@@ -23,37 +23,42 @@
static const struct data
{
struct sv_expf_data expf_consts;
- uint32_t special_bound;
+ float special_bound;
} data = {
.expf_consts = SV_EXPF_DATA,
/* 0x1.5a92d8p+6: expf overflows above this, so have to use special case. */
- .special_bound = 0x42ad496c,
+ .special_bound = 0x1.5a92d8p+6,
};
static svfloat32_t NOINLINE
-special_case (svfloat32_t x, svfloat32_t y, svbool_t pg)
+special_case (svfloat32_t x, svfloat32_t half_e, svfloat32_t half_over_e,
+ svbool_t pg)
{
- return sv_call_f32 (coshf, x, y, pg);
+ return sv_call_f32 (coshf, x, svadd_x (svptrue_b32 (), half_e, half_over_e),
+ pg);
}
/* Single-precision vector cosh, using vector expf.
- Maximum error is 1.89 ULP:
- _ZGVsMxv_coshf (-0x1.65898cp+6) got 0x1.f00aep+127
- want 0x1.f00adcp+127. */
+ Maximum error is 2.77 ULP:
+ _ZGVsMxv_coshf(-0x1.5b38f4p+1) got 0x1.e45946p+2
+ want 0x1.e4594cp+2. */
svfloat32_t SV_NAME_F1 (cosh) (svfloat32_t x, svbool_t pg)
{
const struct data *d = ptr_barrier (&data);
- svfloat32_t ax = svabs_x (pg, x);
- svbool_t special = svcmpge (pg, svreinterpret_u32 (ax), d->special_bound);
+ svbool_t special = svacge (pg, x, d->special_bound);
- /* Calculate cosh by exp(x) / 2 + exp(-x) / 2. */
- svfloat32_t t = expf_inline (ax, pg, &d->expf_consts);
- svfloat32_t half_t = svmul_x (pg, t, 0.5);
- svfloat32_t half_over_t = svdivr_x (pg, t, 0.5);
+ /* Calculate cosh by exp(x) / 2 + exp(-x) / 2.
+ Note that x is passed to exp here, rather than |x|. This is to avoid using
+ destructive unary ABS for better register usage. However it means the
+ routine is not exactly symmetrical, as the exp helper is slightly less
+ accurate in the negative range. */
+ svfloat32_t e = expf_inline (x, pg, &d->expf_consts);
+ svfloat32_t half_e = svmul_x (svptrue_b32 (), e, 0.5);
+ svfloat32_t half_over_e = svdivr_x (pg, e, 0.5);
if (__glibc_unlikely (svptest_any (pg, special)))
- return special_case (x, svadd_x (pg, half_t, half_over_t), special);
+ return special_case (x, half_e, half_over_e, special);
- return svadd_x (pg, half_t, half_over_t);
+ return svadd_x (svptrue_b32 (), half_e, half_over_e);
}
@@ -18,74 +18,83 @@
<https://www.gnu.org/licenses/>. */
#include "sv_math.h"
-#include "poly_sve_f32.h"
-/* For x < -SpecialBound, the result is subnormal and not handled correctly by
+/* For x < -Thres, the result is subnormal and not handled correctly by
FEXPA. */
-#define SpecialBound 37.9
+#define Thres 37.9
static const struct data
{
- float poly[5];
- float shift, log10_2, log2_10_hi, log2_10_lo, special_bound;
+ float log2_10_lo, c0, c2, c4;
+ float c1, c3, log10_2;
+ float shift, log2_10_hi, thres;
} data = {
/* Coefficients generated using Remez algorithm with minimisation of relative
error.
