1*f3087befSAndrew Turner /* 2*f3087befSAndrew Turner * Double-precision vector tanpi(x) function. 3*f3087befSAndrew Turner * 4*f3087befSAndrew Turner * Copyright (c) 2024, Arm Limited. 5*f3087befSAndrew Turner * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6*f3087befSAndrew Turner */ 7*f3087befSAndrew Turner 8*f3087befSAndrew Turner #include "v_math.h" 9*f3087befSAndrew Turner #include "test_sig.h" 10*f3087befSAndrew Turner #include "test_defs.h" 11*f3087befSAndrew Turner 12*f3087befSAndrew Turner const static struct v_tanpi_data 13*f3087befSAndrew Turner { 14*f3087befSAndrew Turner float64x2_t c0, c2, c4, c6, c8, c10, c12; 15*f3087befSAndrew Turner double c1, c3, c5, c7, c9, c11, c13, c14; 16*f3087befSAndrew Turner } tanpi_data = { 17*f3087befSAndrew Turner /* Coefficents for tan(pi * x) computed with fpminimax 18*f3087befSAndrew Turner on [ 0x1p-1022 0x1p-2 ] 19*f3087befSAndrew Turner approx rel error: 0x1.7eap-55 20*f3087befSAndrew Turner approx abs error: 0x1.7eap-55. */ 21*f3087befSAndrew Turner .c0 = V2 (0x1.921fb54442d18p1), /* pi. */ 22*f3087befSAndrew Turner .c1 = 0x1.4abbce625be52p3, .c2 = V2 (0x1.466bc6775b0f9p5), 23*f3087befSAndrew Turner .c3 = 0x1.45fff9b426f5ep7, .c4 = V2 (0x1.45f4730dbca5cp9), 24*f3087befSAndrew Turner .c5 = 0x1.45f3265994f85p11, .c6 = V2 (0x1.45f4234b330cap13), 25*f3087befSAndrew Turner .c7 = 0x1.45dca11be79ebp15, .c8 = V2 (0x1.47283fc5eea69p17), 26*f3087befSAndrew Turner .c9 = 0x1.3a6d958cdefaep19, .c10 = V2 (0x1.927896baee627p21), 27*f3087befSAndrew Turner .c11 = -0x1.89333f6acd922p19, .c12 = V2 (0x1.5d4e912bb8456p27), 28*f3087befSAndrew Turner .c13 = -0x1.a854d53ab6874p29, .c14 = 0x1.1b76de7681424p32, 29*f3087befSAndrew Turner }; 30*f3087befSAndrew Turner 31*f3087befSAndrew Turner /* Approximation for double-precision vector tanpi(x) 32*f3087befSAndrew Turner The maximum error is 3.06 ULP: 33*f3087befSAndrew Turner _ZGVnN2v_tanpi(0x1.0a4a07dfcca3ep-1) got -0x1.fa30112702c98p+3 34*f3087befSAndrew Turner want -0x1.fa30112702c95p+3. */ 35*f3087befSAndrew Turner float64x2_t VPCS_ATTR V_NAME_D1 (tanpi) (float64x2_t x) 36*f3087befSAndrew Turner { 37*f3087befSAndrew Turner const struct v_tanpi_data *d = ptr_barrier (&tanpi_data); 38*f3087befSAndrew Turner 39*f3087befSAndrew Turner float64x2_t n = vrndnq_f64 (x); 40*f3087befSAndrew Turner 41*f3087befSAndrew Turner /* inf produces nan that propagates. */ 42*f3087befSAndrew Turner float64x2_t xr = vsubq_f64 (x, n); 43*f3087befSAndrew Turner float64x2_t ar = vabdq_f64 (x, n); 44*f3087befSAndrew Turner uint64x2_t flip = vcgtq_f64 (ar, v_f64 (0.25)); 45*f3087befSAndrew Turner float64x2_t r = vbslq_f64 (flip, vsubq_f64 (v_f64 (0.5), ar), ar); 46*f3087befSAndrew Turner 