on precision requirements specified by the
user, resulting in substantial performance gains. This is an initial proposal to
add a new LLVM IR transformation pass that will translate scalar math calls to
svml calls with the help of the loop vectorizer.

====================
Problem Description
====================

Currently, without the "#pragma clang loop vectorize(enable)", the loop
vectorizer will not vectorize loops with math calls due to cost model reasons.
Additionally, When the loop pragma is used, the loop vectorizer will widen the
math call using an intrinsic, but the resulting code is inefficient because the
intrinsic is replaced with scalarized function calls. Please see the example
below for a simple loop containing a sinf call. For demonstration purposes, the
example was compiled for an xmm target, thus VF = 4 given the float type.

Example: sinf.c

#define N 1000

#pragma clang loop vectorize(enable)
for (i = 0; i < N; i++) {
array[i] = sinf((float)i);
}

Without the loop pragma the loop vectorizer's cost model rejects the loop.

clang -c -ffast-math -O2 -Rpass-analysis=loop-vectorize
-Rpass-missed=loop-vectorize sinf.c

sinf.c:19:3: remark: the cost-model indicates that vectorization is not
beneficial [-Rpass-analysis=loop-vectorize]
for (i = 0; i < N; i++) {
^
sinf.c:19:3: remark: the cost-model indicates that interleaving is not
beneficial and is explicitly disabled or interleave count is set to 1
[-Rpass-analysis=loop-vectorize]

When the the loop pragma is used, the loop is vectorized and the call to
@llvm.sin.v4f32 is generated, but the call is later scalarized with the
additional overhead of unpacking the scalar function arguments from a vector.
This can be seen from inspection of the resulting assembly code just below the
LLVM IR.

vector.body:                                ; preds = %vector.body, %vector.ph
%index = phi i64 [ 0, %vector.ph ], [ %index.next, %vector.body ], !dbg !6
%0 = trunc i64 %index to i32, !dbg !7
%broadcast.splatinsert6 = insertelement <4 x i32> undef, i32 %0, i32 0,
!dbg !7
%broadcast.splat7 = shufflevector <4 x i32> %broadcast.splatinsert6,
<4 x i32> undef, <4 x i32> zeroinitializer, !dbg !7
%induction8 = add <4 x i32> %broadcast.splat7, <i32 0, i32 1, i32 2, i32 3>,
!dbg !7
%1 = sitofp <4 x i32> %induction8 to <4 x float>, !dbg !7
%2 = call <4 x float> @llvm.sin.v4f32(<4 x float> %1), !dbg !8
%3 = getelementptr inbounds float, float* %array, i64 %index, !dbg !9
%4 = bitcast float* %3 to <4 x float>*, !dbg !10
store <4 x float> %2, <4 x float>* %4, align 4, !dbg !10, !tbaa !11
%index.next = add i64 %index, 4, !dbg !6
%5 = icmp eq i64 %index.next, 1000, !dbg !6
br i1 %5, label %middle.block, label %vector.body, !dbg !6, !llvm.loop !15

.LBB0_1:                                # %vector.body
# =>This Inner Loop Header: Depth=1
movd    %ebx, %xmm0
pshufd  \$0, %xmm0, %xmm0        # xmm0 = xmm0[0,0,0,0]
cvtdq2ps        %xmm0, %xmm0
movaps  %xmm0, 16(%rsp)         # 16-byte Spill
shufps  \$231, %xmm0, %xmm0      # xmm0 = xmm0[3,1,2,3]
callq   sinf
movaps  %xmm0, (%rsp)           # 16-byte Spill
movaps  16(%rsp), %xmm0         # 16-byte Reload
shufps  \$229, %xmm0, %xmm0      # xmm0 = xmm0[1,1,2,3]
callq   sinf
unpcklps        (%rsp), %xmm0   # 16-byte Folded Reload
# xmm0 = xmm0[0],mem[0],xmm0[1],mem[1]
movaps  %xmm0, (%rsp)           # 16-byte Spill
movaps  16(%rsp), %xmm0         # 16-byte Reload
callq   sinf
movaps  %xmm0, 32(%rsp)         # 16-byte Spill
movapd  16(%rsp), %xmm0         # 16-byte Reload
shufpd  \$1, %xmm0, %xmm0        # xmm0 = xmm0[1,0]
callq   sinf
movaps  32(%rsp), %xmm1         # 16-byte Reload
unpcklps        %xmm0, %xmm1    # xmm1 = xmm1[0],xmm0[0],xmm1[1],xmm0[1]
unpcklps        (%rsp), %xmm1   # 16-byte Folded Reload
# xmm1 = xmm1[0],mem[0],xmm1[1],mem[1]
movups  %xmm1, (%r14,%rbx,4)
cmpq    \$1000, %rbx             # imm = 0x3E8
jne     .LBB0_1

