Reduce memory access by using lanewise MLA and reduce number of MOVPRFXs.
Move log1pf implementation to inline helper function.
Speedup on Neoverse V1 for log1pf (10%), acoshf (-1%), atanhf (2%), asinhf (2%).
License along with the GNU C Library; if not, see
<https://www.gnu.org/licenses/>. */
+#include "sv_math.h"
+#include "sv_log1pf_inline.h"
+
#define One 0x3f800000
#define Thres 0x20000000 /* asuint(0x1p64) - One. */
-#include "sv_log1pf_inline.h"
-
static svfloat32_t NOINLINE
-special_case (svfloat32_t x, svfloat32_t y, svbool_t special)
+special_case (svfloat32_t xm1, svfloat32_t tmp, svbool_t special)
{
+ svfloat32_t x = svadd_x (svptrue_b32 (), xm1, 1.0f);
+ svfloat32_t y = sv_log1pf_inline (tmp, svptrue_b32 ());
return sv_call_f32 (acoshf, x, y, special);
}
/* Single-precision SVE acosh(x) routine. Implements the same algorithm as
vector acoshf and log1p.
- Maximum error is 2.78 ULPs:
- SV_NAME_F1 (acosh) (0x1.01e996p+0) got 0x1.f45b42p-4
- want 0x1.f45b3cp-4. */
+ Maximum error is 2.47 ULPs:
+ SV_NAME_F1 (acosh) (0x1.01ca76p+0) got 0x1.e435a6p-4
+ want 0x1.e435a2p-4. */
svfloat32_t SV_NAME_F1 (acosh) (svfloat32_t x, const svbool_t pg)
{
svuint32_t ix = svreinterpret_u32 (x);
svfloat32_t xm1 = svsub_x (pg, x, 1.0f);
svfloat32_t u = svmul_x (pg, xm1, svadd_x (pg, x, 1.0f));
- svfloat32_t y = sv_log1pf_inline (svadd_x (pg, xm1, svsqrt_x (pg, u)), pg);
+ svfloat32_t tmp = svadd_x (pg, xm1, svsqrt_x (pg, u));
if (__glibc_unlikely (svptest_any (pg, special)))
- return special_case (x, y, special);
- return y;
+ return special_case (xm1, tmp, special);
+ return sv_log1pf_inline (tmp, pg);
}
#include "sv_math.h"
#include "sv_log1pf_inline.h"
-#define BigBound (0x5f800000) /* asuint(0x1p64). */
+#define BigBound 0x5f800000 /* asuint(0x1p64). */
static svfloat32_t NOINLINE
-special_case (svfloat32_t x, svfloat32_t y, svbool_t special)
+special_case (svuint32_t iax, svuint32_t sign, svfloat32_t y, svbool_t special)
{
+ svfloat32_t x = svreinterpret_f32 (sveor_x (svptrue_b32 (), iax, sign));
+ y = svreinterpret_f32 (
+ svorr_x (svptrue_b32 (), sign, svreinterpret_u32 (y)));
return sv_call_f32 (asinhf, x, y, special);
}
/* Single-precision SVE asinh(x) routine. Implements the same algorithm as
vector asinhf and log1p.
- Maximum error is 2.48 ULPs:
- SV_NAME_F1 (asinh) (0x1.008864p-3) got 0x1.ffbbbcp-4
- want 0x1.ffbbb8p-4. */
+ Maximum error is 1.92 ULPs:
+ SV_NAME_F1 (asinh) (-0x1.0922ecp-1) got -0x1.fd0bccp-2
+ want -0x1.fd0bc8p-2. */
svfloat32_t SV_NAME_F1 (asinh) (svfloat32_t x, const svbool_t pg)
{
svfloat32_t ax = svabs_x (pg, x);
= sv_log1pf_inline (svadd_x (pg, ax, svdiv_x (pg, ax2, d)), pg);
if (__glibc_unlikely (svptest_any (pg, special)))
- return special_case (
- x, svreinterpret_f32 (svorr_x (pg, sign, svreinterpret_u32 (y))),
- special);
+ return special_case (iax, sign, y, special);
return svreinterpret_f32 (svorr_x (pg, sign, svreinterpret_u32 (y)));
}
License along with the GNU C Library; if not, see
<https://www.gnu.org/licenses/>. */
+#include "sv_math.h"
#include "sv_log1pf_inline.h"
#define One (0x3f800000)
#define Half (0x3f000000)
static svfloat32_t NOINLINE
-special_case (svfloat32_t x, svfloat32_t y, svbool_t special)
+special_case (svuint32_t iax, svuint32_t sign, svfloat32_t halfsign,
+ svfloat32_t y, svbool_t special)
{
+ svfloat32_t x = svreinterpret_f32 (sveor_x (svptrue_b32 (), iax, sign));
+ y = svmul_x (svptrue_b32 (), halfsign, y);
return sv_call_f32 (atanhf, x, y, special);
}
/* Approximation for vector single-precision atanh(x) using modified log1p.