rel error: 0x1.89dafa3p-24
abs error: 0x1.167d55p-23 in [-log10(2)/2, log10(2)/2]
maxerr: 0.52 +0.5 ulp. */
- .poly = { 0x1.26bb16p+1f, 0x1.5350d2p+1f, 0x1.04744ap+1f, 0x1.2d8176p+0f,
- 0x1.12b41ap-1f },
+ .c0 = 0x1.26bb16p+1f,
+ .c1 = 0x1.5350d2p+1f,
+ .c2 = 0x1.04744ap+1f,
+ .c3 = 0x1.2d8176p+0f,
+ .c4 = 0x1.12b41ap-1f,
/* 1.5*2^17 + 127, a shift value suitable for FEXPA. */
- .shift = 0x1.903f8p17f,
+ .shift = 0x1.803f8p17f,
.log10_2 = 0x1.a934fp+1,
.log2_10_hi = 0x1.344136p-2,
.log2_10_lo = -0x1.ec10cp-27,
- .special_bound = SpecialBound,
+ .thres = Thres,
};
-static svfloat32_t NOINLINE
-special_case (svfloat32_t x, svfloat32_t y, svbool_t special)
+static inline svfloat32_t
+sv_exp10f_inline (svfloat32_t x, const svbool_t pg, const struct data *d)
{
- return sv_call_f32 (exp10f, x, y, special);
-}
-
-/* Single-precision SVE exp10f routine. Implements the same algorithm
- as AdvSIMD exp10f.
- Worst case error is 1.02 ULPs.
- _ZGVsMxv_exp10f(-0x1.040488p-4) got 0x1.ba5f9ep-1
- want 0x1.ba5f9cp-1. */
-svfloat32_t SV_NAME_F1 (exp10) (svfloat32_t x, const svbool_t pg)
-{
- const struct data *d = ptr_barrier (&data);
/* exp10(x) = 2^(n/N) * 10^r = 2^n * (1 + poly (r)),
with poly(r) in [1/sqrt(2), sqrt(2)] and
x = r + n * log10(2) / N, with r in [-log10(2)/2N, log10(2)/2N]. */
- /* Load some constants in quad-word chunks to minimise memory access (last
- lane is wasted). */
- svfloat32_t log10_2_and_inv = svld1rq (svptrue_b32 (), &d->log10_2);
+ svfloat32_t lane_consts = svld1rq (svptrue_b32 (), &d->log2_10_lo);
/* n = round(x/(log10(2)/N)). */
svfloat32_t shift = sv_f32 (d->shift);
- svfloat32_t z = svmla_lane (shift, x, log10_2_and_inv, 0);
- svfloat32_t n = svsub_x (pg, z, shift);
+ svfloat32_t z = svmad_x (pg, sv_f32 (d->log10_2), x, shift);
+ svfloat32_t n = svsub_x (svptrue_b32 (), z, shift);
/* r = x - n*log10(2)/N. */
- svfloat32_t r = svmls_lane (x, n, log10_2_and_inv, 1);
- r = svmls_lane (r, n, log10_2_and_inv, 2);
+ svfloat32_t r = svmsb_x (pg, sv_f32 (d->log2_10_hi), n, x);
+ r = svmls_lane (r, n, lane_consts, 0);
- svbool_t special = svacgt (pg, x, d->special_bound);
svfloat32_t scale = svexpa (svreinterpret_u32 (z));
/* Polynomial evaluation: poly(r) ~ exp10(r)-1. */
- svfloat32_t r2 = svmul_x (pg, r, r);
- svfloat32_t poly
- = svmla_x (pg, svmul_x (pg, r, d->poly[0]),
- sv_pairwise_poly_3_f32_x (pg, r, r2, d->poly + 1), r2);
-
- if (__glibc_unlikely (svptest_any (pg, special)))
- return special_case (x, svmla_x (pg, scale, scale, poly), special);
+ 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);
+ 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);
return svmla_x (pg, scale, scale, poly);
}
+
+static svfloat32_t NOINLINE
+special_case (svfloat32_t x, svbool_t special, const struct data *d)
+{
+ return sv_call_f32 (exp10f, x, sv_exp10f_inline (x, svptrue_b32 (), d),
+ special);
+}
+
+/* Single-precision SVE exp10f routine. Implements the same algorithm
+ as AdvSIMD exp10f.
+ Worst case error is 1.02 ULPs.