===========================
Proposed New Functionality
===========================

In order to take advantage of the performance benefits of the svml library, the
proposed solution is to introduce a new LLVM IR pass that is capable of
translating the vector math intrinsics to svml calls. As an example, the LLVM IR
above for "vector.body", introduced in the Problem Description section, would
serve as input to the proposed pass and be transformed into the following LLVM
IR. Special attention should be paid to the "__svml_sinf4_ha" call in the LLVM
IR and resulting assembly code snippet.

vector.body:                                   ; preds = %vector.body, %entry
%index = phi i64 [ 0, %entry ], [ %index.next, %vector.body ], !dbg !6
%0 = trunc i64 %index to i32, !dbg !7
%broadcast.splatinsert6 = insertelement <4 x i32> undef, i32 %0, i32 0,
!dbg !7
%broadcast.splat7 = shufflevector <4 x i32> %broadcast.splatinsert6,
<4 x i32> undef, <4 x i32> zeroinitializer, !dbg !7
%induction8 = add <4 x i32> %broadcast.splat7, <i32 0, i32 1, i32 2, i32 3>,
!dbg !7
%1 = sitofp <4 x i32> %induction8 to <4 x float>, !dbg !7
%vcall = call <4 x float> @__svml_sinf4_ha(<4 x float> %1)
%2 = getelementptr inbounds float, float* %array, i64 %index, !dbg !8
%3 = bitcast float* %2 to <4 x float>*, !dbg !9
store <4 x float> %vcall, <4 x float>* %3, align 4, !dbg !9, !tbaa !10
%index.next = add i64 %index, 4, !dbg !6
%4 = icmp eq i64 %index.next, 1000, !dbg !6
br i1 %4, label %for.end, label %vector.body, !dbg !6, !llvm.loop !14

The resulting assembly would appear as:

.LBB0_1:                                # %vector.body
# =>This Inner Loop Header: Depth=1
movd    %ebx, %xmm0
pshufd  \$0, %xmm0, %xmm0        # xmm0 = xmm0[0,0,0,0]
cvtdq2ps        %xmm0, %xmm0
callq   __svml_sinf4_ha
movups  %xmm0, (%r14,%rbx,4)
cmpq    \$1000, %rbx             # imm = 0x3E8
jne     .LBB0_1

In order to perform the translation, several requirements must be met to guide
code generation. Those include:

1) In addition to the -ffast-math flag, support is needed from clang to allow
the user to be able to specify the desired precision requirements. The
additional flags needed include the following, where "imf" is shorthand for
"Intel math function".

