From: Szabolcs Nagy <szabolcs.nagy@arm.com>
To: Joe Ramsay <Joe.Ramsay@arm.com>, <libc-alpha@sourceware.org>
Subject: Re: [PATCH v2] aarch64: Improve vecmath sin routines
Date: Thu, 5 Oct 2023 17:01:02 +0100 [thread overview]
Message-ID: <ZR7dvvqcymJ2DC+N@arm.com> (raw)
In-Reply-To: <20231005093138.7209-1-Joe.Ramsay@arm.com>
The 10/05/2023 10:31, Joe Ramsay wrote:
> * Update ULP comment reflecting a new observed max in [-pi/2, pi/2]
> * Use the same polynomial in AdvSIMD and SVE, rather than FTRIG instructions
> * Improve register use near special-case branch
>
> Also use overloaded intrinsics for SVE.
looks good. committed.
> ---
> Changes from v1:
> * Report new observed global max and max in [-pi/2, pi/2]
> Thanks,
> Joe
> sysdeps/aarch64/fpu/sin_advsimd.c | 10 ++-
> sysdeps/aarch64/fpu/sin_sve.c | 106 ++++++++++++++++--------------
> sysdeps/aarch64/fpu/sinf_sve.c | 44 +++++++------
> 3 files changed, 87 insertions(+), 73 deletions(-)
>
> diff --git a/sysdeps/aarch64/fpu/sin_advsimd.c b/sysdeps/aarch64/fpu/sin_advsimd.c
> index 0389b334cc..3d87a1da79 100644
> --- a/sysdeps/aarch64/fpu/sin_advsimd.c
> +++ b/sysdeps/aarch64/fpu/sin_advsimd.c
> @@ -24,7 +24,6 @@ static const struct data
> float64x2_t poly[7];
> float64x2_t range_val, inv_pi, shift, pi_1, pi_2, pi_3;
> } data = {
> - /* Worst-case error is 2.8 ulp in [-pi/2, pi/2]. */
> .poly = { V2 (-0x1.555555555547bp-3), V2 (0x1.1111111108a4dp-7),
> V2 (-0x1.a01a019936f27p-13), V2 (0x1.71de37a97d93ep-19),
> V2 (-0x1.ae633919987c6p-26), V2 (0x1.60e277ae07cecp-33),
> @@ -52,6 +51,15 @@ special_case (float64x2_t x, float64x2_t y, uint64x2_t odd, uint64x2_t cmp)
> return v_call_f64 (sin, x, y, cmp);
> }
>
> +/* Vector (AdvSIMD) sin approximation.
> + Maximum observed error in [-pi/2, pi/2], where argument is not reduced,
> + is 2.87 ULP:
> + _ZGVnN2v_sin (0x1.921d5c6a07142p+0) got 0x1.fffffffa7dc02p-1
> + want 0x1.fffffffa7dc05p-1
> + Maximum observed error in the entire non-special domain ([-2^23, 2^23])
> + is 3.22 ULP:
> + _ZGVnN2v_sin (0x1.5702447b6f17bp+22) got 0x1.ffdcd125c84fbp-3
> + want 0x1.ffdcd125c84f8p-3. */
> float64x2_t VPCS_ATTR V_NAME_D1 (sin) (float64x2_t x)
> {
> const struct data *d = ptr_barrier (&data);
> diff --git a/sysdeps/aarch64/fpu/sin_sve.c b/sysdeps/aarch64/fpu/sin_sve.c
> index c3f450d0ea..54c8dae286 100644
> --- a/sysdeps/aarch64/fpu/sin_sve.c
> +++ b/sysdeps/aarch64/fpu/sin_sve.c
> @@ -21,20 +21,22 @@
>
> static const struct data
> {
> - double inv_pi, half_pi, inv_pi_over_2, pi_over_2_1, pi_over_2_2, pi_over_2_3,
> - shift;
> + double inv_pi, pi_1, pi_2, pi_3, shift, range_val;
> + double poly[7];
> } data = {
> - /* Polynomial coefficients are hard-wired in the FTMAD instruction. */
