Load the polynomial evaluation coefficients into 2 vectors and use lanewise MLAs.
8% improvement in throughput microbenchmark on Neoverse V1.
Reviewed-by: Wilco Dijkstra <Wilco.Dijkstra@arm.com>
static const struct data
{
+ float64x2_t c0, c2, c4, c6, c8, c10, c12, c14, c16, c18;
float64x2_t pi_over_2;
- float64x2_t poly[20];
+ double c1, c3, c5, c7, c9, c11, c13, c15, c17, c19;
+ uint64x2_t zeroinfnan, minustwo;
} data = {
/* Coefficients of polynomial P such that atan(x)~x+x*P(x^2) on
- the interval [2**-1022, 1.0]. */
- .poly = { V2 (-0x1.5555555555555p-2), V2 (0x1.99999999996c1p-3),
- V2 (-0x1.2492492478f88p-3), V2 (0x1.c71c71bc3951cp-4),
- V2 (-0x1.745d160a7e368p-4), V2 (0x1.3b139b6a88ba1p-4),
- V2 (-0x1.11100ee084227p-4), V2 (0x1.e1d0f9696f63bp-5),
- V2 (-0x1.aebfe7b418581p-5), V2 (0x1.842dbe9b0d916p-5),
- V2 (-0x1.5d30140ae5e99p-5), V2 (0x1.338e31eb2fbbcp-5),
- V2 (-0x1.00e6eece7de8p-5), V2 (0x1.860897b29e5efp-6),
- V2 (-0x1.0051381722a59p-6), V2 (0x1.14e9dc19a4a4ep-7),
- V2 (-0x1.d0062b42fe3bfp-9), V2 (0x1.17739e210171ap-10),
- V2 (-0x1.ab24da7be7402p-13), V2 (0x1.358851160a528p-16), },
+ [2**-1022, 1.0]. */
+ .c0 = V2 (-0x1.5555555555555p-2),
+ .c1 = 0x1.99999999996c1p-3,
+ .c2 = V2 (-0x1.2492492478f88p-3),
+ .c3 = 0x1.c71c71bc3951cp-4,
+ .c4 = V2 (-0x1.745d160a7e368p-4),
+ .c5 = 0x1.3b139b6a88ba1p-4,
+ .c6 = V2 (-0x1.11100ee084227p-4),
+ .c7 = 0x1.e1d0f9696f63bp-5,
+ .c8 = V2 (-0x1.aebfe7b418581p-5),
+ .c9 = 0x1.842dbe9b0d916p-5,
+ .c10 = V2 (-0x1.5d30140ae5e99p-5),
+ .c11 = 0x1.338e31eb2fbbcp-5,
+ .c12 = V2 (-0x1.00e6eece7de8p-5),
+ .c13 = 0x1.860897b29e5efp-6,
+ .c14 = V2 (-0x1.0051381722a59p-6),
+ .c15 = 0x1.14e9dc19a4a4ep-7,
+ .c16 = V2 (-0x1.d0062b42fe3bfp-9),
+ .c17 = 0x1.17739e210171ap-10,
+ .c18 = V2 (-0x1.ab24da7be7402p-13),
+ .c19 = 0x1.358851160a528p-16,
.pi_over_2 = V2 (0x1.921fb54442d18p+0),
+ .zeroinfnan = V2 (2 * 0x7ff0000000000000ul - 1),
+ .minustwo = V2 (0xc000000000000000),
};
#define SignMask v_u64 (0x8000000000000000)
/* Special cases i.e. 0, infinity, NaN (fall back to scalar calls). */
static float64x2_t VPCS_ATTR NOINLINE
-special_case (float64x2_t y, float64x2_t x, float64x2_t ret, uint64x2_t cmp)
+special_case (float64x2_t y, float64x2_t x, float64x2_t ret,
+ uint64x2_t sign_xy, uint64x2_t cmp)
{
+ /* Account for the sign of x and y. */
+ ret = vreinterpretq_f64_u64 (
+ veorq_u64 (vreinterpretq_u64_f64 (ret), sign_xy));
return v_call2_f64 (atan2, y, x, ret, cmp);
}
/* Returns 1 if input is the bit representation of 0, infinity or nan. */
static inline uint64x2_t
-zeroinfnan (uint64x2_t i)
+zeroinfnan (uint64x2_t i, const struct data *d)
{
/* (2 * i - 1) >= (2 * asuint64 (INFINITY) - 1). */
- return vcgeq_u64 (vsubq_u64 (vaddq_u64 (i, i), v_u64 (1)),
- v_u64 (2 * asuint64 (INFINITY) - 1));
+ return vcgeq_u64 (vsubq_u64 (vaddq_u64 (i, i), v_u64 (1)), d->zeroinfnan);
}
/* Fast implementation of vector atan2.