+ _ZGVsMxv_exp10f(-0x1.040488p-4) got 0x1.ba5f9ep-1
+ want 0x1.ba5f9cp-1. */
+svfloat32_t SV_NAME_F1 (exp10) (svfloat32_t x, const svbool_t pg)
+{
+ const struct data *d = ptr_barrier (&data);
+ svbool_t special = svacgt (pg, x, d->thres);
+ if (__glibc_unlikely (svptest_any (special, special)))
+ return special_case (x, special, d);
+ return sv_exp10f_inline (x, pg, d);
+}
@@ -24,54 +24,64 @@
static const struct data
{
- float poly[5];
+ float c0, c2, c4, c1, c3;
float shift, thres;
} data = {
- /* Coefficients copied from the polynomial in AdvSIMD variant, reversed for
- compatibility with polynomial helpers. */
- .poly = { 0x1.62e422p-1f, 0x1.ebf9bcp-3f, 0x1.c6bd32p-5f, 0x1.3ce9e4p-7f,
- 0x1.59977ap-10f },
+ /* Coefficients copied from the polynomial in AdvSIMD variant. */
+ .c0 = 0x1.62e422p-1f,
+ .c1 = 0x1.ebf9bcp-3f,
+ .c2 = 0x1.c6bd32p-5f,
+ .c3 = 0x1.3ce9e4p-7f,
+ .c4 = 0x1.59977ap-10f,
/* 1.5*2^17 + 127. */
- .shift = 0x1.903f8p17f,
+ .shift = 0x1.803f8p17f,
/* Roughly 87.3. For x < -Thres, the result is subnormal and not handled
correctly by FEXPA. */
.thres = Thres,
};
-static svfloat32_t NOINLINE
-special_case (svfloat32_t x, svfloat32_t y, svbool_t special)
-{
- return sv_call_f32 (exp2f, x, y, special);
-}
-
-/* Single-precision SVE exp2f routine. Implements the same algorithm
- as AdvSIMD exp2f.
- Worst case error is 1.04 ULPs.
- SV_NAME_F1 (exp2)(0x1.943b9p-1) got 0x1.ba7eb2p+0
- want 0x1.ba7ebp+0. */
-svfloat32_t SV_NAME_F1 (exp2) (svfloat32_t x, const svbool_t pg)
+static inline svfloat32_t
+sv_exp2f_inline (svfloat32_t x, const svbool_t pg, const struct data *d)
{
- const struct data *d = ptr_barrier (&data);
/* exp2(x) = 2^n (1 + poly(r)), with 1 + poly(r) in [1/sqrt(2),sqrt(2)]
x = n + r, with r in [-1/2, 1/2]. */
- svfloat32_t shift = sv_f32 (d->shift);
- svfloat32_t z = svadd_x (pg, x, shift);
- svfloat32_t n = svsub_x (pg, z, shift);
- svfloat32_t r = svsub_x (pg, x, n);
+ svfloat32_t z = svadd_x (svptrue_b32 (), x, d->shift);
+ svfloat32_t n = svsub_x (svptrue_b32 (), z, d->shift);
+ svfloat32_t r = svsub_x (svptrue_b32 (), x, n);
- svbool_t special = svacgt (pg, x, d->thres);
svfloat32_t scale = svexpa (svreinterpret_u32 (z));
/* Polynomial evaluation: poly(r) ~ exp2(r)-1.
Evaluate polynomial use hybrid scheme - offset ESTRIN by 1 for
coefficients 1 to 4, and apply most significant coefficient directly. */
- svfloat32_t r2 = svmul_x (pg, r, r);
- svfloat32_t p14 = sv_pairwise_poly_3_f32_x (pg, r, r2, d->poly + 1);
- svfloat32_t p0 = svmul_x (pg, r, d->poly[0]);
+ svfloat32_t even_coeffs = svld1rq (svptrue_b32 (), &d->c0);
+ svfloat32_t r2 = svmul_x (svptrue_b32 (), r, r);
+ svfloat32_t p12 = svmla_lane (sv_f32 (d->c1), r, even_coeffs, 1);
+ svfloat32_t p34 = svmla_lane (sv_f32 (d->c3), r, even_coeffs, 2);
+ svfloat32_t p14 = svmla_x (pg, p12, r2, p34);
+ svfloat32_t p0 = svmul_lane (r, even_coeffs, 0);
svfloat32_t poly = svmla_x (pg, p0, r2, p14);
- if (__glibc_unlikely (svptest_any (pg, special)))
- return special_case (x, svmla_x (pg, scale, scale, poly), special);
-
return svmla_x (pg, scale, scale, poly);
}
+
+static svfloat32_t NOINLINE
+special_case (svfloat32_t x, svbool_t special, const struct data *d)
+{
+ return sv_call_f32 (exp2f, x, sv_exp2f_inline (x, svptrue_b32 (), d),
+ special);
+}
+
+/* Single-precision SVE exp2f routine. Implements the same algorithm
+ as AdvSIMD exp2f.