> + .poly = { -0x1.555555555547bp-3, 0x1.1111111108a4dp-7, -0x1.a01a019936f27p-13,
> + 0x1.71de37a97d93ep-19, -0x1.ae633919987c6p-26,
> + 0x1.60e277ae07cecp-33, -0x1.9e9540300a1p-41, },
> +
> .inv_pi = 0x1.45f306dc9c883p-2,
> - .half_pi = 0x1.921fb54442d18p+0,
> - .inv_pi_over_2 = 0x1.45f306dc9c882p-1,
> - .pi_over_2_1 = 0x1.921fb50000000p+0,
> - .pi_over_2_2 = 0x1.110b460000000p-26,
> - .pi_over_2_3 = 0x1.1a62633145c07p-54,
> - .shift = 0x1.8p52
> + .pi_1 = 0x1.921fb54442d18p+1,
> + .pi_2 = 0x1.1a62633145c06p-53,
> + .pi_3 = 0x1.c1cd129024e09p-106,
> + .shift = 0x1.8p52,
> + .range_val = 0x1p23,
> };
>
> -#define RangeVal 0x4160000000000000 /* asuint64 (0x1p23). */
> +#define C(i) sv_f64 (d->poly[i])
>
> static svfloat64_t NOINLINE
> special_case (svfloat64_t x, svfloat64_t y, svbool_t cmp)
> @@ -42,56 +44,58 @@ special_case (svfloat64_t x, svfloat64_t y, svbool_t cmp)
> return sv_call_f64 (sin, x, y, cmp);
> }
>
> -/* A fast SVE implementation of sin based on trigonometric
> - instructions (FTMAD, FTSSEL, FTSMUL).
> - Maximum observed error in 2.52 ULP:
> - SV_NAME_D1 (sin)(0x1.2d2b00df69661p+19) got 0x1.10ace8f3e786bp-40
> - want 0x1.10ace8f3e7868p-40. */
> +/* A fast SVE implementation of sin.
> + Maximum observed error in [-pi/2, pi/2], where argument is not reduced,
> + is 2.87 ULP:
> + _ZGVsMxv_sin (0x1.921d5c6a07142p+0) got 0x1.fffffffa7dc02p-1
> + want 0x1.fffffffa7dc05p-1
> + Maximum observed error in the entire non-special domain ([-2^23, 2^23])
> + is 3.22 ULP:
> + _ZGVsMxv_sin (0x1.5702447b6f17bp+22) got 0x1.ffdcd125c84fbp-3
> + want 0x1.ffdcd125c84f8p-3. */
> svfloat64_t SV_NAME_D1 (sin) (svfloat64_t x, const svbool_t pg)
> {
> const struct data *d = ptr_barrier (&data);
>
> - svfloat64_t r = svabs_f64_x (pg, x);
> - svuint64_t sign
> - = sveor_u64_x (pg, svreinterpret_u64_f64 (x), svreinterpret_u64_f64 (r));
> - svbool_t cmp = svcmpge_n_u64 (pg, svreinterpret_u64_f64 (r), RangeVal);
> + /* Load some values in quad-word chunks to minimise memory access. */
> + const svbool_t ptrue = svptrue_b64 ();
> + svfloat64_t shift = sv_f64 (d->shift);
> + svfloat64_t inv_pi_and_pi1 = svld1rq (ptrue, &d->inv_pi);
> + svfloat64_t pi2_and_pi3 = svld1rq (ptrue, &d->pi_2);
>
> - /* Load first two pio2-related constants to one vector. */
> - svfloat64_t invpio2_and_pio2_1
> - = svld1rq_f64 (svptrue_b64 (), &d->inv_pi_over_2);
> + /* n = rint(|x|/pi). */
> + svfloat64_t n = svmla_lane (shift, x, inv_pi_and_pi1, 0);
> + svuint64_t odd = svlsl_x (pg, svreinterpret_u64 (n), 63);
> + n = svsub_x (pg, n, shift);
>
> - /* n = rint(|x|/(pi/2)). */
> - svfloat64_t q = svmla_lane_f64 (sv_f64 (d->shift), r, invpio2_and_pio2_1, 0);
