SIMD: Add sum intrinsics for float/double.

[Qiyu8]

The origin PR is too large to review, So I will split to several small PRs, Here is the sum intrinsics that was about to used in einsum, The intrinsics has been fully discussed and tested.

[mattip]

@seiko2plus looks ok?

[seiko2plus]

Suggested change

	// Horizontal add: Calculates the sum of all vector elements.
	NPY_FINLINE float npyv_sum_f32(float32x4_t a)
	{
	float32x2_t r = vadd_f32(vget_high_f32(a), vget_low_f32(a));
	return vget_lane_f32(vpadd_f32(r, r), 0);
	}
	#ifdef __aarch64__
	NPY_FINLINE double npyv_sum_f64(float64x2_t a)
	{
	return vget_lane_f64(vget_low_f64(a) + vget_high_f64(a), 0);
	}
	#endif
	// Horizontal add: Calculates the sum of all vector elements.
	#if NPY_SIMD_F64
	#define npyv_sum_f32 vaddvq_f32
	#define npyv_sum_f64 vaddvq_f64
	#else
	NPY_FINLINE float npyv_sum_f32(npyv_f32 a)
	{
	float32x2_t r = vadd_f32(vget_high_f32(a), vget_low_f32(a));
	return vget_lane_f32(vpadd_f32(r, r), 0);
	}
	#endif

EDIT: bring vpadd_f32 again as it was, It should perform better than extracting two scalars.

[seiko2plus]

Suggested change

	NPY_FINLINE float npyv_sum_f32(npyv_f32 a)
	{
	return vec_extract(a, 0) + vec_extract(a, 1) +
	vec_extract(a, 2) + vec_extract(a, 3);
	}
	NPY_FINLINE float npyv_sum_f32(npyv_f32 a)
	{
	npyv_f32 sum = vec_add(a, npyv_combineh_f32(a, a));
	return vec_extract(sum, 0) + vec_extract(sum, 1);
	}

EDIT: my bad, fix swaping the highest half

[seiko2plus]

please, move the intrinsics inside the header guard _NPY_SIMD_AVX2_ARITHMETIC_H,
same thing for other SIMD extensions.

[seiko2plus]

I prefer adding a testing unit for any new intrinsics to keep things under control.
@Qiyu8 please could you add a testing case for them?
If yes, then you have to add new methods for the new intrinsics within _simd.dispatch.c.src. for example:

// try to follow the current defentions in the way of sorting the source
// this how you should define the new python methods
SIMD_IMPL_INTRIN_1(sum_f32, f32, vf32)
#if NPY_SIMD_F64
SIMD_IMPL_INTRIN_1(sum_f64, f64, vf64)
#endif
// and that how we attach them
SIMD_INTRIN_DEF(sum_f32)
#if NPY_SIMD_F64
SIMD_INTRIN_DEF(sum_f64)
#endif

Once you get done bringing the new methods to _simd module, go to test_simd.py and add testing cases for them. for example:

def test_reduce(self):
    data = self._data()
    vdata = self.load(data)
    # reduce sum
    data_sum = sum(data)
    vsum = self.sum(vdata)
    assert vsum == data_sum

You can also have some fun and try to use _simd module as a tool for designing and discovering, for example

# 1- bring the baseline via dict `targets` or attribute `baseline`
from numpy.core._simd import targets, baseline
npyv = targets["baseline"] # or baseline
# you can also dump `targets` to get the supported SIMD extensions
# by default build option `--simd-test` contains the most common SIMD extentions
if not npyv.simd: # equivalent to C def `NPY_SIMD`
    print((
        "How that possible? changed the default build settings?\n"
        "maybe you running it under armhf, then get targets['NEON']"
    ))
    return

a = npyv.load_f32(range(npyv.nlanes_f32))
print("sum of f32", npyv.sum_f32(a))

if npyv.simd_f64: # equivalent to C def `NPY_SIMD_F64`
    b = npyv.load_f64(range(npyv.nlanes_f64))
    print("sum of f64", npyv.sum_f64(b))

EDIT: improve the examples

[Qiyu8]

@seiko2plus Thanks for your detailed recommendations, The _simd.dispatch.c.src provides perfect functional test interface for universal intrinsics, we should write a doc such as how to write a simd test because the additional complexity compared to regular apis.

[seiko2plus]

LGTM, Thank you.

[mattip]

nice!

[mattip]

Thanks @Qiyu8