Use unpredicated muls, use absolute compare and improve memory access.
Expm1f, sinhf and tanhf show 7%, 5% and 1% improvement in throughput
microbenchmark on Neoverse V1.
<https://www.gnu.org/licenses/>. */
#include "sv_math.h"
-#include "poly_sve_f32.h"
/* Largest value of x for which expm1(x) should round to -1. */
#define SpecialBound 0x1.5ebc4p+6f
/* These 4 are grouped together so they can be loaded as one quadword, then
used with _lane forms of svmla/svmls. */
float c2, c4, ln2_hi, ln2_lo;
- float c0, c1, c3, inv_ln2, special_bound, shift;
+ float c0, inv_ln2, c1, c3, special_bound;
} data = {
/* Generated using fpminimax. */
.c0 = 0x1.fffffep-2, .c1 = 0x1.5554aep-3,
.c2 = 0x1.555736p-5, .c3 = 0x1.12287cp-7,
- .c4 = 0x1.6b55a2p-10,
+ .c4 = 0x1.6b55a2p-10, .inv_ln2 = 0x1.715476p+0f,
+ .special_bound = SpecialBound, .ln2_lo = 0x1.7f7d1cp-20f,
+ .ln2_hi = 0x1.62e4p-1f,
- .special_bound = SpecialBound, .shift = 0x1.8p23f,
- .inv_ln2 = 0x1.715476p+0f, .ln2_hi = 0x1.62e4p-1f,
- .ln2_lo = 0x1.7f7d1cp-20f,
};
-#define C(i) sv_f32 (d->c##i)
-
static svfloat32_t NOINLINE
special_case (svfloat32_t x, svbool_t pg)
{
and f = x - i * ln2, then f is in [-ln2/2, ln2/2].
exp(x) - 1 = 2^i * (expm1(f) + 1) - 1
where 2^i is exact because i is an integer. */
- svfloat32_t j = svmla_x (pg, sv_f32 (d->shift), x, d->inv_ln2);
- j = svsub_x (pg, j, d->shift);
- svint32_t i = svcvt_s32_x (pg, j);
+ svfloat32_t j = svmul_x (svptrue_b32 (), x, d->inv_ln2);
+ j = svrinta_x (pg, j);
svfloat32_t f = svmls_lane (x, j, lane_constants, 2);
f = svmls_lane (f, j, lane_constants, 3);
x + ax^2 + bx^3 + cx^4 ....
So we calculate the polynomial P(f) = a + bf + cf^2 + ...
and assemble the approximation expm1(f) ~= f + f^2 * P(f). */
- svfloat32_t p12 = svmla_lane (C (1), f, lane_constants, 0);
- svfloat32_t p34 = svmla_lane (C (3), f, lane_constants, 1);
- svfloat32_t f2 = svmul_x (pg, f, f);
+ svfloat32_t p12 = svmla_lane (sv_f32 (d->c1), f, lane_constants, 0);
+ svfloat32_t p34 = svmla_lane (sv_f32 (d->c3), f, lane_constants, 1);
+ svfloat32_t f2 = svmul_x (svptrue_b32 (), f, f);
svfloat32_t p = svmla_x (pg, p12, f2, p34);
- p = svmla_x (pg, C (0), f, p);
+
+ p = svmla_x (pg, sv_f32 (d->c0), f, p);
p = svmla_x (pg, f, f2, p);
/* Assemble the result.
expm1(x) ~= 2^i * (p + 1) - 1
Let t = 2^i. */
- svfloat32_t t = svreinterpret_f32 (
- svadd_x (pg, svreinterpret_u32 (svlsl_x (pg, i, 23)), 0x3f800000));
- return svmla_x (pg, svsub_x (pg, t, 1), p, t);
+ svfloat32_t t = svscale_x (pg, sv_f32 (1.0f), svcvt_s32_x (pg, j));
+ return svmla_x (pg, svsub_x (pg, t, 1.0f), p, t);
}
if (__glibc_unlikely (svptest_any (pg, special)))
return special_case (x, svmul_x (pg, t, halfsign), special);
- return svmul_x (pg, t, halfsign);
+ return svmul_x (svptrue_b32 (), t, halfsign);
}
/* These 4 are grouped together so they can be loaded as one quadword, then
used with _lane forms of svmla/svmls. */
float32_t c2, c4, ln2_hi, ln2_lo;
- float32_t c0, c1, c3, inv_ln2, shift;
+ float c0, inv_ln2, c1, c3, special_bound;
};
/* Coefficients generated using fpminimax. */
#define SV_EXPM1F_DATA \
{ \
- .c0 = 0x1.fffffep-2, .c1 = 0x1.5554aep-3, .c2 = 0x1.555736p-5, \
- .c3 = 0x1.12287cp-7, .c4 = 0x1.6b55a2p-10, \
+ .c0 = 0x1.fffffep-2, .c1 = 0x1.5554aep-3, .inv_ln2 = 0x1.715476p+0f, \
+ .c2 = 0x1.555736p-5, .c3 = 0x1.12287cp-7, \
\
- .shift = 0x1.8p23f, .inv_ln2 = 0x1.715476p+0f, .ln2_hi = 0x1.62e4p-1f, \
- .ln2_lo = 0x1.7f7d1cp-20f, \
+ .c4 = 0x1.6b55a2p-10, .ln2_lo = 0x1.7f7d1cp-20f, .ln2_hi = 0x1.62e4p-1f, \
}
-#define C(i) sv_f32 (d->c##i)
-
static inline svfloat32_t
expm1f_inline (svfloat32_t x, svbool_t pg, const struct sv_expm1f_data *d)
{
and f = x - i * ln2, then f is in [-ln2/2, ln2/2].
