diff --git a/sysdeps/aarch64/fpu/atan2_advsimd.c b/sysdeps/aarch64/fpu/atan2_advsimd.c index b1e7a9b8fc..1a8f02109f 100644 --- a/sysdeps/aarch64/fpu/atan2_advsimd.c +++ b/sysdeps/aarch64/fpu/atan2_advsimd.c @@ -23,40 +23,57 @@ 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. @@ -66,12 +83,13 @@ zeroinfnan (uint64x2_t i) 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); @@ -81,18 +99,18 @@ float64x2_t VPCS_ATTR V_NAME_D2 (atan2) (float64x2_t y, float64x2_t x) 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 @@ -103,20 +121,52 @@ float64x2_t VPCS_ATTR V_NAME_D2 (atan2) (float64x2_t y, float64x2_t x) 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; } diff --git a/sysdeps/aarch64/fpu/atan2f_advsimd.c b/sysdeps/aarch64/fpu/atan2f_advsimd.c index 56e610caf1..88daacd76c 100644 --- a/sysdeps/aarch64/fpu/atan2f_advsimd.c +++ b/sysdeps/aarch64/fpu/atan2f_advsimd.c @@ -22,34 +22,39 @@ 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 @@ -58,12 +63,13 @@ zeroinfnan (uint32x4_t i) 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); @@ -77,14 +83,14 @@ float32x4_t VPCS_ATTR NOINLINE V_NAME_F2 (atan2) (float32x4_t y, float32x4_t x) /* 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, @@ -96,23 +102,27 @@ float32x4_t VPCS_ATTR NOINLINE V_NAME_F2 (atan2) (float32x4_t y, float32x4_t x) 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) diff --git a/sysdeps/aarch64/fpu/atan_advsimd.c b/sysdeps/aarch64/fpu/atan_advsimd.c index a962be0f78..14f1809796 100644 --- a/sysdeps/aarch64/fpu/atan_advsimd.c +++ b/sysdeps/aarch64/fpu/atan_advsimd.c @@ -22,21 +22,22 @@ 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), }; @@ -52,6 +53,11 @@ static const struct data 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 @@ -90,9 +96,35 @@ float64x2_t VPCS_ATTR V_NAME_D1 (atan) (float64x2_t x) 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));