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AArch64: Improve codegen of AdvSIMD logf function family
Load the polynomial evaluation coefficients into 2 vectors and use lanewise MLAs.
8% improvement in throughput microbenchmark on Neoverse V1 for log2 and log,
and 2% for log10.
Reviewed-by: Wilco Dijkstra <Wilco.Dijkstra@arm.com>
(cherry picked from commit d6e034f5b2)
This commit is contained in:
Joana Cruz
Wilco Dijkstra
parent
72156cb90b
commit
dcd1229e5b
3 changed files with 66 additions and 40 deletions
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@ -18,21 +18,25 @@
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<https://www.gnu.org/licenses/>. */
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#include "v_math.h"
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#include "poly_advsimd_f32.h"
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static const struct data
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{
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float32x4_t c0, c2, c4, c6, inv_ln10, ln2;
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uint32x4_t off, offset_lower_bound;
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uint16x8_t special_bound;
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uint32x4_t mantissa_mask;
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float32x4_t poly[8];
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float32x4_t inv_ln10, ln2;
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float c1, c3, c5, c7;
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} data = {
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/* Use order 9 for log10(1+x), i.e. order 8 for log10(1+x)/x, with x in
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[-1/3, 1/3] (offset=2/3). Max. relative error: 0x1.068ee468p-25. */
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.poly = { V4 (-0x1.bcb79cp-3f), V4 (0x1.2879c8p-3f), V4 (-0x1.bcd472p-4f),
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V4 (0x1.6408f8p-4f), V4 (-0x1.246f8p-4f), V4 (0x1.f0e514p-5f),
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V4 (-0x1.0fc92cp-4f), V4 (0x1.f5f76ap-5f) },
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.c0 = V4 (-0x1.bcb79cp-3f),
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.c1 = 0x1.2879c8p-3f,
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.c2 = V4 (-0x1.bcd472p-4f),
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.c3 = 0x1.6408f8p-4f,
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.c4 = V4 (-0x1.246f8p-4f),
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.c5 = 0x1.f0e514p-5f,
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.c6 = V4 (-0x1.0fc92cp-4f),
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.c7 = 0x1.f5f76ap-5f,
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.ln2 = V4 (0x1.62e43p-1f),
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.inv_ln10 = V4 (0x1.bcb7b2p-2f),
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/* Lower bound is the smallest positive normal float 0x00800000. For
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@ -62,7 +66,7 @@ special_case (float32x4_t y, uint32x4_t u_off, float32x4_t p, float32x4_t r2,
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float32x4_t VPCS_ATTR NOINLINE V_NAME_F1 (log10) (float32x4_t x)
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{
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const struct data *d = ptr_barrier (&data);
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float32x4_t c1357 = vld1q_f32 (&d->c1);
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/* To avoid having to mov x out of the way, keep u after offset has been
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applied, and recover x by adding the offset back in the special-case
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handler. */
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@ -81,7 +85,16 @@ float32x4_t VPCS_ATTR NOINLINE V_NAME_F1 (log10) (float32x4_t x)
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/* y = log10(1+r) + n * log10(2). */
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float32x4_t r2 = vmulq_f32 (r, r);
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float32x4_t poly = v_pw_horner_7_f32 (r, r2, d->poly);
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float32x4_t c01 = vfmaq_laneq_f32 (d->c0, r, c1357, 0);
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float32x4_t c23 = vfmaq_laneq_f32 (d->c2, r, c1357, 1);
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float32x4_t c45 = vfmaq_laneq_f32 (d->c4, r, c1357, 2);
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float32x4_t c67 = vfmaq_laneq_f32 (d->c6, r, c1357, 3);
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float32x4_t p47 = vfmaq_f32 (c45, r2, c67);
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float32x4_t p27 = vfmaq_f32 (c23, r2, p47);
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float32x4_t poly = vfmaq_f32 (c01, r2, p27);
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/* y = Log10(2) * n + poly * InvLn(10). */
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float32x4_t y = vfmaq_f32 (r, d->ln2, n);
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y = vmulq_f32 (y, d->inv_ln10);
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@ -18,22 +18,27 @@
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<https://www.gnu.org/licenses/>. */
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#include "v_math.h"
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#include "poly_advsimd_f32.h"
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static const struct data
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{
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float32x4_t c0, c2, c4, c6, c8;
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uint32x4_t off, offset_lower_bound;
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uint16x8_t special_bound;
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uint32x4_t mantissa_mask;
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float32x4_t poly[9];
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float c1, c3, c5, c7;
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} data = {
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/* Coefficients generated using Remez algorithm approximate
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log2(1+r)/r for r in [ -1/3, 1/3 ].
