1 /* 2 * Double-precision vector tanpi(x) function. 3 * 4 * Copyright (c) 2024, Arm Limited. 5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6 */ 7 8 #include "sv_math.h" 9 #include "test_sig.h" 10 #include "test_defs.h" 11 12 const static struct v_tanpi_data 13 { 14 double c0, c2, c4, c6, c8, c10, c12; 15 double c1, c3, c5, c7, c9, c11, c13, c14; 16 } tanpi_data = { 17 /* Coefficents for tan(pi * x) computed with fpminimax 18 on [ 0x1p-1022 0x1p-2 ] 19 approx rel error: 0x1.7eap-55 20 approx abs error: 0x1.7eap-55. */ 21 .c0 = 0x1.921fb54442d18p1, /* pi. */ 22 .c1 = 0x1.4abbce625be52p3, .c2 = 0x1.466bc6775b0f9p5, 23 .c3 = 0x1.45fff9b426f5ep7, .c4 = 0x1.45f4730dbca5cp9, 24 .c5 = 0x1.45f3265994f85p11, .c6 = 0x1.45f4234b330cap13, 25 .c7 = 0x1.45dca11be79ebp15, .c8 = 0x1.47283fc5eea69p17, 26 .c9 = 0x1.3a6d958cdefaep19, .c10 = 0x1.927896baee627p21, 27 .c11 = -0x1.89333f6acd922p19, .c12 = 0x1.5d4e912bb8456p27, 28 .c13 = -0x1.a854d53ab6874p29, .c14 = 0x1.1b76de7681424p32, 29 }; 30 31 /* Approximation for double-precision vector tanpi(x) 32 The maximum error is 3.06 ULP: 33 _ZGVsMxv_tanpi(0x1.0a4a07dfcca3ep-1) got -0x1.fa30112702c98p+3 34 want -0x1.fa30112702c95p+3. */ 35 svfloat64_t SV_NAME_D1 (tanpi) (svfloat64_t x, const svbool_t pg) 36 { 37 const struct v_tanpi_data *d = ptr_barrier (&tanpi_data); 38 39 svfloat64_t n = svrintn_x (pg, x); 40 41 /* inf produces nan that propagates. */ 42 svfloat64_t xr = svsub_x (pg, x, n); 43 svfloat64_t ar = svabd_x (pg, x, n); 44 svbool_t flip = svcmpgt (pg, ar, 0.25); 45 svfloat64_t r = svsel (flip, svsubr_x (pg, ar, 0.5), ar); 46 47 /* Order-14 pairwise Horner. */ 48 svfloat64_t r2 = svmul_x (pg, r, r); 49 svfloat64_t r4 = svmul_x (pg, r2, r2); 50 51 svfloat64_t c_1_3 = svld1rq (pg, &d->c1); 52 svfloat64_t c_5_7 = svld1rq (pg, &d->c5); 53 svfloat64_t c_9_11 = svld1rq (pg, &d->c9); 54 svfloat64_t c_13_14 = svld1rq (pg, &d->c13); 55 svfloat64_t p01 = svmla_lane (sv_f64 (d->c0), r2, c_1_3, 0); 56 svfloat64_t p23 = svmla_lane (sv_f64 (d->c2), r2, c_1_3, 1); 57 svfloat64_t p45 = svmla_lane (sv_f64 (d->c4), r2, c_5_7, 0); 58 svfloat64_t p67 = svmla_lane (sv_f64 (d->c6), r2, c_5_7, 1); 59 svfloat64_t p89 = svmla_lane (sv_f64 (d->c8), r2, c_9_11, 0); 60 svfloat64_t p1011 = svmla_lane (sv_f64 (d->c10), r2, c_9_11, 1); 61 svfloat64_t p1213 = svmla_lane (sv_f64 (d->c12), r2, c_13_14, 0); 62 63 svfloat64_t p = svmla_lane (p1213, r4, c_13_14, 1); 64 p = svmad_x (pg, p, r4, p1011); 65 p = svmad_x (pg, p, r4, p89); 66 p = svmad_x (pg, p, r4, p67); 67 p = svmad_x (pg, p, r4, p45); 68 p = svmad_x (pg, p, r4, p23); 69 p = svmad_x (pg, p, r4, p01); 70 p = svmul_x (pg, r, p); 71 72 svfloat64_t p_recip = svdivr_x (pg, p, 1.0); 73 svfloat64_t y = svsel (flip, p_recip, p); 74 75 svuint64_t sign 76 = sveor_x (pg, svreinterpret_u64 (xr), svreinterpret_u64 (ar)); 77 return svreinterpret_f64 (svorr_x (pg, svreinterpret_u64 (y), sign)); 78 } 79 80 #if WANT_TRIGPI_TESTS 81 TEST_DISABLE_FENV (SV_NAME_D1 (tanpi)) 82 TEST_ULP (SV_NAME_D1 (tanpi), 2.57) 83 TEST_SYM_INTERVAL (SV_NAME_D1 (tanpi), 0, 0x1p-31, 50000) 84 TEST_SYM_INTERVAL (SV_NAME_D1 (tanpi), 0x1p-31, 0.5, 50000) 85 TEST_SYM_INTERVAL (SV_NAME_D1 (tanpi), 0.5, 1.0, 200000) 86 TEST_SYM_INTERVAL (SV_NAME_D1 (tanpi), 1.0, 0x1p23, 50000) 87 TEST_SYM_INTERVAL (SV_NAME_D1 (tanpi), 0x1p23, inf, 50000) 88 #endif 89 CLOSE_SVE_ATTR 90