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aarch64: Improve vecmath sin routines
* 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.
This commit is contained in:
Joe Ramsay
Szabolcs Nagy
parent
820948edd9
commit
8014d1e832
@ -24,7 +24,6 @@ static const struct data
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float64x2_t poly[7];
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float64x2_t range_val, inv_pi, shift, pi_1, pi_2, pi_3;
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} data = {
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/* Worst-case error is 2.8 ulp in [-pi/2, pi/2]. */
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.poly = { V2 (-0x1.555555555547bp-3), V2 (0x1.1111111108a4dp-7),
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V2 (-0x1.a01a019936f27p-13), V2 (0x1.71de37a97d93ep-19),
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V2 (-0x1.ae633919987c6p-26), V2 (0x1.60e277ae07cecp-33),
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@ -52,6 +51,15 @@ special_case (float64x2_t x, float64x2_t y, uint64x2_t odd, uint64x2_t cmp)
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return v_call_f64 (sin, x, y, cmp);
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}
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/* Vector (AdvSIMD) sin approximation.
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Maximum observed error in [-pi/2, pi/2], where argument is not reduced,
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is 2.87 ULP:
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_ZGVnN2v_sin (0x1.921d5c6a07142p+0) got 0x1.fffffffa7dc02p-1
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want 0x1.fffffffa7dc05p-1
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Maximum observed error in the entire non-special domain ([-2^23, 2^23])
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is 3.22 ULP:
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_ZGVnN2v_sin (0x1.5702447b6f17bp+22) got 0x1.ffdcd125c84fbp-3
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want 0x1.ffdcd125c84f8p-3. */
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float64x2_t VPCS_ATTR V_NAME_D1 (sin) (float64x2_t x)
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{
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const struct data *d = ptr_barrier (&data);
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@ -21,20 +21,22 @@
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static const struct data
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{
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double inv_pi, half_pi, inv_pi_over_2, pi_over_2_1, pi_over_2_2, pi_over_2_3,
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shift;
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double inv_pi, pi_1, pi_2, pi_3, shift, range_val;
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double poly[7];
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} data = {
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/* Polynomial coefficients are hard-wired in the FTMAD instruction. */
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.poly = { -0x1.555555555547bp-3, 0x1.1111111108a4dp-7, -0x1.a01a019936f27p-13,
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0x1.71de37a97d93ep-19, -0x1.ae633919987c6p-26,
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0x1.60e277ae07cecp-33, -0x1.9e9540300a1p-41, },
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.inv_pi = 0x1.45f306dc9c883p-2,
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.half_pi = 0x1.921fb54442d18p+0,
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.inv_pi_over_2 = 0x1.45f306dc9c882p-1,
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.pi_over_2_1 = 0x1.921fb50000000p+0,
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.pi_over_2_2 = 0x1.110b460000000p-26,
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.pi_over_2_3 = 0x1.1a62633145c07p-54,
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.shift = 0x1.8p52
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.pi_1 = 0x1.921fb54442d18p+1,
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.pi_2 = 0x1.1a62633145c06p-53,
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.pi_3 = 0x1.c1cd129024e09p-106,
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.shift = 0x1.8p52,
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.range_val = 0x1p23,
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};
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#define RangeVal 0x4160000000000000 /* asuint64 (0x1p23). */
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#define C(i) sv_f64 (d->poly[i])
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static svfloat64_t NOINLINE
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special_case (svfloat64_t x, svfloat64_t y, svbool_t cmp)
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@ -42,56 +44,58 @@ special_case (svfloat64_t x, svfloat64_t y, svbool_t cmp)
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return sv_call_f64 (sin, x, y, cmp);
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}
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/* A fast SVE implementation of sin based on trigonometric
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instructions (FTMAD, FTSSEL, FTSMUL).
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Maximum observed error in 2.52 ULP:
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SV_NAME_D1 (sin)(0x1.2d2b00df69661p+19) got 0x1.10ace8f3e786bp-40
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want 0x1.10ace8f3e7868p-40. */
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/* A fast SVE implementation of sin.