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rel error: 0x1.c4c4b0cp-26. */
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.poly = { V4 (0x1.715476p0f), /* (float)(1 / ln(2)). */
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V4 (-0x1.715458p-1f), V4 (0x1.ec701cp-2f), V4 (-0x1.7171a4p-2f),
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V4 (0x1.27a0b8p-2f), V4 (-0x1.e5143ep-3f), V4 (0x1.9d8ecap-3f),
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V4 (-0x1.c675bp-3f), V4 (0x1.9e495p-3f) },
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.c0 = V4 (0x1.715476p0f), /* (float)(1 / ln(2)). */
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.c1 = -0x1.715458p-1f,
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.c2 = V4 (0x1.ec701cp-2f),
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.c3 = -0x1.7171a4p-2f,
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.c4 = V4 (0x1.27a0b8p-2f),
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.c5 = -0x1.e5143ep-3f,
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.c6 = V4 (0x1.9d8ecap-3f),
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.c7 = -0x1.c675bp-3f,
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.c8 = V4 (0x1.9e495p-3f),
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/* Lower bound is the smallest positive normal float 0x00800000. For
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optimised register use subnormals are detected after offset has been
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subtracted, so lower bound is 0x0080000 - offset (which wraps around). */
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@ -79,11 +84,21 @@ float32x4_t VPCS_ATTR NOINLINE V_NAME_F1 (log2) (float32x4_t x)
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/* y = log2(1+r) + n. */
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float32x4_t r2 = vmulq_f32 (r, r);
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float32x4_t p = v_pw_horner_8_f32 (r, r2, d->poly);
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float32x4_t c1357 = vld1q_f32 (&d->c1);
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float32x4_t c01 = vfmaq_laneq_f32 (d->c0, r, c1357, 0);
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float32x4_t c23 = vfmaq_laneq_f32 (d->c2, r, c1357, 1);
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float32x4_t c45 = vfmaq_laneq_f32 (d->c4, r, c1357, 2);
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float32x4_t c67 = vfmaq_laneq_f32 (d->c6, r, c1357, 3);
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float32x4_t p68 = vfmaq_f32 (c67, r2, d->c8);
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float32x4_t p48 = vfmaq_f32 (c45, r2, p68);
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float32x4_t p28 = vfmaq_f32 (c23, r2, p48);
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float32x4_t p = vfmaq_f32 (c01, r2, p28);
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if (__glibc_unlikely (v_any_u16h (special)))
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return special_case (n, u_off, p, r, special, d);
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return vfmaq_f32 (n, p, r);
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}
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libmvec_hidden_def (V_NAME_F1 (log2))
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HALF_WIDTH_ALIAS_F1 (log2)
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@ -21,16 +21,19 @@
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static const struct data
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{
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uint32x4_t off, offset_lower_bound;
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float32x4_t c2, c4, c6, ln2;
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uint32x4_t off, offset_lower_bound, mantissa_mask;
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uint16x8_t special_bound;
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uint32x4_t mantissa_mask;
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float32x4_t poly[7];
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float32x4_t ln2;
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float c1, c3, c5, c0;
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} data = {
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/* 3.34 ulp error. */
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.poly = { V4 (-0x1.3e737cp-3f), V4 (0x1.5a9aa2p-3f), V4 (-0x1.4f9934p-3f),
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V4 (0x1.961348p-3f), V4 (-0x1.00187cp-2f), V4 (0x1.555d7cp-2f),
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V4 (-0x1.ffffc8p-2f) },
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.c0 = -0x1.3e737cp-3f,
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.c1 = 0x1.5a9aa2p-3f,
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.c2 = V4 (-0x1.4f9934p-3f),
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.c3 = 0x1.961348p-3f,
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.c4 = V4 (-0x1.00187cp-2f),
