1 /* 2 * Single-precision vector tan(x) function. 3 * 4 * Copyright (c) 2021-2023, Arm Limited. 5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6 */ 7 8 #include "v_math.h" 9 #include "estrinf.h" 10 #include "pl_sig.h" 11 #include "pl_test.h" 12 13 #if V_SUPPORTED 14 15 /* Constants. */ 16 #define NegPio2_1 (v_f32 (-0x1.921fb6p+0f)) 17 #define NegPio2_2 (v_f32 (0x1.777a5cp-25f)) 18 #define NegPio2_3 (v_f32 (0x1.ee59dap-50f)) 19 #define InvPio2 (v_f32 (0x1.45f306p-1f)) 20 #define RangeVal (0x47000000) /* asuint32(0x1p15f). */ 21 #define TinyBound (0x30000000) /* asuint32 (0x1p-31). */ 22 #define Shift (v_f32 (0x1.8p+23f)) 23 #define AbsMask (v_u32 (0x7fffffff)) 24 25 #define poly(i) v_f32 (__tanf_poly_data.poly_tan[i]) 26 27 /* Special cases (fall back to scalar calls). */ 28 VPCS_ATTR 29 NOINLINE static v_f32_t 30 specialcase (v_f32_t x, v_f32_t y, v_u32_t cmp) 31 { 32 return v_call_f32 (tanf, x, y, cmp); 33 } 34 35 /* Use a full Estrin scheme to evaluate polynomial. */ 36 static inline v_f32_t 37 eval_poly (v_f32_t z) 38 { 39 v_f32_t z2 = z * z; 40 #if WANT_SIMD_EXCEPT 41 /* Tiny z (<= 0x1p-31) will underflow when calculating z^4. If fp exceptions 42 are to be triggered correctly, sidestep this by fixing such lanes to 0. */ 43 v_u32_t will_uflow = v_cond_u32 ((v_as_u32_f32 (z) & AbsMask) <= TinyBound); 44 if (unlikely (v_any_u32 (will_uflow))) 45 z2 = v_sel_f32 (will_uflow, v_f32 (0), z2); 46 #endif 47 v_f32_t z4 = z2 * z2; 48 return ESTRIN_5 (z, z2, z4, poly); 49 } 50 51 /* Fast implementation of Neon tanf. 52 Maximum error is 3.45 ULP: 53 __v_tanf(-0x1.e5f0cap+13) got 0x1.ff9856p-1 54 want 0x1.ff9850p-1. */ 55 VPCS_ATTR 56 v_f32_t V_NAME (tanf) (v_f32_t x) 57 { 58 v_f32_t special_arg = x; 59 v_u32_t ix = v_as_u32_f32 (x); 60 v_u32_t iax = ix & AbsMask; 61 62 /* iax >= RangeVal means x, if not inf or NaN, is too large to perform fast 63 regression. */ 64 #if WANT_SIMD_EXCEPT 65 /* If fp exceptions are to be triggered correctly, also special-case tiny 66 input, as this will load to overflow later. Fix any special lanes to 1 to 67 prevent any exceptions being triggered. */ 68 v_u32_t special = v_cond_u32 (iax - TinyBound >= RangeVal - TinyBound); 69 if (unlikely (v_any_u32 (special))) 70 x = v_sel_f32 (special, v_f32 (1.0f), x); 71 #else 72 /* Otherwise, special-case large and special values. */ 73 v_u32_t special = v_cond_u32 (iax >= RangeVal); 74 #endif 75 76 /* n = rint(x/(pi/2)). */ 77 v_f32_t q = v_fma_f32 (InvPio2, x, Shift); 78 v_f32_t n = q - Shift; 79 /* n is representable as a signed integer, simply convert it. */ 80 v_s32_t in = v_round_s32 (n); 81 /* Determine if x lives in an interval, where |tan(x)| grows to infinity. */ 82 v_s32_t alt = in & 1; 83 v_u32_t pred_alt = (alt != 0); 84 85 /* r = x - n * (pi/2) (range reduction into -pi./4 .. pi/4). */ 86 v_f32_t r; 87 r = v_fma_f32 (NegPio2_1, n, x); 88 r = v_fma_f32 (NegPio2_2, n, r); 89 r = v_fma_f32 (NegPio2_3, n, r); 90 91 /* If x lives in an interval, where |tan(x)| 92 - is finite, then use a polynomial approximation of the form 93 tan(r) ~ r + r^3 * P(r^2) = r + r * r^2 * P(r^2). 94 - grows to infinity then use symmetries of tangent and the identity 95 tan(r) = cotan(pi/2 - r) to express tan(x) as 1/tan(-r). Finally, use 96 the same polynomial approximation of tan as above. */ 97 98 /* Perform additional reduction if required. */ 99 v_f32_t z = v_sel_f32 (pred_alt, -r, r); 100 101 /* Evaluate polynomial approximation of tangent on [-pi/4, pi/4]. */ 102 v_f32_t z2 = r * r; 103 v_f32_t p = eval_poly (z2); 104 v_f32_t y = v_fma_f32 (z * z2, p, z); 105 106 /* Compute reciprocal and apply if required. */ 107 v_f32_t inv_y = v_div_f32 (v_f32 (1.0f), y); 108 y = v_sel_f32 (pred_alt, inv_y, y); 109 110 /* Fast reduction does not handle the x = -0.0 case well, 111 therefore it is fixed here. */ 112 y = v_sel_f32 (x == v_f32 (-0.0), x, y); 113 114 if (unlikely (v_any_u32 (special))) 115 return specialcase (special_arg, y, special); 116 return y; 117 } 118 VPCS_ALIAS 119 120 PL_SIG (V, F, 1, tan, -3.1, 3.1) 121 PL_TEST_ULP (V_NAME (tanf), 2.96) 122 PL_TEST_EXPECT_FENV (V_NAME (tanf), WANT_SIMD_EXCEPT) 123 PL_TEST_INTERVAL (V_NAME (tanf), -0.0, -0x1p126, 100) 124 PL_TEST_INTERVAL (V_NAME (tanf), 0x1p-149, 0x1p-126, 4000) 125 PL_TEST_INTERVAL (V_NAME (tanf), 0x1p-126, 0x1p-23, 50000) 126 PL_TEST_INTERVAL (V_NAME (tanf), 0x1p-23, 0.7, 50000) 127 PL_TEST_INTERVAL (V_NAME (tanf), 0.7, 1.5, 50000) 128 PL_TEST_INTERVAL (V_NAME (tanf), 1.5, 100, 50000) 129 PL_TEST_INTERVAL (V_NAME (tanf), 100, 0x1p17, 50000) 130 PL_TEST_INTERVAL (V_NAME (tanf), 0x1p17, inf, 50000) 131 #endif 132