want 0x1.92d628ab678cfp-1. */
float64x2_t VPCS_ATTR V_NAME_D2 (atan2) (float64x2_t y, float64x2_t x)
{
- const struct data *data_ptr = ptr_barrier (&data);
+ const struct data *d = ptr_barrier (&data);
uint64x2_t ix = vreinterpretq_u64_f64 (x);
uint64x2_t iy = vreinterpretq_u64_f64 (y);
- uint64x2_t special_cases = vorrq_u64 (zeroinfnan (ix), zeroinfnan (iy));
+ uint64x2_t special_cases
+ = vorrq_u64 (zeroinfnan (ix, d), zeroinfnan (iy, d));
uint64x2_t sign_x = vandq_u64 (ix, SignMask);
uint64x2_t sign_y = vandq_u64 (iy, SignMask);
float64x2_t ay = vabsq_f64 (y);
uint64x2_t pred_xlt0 = vcltzq_f64 (x);
- uint64x2_t pred_aygtax = vcgtq_f64 (ay, ax);
+ uint64x2_t pred_aygtax = vcagtq_f64 (y, x);
/* Set up z for call to atan. */
float64x2_t n = vbslq_f64 (pred_aygtax, vnegq_f64 (ax), ay);
- float64x2_t d = vbslq_f64 (pred_aygtax, ay, ax);
- float64x2_t z = vdivq_f64 (n, d);
+ float64x2_t q = vbslq_f64 (pred_aygtax, ay, ax);
+ float64x2_t z = vdivq_f64 (n, q);
/* Work out the correct shift. */
- float64x2_t shift = vreinterpretq_f64_u64 (
- vandq_u64 (pred_xlt0, vreinterpretq_u64_f64 (v_f64 (-2.0))));
+ float64x2_t shift
+ = vreinterpretq_f64_u64 (vandq_u64 (pred_xlt0, d->minustwo));
shift = vbslq_f64 (pred_aygtax, vaddq_f64 (shift, v_f64 (1.0)), shift);
- shift = vmulq_f64 (shift, data_ptr->pi_over_2);
+ shift = vmulq_f64 (shift, d->pi_over_2);
/* Calculate the polynomial approximation.
Use split Estrin scheme for P(z^2) with deg(P)=19. Use split instead of
float64x2_t x2 = vmulq_f64 (z2, z2);
float64x2_t x4 = vmulq_f64 (x2, x2);
float64x2_t x8 = vmulq_f64 (x4, x4);
- float64x2_t ret
- = vfmaq_f64 (v_estrin_7_f64 (z2, x2, x4, data_ptr->poly),
- v_estrin_11_f64 (z2, x2, x4, x8, data_ptr->poly + 8), x8);
+
+ float64x2_t c13 = vld1q_f64 (&d->c1);
+ float64x2_t c57 = vld1q_f64 (&d->c5);
+ float64x2_t c911 = vld1q_f64 (&d->c9);
+ float64x2_t c1315 = vld1q_f64 (&d->c13);
+ float64x2_t c1719 = vld1q_f64 (&d->c17);
+
+ /* estrin_7. */
+ float64x2_t p01 = vfmaq_laneq_f64 (d->c0, z2, c13, 0);
+ float64x2_t p23 = vfmaq_laneq_f64 (d->c2, z2, c13, 1);
+ float64x2_t p03 = vfmaq_f64 (p01, x2, p23);
+
+ float64x2_t p45 = vfmaq_laneq_f64 (d->c4, z2, c57, 0);
+ float64x2_t p67 = vfmaq_laneq_f64 (d->c6, z2, c57, 1);
+ float64x2_t p47 = vfmaq_f64 (p45, x2, p67);
+
+ float64x2_t p07 = vfmaq_f64 (p03, x4, p47);
+
+ /* estrin_11. */
+ float64x2_t p89 = vfmaq_laneq_f64 (d->c8, z2, c911, 0);
+ float64x2_t p1011 = vfmaq_laneq_f64 (d->c10, z2, c911, 1);
+ float64x2_t p811 = vfmaq_f64 (p89, x2, p1011);
+
+ float64x2_t p1213 = vfmaq_laneq_f64 (d->c12, z2, c1315, 0);
+ float64x2_t p1415 = vfmaq_laneq_f64 (d->c14, z2, c1315, 1);
+ float64x2_t p1215 = vfmaq_f64 (p1213, x2, p1415);
+
+ float64x2_t p1617 = vfmaq_laneq_f64 (d->c16, z2, c1719, 0);
+ float64x2_t p1819 = vfmaq_laneq_f64 (d->c18, z2, c1719, 1);
+ float64x2_t p1619 = vfmaq_f64 (p1617, x2, p1819);
+
+ float64x2_t p815 = vfmaq_f64 (p811, x4, p1215);
+ float64x2_t p819 = vfmaq_f64 (p815, x8, p1619);
+
+ float64x2_t ret = vfmaq_f64 (p07, p819, x8);
/* Finalize. y = shift + z + z^3 * P(z^2). */
ret = vfmaq_f64 (z, ret, vmulq_f64 (z2, z));
ret = vaddq_f64 (ret, shift);
+ if (__glibc_unlikely (v_any_u64 (special_cases)))
