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Diffstat (limited to 'math/aarch64/sve/tanf.c')
| -rw-r--r-- | math/aarch64/sve/tanf.c | 117 |
1 files changed, 117 insertions, 0 deletions
diff --git a/math/aarch64/sve/tanf.c b/math/aarch64/sve/tanf.c new file mode 100644 index 000000000000..d34fc2fc1a4e --- /dev/null +++ b/math/aarch64/sve/tanf.c @@ -0,0 +1,117 @@ +/* + * Single-precision vector tan(x) function. + * + * Copyright (c) 2020-2024, Arm Limited. + * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception + */ + +#include "sv_math.h" +#include "test_sig.h" +#include "test_defs.h" + +static const struct data +{ + 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_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); + + svfloat32_t odd_coeffs = svld1rq (svptrue_b32 (), &d->c1); + svfloat32_t pi_vals = svld1rq (svptrue_b32 (), &d->pio2_1); + + /* n = rint(x/(pi/2)). */ + svfloat32_t n = svrintn_x (pg, svmul_lane (x, pi_vals, 3)); + /* n is already a signed integer, simply convert it. */ + svint32_t in = svcvt_s32_x (pg, n); + /* Determine if x lives in an interval, where |tan(x)| grows to infinity. */ + 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). */ + 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 + tan(r) ~ r + r^3 * P(r^2) = r + r * r^2 * P(r^2). + - grows to infinity then use symmetries of tangent and the identity + tan(r) = cotan(pi/2 - r) to express tan(x) as 1/tan(-r). Finally, use + the same polynomial approximation of tan as above. */ + + /* Perform additional reduction if required. */ + svfloat32_t z = svneg_m (r, pred_alt, r); + + /* Evaluate polynomial approximation of tangent on [-pi/4, pi/4], + using Estrin on z^2. */ + svfloat32_t z2 = svmul_x (svptrue_b32 (), r, r); + 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); + + 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)); + + /* No need to pass pg to specialcase here since cmp is a strict subset, + guaranteed by the cmpge above. */ + + /* Determine whether input is too large to perform fast regression. */ + svbool_t cmp = svacge (pg, x, d->range_val); + if (unlikely (svptest_any (pg, cmp))) + return special_case (x, svdivr_x (pg, y, 1.0f), cmp); + + svfloat32_t inv_y = svdivr_x (pg, y, 1.0f); + return svsel (pred_alt, inv_y, y); +} + +TEST_SIG (SV, F, 1, tan, -3.1, 3.1) +TEST_ULP (SV_NAME_F1 (tan), 2.96) +TEST_DISABLE_FENV (SV_NAME_F1 (tan)) +TEST_INTERVAL (SV_NAME_F1 (tan), -0.0, -0x1p126, 100) +TEST_INTERVAL (SV_NAME_F1 (tan), 0x1p-149, 0x1p-126, 4000) +TEST_INTERVAL (SV_NAME_F1 (tan), 0x1p-126, 0x1p-23, 50000) +TEST_INTERVAL (SV_NAME_F1 (tan), 0x1p-23, 0.7, 50000) +TEST_INTERVAL (SV_NAME_F1 (tan), 0.7, 1.5, 50000) +TEST_INTERVAL (SV_NAME_F1 (tan), 1.5, 100, 50000) +TEST_INTERVAL (SV_NAME_F1 (tan), 100, 0x1p17, 50000) +TEST_INTERVAL (SV_NAME_F1 (tan), 0x1p17, inf, 50000) +CLOSE_SVE_ATTR |