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AArch64: Optimize algorithm in users of SVE expf helper 

Polynomial order was unnecessarily high, unlocking multiple
optimizations.
Max error for new SVE expf is 0.88 +0.5ULP.
Max error for new SVE coshf is 2.56 +0.5ULP.
Performance improvement on Neoverse V1: expf (30%), coshf (26%).

Reviewed-by: Wilco Dijkstra  <Wilco.Dijkstra@arm.com>
This commit is contained in:
Pierre Blanchard 2025-03-18 17:07:31 +00:00 committed by Wilco Dijkstra
parent 9f551e28a7
commit cf56eb28fa
3 changed files with 16 additions and 26 deletions
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6
sysdeps/aarch64/fpu/coshf_sve.c
View File

@ -39,9 +39,9 @@ special_case (svfloat32_t x, svfloat32_t half_e, svfloat32_t half_over_e,
}
/* Single-precision vector cosh, using vector expf.
Maximum error is 2.77 ULP:
_ZGVsMxv_coshf(-0x1.5b38f4p+1) got 0x1.e45946p+2
want 0x1.e4594cp+2. */
Maximum error is 2.56 +0.5 ULP:
_ZGVsMxv_coshf(-0x1.5b40f4p+1) got 0x1.e47748p+2
want 0x1.e4774ep+2. */
svfloat32_t SV_NAME_F1 (cosh) (svfloat32_t x, svbool_t pg)
{
const struct data *d = ptr_barrier (&data);

6
sysdeps/aarch64/fpu/expf_sve.c
View File

@ -40,9 +40,9 @@ special_case (svfloat32_t x, svbool_t special, const struct sv_expf_data *d)
}
/* Optimised single-precision SVE exp function.
Worst-case error is 1.04 ulp:
SV_NAME_F1 (exp)(0x1.a8eda4p+1) got 0x1.ba74bcp+4
want 0x1.ba74bap+4. */
Worst-case error is 0.88 +0.50 ULP:
_ZGVsMxv_expf(-0x1.bba276p-6) got 0x1.f25288p-1
want 0x1.f2528ap-1. */
svfloat32_t SV_NAME_F1 (exp) (svfloat32_t x, const svbool_t pg)
{
const struct data *d = ptr_barrier (&data);

30
sysdeps/aarch64/fpu/sv_expf_inline.h
View File

@ -24,50 +24,40 @@
struct sv_expf_data
{
float c1, c3, inv_ln2;
float ln2_lo, c0, c2, c4;
float ln2_hi, shift;
float ln2_hi, ln2_lo, c1, null;
float inv_ln2, shift;
};
/* Coefficients copied from the polynomial in AdvSIMD variant, reversed for
compatibility with polynomial helpers. Shift is 1.5*2^17 + 127. */
/* Shift is 1.5*2^17 + 127. */
#define SV_EXPF_DATA \
{ \
/* Coefficients copied from the polynomial in AdvSIMD variant. */ \
.c0 = 0x1.ffffecp-1f, .c1 = 0x1.fffdb6p-2f, .c2 = 0x1.555e66p-3f, \
.c3 = 0x1.573e2ep-5f, .c4 = 0x1.0e4020p-7f, .inv_ln2 = 0x1.715476p+0f, \
.ln2_hi = 0x1.62e4p-1f, .ln2_lo = 0x1.7f7d1cp-20f, \
.shift = 0x1.803f8p17f, \
.c1 = 0.5f, .inv_ln2 = 0x1.715476p+0f, .ln2_hi = 0x1.62e4p-1f, \
.ln2_lo = 0x1.7f7d1cp-20f, .shift = 0x1.803f8p17f, \
}
#define C(i) sv_f32 (d->poly[i])
static inline svfloat32_t
expf_inline (svfloat32_t x, const svbool_t pg, const struct sv_expf_data *d)
{
/* exp(x) = 2^n (1 + poly(r)), with 1 + poly(r) in [1/sqrt(2),sqrt(2)]
x = ln2*n + r, with r in [-ln2/2, ln2/2]. */
svfloat32_t lane_consts = svld1rq (svptrue_b32 (), &d->ln2_lo);
svfloat32_t lane_consts = svld1rq (svptrue_b32 (), &d->ln2_hi);
/* n = round(x/(ln2/N)). */
svfloat32_t z = svmad_x (pg, sv_f32 (d->inv_ln2), x, d->shift);
svfloat32_t n = svsub_x (pg, z, d->shift);
/* r = x - n*ln2/N. */
svfloat32_t r = svmsb_x (pg, sv_f32 (d->ln2_hi), n, x);
svfloat32_t r = x;
r = svmls_lane (r, n, lane_consts, 0);
r = svmls_lane (r, n, lane_consts, 1);
/* scale = 2^(n/N). */
svfloat32_t scale = svexpa (svreinterpret_u32 (z));
/* poly(r) = exp(r) - 1 ~= C0 r + C1 r^2 + C2 r^3 + C3 r^4 + C4 r^5. */
svfloat32_t p12 = svmla_lane (sv_f32 (d->c1), r, lane_consts, 2);
svfloat32_t p34 = svmla_lane (sv_f32 (d->c3), r, lane_consts, 3);
/* poly(r) = exp(r) - 1 ~= r + 0.5 r^2. */
svfloat32_t r2 = svmul_x (svptrue_b32 (), r, r);
svfloat32_t p14 = svmla_x (pg, p12, p34, r2);
svfloat32_t p0 = svmul_lane (r, lane_consts, 1);
svfloat32_t poly = svmla_x (pg, p0, r2, p14);
svfloat32_t poly = svmla_lane (r, r2, lane_consts, 2);
return svmla_x (pg, scale, scale, poly);
}