+ Worst case error is 1.04 ULPs.
+ _ZGVsMxv_exp2f(-0x1.af994ap-3) got 0x1.ba6a66p-1
+ want 0x1.ba6a64p-1. */
+svfloat32_t SV_NAME_F1 (exp2) (svfloat32_t x, const svbool_t pg)
+{
+ const struct data *d = ptr_barrier (&data);
+ svbool_t special = svacgt (pg, x, d->thres);
+ if (__glibc_unlikely (svptest_any (special, special)))
+ return special_case (x, special, d);
+ return sv_exp2f_inline (x, pg, d);
+}
@@ -18,33 +18,25 @@
<https://www.gnu.org/licenses/>. */
#include "sv_math.h"
+#include "sv_expf_inline.h"
+
+/* Roughly 87.3. For x < -Thres, the result is subnormal and not handled
+ correctly by FEXPA. */
+#define Thres 0x1.5d5e2ap+6f
static const struct data
{
- float poly[5];
- float inv_ln2, ln2_hi, ln2_lo, shift, thres;
+ struct sv_expf_data d;
+ float thres;
} data = {
- /* Coefficients copied from the polynomial in AdvSIMD variant, reversed for
- compatibility with polynomial helpers. */
- .poly = { 0x1.ffffecp-1f, 0x1.fffdb6p-2f, 0x1.555e66p-3f, 0x1.573e2ep-5f,
- 0x1.0e4020p-7f },
- .inv_ln2 = 0x1.715476p+0f,
- .ln2_hi = 0x1.62e4p-1f,
- .ln2_lo = 0x1.7f7d1cp-20f,
- /* 1.5*2^17 + 127. */
- .shift = 0x1.903f8p17f,
- /* Roughly 87.3. For x < -Thres, the result is subnormal and not handled
- correctly by FEXPA. */
- .thres = 0x1.5d5e2ap+6f,
+ .d = SV_EXPF_DATA,
+ .thres = Thres,
};
-#define C(i) sv_f32 (d->poly[i])
-#define ExponentBias 0x3f800000
-
static svfloat32_t NOINLINE
-special_case (svfloat32_t x, svfloat32_t y, svbool_t special)
+special_case (svfloat32_t x, svbool_t special, const struct sv_expf_data *d)
{
- return sv_call_f32 (expf, x, y, special);
+ return sv_call_f32 (expf, x, expf_inline (x, svptrue_b32 (), d), special);
}
/* Optimised single-precision SVE exp function.