- The maximum error is 2.28 ULP:
- _ZGVsMxv_atanhf(0x1.ff1194p-5) got 0x1.ffbbbcp-5
- want 0x1.ffbbb6p-5. */
+ The maximum error is 1.99 ULP:
+ _ZGVsMxv_atanhf(0x1.f1583p-5) got 0x1.f1f4fap-5
+ want 0x1.f1f4f6p-5. */
svfloat32_t SV_NAME_F1 (atanh) (svfloat32_t x, const svbool_t pg)
{
svfloat32_t ax = svabs_x (pg, x);
y = sv_log1pf_inline (y, pg);
if (__glibc_unlikely (svptest_any (pg, special)))
- return special_case (x, svmul_x (pg, halfsign, y), special);
+ return special_case (iax, sign, halfsign, y, special);
return svmul_x (pg, halfsign, y);
}
<https://www.gnu.org/licenses/>. */
#include "sv_math.h"
-#include "poly_sve_f32.h"
-
-static const struct data
-{
- float poly[8];
- float ln2, exp_bias;
- uint32_t four, three_quarters;
-} data = {.poly = {/* Do not store first term of polynomial, which is -0.5, as
- this can be fmov-ed directly instead of including it in
- the main load-and-mla polynomial schedule. */
- 0x1.5555aap-2f, -0x1.000038p-2f, 0x1.99675cp-3f,
- -0x1.54ef78p-3f, 0x1.28a1f4p-3f, -0x1.0da91p-3f,
- 0x1.abcb6p-4f, -0x1.6f0d5ep-5f},
- .ln2 = 0x1.62e43p-1f,
- .exp_bias = 0x1p-23f,
- .four = 0x40800000,
- .three_quarters = 0x3f400000};
-
-#define SignExponentMask 0xff800000
+#include "sv_log1pf_inline.h"
static svfloat32_t NOINLINE
-special_case (svfloat32_t x, svfloat32_t y, svbool_t special)
+special_case (svfloat32_t x, svbool_t special)
{
- return sv_call_f32 (log1pf, x, y, special);
+ return sv_call_f32 (log1pf, x, sv_log1pf_inline (x, svptrue_b32 ()),
+ special);
}
/* Vector log1pf approximation using polynomial on reduced interval. Worst-case
want 0x1.9f323ep-2. */
svfloat32_t SV_NAME_F1 (log1p) (svfloat32_t x, svbool_t pg)
{
- const struct data *d = ptr_barrier (&data);
/* x < -1, Inf/Nan. */
svbool_t special = svcmpeq (pg, svreinterpret_u32 (x), 0x7f800000);
special = svorn_z (pg, special, svcmpge (pg, x, -1));
- /* With x + 1 = t * 2^k (where t = m + 1 and k is chosen such that m
- is in [-0.25, 0.5]):
- log1p(x) = log(t) + log(2^k) = log1p(m) + k*log(2).