-fimf-absolute-error=value[:funclist]
define the maximum allowable absolute error for math library
function results
value    - a positive, floating-point number conforming to the
format [digits][.digits][{e|E}[sign]digits]
funclist - optional comma separated list of one or more math
library functions to which the attribute should be
applied

-fimf-accuracy-bits=bits[:funclist]
define the relative error, measured by the number of correct bits,
for math library function results
bits     - a positive, floating-point number
funclist - optional comma separated list of one or more math
library functions to which the attribute should be
applied

-fimf-arch-consistency=value[:funclist]
ensures that the math library functions produce consistent results
across different implementations of the same architecture
value    - true or false
funclist - optional comma separated list of one or more math
library functions to which the attribute should be
applied

-fimf-max-error=ulps[:funclist]
defines the maximum allowable relative error, measured in ulps, for
math library function results
ulps     - a positive, floating-point number conforming to the
format [digits][.digits][{e|E}[sign]digits]
funclist - optional comma separated list of one or more math
library functions to which the attribute should be
applied

-fimf-precision=value[:funclist]
defines the accuracy (precision) for math library functions
value    - defined as one of the following values
high   - equivalent to max-error = 0.6
medium - equivalent to max-error = 4
low    - equivalent to accuracy-bits = 11 (single
precision); accuracy-bits = 26 (double
precision)
funclist - optional comma separated list of one or more math
library functions to which the attribute should be
applied

-fimf-domain-exclusion=classlist[:funclist]
indicates the input arguments domain on which math functions
must provide correct results.
classlist - defined as one of the following values
nans, infinities, denormals, zeros
all, none, common
funclist - optional list of one or more math library
functions to which the attribute should be applied.

Information from the flags can then be encoded as function attributes at each
call site. In the future, this functionality will enable more fine-grained
control over specifying precision for individual calls/regions, instead of
setting the precision requirements for all call instances of a function. Please
note that the example translation presented so far does not have the IMF
attributes attached to the @llvm.sin.v4f32 call, and as a result the default is
set to an svml variant marked with "_ha" (max-error = 0.6), which is short for
high accuracy. Other supported variants will include low precision, enhanced
performance, bitwise reproducible, and correctly rounded. Please refer to the
IEEE-754 standard for additional information regarding supported precisions.
The compiler will select the most appropriate variant based on the IMF
attributes. See #2.

2) An interface to query for the appropriate svml function variant based on the
scalar function name and IMF attributes.

3) For calls to math functions that store to memory (e.g., sincos), additional
analysis of the pointer arguments is beneficial in order to generate the best

======================
GCC/ICC compatibility
======================

The initial implementation will involve the translation of 6 svml functions,
which include sin, cos, log, pow, exp, and sincos (both single and double
precision variants). Support for these functions matches the current
capabilities of GCC and a subset of ICC. As more functions become open-sourced,
the plan is to support them as part of the final solution determined from this
proposal. The flags referenced in the Proposed New Functionality section are
required to maintain icc compatibility.

=======================
Current Implementation
=======================

To evaluate the feasibility of this proposal, a prototype transform pass has
been developed, which performs the following:

1) Searches for vector math intrinsics as candidates for translation to svml.

2) Reads function attributes to obtain precision requirements for the call. If
none, default to attributes that will force the selection of a high accuracy
variant.

3) Since the vector factor of the intrinsic can be wider than what is legally
supported by the target, type legalization is performed so that the correct
svml variant is selected. For example, if a call to
@llvm.sin.v8f32(<8 x float> %1) is made for an xmm target, the pass will
generate two __svml_sinf4 calls and will do the appropriate splitting of %1
to create the new arguments for each call. In addition, the multiple return
vectors are recombined and users of the original return vector are updated.
The pass is also capable of handling less than full vector cases. E.g.,
@llvm.sin.v2f32.

4) Special handling for sincos since the results are stored to a double wide
vector and additional analysis is needed to optimize the stores to memory.
Additional shuffling is required to obtain the sin and cos results from
the double wide vector.

5) Vector intrinsics that are not translated to svml are scalarized.

6) The loop vectorizer has been taught to allow widening of sincos and
additional utilities have been written to analyze arguments for sincos.

=========
Feedback
=========

For those who are interested in this topic, I would like to ask for your review
of this proposal and would definitely appreciate any/all feedback on the
proposed approach. Help is also very welcome and much appreciated in the
development process.
```