47*f3087befSAndrew Turner /* Order-14 pairwise Horner. */ 48*f3087befSAndrew Turner float64x2_t r2 = vmulq_f64 (r, r); 49*f3087befSAndrew Turner float64x2_t r4 = vmulq_f64 (r2, r2); 50*f3087befSAndrew Turner 51*f3087befSAndrew Turner float64x2_t c_1_3 = vld1q_f64 (&d->c1); 52*f3087befSAndrew Turner float64x2_t c_5_7 = vld1q_f64 (&d->c5); 53*f3087befSAndrew Turner float64x2_t c_9_11 = vld1q_f64 (&d->c9); 54*f3087befSAndrew Turner float64x2_t c_13_14 = vld1q_f64 (&d->c13); 55*f3087befSAndrew Turner float64x2_t p01 = vfmaq_laneq_f64 (d->c0, r2, c_1_3, 0); 56*f3087befSAndrew Turner float64x2_t p23 = vfmaq_laneq_f64 (d->c2, r2, c_1_3, 1); 57*f3087befSAndrew Turner float64x2_t p45 = vfmaq_laneq_f64 (d->c4, r2, c_5_7, 0); 58*f3087befSAndrew Turner float64x2_t p67 = vfmaq_laneq_f64 (d->c6, r2, c_5_7, 1); 59*f3087befSAndrew Turner float64x2_t p89 = vfmaq_laneq_f64 (d->c8, r2, c_9_11, 0); 60*f3087befSAndrew Turner float64x2_t p1011 = vfmaq_laneq_f64 (d->c10, r2, c_9_11, 1); 61*f3087befSAndrew Turner float64x2_t p1213 = vfmaq_laneq_f64 (d->c12, r2, c_13_14, 0); 62*f3087befSAndrew Turner 63*f3087befSAndrew Turner float64x2_t p = vfmaq_laneq_f64 (p1213, r4, c_13_14, 1); 64*f3087befSAndrew Turner p = vfmaq_f64 (p1011, r4, p); 65*f3087befSAndrew Turner p = vfmaq_f64 (p89, r4, p); 66*f3087befSAndrew Turner p = vfmaq_f64 (p67, r4, p); 67*f3087befSAndrew Turner p = vfmaq_f64 (p45, r4, p); 68*f3087befSAndrew Turner p = vfmaq_f64 (p23, r4, p); 69*f3087befSAndrew Turner p = vfmaq_f64 (p01, r4, p); 70*f3087befSAndrew Turner p = vmulq_f64 (r, p); 71*f3087befSAndrew Turner 72*f3087befSAndrew Turner float64x2_t p_recip = vdivq_f64 (v_f64 (1.0), p); 73*f3087befSAndrew Turner float64x2_t y = vbslq_f64 (flip, p_recip, p); 74*f3087befSAndrew Turner 75*f3087befSAndrew Turner uint64x2_t sign 76*f3087befSAndrew Turner = veorq_u64 (vreinterpretq_u64_f64 (xr), vreinterpretq_u64_f64 (ar)); 77*f3087befSAndrew Turner return vreinterpretq_f64_u64 (vorrq_u64 (vreinterpretq_u64_f64 (y), sign)); 78*f3087befSAndrew Turner } 79*f3087befSAndrew Turner 80*f3087befSAndrew Turner #if WANT_TRIGPI_TESTS 81*f3087befSAndrew Turner TEST_DISABLE_FENV (V_NAME_D1 (tanpi)) 82*f3087befSAndrew Turner TEST_ULP (V_NAME_D1 (tanpi), 2.57) 83*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_D1 (tanpi), 0, 0x1p-31, 50000) 84*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_D1 (tanpi), 0x1p-31, 0.5, 50000) 85*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_D1 (tanpi), 0.5, 1.0, 200000) 86*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_D1 (tanpi), 1.0, 0x1p23, 50000) 87*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_D1 (tanpi), 0x1p23, inf, 50000) 88*f3087befSAndrew Turner #endif 89