-
- We approximate log1p(m) with a polynomial, then scale by
- k*log(2). Instead of doing this directly, we use an intermediate
- scale factor s = 4*k*log(2) to ensure the scale is representable
- as a normalised fp32 number. */
- svfloat32_t m = svadd_x (pg, x, 1);
-
- /* Choose k to scale x to the range [-1/4, 1/2]. */
- svint32_t k
- = svand_x (pg, svsub_x (pg, svreinterpret_s32 (m), d->three_quarters),
- sv_s32 (SignExponentMask));
-
- /* Scale x by exponent manipulation. */
- svfloat32_t m_scale = svreinterpret_f32 (
- svsub_x (pg, svreinterpret_u32 (x), svreinterpret_u32 (k)));
-
- /* Scale up to ensure that the scale factor is representable as normalised
- fp32 number, and scale m down accordingly. */
- svfloat32_t s = svreinterpret_f32 (svsubr_x (pg, k, d->four));
- m_scale = svadd_x (pg, m_scale, svmla_x (pg, sv_f32 (-1), s, 0.25));
-
- /* Evaluate polynomial on reduced interval. */
- svfloat32_t ms2 = svmul_x (pg, m_scale, m_scale),
- ms4 = svmul_x (pg, ms2, ms2);
- svfloat32_t p = sv_estrin_7_f32_x (pg, m_scale, ms2, ms4, d->poly);
- p = svmad_x (pg, m_scale, p, -0.5);
- p = svmla_x (pg, m_scale, m_scale, svmul_x (pg, m_scale, p));
-
- /* The scale factor to be applied back at the end - by multiplying float(k)
- by 2^-23 we get the unbiased exponent of k. */
- svfloat32_t scale_back = svmul_x (pg, svcvt_f32_x (pg, k), d->exp_bias);
-
- /* Apply the scaling back. */
- svfloat32_t y = svmla_x (pg, p, scale_back, d->ln2);
-
if (__glibc_unlikely (svptest_any (pg, special)))
- return special_case (x, y, special);
+ return special_case (x, special);
- return y;
+ return sv_log1pf_inline (x, pg);
}
strong_alias (SV_NAME_F1 (log1p), SV_NAME_F1 (logp1))
#include "sv_math.h"
#include "vecmath_config.h"
-#include "poly_sve_f32.h"
+
+#define SignExponentMask 0xff800000
static const struct sv_log1pf_data
{
- float32_t poly[9];
- float32_t ln2;
- float32_t scale_back;
+ float c0, c2, c4, c6;
+ float c1, c3, c5, c7;
+ float ln2, exp_bias, quarter;
+ uint32_t four, three_quarters;
} sv_log1pf_data = {
- /* Polynomial generated using FPMinimax in [-0.25, 0.5]. */
- .poly = { -0x1p-1f, 0x1.5555aap-2f, -0x1.000038p-2f, 0x1.99675cp-3f,
- -0x1.54ef78p-3f, 0x1.28a1f4p-3f, -0x1.0da91p-3f, 0x1.abcb6p-4f,
- -0x1.6f0d5ep-5f },
- .scale_back = 0x1.0p-23f,
- .ln2 = 0x1.62e43p-1f,
+ /* Do not store first term of polynomial, which is -0.5, as
+ this can be fmov-ed directly instead of including it in
+ the main load-and-mla polynomial schedule. */
+ .c0 = 0x1.5555aap-2f, .c1 = -0x1.000038p-2f, .c2 = 0x1.99675cp-3f,
+ .c3 = -0x1.54ef78p-3f, .c4 = 0x1.28a1f4p-3f, .c5 = -0x1.0da91p-3f,
+ .c6 = 0x1.abcb6p-4f, .c7 = -0x1.6f0d5ep-5f, .ln2 = 0x1.62e43p-1f,
+ .exp_bias = 0x1p-23f, .quarter = 0x1p-2f, .four = 0x40800000,
+ .three_quarters = 0x3f400000,
};
-static inline svfloat32_t
-eval_poly (svfloat32_t m, const float32_t *c, svbool_t pg)
-{
- svfloat32_t p_12 = svmla_x (pg, sv_f32 (c[0]), m, sv_f32 (c[1]));
- svfloat32_t m2 = svmul_x (pg, m, m);
- svfloat32_t q = svmla_x (pg, m, m2, p_12);