+ return special_case (y, x, ret, sign_xy, special_cases);
+
/* Account for the sign of x and y. */
ret = vreinterpretq_f64_u64 (
veorq_u64 (vreinterpretq_u64_f64 (ret), sign_xy));
- if (__glibc_unlikely (v_any_u64 (special_cases)))
- return special_case (y, x, ret, special_cases);
-
return ret;
}
static const struct data
{
- float32x4_t poly[8];
- float32x4_t pi_over_2;
+ float32x4_t c0, pi_over_2, c4, c6, c2;
+ float c1, c3, c5, c7;
+ uint32x4_t comp_const;
} data = {
/* Coefficients of polynomial P such that atan(x)~x+x*P(x^2) on
[2**-128, 1.0].
Generated using fpminimax between FLT_MIN and 1. */
- .poly = { V4 (-0x1.55555p-2f), V4 (0x1.99935ep-3f), V4 (-0x1.24051ep-3f),
- V4 (0x1.bd7368p-4f), V4 (-0x1.491f0ep-4f), V4 (0x1.93a2c0p-5f),
- V4 (-0x1.4c3c60p-6f), V4 (0x1.01fd88p-8f) },
- .pi_over_2 = V4 (0x1.921fb6p+0f),
+ .c0 = V4 (-0x1.55555p-2f), .c1 = 0x1.99935ep-3f,
+ .c2 = V4 (-0x1.24051ep-3f), .c3 = 0x1.bd7368p-4f,
+ .c4 = V4 (-0x1.491f0ep-4f), .c5 = 0x1.93a2c0p-5f,
+ .c6 = V4 (-0x1.4c3c60p-6f), .c7 = 0x1.01fd88p-8f,
+ .pi_over_2 = V4 (0x1.921fb6p+0f), .comp_const = V4 (2 * 0x7f800000lu - 1),
};
#define SignMask v_u32 (0x80000000)
/* Special cases i.e. 0, infinity and nan (fall back to scalar calls). */
static float32x4_t VPCS_ATTR NOINLINE
-special_case (float32x4_t y, float32x4_t x, float32x4_t ret, uint32x4_t cmp)
+special_case (float32x4_t y, float32x4_t x, float32x4_t ret,
+ uint32x4_t sign_xy, uint32x4_t cmp)
{
+ /* Account for the sign of y. */
+ ret = vreinterpretq_f32_u32 (
+ veorq_u32 (vreinterpretq_u32_f32 (ret), sign_xy));
return v_call2_f32 (atan2f, y, x, ret, cmp);
}
/* Returns 1 if input is the bit representation of 0, infinity or nan. */
static inline uint32x4_t
-zeroinfnan (uint32x4_t i)
+zeroinfnan (uint32x4_t i, const struct data *d)
{
/* 2 * i - 1 >= 2 * 0x7f800000lu - 1. */
- return vcgeq_u32 (vsubq_u32 (vmulq_n_u32 (i, 2), v_u32 (1)),
- v_u32 (2 * 0x7f800000lu - 1));
+ return vcgeq_u32 (vsubq_u32 (vmulq_n_u32 (i, 2), v_u32 (1)), d->comp_const);
}
/* Fast implementation of vector atan2f. Maximum observed error is
want 0x1.967f00p-1. */
float32x4_t VPCS_ATTR NOINLINE V_NAME_F2 (atan2) (float32x4_t y, float32x4_t x)
{
- const struct data *data_ptr = ptr_barrier (&data);
+ const struct data *d = ptr_barrier (&data);
uint32x4_t ix = vreinterpretq_u32_f32 (x);
uint32x4_t iy = vreinterpretq_u32_f32 (y);
- uint32x4_t special_cases = vorrq_u32 (zeroinfnan (ix), zeroinfnan (iy));
+ uint32x4_t special_cases
+ = vorrq_u32 (zeroinfnan (ix, d), zeroinfnan (iy, d));
uint32x4_t sign_x = vandq_u32 (ix, SignMask);
uint32x4_t sign_y = vandq_u32 (iy, SignMask);
/* Set up z for call to atanf. */
float32x4_t n = vbslq_f32 (pred_aygtax, vnegq_f32 (ax), ay);
- float32x4_t d = vbslq_f32 (pred_aygtax, ay, ax);
- float32x4_t z = vdivq_f32 (n, d);
+ float32x4_t q = vbslq_f32 (pred_aygtax, ay, ax);
+ float32x4_t z = vdivq_f32 (n, q);
/* Work out the correct shift. */
float32x4_t shift = vreinterpretq_f32_u32 (
vandq_u32 (pred_xlt0, vreinterpretq_u32_f32 (v_f32 (-2.0f))));
shift = vbslq_f32 (pred_aygtax, vaddq_f32 (shift, v_f32 (1.0f)), shift);
- shift = vmulq_f32 (shift, data_ptr->pi_over_2);
+ shift = vmulq_f32 (shift, d->pi_over_2);
/* Calculate the polynomial approximation.
