diff options
Diffstat (limited to 'pl/math/sv_tanf_3u5.c')
| -rw-r--r-- | pl/math/sv_tanf_3u5.c | 141 |
1 files changed, 74 insertions, 67 deletions
diff --git a/pl/math/sv_tanf_3u5.c b/pl/math/sv_tanf_3u5.c index cca43bd886fd..6b8cd1e64b44 100644 --- a/pl/math/sv_tanf_3u5.c +++ b/pl/math/sv_tanf_3u5.c @@ -9,63 +9,67 @@ #include "pl_sig.h" #include "pl_test.h" -#if SV_SUPPORTED - -/* Constants. */ -#define NegPio2_1 (sv_f32 (-0x1.921fb6p+0f)) -#define NegPio2_2 (sv_f32 (0x1.777a5cp-25f)) -#define NegPio2_3 (sv_f32 (0x1.ee59dap-50f)) -#define InvPio2 (sv_f32 (0x1.45f306p-1f)) -#define RangeVal (sv_f32 (0x1p15f)) -#define Shift (sv_f32 (0x1.8p+23f)) - -#define poly(i) sv_f32 (__tanf_poly_data.poly_tan[i]) - -/* Use full Estrin's scheme to evaluate polynomial. */ -static inline sv_f32_t -eval_poly (svbool_t pg, sv_f32_t z) +static const struct data { - sv_f32_t z2 = svmul_f32_x (pg, z, z); - sv_f32_t z4 = svmul_f32_x (pg, z2, z2); - sv_f32_t y_10 = sv_fma_f32_x (pg, z, poly (1), poly (0)); - sv_f32_t y_32 = sv_fma_f32_x (pg, z, poly (3), poly (2)); - sv_f32_t y_54 = sv_fma_f32_x (pg, z, poly (5), poly (4)); - sv_f32_t y_32_10 = sv_fma_f32_x (pg, z2, y_32, y_10); - sv_f32_t y = sv_fma_f32_x (pg, z4, y_54, y_32_10); - return y; -} - -static NOINLINE sv_f32_t -__sv_tanf_specialcase (sv_f32_t x, sv_f32_t y, svbool_t cmp) + float pio2_1, pio2_2, pio2_3, invpio2; + float c1, c3, c5; + float c0, c2, c4, range_val, shift; +} data = { + /* Coefficients generated using: + poly = fpminimax((tan(sqrt(x))-sqrt(x))/x^(3/2), + deg, + [|single ...|], + [a*a;b*b]); + optimize relative error + final prec : 23 bits + deg : 5 + a : 0x1p-126 ^ 2 + b : ((pi) / 0x1p2) ^ 2 + dirty rel error: 0x1.f7c2e4p-25 + dirty abs error: 0x1.f7c2ecp-25. */ + .c0 = 0x1.55555p-2, .c1 = 0x1.11166p-3, + .c2 = 0x1.b88a78p-5, .c3 = 0x1.7b5756p-6, + .c4 = 0x1.4ef4cep-8, .c5 = 0x1.0e1e74p-7, + + .pio2_1 = 0x1.921fb6p+0f, .pio2_2 = -0x1.777a5cp-25f, + .pio2_3 = -0x1.ee59dap-50f, .invpio2 = 0x1.45f306p-1f, + .range_val = 0x1p15f, .shift = 0x1.8p+23f +}; + +static svfloat32_t NOINLINE +special_case (svfloat32_t x, svfloat32_t y, svbool_t cmp) { return sv_call_f32 (tanf, x, y, cmp); } /* Fast implementation of SVE tanf. Maximum error is 3.45 ULP: - __sv_tanf(-0x1.e5f0cap+13) got 0x1.ff9856p-1 - want 0x1.ff9850p-1. */ -sv_f32_t -__sv_tanf_x (sv_f32_t x, const svbool_t pg) + SV_NAME_F1 (tan)(-0x1.e5f0cap+13) got 0x1.ff9856p-1 + want 0x1.ff9850p-1. */ +svfloat32_t SV_NAME_F1 (tan) (svfloat32_t x, const svbool_t pg) { + const struct data *d = ptr_barrier (&data); + /* Determine whether input is too large to perform fast regression. */ - svbool_t cmp = svacge_f32 (pg, x, RangeVal); - svbool_t pred_minuszero = svcmpeq_f32 (pg, x, sv_f32 (-0.0)); + svbool_t cmp = svacge (pg, x, d->range_val); + + svfloat32_t odd_coeffs = svld1rq (svptrue_b32 (), &d->c1); + svfloat32_t pi_vals = svld1rq (svptrue_b32 (), &d->pio2_1); /* n = rint(x/(pi/2)). */ - sv_f32_t q = sv_fma_f32_x (pg, InvPio2, x, Shift); - sv_f32_t n = svsub_f32_x (pg, q, Shift); + svfloat32_t q = svmla_lane (sv_f32 (d->shift), x, pi_vals, 3); + svfloat32_t n = svsub_x (pg, q, d->shift); /* n is already a signed integer, simply convert it. */ - sv_s32_t in = sv_to_s32_f32_x (pg, n); + svint32_t in = svcvt_s32_x (pg, n); /* Determine if x lives in an interval, where |tan(x)| grows to