mirror of git://sourceware.org/git/glibc.git
AArch64: Improve codegen SVE log1p helper
Improve codegen by packing coefficients. 4% and 2% improvement in throughput microbenchmark on Neoverse V1, for acosh and atanh respectively. Reviewed-by: Wilco Dijkstra <Wilco.Dijkstra@arm.com>
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Luna Lamb
Wilco Dijkstra
parent
dee22d2a81
commit
6849c5b791
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@ -30,10 +30,10 @@ special_case (svfloat64_t x, svfloat64_t y, svbool_t special)
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}
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/* SVE approximation for double-precision acosh, based on log1p.
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The largest observed error is 3.19 ULP in the region where the
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The largest observed error is 3.14 ULP in the region where the
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argument to log1p falls in the k=0 interval, i.e. x close to 1:
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SV_NAME_D1 (acosh)(0x1.1e4388d4ca821p+0) got 0x1.ed23399f5137p-2
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want 0x1.ed23399f51373p-2. */
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SV_NAME_D1 (acosh)(0x1.1e80ed12f0ad1p+0) got 0x1.ef0cee7c33ce1p-2
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want 0x1.ef0cee7c33ce4p-2. */
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svfloat64_t SV_NAME_D1 (acosh) (svfloat64_t x, const svbool_t pg)
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{
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/* (ix - One) >= (BigBound - One). */
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@ -30,7 +30,7 @@ special_case (svfloat64_t x, svfloat64_t y, svbool_t special)
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}
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/* SVE approximation for double-precision atanh, based on log1p.
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The greatest observed error is 2.81 ULP:
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The greatest observed error is 3.3 ULP:
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_ZGVsMxv_atanh(0x1.ffae6288b601p-6) got 0x1.ffd8ff31b5019p-6
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want 0x1.ffd8ff31b501cp-6. */
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svfloat64_t SV_NAME_D1 (atanh) (svfloat64_t x, const svbool_t pg)
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@ -42,7 +42,6 @@ svfloat64_t SV_NAME_D1 (atanh) (svfloat64_t x, const svbool_t pg)
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svfloat64_t halfsign = svreinterpret_f64 (svorr_x (pg, sign, Half));
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/* It is special if iax >= 1. */
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// svbool_t special = svcmpge (pg, iax, One);
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svbool_t special = svacge (pg, x, 1.0);
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/* Computation is performed based on the following sequence of equality:
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@ -21,11 +21,12 @@
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#define AARCH64_FPU_SV_LOG1P_INLINE_H
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#include "sv_math.h"
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#include "poly_sve_f64.h"
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static const struct sv_log1p_data
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{
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double poly[19], ln2[2];
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double c0, c2, c4, c6, c8, c10, c12, c14, c16;
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double c1, c3, c5, c7, c9, c11, c13, c15, c17, c18;
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double ln2_lo, ln2_hi;
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uint64_t hf_rt2_top;
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uint64_t one_m_hf_rt2_top;
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uint32_t bottom_mask;
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@ -33,15 +34,30 @@ static const struct sv_log1p_data
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} sv_log1p_data = {
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/* Coefficients generated using Remez, deg=20, in [sqrt(2)/2-1, sqrt(2)-1].
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*/
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.poly = { -0x1.ffffffffffffbp-2, 0x1.55555555551a9p-2, -0x1.00000000008e3p-2,
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0x1.9999999a32797p-3, -0x1.555555552fecfp-3, 0x1.249248e071e5ap-3,
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-0x1.ffffff8bf8482p-4, 0x1.c71c8f07da57ap-4, -0x1.9999ca4ccb617p-4,
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0x1.7459ad2e1dfa3p-4, -0x1.554d2680a3ff2p-4, 0x1.3b4c54d487455p-4,
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-0x1.2548a9ffe80e6p-4, 0x1.0f389a24b2e07p-4, -0x1.eee4db15db335p-5,
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0x1.e95b494d4a5ddp-5, -0x1.15fdf07cb7c73p-4, 0x1.0310b70800fcfp-4,
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-0x1.cfa7385bdb37ep-6 },
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.ln2 = { 0x1.62e42fefa3800p-1, 0x1.ef35793c76730p-45 },
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.c0 = -0x1.ffffffffffffbp-2,
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.c1 = 0x1.55555555551a9p-2,
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.c2 = -0x1.00000000008e3p-2,
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.c3 = 0x1.9999999a32797p-3,
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.c4 = -0x1.555555552fecfp-3,
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.c5 = 0x1.249248e071e5ap-3,
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.c6 = -0x1.ffffff8bf8482p-4,
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.c7 = 0x1.c71c8f07da57ap-4,
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.c8 = -0x1.9999ca4ccb617p-4,
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.c9 = 0x1.7459ad2e1dfa3p-4,
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.c10 = -0x1.554d2680a3ff2p-4,
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.c11 = 0x1.3b4c54d487455p-4,
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.c12 = -0x1.2548a9ffe80e6p-4,
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.c13 = 0x1.0f389a24b2e07p-4,
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.c14 = -0x1.eee4db15db335p-5,
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.c15 = 0x1.e95b494d4a5ddp-5,
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.c16 = -0x1.15fdf07cb7c73p-4,
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.c17 = 0x1.0310b70800fcfp-4,
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.c18 = -0x1.cfa7385bdb37ep-6,
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.ln2_lo = 0x1.62e42fefa3800p-1,
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.ln2_hi = 0x1.ef35793c76730p-45,
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/* top32(asuint64(sqrt(2)/2)) << 32. */
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.hf_rt2_top = 0x3fe6a09e00000000,
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/* (top32(asuint64(1)) - top32(asuint64(sqrt(2)/2))) << 32. */
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.one_m_hf_rt2_top = 0x00095f6200000000,
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.bottom_mask = 0xffffffff,
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.one_top = 0x3ff
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@ -51,14 +67,14 @@ static inline svfloat64_t
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sv_log1p_inline (svfloat64_t x, const svbool_t pg)
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{
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/* Helper for calculating log(x + 1). Adapted from v_log1p_inline.h, which
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differs from v_log1p_2u5.c by:
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differs from advsimd/log1p.c by:
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- No special-case handling - this should be dealt with by the caller.
