1 /* 2 * Double-precision SVE cos(x) function. 3 * 4 * Copyright (c) 2019-2023, Arm Limited. 5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6 */ 7 8 #include "sv_math.h" 9 #include "pl_sig.h" 10 #include "pl_test.h" 11 12 static const struct data 13 { 14 double inv_pio2, pio2_1, pio2_2, pio2_3, shift; 15 } data = { 16 /* Polynomial coefficients are hardwired in FTMAD instructions. */ 17 .inv_pio2 = 0x1.45f306dc9c882p-1, 18 .pio2_1 = 0x1.921fb50000000p+0, 19 .pio2_2 = 0x1.110b460000000p-26, 20 .pio2_3 = 0x1.1a62633145c07p-54, 21 /* Original shift used in AdvSIMD cos, 22 plus a contribution to set the bit #0 of q 23 as expected by trigonometric instructions. */ 24 .shift = 0x1.8000000000001p52 25 }; 26 27 #define RangeVal 0x4160000000000000 /* asuint64 (0x1p23). */ 28 29 static svfloat64_t NOINLINE 30 special_case (svfloat64_t x, svfloat64_t y, svbool_t oob) 31 { 32 return sv_call_f64 (cos, x, y, oob); 33 } 34 35 /* A fast SVE implementation of cos based on trigonometric 36 instructions (FTMAD, FTSSEL, FTSMUL). 37 Maximum measured error: 2.108 ULPs. 38 SV_NAME_D1 (cos)(0x1.9b0ba158c98f3p+7) got -0x1.fddd4c65c7f07p-3 39 want -0x1.fddd4c65c7f05p-3. */ 40 svfloat64_t SV_NAME_D1 (cos) (svfloat64_t x, const svbool_t pg) 41 { 42 const struct data *d = ptr_barrier (&data); 43 44 svfloat64_t r = svabs_x (pg, x); 45 svbool_t oob = svcmpge (pg, svreinterpret_u64 (r), RangeVal); 46 47 /* Load some constants in quad-word chunks to minimise memory access. */ 48 svbool_t ptrue = svptrue_b64 (); 49 svfloat64_t invpio2_and_pio2_1 = svld1rq (ptrue, &d->inv_pio2); 50 svfloat64_t pio2_23 = svld1rq (ptrue, &d->pio2_2); 51 52 /* n = rint(|x|/(pi/2)). */ 53 svfloat64_t q = svmla_lane (sv_f64 (d->shift), r, invpio2_and_pio2_1, 0); 54 svfloat64_t n = svsub_x (pg, q, d->shift); 55 56 /* r = |x| - n*(pi/2) (range reduction into -pi/4 .. pi/4). */ 57 r = svmls_lane (r, n, invpio2_and_pio2_1, 1); 58 r = svmls_lane (r, n, pio2_23, 0); 59 r = svmls_lane (r, n, pio2_23, 1); 60 61 /* cos(r) poly approx. */ 62 svfloat64_t r2 = svtsmul (r, svreinterpret_u64 (q)); 63 svfloat64_t y = sv_f64 (0.0); 64 y = svtmad (y, r2, 7); 65 y = svtmad (y, r2, 6); 66 y = svtmad (y, r2, 5); 67 y = svtmad (y, r2, 4); 68 y = svtmad (y, r2, 3); 69 y = svtmad (y, r2, 2); 70 y = svtmad (y, r2, 1); 71 y = svtmad (y, r2, 0); 72 73 /* Final multiplicative factor: 1.0 or x depending on bit #0 of q. */ 74 svfloat64_t f = svtssel (r, svreinterpret_u64 (q)); 75 76 if (unlikely (svptest_any (pg, oob))) 77 return special_case (x, svmul_x (svnot_z (pg, oob), y, f), oob); 78 79 /* Apply factor. */ 80 return svmul_x (pg, f, y); 81 } 82 83 PL_SIG (SV, D, 1, cos, -3.1, 3.1) 84 PL_TEST_ULP (SV_NAME_D1 (cos), 1.61) 85 PL_TEST_INTERVAL (SV_NAME_D1 (cos), 0, 0xffff0000, 10000) 86 PL_TEST_INTERVAL (SV_NAME_D1 (cos), 0x1p-4, 0x1p4, 500000) 87