Use 2-level Estrin scheme for P(z^2) with deg(P)=7. However,
float32x4_t z2 = vmulq_f32 (z, z);
float32x4_t z4 = vmulq_f32 (z2, z2);
- float32x4_t ret = vfmaq_f32 (
- v_pairwise_poly_3_f32 (z2, z4, data_ptr->poly), z4,
- vmulq_f32 (z4, v_pairwise_poly_3_f32 (z2, z4, data_ptr->poly + 4)));
+ float32x4_t c1357 = vld1q_f32 (&d->c1);
+ float32x4_t p01 = vfmaq_laneq_f32 (d->c0, z2, c1357, 0);
+ float32x4_t p23 = vfmaq_laneq_f32 (d->c2, z2, c1357, 1);
+ float32x4_t p45 = vfmaq_laneq_f32 (d->c4, z2, c1357, 2);
+ float32x4_t p67 = vfmaq_laneq_f32 (d->c6, z2, c1357, 3);
+ float32x4_t p03 = vfmaq_f32 (p01, z4, p23);
+ float32x4_t p47 = vfmaq_f32 (p45, z4, p67);
+
+ float32x4_t ret = vfmaq_f32 (p03, z4, vmulq_f32 (z4, p47));
/* y = shift + z * P(z^2). */
ret = vaddq_f32 (vfmaq_f32 (z, ret, vmulq_f32 (z2, z)), shift);
- /* Account for the sign of y. */
- ret = vreinterpretq_f32_u32 (
- veorq_u32 (vreinterpretq_u32_f32 (ret), sign_xy));
-
if (__glibc_unlikely (v_any_u32 (special_cases)))
{
- return special_case (y, x, ret, special_cases);
+ return special_case (y, x, ret, sign_xy, special_cases);
}
- return ret;
+ /* Account for the sign of y. */
+ return vreinterpretq_f32_u32 (
+ veorq_u32 (vreinterpretq_u32_f32 (ret), sign_xy));
}
libmvec_hidden_def (V_NAME_F2 (atan2))
HALF_WIDTH_ALIAS_F2(atan2)
static const struct data
{
+ float64x2_t c0, c2, c4, c6, c8, c10, c12, c14, c16, c18;
float64x2_t pi_over_2;
- float64x2_t poly[20];
+ double c1, c3, c5, c7, c9, c11, c13, c15, c17, c19;
} data = {
/* Coefficients of polynomial P such that atan(x)~x+x*P(x^2) on
[2**-1022, 1.0]. */
- .poly = { V2 (-0x1.5555555555555p-2), V2 (0x1.99999999996c1p-3),
- V2 (-0x1.2492492478f88p-3), V2 (0x1.c71c71bc3951cp-4),
- V2 (-0x1.745d160a7e368p-4), V2 (0x1.3b139b6a88ba1p-4),
- V2 (-0x1.11100ee084227p-4), V2 (0x1.e1d0f9696f63bp-5),
- V2 (-0x1.aebfe7b418581p-5), V2 (0x1.842dbe9b0d916p-5),
- V2 (-0x1.5d30140ae5e99p-5), V2 (0x1.338e31eb2fbbcp-5),
- V2 (-0x1.00e6eece7de8p-5), V2 (0x1.860897b29e5efp-6),
- V2 (-0x1.0051381722a59p-6), V2 (0x1.14e9dc19a4a4ep-7),
- V2 (-0x1.d0062b42fe3bfp-9), V2 (0x1.17739e210171ap-10),
- V2 (-0x1.ab24da7be7402p-13), V2 (0x1.358851160a528p-16), },
+ .c0 = V2 (-0x1.5555555555555p-2), .c1 = 0x1.99999999996c1p-3,
+ .c2 = V2 (-0x1.2492492478f88p-3), .c3 = 0x1.c71c71bc3951cp-4,
+ .c4 = V2 (-0x1.745d160a7e368p-4), .c5 = 0x1.3b139b6a88ba1p-4,