> - svfloat64_t n = svsub_n_f64_x (pg, q, d->shift);
> + /* r = |x| - n*(pi/2) (range reduction into -pi/2 .. pi/2). */
> + svfloat64_t r = x;
> + r = svmls_lane (r, n, inv_pi_and_pi1, 1);
> + r = svmls_lane (r, n, pi2_and_pi3, 0);
> + r = svmls_lane (r, n, pi2_and_pi3, 1);
>
> - /* r = |x| - n*(pi/2) (range reduction into -pi/4 .. pi/4). */
> - r = svmls_lane_f64 (r, n, invpio2_and_pio2_1, 1);
> - r = svmls_n_f64_x (pg, r, n, d->pi_over_2_2);
> - r = svmls_n_f64_x (pg, r, n, d->pi_over_2_3);
> + /* sin(r) poly approx. */
> + svfloat64_t r2 = svmul_x (pg, r, r);
> + svfloat64_t r3 = svmul_x (pg, r2, r);
> + svfloat64_t r4 = svmul_x (pg, r2, r2);
>
> - /* Final multiplicative factor: 1.0 or x depending on bit #0 of q. */
> - svfloat64_t f = svtssel_f64 (r, svreinterpret_u64_f64 (q));
> + svfloat64_t t1 = svmla_x (pg, C (4), C (5), r2);
> + svfloat64_t t2 = svmla_x (pg, C (2), C (3), r2);
> + svfloat64_t t3 = svmla_x (pg, C (0), C (1), r2);
>
> - /* sin(r) poly approx. */
> - svfloat64_t r2 = svtsmul_f64 (r, svreinterpret_u64_f64 (q));
> - svfloat64_t y = sv_f64 (0.0);
> - y = svtmad_f64 (y, r2, 7);
> - y = svtmad_f64 (y, r2, 6);
> - y = svtmad_f64 (y, r2, 5);
> - y = svtmad_f64 (y, r2, 4);
> - y = svtmad_f64 (y, r2, 3);
> - y = svtmad_f64 (y, r2, 2);
> - y = svtmad_f64 (y, r2, 1);
> - y = svtmad_f64 (y, r2, 0);
> -
> - /* Apply factor. */
> - y = svmul_f64_x (pg, f, y);
> -
> - /* sign = y^sign. */
> - y = svreinterpret_f64_u64 (
> - sveor_u64_x (pg, svreinterpret_u64_f64 (y), sign));
> + svfloat64_t y = svmla_x (pg, t1, C (6), r4);
> + y = svmla_x (pg, t2, y, r4);
> + y = svmla_x (pg, t3, y, r4);
> + y = svmla_x (pg, r, y, r3);
>
> + svbool_t cmp = svacle (pg, x, d->range_val);
> + cmp = svnot_z (pg, cmp);
> if (__glibc_unlikely (svptest_any (pg, cmp)))
> - return special_case (x, y, cmp);
> - return y;
> + return special_case (x,
> + svreinterpret_f64 (sveor_z (
> + svnot_z (pg, cmp), svreinterpret_u64 (y), odd)),
> + cmp);
> +
> + /* Copy sign. */
> + return svreinterpret_f64 (sveor_z (pg, svreinterpret_u64 (y), odd));
> }
> diff --git a/sysdeps/aarch64/fpu/sinf_sve.c b/sysdeps/aarch64/fpu/sinf_sve.c
> index 4d2ce7a846..590881c14b 100644
> --- a/sysdeps/aarch64/fpu/sinf_sve.c
> +++ b/sysdeps/aarch64/fpu/sinf_sve.c
> @@ -23,7 +23,7 @@ static const struct data
> {
> float poly[4];
> /* Pi-related values to be loaded as one quad-word and used with
> - svmla_lane_f32. */
> + svmla_lane. */
> float negpi1, negpi2, negpi3, invpi;
> float shift;
> } data = {
> @@ -57,40 +57,42 @@ svfloat32_t SV_NAME_F1 (sin) (svfloat32_t x, const svbool_t pg)
> {
> const struct data *d = ptr_barrier (&data);
>
> - svfloat32_t ax = svabs_f32_x (pg, x);
