diff options
Diffstat (limited to 'pl/math/v_tan_3u5.c')
| -rw-r--r-- | pl/math/v_tan_3u5.c | 120 |
1 files changed, 0 insertions, 120 deletions
diff --git a/pl/math/v_tan_3u5.c b/pl/math/v_tan_3u5.c deleted file mode 100644 index c431c8c4889e..000000000000 --- a/pl/math/v_tan_3u5.c +++ /dev/null @@ -1,120 +0,0 @@ -/* - * Double-precision vector tan(x) function. - * - * Copyright (c) 2023, Arm Limited. - * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception - */ - -#include "v_math.h" -#include "poly_advsimd_f64.h" -#include "pl_sig.h" -#include "pl_test.h" - -static const struct data -{ - float64x2_t poly[9]; - float64x2_t half_pi, two_over_pi, shift; -#if !WANT_SIMD_EXCEPT - float64x2_t range_val; -#endif -} data = { - /* Coefficients generated using FPMinimax. */ - .poly = { V2 (0x1.5555555555556p-2), V2 (0x1.1111111110a63p-3), - V2 (0x1.ba1ba1bb46414p-5), V2 (0x1.664f47e5b5445p-6), - V2 (0x1.226e5e5ecdfa3p-7), V2 (0x1.d6c7ddbf87047p-9), - V2 (0x1.7ea75d05b583ep-10), V2 (0x1.289f22964a03cp-11), - V2 (0x1.4e4fd14147622p-12) }, - .half_pi = { 0x1.921fb54442d18p0, 0x1.1a62633145c07p-54 }, - .two_over_pi = V2 (0x1.45f306dc9c883p-1), - .shift = V2 (0x1.8p52), -#if !WANT_SIMD_EXCEPT - .range_val = V2 (0x1p23), -#endif -}; - -#define RangeVal 0x4160000000000000 /* asuint64(0x1p23). */ -#define TinyBound 0x3e50000000000000 /* asuint64(2^-26). */ -#define Thresh 0x310000000000000 /* RangeVal - TinyBound. */ - -/* Special cases (fall back to scalar calls). */ -static float64x2_t VPCS_ATTR NOINLINE -special_case (float64x2_t x) -{ - return v_call_f64 (tan, x, x, v_u64 (-1)); -} - -/* Vector approximation for double-precision tan. - Maximum measured error is 3.48 ULP: - _ZGVnN2v_tan(0x1.4457047ef78d8p+20) got -0x1.f6ccd8ecf7dedp+37 - want -0x1.f6ccd8ecf7deap+37. */ -float64x2_t VPCS_ATTR V_NAME_D1 (tan) (float64x2_t x) -{ - const struct data *dat = ptr_barrier (&data); - /* Our argument reduction cannot calculate q with sufficient accuracy for - very large inputs. Fall back to scalar routine for all lanes if any are - too large, or Inf/NaN. If fenv exceptions are expected, also fall back for - tiny input to avoid underflow. */ -#if WANT_SIMD_EXCEPT - uint64x2_t iax = vreinterpretq_u64_f64 (vabsq_f64 (x)); - /* iax - tiny_bound > range_val - tiny_bound. */ - uint64x2_t special - = vcgtq_u64 (vsubq_u64 (iax, v_u64 (TinyBound)), v_u64 (Thresh)); - if (unlikely (v_any_u64 (special))) - return special_case (x); -#endif - - /* q = nearest integer to 2 * x / pi. */ - float64x2_t q - = vsubq_f64 (vfmaq_f64 (dat->shift, x, dat->two_over_pi), dat->shift); - int64x2_t qi = vcvtq_s64_f64 (q); - - /* Use q to reduce x to r in [-pi/4, pi/4], by: - r = x - q * pi/2, in extended precision. */ - float64x2_t r = x; - r = vfmsq_laneq_f64 (r, q, dat->half_pi, 0); - r = vfmsq_laneq_f64 (r, q, dat->half_pi, 1); - /* Further reduce r to [-pi/8, pi/8], to be reconstructed using double angle - formula. */ - r = vmulq_n_f64 (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)). */ - float64x2_t r2 = vmulq_f64 (r, r), r4 = vmulq_f64 (r2, r2), - r8 = vmulq_f64 (r4, r4); - /* Offset coefficients to evaluate from C1 onwards. */ - float64x2_t p = v_estrin_7_f64 (r2, r4, r8, dat->poly + 1); - p = vfmaq_f64 (dat->poly[0], p, r2); - p = vfmaq_f64 (r, r2, vmulq_f64 (p, r)); - - /* 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 (hence quadrant). - */ - float64x2_t n = vfmaq_f64 (v_f64 (-1), p, p); - float64x2_t d = vaddq_f64 (p, p); - - uint64x2_t no_recip = vtstq_u64 (vreinterpretq_u64_s64 (qi), v_u64 (1)); - -#if !WANT_SIMD_EXCEPT - uint64x2_t special = vcageq_f64 (x, dat->range_val); - if (unlikely (v_any_u64 (special))) - return special_case (x); -#endif - - return vdivq_f64 (vbslq_f64 (no_recip, n, vnegq_f64 (d)), - vbslq_f64 (no_recip, d, n)); -} - -PL_SIG (V, D, 1, tan, -3.1, 3.1) -PL_TEST_ULP (V_NAME_D1 (tan), 2.99) -PL_TEST_EXPECT_FENV (V_NAME_D1 (tan), WANT_SIMD_EXCEPT) -PL_TEST_SYM_INTERVAL (V_NAME_D1 (tan), 0, TinyBound, 5000) -PL_TEST_SYM_INTERVAL (V_NAME_D1 (tan), TinyBound, RangeVal, 100000) -PL_TEST_SYM_INTERVAL (V_NAME_D1 (tan), RangeVal, inf, 5000) |