exp(x) - 1 = 2^i * (expm1(f) + 1) - 1
where 2^i is exact because i is an integer. */
- svfloat32_t j = svmla_x (pg, sv_f32 (d->shift), x, d->inv_ln2);
- j = svsub_x (pg, j, d->shift);
- svint32_t i = svcvt_s32_x (pg, j);
+ svfloat32_t j = svmul_x (svptrue_b32 (), x, d->inv_ln2);
+ j = svrinta_x (pg, j);
svfloat32_t f = svmls_lane (x, j, lane_constants, 2);
f = svmls_lane (f, j, lane_constants, 3);
x + ax^2 + bx^3 + cx^4 ....
So we calculate the polynomial P(f) = a + bf + cf^2 + ...
and assemble the approximation expm1(f) ~= f + f^2 * P(f). */
- svfloat32_t p12 = svmla_lane (C (1), f, lane_constants, 0);
- svfloat32_t p34 = svmla_lane (C (3), f, lane_constants, 1);
- svfloat32_t f2 = svmul_x (pg, f, f);
+ svfloat32_t p12 = svmla_lane (sv_f32 (d->c1), f, lane_constants, 0);
+ svfloat32_t p34 = svmla_lane (sv_f32 (d->c3), f, lane_constants, 1);
+ svfloat32_t f2 = svmul_x (svptrue_b32 (), f, f);
svfloat32_t p = svmla_x (pg, p12, f2, p34);
- p = svmla_x (pg, C (0), f, p);
+ p = svmla_x (pg, sv_f32 (d->c0), f, p);
p = svmla_x (pg, f, f2, p);
/* Assemble the result.
expm1(x) ~= 2^i * (p + 1) - 1
Let t = 2^i. */
- svfloat32_t t = svscale_x (pg, sv_f32 (1), i);
- return svmla_x (pg, svsub_x (pg, t, 1), p, t);
+ svfloat32_t t = svscale_x (pg, sv_f32 (1.0f), svcvt_s32_x (pg, j));
+ return svmla_x (pg, svsub_x (pg, t, 1.0f), p, t);
}
#endif
#include "sv_expm1f_inline.h"
+/* Largest value of x for which tanhf(x) rounds to 1 (or -1 for negative). */
+#define BoringBound 0x1.205966p+3f
+
static const struct data
{
struct sv_expm1f_data expm1f_consts;
- uint32_t boring_bound, onef;
+ uint32_t onef, special_bound;
+ float boring_bound;
} data = {
.expm1f_consts = SV_EXPM1F_DATA,
- /* 0x1.205966p+3, above which tanhf rounds to 1 (or -1 for negative). */
- .boring_bound = 0x41102cb3,
.onef = 0x3f800000,
+ .special_bound = 0x7f800000,
+ .boring_bound = BoringBound,
};
static svfloat32_t NOINLINE
-special_case (svfloat32_t x, svfloat32_t y, svbool_t special)
+special_case (svfloat32_t x, svbool_t pg, svbool_t is_boring,
+ svfloat32_t boring, svfloat32_t q, svbool_t special)
{
+ svfloat32_t y
+ = svsel_f32 (is_boring, boring, svdiv_x (pg, q, svadd_x (pg, q, 2.0)));
return sv_call_f32 (tanhf, x, y, special);
}
svfloat32_t ax = svabs_x (pg, x);
svuint32_t iax = svreinterpret_u32 (ax);
svuint32_t sign = sveor_x (pg, svreinterpret_u32 (x), iax);
- svbool_t is_boring = svcmpgt (pg, iax, d->boring_bound);
svfloat32_t boring = svreinterpret_f32 (svorr_x (pg, sign, d->onef));
-
- svbool_t special = svcmpgt (pg, iax, 0x7f800000);
+ svbool_t special = svcmpgt (pg, iax, d->special_bound);
+ svbool_t is_boring = svacgt (pg, x, d->boring_bound);
/* tanh(x) = (e^2x - 1) / (e^2x + 1). */
- svfloat32_t q = expm1f_inline (svmul_x (pg, x, 2.0), pg, &d->expm1f_consts);
- svfloat32_t y = svdiv_x (pg, q, svadd_x (pg, q, 2.0));
+ svfloat32_t q = expm1f_inline (svmul_x (svptrue_b32 (), x, 2.0), pg,
+ &d->expm1f_consts);
+
if (__glibc_unlikely (svptest_any (pg, special)))
- return special_case (x, svsel_f32 (is_boring, boring, y), special);
+ return special_case (x, pg, is_boring, boring, q, special);
+ svfloat32_t y = svdiv_x (pg, q, svadd_x (pg, q, 2.0));
return svsel_f32 (is_boring, boring, y);
}
projects / thirdparty / glibc.git / commitdiff
