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 static const struct data 13 { 14 float neg_pio2_1, neg_pio2_2, neg_pio2_3, inv_pio2, shift; 15 } data = { 16 /* Polynomial coefficients are hard-wired in FTMAD instructions. */ 17 .neg_pio2_1 = -0x1.921fb6p+0f, 18 .neg_pio2_2 = 0x1.777a5cp-25f, 19 .neg_pio2_3 = 0x1.ee59dap-50f, 20 .inv_pio2 = 0x1.45f306p-1f, 21 /* Original shift used in AdvSIMD cosf, 22 plus a contribution to set the bit #0 of q 23 as expected by trigonometric instructions. */ 24 .shift = 0x1.800002p+23f 25 }; 26 27 #define RangeVal 0x49800000 /* asuint32(0x1p20f). */ 28 29 static svfloat32_t NOINLINE 30 special_case (svfloat32_t x, svfloat32_t y, svbool_t oob) 31 { 32 return sv_call_f32 (cosf, x, y, oob); 33 } 34 35 /* A fast SVE implementation of cosf based on trigonometric 36 instructions (FTMAD, FTSSEL, FTSMUL). 37 Maximum measured error: 2.06 ULPs. 38 SV_NAME_F1 (cos)(0x1.dea2f2p+19) got 0x1.fffe7ap-6 39 want 0x1.fffe76p-6. */ 40 svfloat32_t SV_NAME_F1 (cos) (svfloat32_t x, const svbool_t pg) 41 { 42 const struct data *d = ptr_barrier (&data); 43 44 svfloat32_t r = svabs_x (pg, x); 45 svbool_t oob = svcmpge (pg, svreinterpret_u32 (r), RangeVal); 46 47 /* Load some constants in quad-word chunks to minimise memory access. */ 48 svfloat32_t negpio2_and_invpio2 = svld1rq (svptrue_b32 (), &d->neg_pio2_1); 49 50 /* n = rint(|x|/(pi/2)). */ 51 svfloat32_t q = svmla_lane (sv_f32 (d->shift), r, negpio2_and_invpio2, 3); 52 svfloat32_t n = svsub_x (pg, q, d->shift); 53 54 /* r = |x| - n*(pi/2) (range reduction into -pi/4 .. pi/4). */ 55 r = svmla_lane (r, n, negpio2_and_invpio2, 0); 56 r = svmla_lane (r, n, negpio2_and_invpio2, 1); 57 r = svmla_lane (r, n, negpio2_and_invpio2, 2); 58 59 /* Final multiplicative factor: 1.0 or x depending on bit #0 of q. */ 60 svfloat32_t f = svtssel (r, svreinterpret_u32 (q)); 61 62 /* cos(r) poly approx. */ 63 svfloat32_t r2 = svtsmul (r, svreinterpret_u32 (q)); 64 svfloat32_t y = sv_f32 (0.0f); 65 y = svtmad (y, r2, 4); 66 y = svtmad (y, r2, 3); 67 y = svtmad (y, r2, 2); 68 y = svtmad (y, r2, 1); 69 y = svtmad (y, r2, 0); 70 71 if (unlikely (svptest_any (pg, oob))) 72 return special_case (x, svmul_x (svnot_z (pg, oob), f, y), oob); 73 /* Apply factor. */ 74 return svmul_x (pg, f, y); 75 } 76 77 PL_SIG (SV, F, 1, cos, -3.1, 3.1) 78 PL_TEST_ULP (SV_NAME_F1 (cos), 1.57) 79 PL_TEST_INTERVAL (SV_NAME_F1 (cos), 0, 0xffff0000, 10000) 80 PL_TEST_INTERVAL (SV_NAME_F1 (cos), 0x1p-4, 0x1p4, 500000) 81