@@ -54,36 +46,8 @@ special_case (svfloat32_t x, svfloat32_t y, svbool_t special)
svfloat32_t SV_NAME_F1 (exp) (svfloat32_t x, const svbool_t pg)
{
const struct data *d = ptr_barrier (&data);
-
- /* 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]. */
-
- /* Load some constants in quad-word chunks to minimise memory access (last
- lane is wasted). */
- svfloat32_t invln2_and_ln2 = svld1rq (svptrue_b32 (), &d->inv_ln2);
-
- /* n = round(x/(ln2/N)). */
- svfloat32_t z = svmla_lane (sv_f32 (d->shift), x, invln2_and_ln2, 0);
- svfloat32_t n = svsub_x (pg, z, d->shift);
-
- /* r = x - n*ln2/N. */
- svfloat32_t r = svmls_lane (x, n, invln2_and_ln2, 1);
- r = svmls_lane (r, n, invln2_and_ln2, 2);
-
- /* scale = 2^(n/N). */
svbool_t is_special_case = svacgt (pg, x, d->thres);
- svfloat32_t scale = svexpa (svreinterpret_u32 (z));
-
- /* y = exp(r) - 1 ~= r + C0 r^2 + C1 r^3 + C2 r^4 + C3 r^5 + C4 r^6. */
- svfloat32_t p12 = svmla_x (pg, C (1), C (2), r);
- svfloat32_t p34 = svmla_x (pg, C (3), C (4), r);
- svfloat32_t r2 = svmul_x (pg, r, r);
- svfloat32_t p14 = svmla_x (pg, p12, p34, r2);
- svfloat32_t p0 = svmul_x (pg, r, C (0));
- svfloat32_t poly = svmla_x (pg, p0, r2, p14);
-
if (__glibc_unlikely (svptest_any (pg, is_special_case)))
- return special_case (x, svmla_x (pg, scale, scale, poly), is_special_case);
-
- return svmla_x (pg, scale, scale, poly);
+ return special_case (x, is_special_case, &d->d);
+ return expf_inline (x, pg, &d->d);
}
@@ -24,19 +24,20 @@
struct sv_expf_data
{
- float poly[5];
- float inv_ln2, ln2_hi, ln2_lo, shift;
+ float c1, c3, inv_ln2;
+ float ln2_lo, c0, c2, c4;
+ float ln2_hi, shift;
};
/* Coefficients copied from the polynomial in AdvSIMD variant, reversed for
compatibility with polynomial helpers. Shift is 1.5*2^17 + 127. */
#define SV_EXPF_DATA \
{ \
- .poly = { 0x1.ffffecp-1f, 0x1.fffdb6p-2f, 0x1.555e66p-3f, 0x1.573e2ep-5f, \
- 0x1.0e4020p-7f }, \
- \
- .inv_ln2 = 0x1.715476p+0f, .ln2_hi = 0x1.62e4p-1f, \
- .ln2_lo = 0x1.7f7d1cp-20f, .shift = 0x1.803f8p17f, \
+ /* 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, \
}
#define C(i) sv_f32 (d->poly[i])
@@ -47,26 +48,25 @@ 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]. */
- /* Load some constants in quad-word chunks to minimise memory access. */
- svfloat32_t c4_invln2_and_ln2 = svld1rq (svptrue_b32 (), &d->poly[4]);
+ svfloat32_t lane_consts = svld1rq (svptrue_b32 (), &d->ln2_lo);
/* n = round(x/(ln2/N)). */
- svfloat32_t z = svmla_lane (sv_f32 (d->shift), x, c4_invln2_and_ln2, 1);
+ 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 = svmls_lane (x, n, c4_invln2_and_ln2, 2);
- r = svmls_lane (r, n, c4_invln2_and_ln2, 3);
+ svfloat32_t r = svmsb_x (pg, sv_f32 (d->ln2_hi), n, x);
+ r = svmls_lane (r, n, lane_consts, 0);
/* scale = 2^(n/N). */
- svfloat32_t scale = svexpa (svreinterpret_u32_f32 (z));
+ svfloat32_t scale = svexpa (svreinterpret_u32 (z));
/* y = exp(r) - 1 ~= r + C0 r^2 + C1 r^3 + C2 r^4 + C3 r^5 + C4 r^6. */
- svfloat32_t p12 = svmla_x (pg, C (1), C (2), r);
- svfloat32_t p34 = svmla_lane (C (3), r, c4_invln2_and_ln2, 0);
- svfloat32_t r2 = svmul_f32_x (pg, r, r);
+ 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);
+ svfloat32_t r2 = svmul_x (svptrue_b32 (), r, r);
svfloat32_t p14 = svmla_x (pg, p12, p34, r2);
- svfloat32_t p0 = svmul_f32_x (pg, r, C (0));
+ svfloat32_t p0 = svmul_lane (r, lane_consts, 1);
svfloat32_t poly = svmla_x (pg, p0, r2, p14);
return svmla_x (pg, scale, scale, poly);