+ .c6 = V2 (-0x1.11100ee084227p-4), .c7 = 0x1.e1d0f9696f63bp-5,
+ .c8 = V2 (-0x1.aebfe7b418581p-5), .c9 = 0x1.842dbe9b0d916p-5,
+ .c10 = V2 (-0x1.5d30140ae5e99p-5), .c11 = 0x1.338e31eb2fbbcp-5,
+ .c12 = V2 (-0x1.00e6eece7de8p-5), .c13 = 0x1.860897b29e5efp-6,
+ .c14 = V2 (-0x1.0051381722a59p-6), .c15 = 0x1.14e9dc19a4a4ep-7,
+ .c16 = V2 (-0x1.d0062b42fe3bfp-9), .c17 = 0x1.17739e210171ap-10,
+ .c18 = V2 (-0x1.ab24da7be7402p-13), .c19 = 0x1.358851160a528p-16,
.pi_over_2 = V2 (0x1.921fb54442d18p+0),
};
float64x2_t VPCS_ATTR V_NAME_D1 (atan) (float64x2_t x)
{
const struct data *d = ptr_barrier (&data);
+ float64x2_t c13 = vld1q_f64 (&d->c1);
+ float64x2_t c57 = vld1q_f64 (&d->c5);
+ float64x2_t c911 = vld1q_f64 (&d->c9);
+ float64x2_t c1315 = vld1q_f64 (&d->c13);
+ float64x2_t c1719 = vld1q_f64 (&d->c17);
/* Small cases, infs and nans are supported by our approximation technique,
but do not set fenv flags correctly. Only trigger special case if we need
float64x2_t x2 = vmulq_f64 (z2, z2);
float64x2_t x4 = vmulq_f64 (x2, x2);
float64x2_t x8 = vmulq_f64 (x4, x4);
- float64x2_t y
- = vfmaq_f64 (v_estrin_7_f64 (z2, x2, x4, d->poly),
- v_estrin_11_f64 (z2, x2, x4, x8, d->poly + 8), x8);
+
+ /* estrin_7. */
+ float64x2_t p01 = vfmaq_laneq_f64 (d->c0, z2, c13, 0);
+ float64x2_t p23 = vfmaq_laneq_f64 (d->c2, z2, c13, 1);
+ float64x2_t p03 = vfmaq_f64 (p01, x2, p23);
+
+ float64x2_t p45 = vfmaq_laneq_f64 (d->c4, z2, c57, 0);
+ float64x2_t p67 = vfmaq_laneq_f64 (d->c6, z2, c57, 1);
+ float64x2_t p47 = vfmaq_f64 (p45, x2, p67);
+
+ float64x2_t p07 = vfmaq_f64 (p03, x4, p47);
+
+ /* estrin_11. */
+ float64x2_t p89 = vfmaq_laneq_f64 (d->c8, z2, c911, 0);
+ float64x2_t p1011 = vfmaq_laneq_f64 (d->c10, z2, c911, 1);
+ float64x2_t p811 = vfmaq_f64 (p89, x2, p1011);
+
+ float64x2_t p1213 = vfmaq_laneq_f64 (d->c12, z2, c1315, 0);
+ float64x2_t p1415 = vfmaq_laneq_f64 (d->c14, z2, c1315, 1);
+ float64x2_t p1215 = vfmaq_f64 (p1213, x2, p1415);
+
+ float64x2_t p1617 = vfmaq_laneq_f64 (d->c16, z2, c1719, 0);
+ float64x2_t p1819 = vfmaq_laneq_f64 (d->c18, z2, c1719, 1);
+ float64x2_t p1619 = vfmaq_f64 (p1617, x2, p1819);
+
+ float64x2_t p815 = vfmaq_f64 (p811, x4, p1215);
+ float64x2_t p819 = vfmaq_f64 (p815, x8, p1619);
+
+ float64x2_t y = vfmaq_f64 (p07, p819, x8);
/* Finalize. y = shift + z + z^3 * P(z^2). */
y = vfmaq_f64 (az, y, vmulq_f64 (z2, az));
projects / thirdparty / glibc.git / commitdiff
