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 #if SV_SUPPORTED 13 14 #define InvPio2 (sv_f64 (0x1.45f306dc9c882p-1)) 15 #define NegPio2_1 (sv_f64 (-0x1.921fb50000000p+0)) 16 #define NegPio2_2 (sv_f64 (-0x1.110b460000000p-26)) 17 #define NegPio2_3 (sv_f64 (-0x1.1a62633145c07p-54)) 18 /* Original shift used in Neon cos, 19 plus a contribution to set the bit #0 of q 20 as expected by trigonometric instructions. */ 21 #define Shift (sv_f64 (0x1.8000000000001p52)) 22 #define RangeVal (sv_f64 (0x1p23)) 23 #define AbsMask (0x7fffffffffffffff) 24 25 static NOINLINE sv_f64_t 26 __sv_cos_specialcase (sv_f64_t x, sv_f64_t y, svbool_t cmp) 27 { 28 return sv_call_f64 (cos, x, y, cmp); 29 } 30 31 /* A fast SVE implementation of cos based on trigonometric 32 instructions (FTMAD, FTSSEL, FTSMUL). 33 Maximum measured error: 2.108 ULPs. 34 __sv_cos(0x1.9b0ba158c98f3p+7) got -0x1.fddd4c65c7f07p-3 35 want -0x1.fddd4c65c7f05p-3. */ 36 sv_f64_t 37 __sv_cos_x (sv_f64_t x, const svbool_t pg) 38 { 39 sv_f64_t n, r, r2, y; 40 svbool_t cmp; 41 42 r = sv_as_f64_u64 (svand_n_u64_x (pg, sv_as_u64_f64 (x), AbsMask)); 43 cmp = svcmpge_u64 (pg, sv_as_u64_f64 (r), sv_as_u64_f64 (RangeVal)); 44 45 /* n = rint(|x|/(pi/2)). */ 46 sv_f64_t q = sv_fma_f64_x (pg, InvPio2, r, Shift); 47 n = svsub_f64_x (pg, q, Shift); 48 49 /* r = |x| - n*(pi/2) (range reduction into -pi/4 .. pi/4). */ 50 r = sv_fma_f64_x (pg, NegPio2_1, n, r); 51 r = sv_fma_f64_x (pg, NegPio2_2, n, r); 52 r = sv_fma_f64_x (pg, NegPio2_3, n, r); 53 54 /* cos(r) poly approx. */ 55 r2 = svtsmul_f64 (r, sv_as_u64_f64 (q)); 56 y = sv_f64 (0.0); 57 y = svtmad_f64 (y, r2, 7); 58 y = svtmad_f64 (y, r2, 6); 59 y = svtmad_f64 (y, r2, 5); 60 y = svtmad_f64 (y, r2, 4); 61 y = svtmad_f64 (y, r2, 3); 62 y = svtmad_f64 (y, r2, 2); 63 y = svtmad_f64 (y, r2, 1); 64 y = svtmad_f64 (y, r2, 0); 65 66 /* Final multiplicative factor: 1.0 or x depending on bit #0 of q. */ 67 sv_f64_t f = svtssel_f64 (r, sv_as_u64_f64 (q)); 68 /* Apply factor. */ 69 y = svmul_f64_x (pg, f, y); 70 71 /* No need to pass pg to specialcase here since cmp is a strict subset, 72 guaranteed by the cmpge above. */ 73 if (unlikely (svptest_any (pg, cmp))) 74 return __sv_cos_specialcase (x, y, cmp); 75 return y; 76 } 77 78 PL_ALIAS (__sv_cos_x, _ZGVsMxv_cos) 79 80 PL_SIG (SV, D, 1, cos, -3.1, 3.1) 81 PL_TEST_ULP (__sv_cos, 1.61) 82 PL_TEST_INTERVAL (__sv_cos, 0, 0xffff0000, 10000) 83 PL_TEST_INTERVAL (__sv_cos, 0x1p-4, 0x1p4, 500000) 84 #endif 85