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.c5 = 0x1.555d7cp-2f,
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.c6 = V4 (-0x1.ffffc8p-2f),
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.ln2 = V4 (0x1.62e43p-1f),
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/* Lower bound is the smallest positive normal float 0x00800000. For
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optimised register use subnormals are detected after offset has been
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@ -41,8 +44,6 @@ static const struct data
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.mantissa_mask = V4 (0x007fffff)
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};
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#define P(i) d->poly[7 - i]
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static float32x4_t VPCS_ATTR NOINLINE
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special_case (float32x4_t p, uint32x4_t u_off, float32x4_t y, float32x4_t r2,
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uint16x4_t cmp, const struct data *d)
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@ -55,33 +56,30 @@ special_case (float32x4_t p, uint32x4_t u_off, float32x4_t y, float32x4_t r2,
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float32x4_t VPCS_ATTR NOINLINE V_NAME_F1 (log) (float32x4_t x)
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{
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const struct data *d = ptr_barrier (&data);
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float32x4_t n, p, q, r, r2, y;
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uint32x4_t u, u_off;
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uint16x4_t cmp;
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float32x4_t c1350 = vld1q_f32 (&d->c1);
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/* To avoid having to mov x out of the way, keep u after offset has been
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applied, and recover x by adding the offset back in the special-case
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handler. */
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u_off = vreinterpretq_u32_f32 (x);
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uint32x4_t u_off = vsubq_u32 (vreinterpretq_u32_f32 (x), d->off);
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/* x = 2^n * (1+r), where 2/3 < 1+r < 4/3. */
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u_off = vsubq_u32 (u_off, d->off);
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n = vcvtq_f32_s32 (
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float32x4_t n = vcvtq_f32_s32 (
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vshrq_n_s32 (vreinterpretq_s32_u32 (u_off), 23)); /* signextend. */
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u = vandq_u32 (u_off, d->mantissa_mask);
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u = vaddq_u32 (u, d->off);
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r = vsubq_f32 (vreinterpretq_f32_u32 (u), v_f32 (1.0f));
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uint16x4_t cmp = vcge_u16 (vsubhn_u32 (u_off, d->offset_lower_bound),
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vget_low_u16 (d->special_bound));
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cmp = vcge_u16 (vsubhn_u32 (u_off, d->offset_lower_bound),
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vget_low_u16 (d->special_bound));
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uint32x4_t u = vaddq_u32 (vandq_u32 (u_off, d->mantissa_mask), d->off);
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float32x4_t r = vsubq_f32 (vreinterpretq_f32_u32 (u), v_f32 (1.0f));
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/* y = log(1+r) + n*ln2. */
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r2 = vmulq_f32 (r, r);
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float32x4_t r2 = vmulq_f32 (r, r);
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/* n*ln2 + r + r2*(P1 + r*P2 + r2*(P3 + r*P4 + r2*(P5 + r*P6 + r2*P7))). */
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p = vfmaq_f32 (P (5), P (6), r);
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q = vfmaq_f32 (P (3), P (4), r);
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y = vfmaq_f32 (P (1), P (2), r);
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p = vfmaq_f32 (p, P (7), r2);
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float32x4_t p = vfmaq_laneq_f32 (d->c2, r, c1350, 0);
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float32x4_t q = vfmaq_laneq_f32 (d->c4, r, c1350, 1);
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float32x4_t y = vfmaq_laneq_f32 (d->c6, r, c1350, 2);
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p = vfmaq_laneq_f32 (p, r2, c1350, 3);
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q = vfmaq_f32 (q, p, r2);
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y = vfmaq_f32 (y, q, r2);
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p = vfmaq_f32 (r, d->ln2, n);
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