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 "poly_advsimd_f32.h" 10 #include "pl_sig.h" 11 #include "pl_test.h" 12 13 static const struct data 14 { 15 float32x4_t poly[6]; 16 float32x4_t pi_consts; 17 float32x4_t shift; 18 #if !WANT_SIMD_EXCEPT 19 float32x4_t range_val; 20 #endif 21 } data = { 22 /* Coefficients generated using FPMinimax. */ 23 .poly = { V4 (0x1.55555p-2f), V4 (0x1.11166p-3f), V4 (0x1.b88a78p-5f), 24 V4 (0x1.7b5756p-6f), V4 (0x1.4ef4cep-8f), V4 (0x1.0e1e74p-7f) }, 25 /* Stores constants: (-pi/2)_high, (-pi/2)_mid, (-pi/2)_low, and 2/pi. */ 26 .pi_consts 27 = { -0x1.921fb6p+0f, 0x1.777a5cp-25f, 0x1.ee59dap-50f, 0x1.45f306p-1f }, 28 .shift = V4 (0x1.8p+23f), 29 #if !WANT_SIMD_EXCEPT 30 .range_val = V4 (0x1p15f), 31 #endif 32 }; 33 34 #define RangeVal v_u32 (0x47000000) /* asuint32(0x1p15f). */ 35 #define TinyBound v_u32 (0x30000000) /* asuint32 (0x1p-31f). */ 36 #define Thresh v_u32 (0x16000000) /* asuint32(RangeVal) - TinyBound. */ 37 38 /* Special cases (fall back to scalar calls). */ 39 static float32x4_t VPCS_ATTR NOINLINE 40 special_case (float32x4_t x, float32x4_t y, uint32x4_t cmp) 41 { 42 return v_call_f32 (tanf, x, y, cmp); 43 } 44 45 /* Use a full Estrin scheme to evaluate polynomial. */ 46 static inline float32x4_t 47 eval_poly (float32x4_t z, const struct data *d) 48 { 49 float32x4_t z2 = vmulq_f32 (z, z); 50 #if WANT_SIMD_EXCEPT 51 /* Tiny z (<= 0x1p-31) will underflow when calculating z^4. 52 If fp exceptions are to be triggered correctly, 53 sidestep this by fixing such lanes to 0. */ 54 uint32x4_t will_uflow 55 = vcleq_u32 (vreinterpretq_u32_f32 (vabsq_f32 (z)), TinyBound); 56 if (unlikely (v_any_u32 (will_uflow))) 57 z2 = vbslq_f32 (will_uflow, v_f32 (0), z2); 58 #endif 59 float32x4_t z4 = vmulq_f32 (z2, z2); 60 return v_estrin_5_f32 (z, z2, z4, d->poly); 61 } 62 63 /* Fast implementation of AdvSIMD tanf. 64 Maximum error is 3.45 ULP: 65 __v_tanf(-0x1.e5f0cap+13) got 0x1.ff9856p-1 66 want 0x1.ff9850p-1. */ 67 float32x4_t VPCS_ATTR V_NAME_F1 (tan) (float32x4_t x) 68 { 69 const struct data *d = ptr_barrier (&data); 70 float32x4_t special_arg = x; 71 72 /* iax >= RangeVal means x, if not inf or NaN, is too large to perform fast 73 regression. */ 74 #if WANT_SIMD_EXCEPT 75 uint32x4_t iax = vreinterpretq_u32_f32 (vabsq_f32 (x)); 76 /* If fp exceptions are to be triggered correctly, also special-case tiny 77 input, as this will load to overflow later. Fix any special lanes to 1 to 78 prevent any exceptions being triggered. */ 79 uint32x4_t special = vcgeq_u32 (vsubq_u32 (iax, TinyBound), Thresh); 80 if (unlikely (v_any_u32 (special))) 81 x = vbslq_f32 (special, v_f32 (1.0f), x); 82 #else 83 /* Otherwise, special-case large and special values. */ 84 uint32x4_t special = vcageq_f32 (x, d->range_val); 85 #endif 86 87 /* n = rint(x/(pi/2)). */ 88 float32x4_t q = vfmaq_laneq_f32 (d->shift, x, d->pi_consts, 3); 89 float32x4_t n = vsubq_f32 (q, d->shift); 90 /* Determine if x lives in an interval, where |tan(x)| grows to infinity. */ 91 uint32x4_t pred_alt = vtstq_u32 (vreinterpretq_u32_f32 (q), v_u32 (1)); 92 93 /* r = x - n * (pi/2) (range reduction into -pi./4 .. pi/4). */ 94 float32x4_t r; 95 r = vfmaq_laneq_f32 (x, n, d->pi_consts, 0); 96 r = vfmaq_laneq_f32 (r, n, d->pi_consts, 1); 97 r = vfmaq_laneq_f32 (r, n, d->pi_consts, 2); 98 99 /* If x lives in an interval, where |tan(x)| 100 - is finite, then use a polynomial approximation of the form 101 tan(r) ~ r + r^3 * P(r^2) = r + r * r^2 * P(r^2). 102 - grows to infinity then use symmetries of tangent and the identity 103 tan(r) = cotan(pi/2 - r) to express tan(x) as 1/tan(-r). Finally, use 104 the same polynomial approximation of tan as above. */ 105 106 /* Invert sign of r if odd quadrant. */ 107 float32x4_t z = vmulq_f32 (r, vbslq_f32 (pred_alt, v_f32 (-1), v_f32 (1))); 108 109 /* Evaluate polynomial approximation of tangent on [-pi/4, pi/4]. */ 110 float32x4_t z2 = vmulq_f32 (r, r); 111 float32x4_t p = eval_poly (z2, d); 112 float32x4_t y = vfmaq_f32 (z, vmulq_f32 (z, z2), p); 113 114 /* Compute reciprocal and apply if required. */ 115 float32x4_t inv_y = vdivq_f32 (v_f32 (1.0f), y); 116 117 if (unlikely (v_any_u32 (special))) 118 return special_case (special_arg, vbslq_f32 (pred_alt, inv_y, y), special); 119 return vbslq_f32 (pred_alt, inv_y, y); 120 } 121 122 PL_SIG (V, F, 1, tan, -3.1, 3.1) 123 PL_TEST_ULP (V_NAME_F1 (tan), 2.96) 124 PL_TEST_EXPECT_FENV (V_NAME_F1 (tan), WANT_SIMD_EXCEPT) 125 PL_TEST_SYM_INTERVAL (V_NAME_F1 (tan), 0, 0x1p-31, 5000) 126 PL_TEST_SYM_INTERVAL (V_NAME_F1 (tan), 0x1p-31, 0x1p15, 500000) 127 PL_TEST_SYM_INTERVAL (V_NAME_F1 (tan), 0x1p15, inf, 5000) 128