1 /* 2 * Single-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 NegPio2_1 (sv_f32 (-0x1.921fb6p+0f)) 15 #define NegPio2_2 (sv_f32 (0x1.777a5cp-25f)) 16 #define NegPio2_3 (sv_f32 (0x1.ee59dap-50f)) 17 #define RangeVal (sv_f32 (0x1p20f)) 18 #define InvPio2 (sv_f32 (0x1.45f306p-1f)) 19 /* Original shift used in Neon cosf, 20 plus a contribution to set the bit #0 of q 21 as expected by trigonometric instructions. */ 22 #define Shift (sv_f32 (0x1.800002p+23f)) 23 #define AbsMask (0x7fffffff) 24 25 static NOINLINE sv_f32_t 26 __sv_cosf_specialcase (sv_f32_t x, sv_f32_t y, svbool_t cmp) 27 { 28 return sv_call_f32 (cosf, x, y, cmp); 29 } 30 31 /* A fast SVE implementation of cosf based on trigonometric 32 instructions (FTMAD, FTSSEL, FTSMUL). 33 Maximum measured error: 2.06 ULPs. 34 __sv_cosf(0x1.dea2f2p+19) got 0x1.fffe7ap-6 35 want 0x1.fffe76p-6. */ 36 sv_f32_t 37 __sv_cosf_x (sv_f32_t x, const svbool_t pg) 38 { 39 sv_f32_t n, r, r2, y; 40 svbool_t cmp; 41 42 r = sv_as_f32_u32 (svand_n_u32_x (pg, sv_as_u32_f32 (x), AbsMask)); 43 cmp = svcmpge_u32 (pg, sv_as_u32_f32 (r), sv_as_u32_f32 (RangeVal)); 44 45 /* n = rint(|x|/(pi/2)). */ 46 sv_f32_t q = sv_fma_f32_x (pg, InvPio2, r, Shift); 47 n = svsub_f32_x (pg, q, Shift); 48 49 /* r = |x| - n*(pi/2) (range reduction into -pi/4 .. pi/4). */ 50 r = sv_fma_f32_x (pg, NegPio2_1, n, r); 51 r = sv_fma_f32_x (pg, NegPio2_2, n, r); 52 r = sv_fma_f32_x (pg, NegPio2_3, n, r); 53 54 /* Final multiplicative factor: 1.0 or x depending on bit #0 of q. */ 55 sv_f32_t f = svtssel_f32 (r, sv_as_u32_f32 (q)); 56 57 /* cos(r) poly approx. */ 58 r2 = svtsmul_f32 (r, sv_as_u32_f32 (q)); 59 y = sv_f32 (0.0f); 60 y = svtmad_f32 (y, r2, 4); 61 y = svtmad_f32 (y, r2, 3); 62 y = svtmad_f32 (y, r2, 2); 63 y = svtmad_f32 (y, r2, 1); 64 y = svtmad_f32 (y, r2, 0); 65 66 /* Apply factor. */ 67 y = svmul_f32_x (pg, f, y); 68 69 /* No need to pass pg to specialcase here since cmp is a strict subset, 70 guaranteed by the cmpge above. */ 71 if (unlikely (svptest_any (pg, cmp))) 72 return __sv_cosf_specialcase (x, y, cmp); 73 return y; 74 } 75 76 PL_ALIAS (__sv_cosf_x, _ZGVsMxv_cosf) 77 78 PL_SIG (SV, F, 1, cos, -3.1, 3.1) 79 PL_TEST_ULP (__sv_cosf, 1.57) 80 PL_TEST_INTERVAL (__sv_cosf, 0, 0xffff0000, 10000) 81 PL_TEST_INTERVAL (__sv_cosf, 0x1p-4, 0x1p4, 500000) 82 #endif 83