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- Pairwise Horner polynomial evaluation for improved accuracy.
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- Optionally simulate the shortcut for k=0, used in the scalar routine,
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using svsel, for improved accuracy when the argument to log1p is close
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to 0. This feature is enabled by defining WANT_SV_LOG1P_K0_SHORTCUT as 1
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in the source of the caller before including this file.
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See sv_log1p_2u1.c for details of the algorithm. */
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See sve/log1p.c for details of the algorithm. */
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const struct sv_log1p_data *d = ptr_barrier (&sv_log1p_data);
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svfloat64_t m = svadd_x (pg, x, 1);
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svuint64_t mi = svreinterpret_u64 (m);
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@ -79,7 +95,7 @@ sv_log1p_inline (svfloat64_t x, const svbool_t pg)
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svfloat64_t cm;
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#ifndef WANT_SV_LOG1P_K0_SHORTCUT
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#error \
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#error \
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"Cannot use sv_log1p_inline.h without specifying whether you need the k0 shortcut for greater accuracy close to 0"
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#elif WANT_SV_LOG1P_K0_SHORTCUT
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/* Shortcut if k is 0 - set correction term to 0 and f to x. The result is
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@ -96,14 +112,46 @@ sv_log1p_inline (svfloat64_t x, const svbool_t pg)
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#endif
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/* Approximate log1p(f) on the reduced input using a polynomial. */
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svfloat64_t f2 = svmul_x (pg, f, f);
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svfloat64_t p = sv_pw_horner_18_f64_x (pg, f, f2, d->poly);
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svfloat64_t f2 = svmul_x (svptrue_b64 (), f, f),
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f4 = svmul_x (svptrue_b64 (), f2, f2),
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f8 = svmul_x (svptrue_b64 (), f4, f4),
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f16 = svmul_x (svptrue_b64 (), f8, f8);
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svfloat64_t c13 = svld1rq (svptrue_b64 (), &d->c1);
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svfloat64_t c57 = svld1rq (svptrue_b64 (), &d->c5);
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svfloat64_t c911 = svld1rq (svptrue_b64 (), &d->c9);
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svfloat64_t c1315 = svld1rq (svptrue_b64 (), &d->c13);
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svfloat64_t c1718 = svld1rq (svptrue_b64 (), &d->c17);
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/* Order-18 Estrin scheme. */
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svfloat64_t p01 = svmla_lane (sv_f64 (d->c0), f, c13, 0);
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svfloat64_t p23 = svmla_lane (sv_f64 (d->c2), f, c13, 1);
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svfloat64_t p45 = svmla_lane (sv_f64 (d->c4), f, c57, 0);
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svfloat64_t p67 = svmla_lane (sv_f64 (d->c6), f, c57, 1);
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svfloat64_t p03 = svmla_x (pg, p01, f2, p23);
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svfloat64_t p47 = svmla_x (pg, p45, f2, p67);
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svfloat64_t p07 = svmla_x (pg, p03, f4, p47);
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svfloat64_t p89 = svmla_lane (sv_f64 (d->c8), f, c911, 0);
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svfloat64_t p1011 = svmla_lane (sv_f64 (d->c10), f, c911, 1);
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svfloat64_t p1213 = svmla_lane (sv_f64 (d->c12), f, c1315, 0);
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svfloat64_t p1415 = svmla_lane (sv_f64 (d->c14), f, c1315, 1);
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svfloat64_t p811 = svmla_x (pg, p89, f2, p1011);
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svfloat64_t p1215 = svmla_x (pg, p1213, f2, p1415);
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svfloat64_t p815 = svmla_x (pg, p811, f4, p1215);
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svfloat64_t p015 = svmla_x (pg, p07, f8, p815);
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svfloat64_t p1617 = svmla_lane (sv_f64 (d->c16), f, c1718, 0);
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svfloat64_t p1618 = svmla_lane (p1617, f2, c1718, 1);
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svfloat64_t p = svmla_x (pg, p015, f16, p1618);
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/* Assemble log1p(x) = k * log2 + log1p(f) + c/m. */
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svfloat64_t ylo = svmla_x (pg, cm, k, d->ln2[0]);
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svfloat64_t yhi = svmla_x (pg, f, k, d->ln2[1]);
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svfloat64_t ln2_lo_hi = svld1rq (svptrue_b64 (), &d->ln2_lo);
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svfloat64_t ylo = svmla_lane (cm, k, ln2_lo_hi, 0);
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svfloat64_t yhi = svmla_lane (f, k, ln2_lo_hi, 1);
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return svmla_x (pg, svadd_x (pg, ylo, yhi), f2, p);
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return svmad_x (pg, p, f2, svadd_x (pg, ylo, yhi));
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}
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#endif
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