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| 1 | +# Copyright 2025 Arm Limited and/or its affiliates. |
| 2 | +# |
| 3 | +# This source code is licensed under the BSD-style license found in the |
| 4 | +# LICENSE file in the root directory of this source tree. |
| 5 | + |
| 6 | +import logging |
| 7 | +from math import pi |
| 8 | + |
| 9 | +from executorch.backends.arm._passes import ArmPass |
| 10 | +from executorch.exir.dialects._ops import ops as exir_ops |
| 11 | + |
| 12 | + |
| 13 | +edge_atan = exir_ops.edge.aten.atan.default # MI case |
| 14 | + |
| 15 | + |
| 16 | +def _get_atan_ops(op): |
| 17 | + """Return the primitive ops required..""" |
| 18 | + if op is not edge_atan: |
| 19 | + raise RuntimeError(f"Can't decompose atan for op {op}") |
| 20 | + |
| 21 | + return ( |
| 22 | + exir_ops.edge.aten.mul.Tensor, |
| 23 | + exir_ops.edge.aten.mul.Scalar, |
| 24 | + exir_ops.edge.aten.add.Tensor, |
| 25 | + exir_ops.edge.aten.add.Scalar, |
| 26 | + exir_ops.edge.aten.sub.Tensor, |
| 27 | + exir_ops.edge.aten.abs.default, |
| 28 | + exir_ops.edge.aten.gt.Scalar, |
| 29 | + exir_ops.edge.aten.reciprocal.default, |
| 30 | + exir_ops.edge.aten.where.self, |
| 31 | + exir_ops.edge.aten.neg.default, |
| 32 | + ) |
| 33 | + |
| 34 | + |
| 35 | +class DecomposeAtanPass(ArmPass): |
| 36 | + """Decomposes the atan operator into a rational (Padé) approximation.""" |
| 37 | + |
| 38 | + def _rational_approximation(self, z, ops, meta): |
| 39 | + """Creates a (2,1) Padé approximation for atan(x) on [-1, 1].""" |
| 40 | + |
| 41 | + op_mul, op_mul_scalar, op_add, op_add_scalar, _, _, _, op_recip, _, _ = ops |
| 42 | + |
| 43 | + # Coefficients calculated using minimax on the interval [-1, 1]. |
| 44 | + a1 = 0.3529666667 |
| 45 | + a2 = -0.0287666667 |
| 46 | + b1 = 0.6863 |
| 47 | + |
| 48 | + z2 = super().call_operator(op_mul, (z, z), {}, meta, updated=True) |
| 49 | + z4 = super().call_operator(op_mul, (z2, z2), {}, meta, updated=True) |
| 50 | + |
| 51 | + num1 = super().call_operator(op_mul_scalar, (z2, a1), {}, meta, updated=True) |
| 52 | + num2 = super().call_operator(op_mul_scalar, (z4, a2), {}, meta, updated=True) |
| 53 | + num = super().call_operator(op_add_scalar, (num1, 1.0), {}, meta, updated=True) |
| 54 | + num = super().call_operator(op_add, (num, num2), {}, meta, updated=True) |
| 55 | + |
| 56 | + den1 = super().call_operator(op_mul_scalar, (z2, b1), {}, meta, updated=True) |
| 57 | + den = super().call_operator(op_add_scalar, (den1, 1.0), {}, meta, updated=True) |
| 58 | + |
| 59 | + inv_den = super().call_operator(op_recip, (den,), {}, meta, updated=True) |
| 60 | + |
| 61 | + prod = super().call_operator(op_mul, (num, inv_den), {}, meta, updated=True) |
| 62 | + return super().call_operator(op_mul, (z, prod), {}, meta, updated=True) |
| 63 | + |
| 64 | + def call_operator(self, op, args, kwargs, meta): |
| 65 | + if op is not edge_atan: |
| 66 | + return super().call_operator(op, args, kwargs, meta, updated=False) |
| 67 | + |
| 68 | + logging.info( |
| 69 | + f"Approximating atan. This may introduce small numerical errors. For details, see {__file__}." |
| 70 | + ) |
| 71 | + |
| 72 | + ops = _get_atan_ops(op) |
| 73 | + ( |
| 74 | + _, |
| 75 | + op_mul_scalar, |
| 76 | + _, |
| 77 | + op_add_scalar, |
| 78 | + op_sub, |
| 79 | + op_abs, |
| 80 | + op_gt, |
| 81 | + op_recip, |
| 82 | + op_where, |
| 83 | + op_neg, |
| 84 | + ) = ops |
| 85 | + |
| 86 | + x = args[0] |
| 87 | + |
| 88 | + # |x| > 1 is reduced to [0, 1] using atan(x) = pi/2 - atan(1/x) and atan(-x) = -atan(x). |
| 89 | + |
| 90 | + abs_x = super().call_operator(op_abs, (x,), {}, meta, updated=True) |
| 91 | + mask_hi = super().call_operator(op_gt, (abs_x, 1.0), {}, meta, updated=True) |
| 92 | + |
| 93 | + inv_x = super().call_operator(op_recip, (abs_x,), {}, meta, updated=True) |
| 94 | + z = super().call_operator( |
| 95 | + op_where, (mask_hi, inv_x, abs_x), {}, meta, updated=True |
| 96 | + ) |
| 97 | + |
| 98 | + atan_z = self._rational_approximation(z, ops, meta) |
| 99 | + |
| 100 | + zero_tensor = super().call_operator( |
| 101 | + op_mul_scalar, (x, 0.0), {}, meta, updated=True |
| 102 | + ) |
| 103 | + half_pi_tensor = super().call_operator( |
| 104 | + op_add_scalar, (zero_tensor, pi / 2), {}, meta, updated=True |
| 105 | + ) |
| 106 | + |
| 107 | + diff = super().call_operator( |
| 108 | + op_sub, (half_pi_tensor, atan_z), {}, meta, updated=True |
| 109 | + ) |
| 110 | + atan_abs = super().call_operator( |
| 111 | + op_where, (mask_hi, diff, atan_z), {}, meta, updated=True |
| 112 | + ) |
| 113 | + |
| 114 | + mask_pos = super().call_operator(op_gt, (x, 0.0), {}, meta, updated=True) |
| 115 | + neg_val = super().call_operator(op_neg, (atan_abs,), {}, meta, updated=True) |
| 116 | + |
| 117 | + return super().call_operator( |
| 118 | + op_where, (mask_pos, atan_abs, neg_val), {}, meta, updated=True |
| 119 | + ) |
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