> - svuint32_t sign = sveor_u32_x (pg, svreinterpret_u32_f32 (x),
> - svreinterpret_u32_f32 (ax));
> - svbool_t cmp = svcmpge_n_u32 (pg, svreinterpret_u32_f32 (ax), RangeVal);
> + svfloat32_t ax = svabs_x (pg, x);
> + svuint32_t sign
> + = sveor_x (pg, svreinterpret_u32 (x), svreinterpret_u32 (ax));
> + svbool_t cmp = svcmpge (pg, svreinterpret_u32 (ax), RangeVal);
>
> /* pi_vals are a quad-word of helper values - the first 3 elements contain
> -pi in extended precision, the last contains 1 / pi. */
> - svfloat32_t pi_vals = svld1rq_f32 (svptrue_b32 (), &d->negpi1);
> + svfloat32_t pi_vals = svld1rq (svptrue_b32 (), &d->negpi1);
>
> /* n = rint(|x|/pi). */
> - svfloat32_t n = svmla_lane_f32 (sv_f32 (d->shift), ax, pi_vals, 3);
> - svuint32_t odd = svlsl_n_u32_x (pg, svreinterpret_u32_f32 (n), 31);
> - n = svsub_n_f32_x (pg, n, d->shift);
> + svfloat32_t n = svmla_lane (sv_f32 (d->shift), ax, pi_vals, 3);
> + svuint32_t odd = svlsl_x (pg, svreinterpret_u32 (n), 31);
> + n = svsub_x (pg, n, d->shift);
>
> /* r = |x| - n*pi (range reduction into -pi/2 .. pi/2). */
> svfloat32_t r;
> - r = svmla_lane_f32 (ax, n, pi_vals, 0);
> - r = svmla_lane_f32 (r, n, pi_vals, 1);
> - r = svmla_lane_f32 (r, n, pi_vals, 2);
> + r = svmla_lane (ax, n, pi_vals, 0);
> + r = svmla_lane (r, n, pi_vals, 1);
> + r = svmla_lane (r, n, pi_vals, 2);
>
> /* sin(r) approx using a degree 9 polynomial from the Taylor series
> expansion. Note that only the odd terms of this are non-zero. */
> - svfloat32_t r2 = svmul_f32_x (pg, r, r);
> + svfloat32_t r2 = svmul_x (pg, r, r);
> svfloat32_t y;
> - y = svmla_f32_x (pg, C (2), r2, C (3));
> - y = svmla_f32_x (pg, C (1), r2, y);
> - y = svmla_f32_x (pg, C (0), r2, y);
> - y = svmla_f32_x (pg, r, r, svmul_f32_x (pg, y, r2));
> + y = svmla_x (pg, C (2), r2, C (3));
> + y = svmla_x (pg, C (1), r2, y);
> + y = svmla_x (pg, C (0), r2, y);
> + y = svmla_x (pg, r, r, svmul_x (pg, y, r2));
>
> /* sign = y^sign^odd. */
> - y = svreinterpret_f32_u32 (sveor_u32_x (pg, svreinterpret_u32_f32 (y),
> - sveor_u32_x (pg, sign, odd)));
> + sign = sveor_x (pg, sign, odd);
>
> if (__glibc_unlikely (svptest_any (pg, cmp)))
> - return special_case (x, y, cmp);
> - return y;
> + return special_case (x,
> + svreinterpret_f32 (sveor_x (
> + svnot_z (pg, cmp), svreinterpret_u32 (y), sign)),
> + cmp);
> + return svreinterpret_f32 (sveor_x (pg, svreinterpret_u32 (y), sign));
> }
> --
> 2.27.0
>
prev parent reply other threads:[~2023-10-05 16:01 UTC|newest]
Thread overview: 3+ messages / expand[flat|nested] mbox.gz Atom feed top
2023-10-05 9:31 Joe Ramsay
2023-10-05 12:31 ` Paul Zimmermann
2023-10-05 16:01 ` Szabolcs Nagy [this message]
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