- svfloat32_t p = sv_pw_horner_6_f32_x (pg, m, m2, c + 2);
- p = svmul_x (pg, m2, p);
-
- return svmla_x (pg, q, m2, p);
-}
-
static inline svfloat32_t
sv_log1pf_inline (svfloat32_t x, svbool_t pg)
{
const struct sv_log1pf_data *d = ptr_barrier (&sv_log1pf_data);
- svfloat32_t m = svadd_x (pg, x, 1.0f);
-
- svint32_t ks = svsub_x (pg, svreinterpret_s32 (m),
- svreinterpret_s32 (svdup_f32 (0.75f)));
- ks = svand_x (pg, ks, 0xff800000);
- svuint32_t k = svreinterpret_u32 (ks);
- svfloat32_t s = svreinterpret_f32 (
- svsub_x (pg, svreinterpret_u32 (svdup_f32 (4.0f)), k));
-
- svfloat32_t m_scale
- = svreinterpret_f32 (svsub_x (pg, svreinterpret_u32 (x), k));
- m_scale
- = svadd_x (pg, m_scale, svmla_x (pg, sv_f32 (-1.0f), sv_f32 (0.25f), s));
- svfloat32_t p = eval_poly (m_scale, d->poly, pg);
- svfloat32_t scale_back = svmul_x (pg, svcvt_f32_x (pg, k), d->scale_back);
- return svmla_x (pg, p, scale_back, d->ln2);
+ /* With x + 1 = t * 2^k (where t = m + 1 and k is chosen such that m
+ is in [-0.25, 0.5]):
+ log1p(x) = log(t) + log(2^k) = log1p(m) + k*log(2).
+
+ We approximate log1p(m) with a polynomial, then scale by
+ k*log(2). Instead of doing this directly, we use an intermediate
+ scale factor s = 4*k*log(2) to ensure the scale is representable
+ as a normalised fp32 number. */
+ svfloat32_t m = svadd_x (pg, x, 1);
+
+ /* Choose k to scale x to the range [-1/4, 1/2]. */
+ svint32_t k
+ = svand_x (pg, svsub_x (pg, svreinterpret_s32 (m), d->three_quarters),
+ sv_s32 (SignExponentMask));
+
+ /* Scale x by exponent manipulation. */
+ svfloat32_t m_scale = svreinterpret_f32 (
+ svsub_x (pg, svreinterpret_u32 (x), svreinterpret_u32 (k)));
+
+ /* Scale up to ensure that the scale factor is representable as normalised
+ fp32 number, and scale m down accordingly. */
+ svfloat32_t s = svreinterpret_f32 (svsubr_x (pg, k, d->four));
+ svfloat32_t fconst = svld1rq_f32 (svptrue_b32 (), &d->ln2);
+ m_scale = svadd_x (pg, m_scale, svmla_lane_f32 (sv_f32 (-1), s, fconst, 2));
+
+ /* Evaluate polynomial on reduced interval. */
+ svfloat32_t ms2 = svmul_x (svptrue_b32 (), m_scale, m_scale);
+
+ svfloat32_t c1357 = svld1rq_f32 (svptrue_b32 (), &d->c1);
+ svfloat32_t p01 = svmla_lane_f32 (sv_f32 (d->c0), m_scale, c1357, 0);
+ svfloat32_t p23 = svmla_lane_f32 (sv_f32 (d->c2), m_scale, c1357, 1);
+ svfloat32_t p45 = svmla_lane_f32 (sv_f32 (d->c4), m_scale, c1357, 2);
+ svfloat32_t p67 = svmla_lane_f32 (sv_f32 (d->c6), m_scale, c1357, 3);
+
+ svfloat32_t p = svmla_x (pg, p45, p67, ms2);
+ p = svmla_x (pg, p23, p, ms2);
+ p = svmla_x (pg, p01, p, ms2);
+
+ p = svmad_x (pg, m_scale, p, -0.5);
+ p = svmla_x (pg, m_scale, m_scale, svmul_x (pg, m_scale, p));
+
+ /* The scale factor to be applied back at the end - by multiplying float(k)
+ by 2^-23 we get the unbiased exponent of k. */
+ svfloat32_t scale_back = svmul_lane_f32 (svcvt_f32_x (pg, k), fconst, 1);
+ return svmla_lane_f32 (p, scale_back, fconst, 0);
}
#endif
projects / thirdparty / glibc.git / commitdiff
