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Diffstat (limited to 'math/aarch64/sve/tan.c')
| -rw-r--r-- | math/aarch64/sve/tan.c | 131 |
1 files changed, 131 insertions, 0 deletions
diff --git a/math/aarch64/sve/tan.c b/math/aarch64/sve/tan.c new file mode 100644 index 000000000000..1dfc5c422d5e --- /dev/null +++ b/math/aarch64/sve/tan.c @@ -0,0 +1,131 @@ +/* + * Double-precision SVE tan(x) function. + * + * Copyright (c) 2023-2024, 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 +{ + double c2, c4, c6, c8; + double poly_1357[4]; + double c0, inv_half_pi; + double half_pi_hi, half_pi_lo, range_val; +} data = { + /* Polynomial generated with FPMinimax. */ + .c2 = 0x1.ba1ba1bb46414p-5, + .c4 = 0x1.226e5e5ecdfa3p-7, + .c6 = 0x1.7ea75d05b583ep-10, + .c8 = 0x1.4e4fd14147622p-12, + .poly_1357 = { 0x1.1111111110a63p-3, 0x1.664f47e5b5445p-6, + 0x1.d6c7ddbf87047p-9, 0x1.289f22964a03cp-11 }, + .c0 = 0x1.5555555555556p-2, + .inv_half_pi = 0x1.45f306dc9c883p-1, + .half_pi_hi = 0x1.921fb54442d18p0, + .half_pi_lo = 0x1.1a62633145c07p-54, + .range_val = 0x1p23, +}; + +static svfloat64_t NOINLINE +special_case (svfloat64_t x, svfloat64_t p, svfloat64_t q, svbool_t pg, + svbool_t special) +{ + svbool_t use_recip = svcmpeq ( + pg, svand_x (pg, svreinterpret_u64 (svcvt_s64_x (pg, q)), 1), 0); + + svfloat64_t n = svmad_x (pg, p, p, -1); + svfloat64_t d = svmul_x (svptrue_b64 (), p, 2); + svfloat64_t swap = n; + n = svneg_m (n, use_recip, d); + d = svsel (use_recip, swap, d); + svfloat64_t y = svdiv_x (svnot_z (pg, special), n, d); + return sv_call_f64 (tan, x, y, special); +} + +/* Vector approximation for double-precision tan. + Maximum measured error is 3.48 ULP: + _ZGVsMxv_tan(0x1.4457047ef78d8p+20) got -0x1.f6ccd8ecf7dedp+37 + want -0x1.f6ccd8ecf7deap+37. */ +svfloat64_t SV_NAME_D1 (tan) (svfloat64_t x, svbool_t pg) +{ + const struct data *dat = ptr_barrier (&data); + svfloat64_t half_pi_c0 = svld1rq (svptrue_b64 (), &dat->c0); + /* q = nearest integer to 2 * x / pi. */ + svfloat64_t q = svmul_lane (x, half_pi_c0, 1); + q = svrinta_x (pg, q); + + /* Use q to reduce x to r in [-pi/4, pi/4], by: + r = x - q * pi/2, in extended precision. */ + svfloat64_t r = x; + svfloat64_t half_pi = svld1rq (svptrue_b64 (), &dat->half_pi_hi); + r = svmls_lane (r, q, half_pi, 0); + r = svmls_lane (r, q, half_pi, 1); + /* Further reduce r to [-pi/8, pi/8], to be reconstructed using double angle + formula. */ + r = svmul_x (svptrue_b64 (), r, 0.5); + + /* Approximate tan(r) using order 8 polynomial. + tan(x) is odd, so polynomial has the form: + tan(x) ~= x + C0 * x^3 + C1 * x^5 + C3 * x^7 + ... + Hence we first approximate P(r) = C1 + C2 * r^2 + C3 * r^4 + ... + Then compute the approximation by: + tan(r) ~= r + r^3 * (C0 + r^2 * P(r)). */ + + svfloat64_t r2 = svmul_x (svptrue_b64 (), r, r); + svfloat64_t r4 = svmul_x (svptrue_b64 (), r2, r2); + svfloat64_t r8 = svmul_x (svptrue_b64 (), r4, r4); + /* Use offset version coeff array by 1 to evaluate from C1 onwards. */ + svfloat64_t C_24 = svld1rq (svptrue_b64 (), &dat->c2); + svfloat64_t C_68 = svld1rq (svptrue_b64 (), &dat->c6); + + /* Use offset version coeff array by 1 to evaluate from C1 onwards. */ + svfloat64_t p01 = svmla_lane (sv_f64 (dat->poly_1357[0]), r2, C_24, 0); + svfloat64_t p23 = svmla_lane_f64 (sv_f64 (dat->poly_1357[1]), r2, C_24, 1); + svfloat64_t p03 = svmla_x (pg, p01, p23, r4); + + svfloat64_t p45 = svmla_lane (sv_f64 (dat->poly_1357[2]), r2, C_68, 0); + svfloat64_t p67 = svmla_lane (sv_f64 (dat->poly_1357[3]), r2, C_68, 1); + svfloat64_t p47 = svmla_x (pg, p45, p67, r4); + + svfloat64_t p = svmla_x (pg, p03, p47, r8); + + svfloat64_t z = svmul_x (svptrue_b64 (), p, r); + z = svmul_x (svptrue_b64 (), r2, z); + z = svmla_lane (z, r, half_pi_c0, 0); + p = svmla_x (pg, r, r2, z); + + /* Recombination uses double-angle formula: + tan(2x) = 2 * tan(x) / (1 - (tan(x))^2) + and reciprocity around pi/2: + tan(x) = 1 / (tan(pi/2 - x)) + to assemble result using change-of-sign and conditional selection of + numerator/denominator dependent on odd/even-ness of q (quadrant). */ + + /* Invert condition to catch NaNs and Infs as well as large values. */ + svbool_t special = svnot_z (pg, svaclt (pg, x, dat->range_val)); + + if (unlikely (svptest_any (pg, special))) + { + return special_case (x, p, q, pg, special); + } + svbool_t use_recip = svcmpeq ( + pg, svand_x (pg, svreinterpret_u64 (svcvt_s64_x (pg, q)), 1), 0); + + svfloat64_t n = svmad_x (pg, p, p, -1); + svfloat64_t d = svmul_x (svptrue_b64 (), p, 2); + svfloat64_t swap = n; + n = svneg_m (n, use_recip, d); + d = svsel (use_recip, swap, d); + return svdiv_x (pg, n, d); +} + +TEST_SIG (SV, D, 1, tan, -3.1, 3.1) +TEST_ULP (SV_NAME_D1 (tan), 2.99) +TEST_DISABLE_FENV (SV_NAME_D1 (tan)) +TEST_SYM_INTERVAL (SV_NAME_D1 (tan), 0, 0x1p23, 500000) +TEST_SYM_INTERVAL (SV_NAME_D1 (tan), 0x1p23, inf, 5000) +CLOSE_SVE_ATTR |