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Maximum observed error in [-pi/2, pi/2], where argument is not reduced,
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is 2.87 ULP:
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_ZGVsMxv_sin (0x1.921d5c6a07142p+0) got 0x1.fffffffa7dc02p-1
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want 0x1.fffffffa7dc05p-1
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Maximum observed error in the entire non-special domain ([-2^23, 2^23])
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is 3.22 ULP:
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_ZGVsMxv_sin (0x1.5702447b6f17bp+22) got 0x1.ffdcd125c84fbp-3
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want 0x1.ffdcd125c84f8p-3. */
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svfloat64_t SV_NAME_D1 (sin) (svfloat64_t x, const svbool_t pg)
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{
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const struct data *d = ptr_barrier (&data);
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svfloat64_t r = svabs_f64_x (pg, x);
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svuint64_t sign
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= sveor_u64_x (pg, svreinterpret_u64_f64 (x), svreinterpret_u64_f64 (r));
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svbool_t cmp = svcmpge_n_u64 (pg, svreinterpret_u64_f64 (r), RangeVal);
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/* Load some values in quad-word chunks to minimise memory access. */
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const svbool_t ptrue = svptrue_b64 ();
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svfloat64_t shift = sv_f64 (d->shift);
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svfloat64_t inv_pi_and_pi1 = svld1rq (ptrue, &d->inv_pi);
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svfloat64_t pi2_and_pi3 = svld1rq (ptrue, &d->pi_2);
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/* Load first two pio2-related constants to one vector. */
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svfloat64_t invpio2_and_pio2_1
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= svld1rq_f64 (svptrue_b64 (), &d->inv_pi_over_2);
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/* n = rint(|x|/pi). */
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svfloat64_t n = svmla_lane (shift, x, inv_pi_and_pi1, 0);
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svuint64_t odd = svlsl_x (pg, svreinterpret_u64 (n), 63);
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n = svsub_x (pg, n, shift);
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/* n = rint(|x|/(pi/2)). */
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svfloat64_t q = svmla_lane_f64 (sv_f64 (d->shift), r, invpio2_and_pio2_1, 0);
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svfloat64_t n = svsub_n_f64_x (pg, q, d->shift);
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/* r = |x| - n*(pi/2) (range reduction into -pi/4 .. pi/4). */
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r = svmls_lane_f64 (r, n, invpio2_and_pio2_1, 1);
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r = svmls_n_f64_x (pg, r, n, d->pi_over_2_2);
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r = svmls_n_f64_x (pg, r, n, d->pi_over_2_3);
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/* Final multiplicative factor: 1.0 or x depending on bit #0 of q. */
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svfloat64_t f = svtssel_f64 (r, svreinterpret_u64_f64 (q));
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/* r = |x| - n*(pi/2) (range reduction into -pi/2 .. pi/2). */
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svfloat64_t r = x;
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r = svmls_lane (r, n, inv_pi_and_pi1, 1);
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r = svmls_lane (r, n, pi2_and_pi3, 0);
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r = svmls_lane (r, n, pi2_and_pi3, 1);
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/* sin(r) poly approx. */
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svfloat64_t r2 = svtsmul_f64 (r, svreinterpret_u64_f64 (q));
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svfloat64_t y = sv_f64 (0.0);
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y = svtmad_f64 (y, r2, 7);
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y = svtmad_f64 (y, r2, 6);
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y = svtmad_f64 (y, r2, 5);
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y = svtmad_f64 (y, r2, 4);
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y = svtmad_f64 (y, r2, 3);
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y = svtmad_f64 (y, r2, 2);
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y = svtmad_f64 (y, r2, 1);
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y = svtmad_f64 (y, r2, 0);
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svfloat64_t r2 = svmul_x (pg, r, r);
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svfloat64_t r3 = svmul_x (pg, r2, r);
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svfloat64_t r4 = svmul_x (pg, r2, r2);
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/* Apply factor. */
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y = svmul_f64_x (pg, f, y);
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svfloat64_t t1 = svmla_x (pg, C (4), C (5), r2);
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svfloat64_t t2 = svmla_x (pg, C (2), C (3), r2);
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svfloat64_t t3 = svmla_x (pg, C (0), C (1), r2);
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/* sign = y^sign. */
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y = svreinterpret_f64_u64 (
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sveor_u64_x (pg, svreinterpret_u64_f64 (y), sign));
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svfloat64_t y = svmla_x (pg, t1, C (6), r4);
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y = svmla_x (pg, t2, y, r4);
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y = svmla_x (pg, t3, y, r4);
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y = svmla_x (pg, r, y, r3);
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svbool_t cmp = svacle (pg, x, d->range_val);
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cmp = svnot_z (pg, cmp);
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if (__glibc_unlikely (svptest_any (pg, cmp)))
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return special_case (x, y, cmp);