infinity. */ - sv_s32_t alt = svand_s32_x (pg, in, sv_s32 (1)); - svbool_t pred_alt = svcmpne_s32 (pg, alt, sv_s32 (0)); + svint32_t alt = svand_x (pg, in, 1); + svbool_t pred_alt = svcmpne (pg, alt, 0); /* r = x - n * (pi/2) (range reduction into 0 .. pi/4). */ - sv_f32_t r; - r = sv_fma_f32_x (pg, NegPio2_1, n, x); - r = sv_fma_f32_x (pg, NegPio2_2, n, r); - r = sv_fma_f32_x (pg, NegPio2_3, n, r); + svfloat32_t r; + r = svmls_lane (x, n, pi_vals, 0); + r = svmls_lane (r, n, pi_vals, 1); + r = svmls_lane (r, n, pi_vals, 2); /* If x lives in an interval, where |tan(x)| - is finite, then use a polynomial approximation of the form @@ -75,38 +79,41 @@ __sv_tanf_x (sv_f32_t x, const svbool_t pg) the same polynomial approximation of tan as above. */ /* Perform additional reduction if required. */ - sv_f32_t z = svneg_f32_m (r, pred_alt, r); + svfloat32_t z = svneg_m (r, pred_alt, r); - /* Evaluate polynomial approximation of tangent on [-pi/4, pi/4]. */ - sv_f32_t z2 = svmul_f32_x (pg, z, z); - sv_f32_t p = eval_poly (pg, z2); - sv_f32_t y = sv_fma_f32_x (pg, svmul_f32_x (pg, z, z2), p, z); + /* Evaluate polynomial approximation of tangent on [-pi/4, pi/4], + using Estrin on z^2. */ + svfloat32_t z2 = svmul_x (pg, z, z); + svfloat32_t p01 = svmla_lane (sv_f32 (d->c0), z2, odd_coeffs, 0); + svfloat32_t p23 = svmla_lane (sv_f32 (d->c2), z2, odd_coeffs, 1); + svfloat32_t p45 = svmla_lane (sv_f32 (d->c4), z2, odd_coeffs, 2); - /* Transform result back, if necessary. */ - sv_f32_t inv_y = svdiv_f32_x (pg, sv_f32 (1.0f), y); - y = svsel_f32 (pred_alt, inv_y, y); + svfloat32_t z4 = svmul_x (pg, z2, z2); + svfloat32_t p = svmla_x (pg, p01, z4, p23); + + svfloat32_t z8 = svmul_x (pg, z4, z4); + p = svmla_x (pg, p, z8, p45); + + svfloat32_t y = svmla_x (pg, z, p, svmul_x (pg, z, z2)); - /* Fast reduction does not handle the x = -0.0 case well, - therefore it is fixed here. */ - y = svsel_f32 (pred_minuszero, x, y); + /* Transform result back, if necessary. */ + svfloat32_t inv_y = svdivr_x (pg, y, 1.0f); /* No need to pass pg to specialcase here since cmp is a strict subset, guaranteed by the cmpge above. */ if (unlikely (svptest_any (pg, cmp))) - return __sv_tanf_specialcase (x, y, cmp); - return y; -} + return special_case (x, svsel (pred_alt, inv_y, y), cmp); -PL_ALIAS (__sv_tanf_x, _ZGVsMxv_tanf) + return svsel (pred_alt, inv_y, y); +} PL_SIG (SV, F, 1, tan, -3.1, 3.1) -PL_TEST_ULP (__sv_tanf, 2.96) -PL_TEST_INTERVAL (__sv_tanf, -0.0, -0x1p126, 100) -PL_TEST_INTERVAL (__sv_tanf, 0x1p-149, 0x1p-126, 4000) -PL_TEST_INTERVAL (__sv_tanf, 0x1p-126, 0x1p-23, 50000) -PL_TEST_INTERVAL (__sv_tanf, 0x1p-23, 0.7, 50000) -PL_TEST_INTERVAL (__sv_tanf, 0.7, 1.5, 50000) -PL_TEST_INTERVAL (__sv_tanf, 1.5, 100, 50000) -PL_TEST_INTERVAL (__sv_tanf, 100, 0x1p17, 50000) -PL_TEST_INTERVAL (__sv_tanf, 0x1p17, inf, 50000) -#endif +PL_TEST_ULP (SV_NAME_F1 (tan), 2.96) +PL_TEST_INTERVAL (SV_NAME_F1 (tan), -0.0, -0x1p126, 100) +PL_TEST_INTERVAL (SV_NAME_F1 (tan), 0x1p-149, 0x1p-126, 4000) +PL_TEST_INTERVAL (SV_NAME_F1 (tan), 0x1p-126, 0x1p-23, 50000) +PL_TEST_INTERVAL (SV_NAME_F1 (tan), 0x1p-23, 0.7, 50000) +PL_TEST_INTERVAL (SV_NAME_F1 (tan), 0.7, 1.5, 50000) +PL_TEST_INTERVAL (SV_NAME_F1 (tan), 1.5, 100, 50000) +PL_TEST_INTERVAL (SV_NAME_F1 (tan), 100, 0x1p17, 50000) +PL_TEST_INTERVAL (SV_NAME_F1 (tan), 0x1p17, inf, 50000) |