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return y;
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return special_case (x,
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svreinterpret_f64 (sveor_z (
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svnot_z (pg, cmp), svreinterpret_u64 (y), odd)),
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cmp);
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/* Copy sign. */
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return svreinterpret_f64 (sveor_z (pg, svreinterpret_u64 (y), odd));
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}
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@ -23,7 +23,7 @@ static const struct data
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{
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float poly[4];
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/* Pi-related values to be loaded as one quad-word and used with
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svmla_lane_f32. */
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svmla_lane. */
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float negpi1, negpi2, negpi3, invpi;
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float shift;
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} data = {
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@ -57,40 +57,42 @@ svfloat32_t SV_NAME_F1 (sin) (svfloat32_t x, const svbool_t pg)
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{
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const struct data *d = ptr_barrier (&data);
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svfloat32_t ax = svabs_f32_x (pg, x);
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svuint32_t sign = sveor_u32_x (pg, svreinterpret_u32_f32 (x),
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svreinterpret_u32_f32 (ax));
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svbool_t cmp = svcmpge_n_u32 (pg, svreinterpret_u32_f32 (ax), RangeVal);
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svfloat32_t ax = svabs_x (pg, x);
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svuint32_t sign
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= sveor_x (pg, svreinterpret_u32 (x), svreinterpret_u32 (ax));
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svbool_t cmp = svcmpge (pg, svreinterpret_u32 (ax), RangeVal);
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/* pi_vals are a quad-word of helper values - the first 3 elements contain
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-pi in extended precision, the last contains 1 / pi. */
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svfloat32_t pi_vals = svld1rq_f32 (svptrue_b32 (), &d->negpi1);
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svfloat32_t pi_vals = svld1rq (svptrue_b32 (), &d->negpi1);
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/* n = rint(|x|/pi). */
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svfloat32_t n = svmla_lane_f32 (sv_f32 (d->shift), ax, pi_vals, 3);
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svuint32_t odd = svlsl_n_u32_x (pg, svreinterpret_u32_f32 (n), 31);
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n = svsub_n_f32_x (pg, n, d->shift);
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svfloat32_t n = svmla_lane (sv_f32 (d->shift), ax, pi_vals, 3);
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svuint32_t odd = svlsl_x (pg, svreinterpret_u32 (n), 31);
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n = svsub_x (pg, n, d->shift);
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/* r = |x| - n*pi (range reduction into -pi/2 .. pi/2). */
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svfloat32_t r;
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r = svmla_lane_f32 (ax, n, pi_vals, 0);
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r = svmla_lane_f32 (r, n, pi_vals, 1);
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r = svmla_lane_f32 (r, n, pi_vals, 2);
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r = svmla_lane (ax, n, pi_vals, 0);
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r = svmla_lane (r, n, pi_vals, 1);
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r = svmla_lane (r, n, pi_vals, 2);
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/* sin(r) approx using a degree 9 polynomial from the Taylor series
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expansion. Note that only the odd terms of this are non-zero. */
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svfloat32_t r2 = svmul_f32_x (pg, r, r);
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svfloat32_t r2 = svmul_x (pg, r, r);
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svfloat32_t y;
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y = svmla_f32_x (pg, C (2), r2, C (3));
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y = svmla_f32_x (pg, C (1), r2, y);
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y = svmla_f32_x (pg, C (0), r2, y);
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y = svmla_f32_x (pg, r, r, svmul_f32_x (pg, y, r2));
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y = svmla_x (pg, C (2), r2, C (3));
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y = svmla_x (pg, C (1), r2, y);
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y = svmla_x (pg, C (0), r2, y);
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y = svmla_x (pg, r, r, svmul_x (pg, y, r2));
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/* sign = y^sign^odd. */
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y = svreinterpret_f32_u32 (sveor_u32_x (pg, svreinterpret_u32_f32 (y),
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sveor_u32_x (pg, sign, odd)));
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sign = sveor_x (pg, sign, odd);
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if (__glibc_unlikely (svptest_any (pg, cmp)))
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return special_case (x, y, cmp);
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return y;
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return special_case (x,
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svreinterpret_f32 (sveor_x (
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svnot_z (pg, cmp), svreinterpret_u32 (y), sign)),
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cmp);
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return svreinterpret_f32 (sveor_x (pg, svreinterpret_u32 (y), sign));
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}
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