prompt: We are currently solving the following issue within our repository. Here is the issue text:
  --- BEGIN ISSUE ---
  rfftfreq
  
  
  --- END ISSUE ---
  
  Below are some code segments, each from a relevant file. One or more of these files may contain bugs.
  --- BEGIN FILES ---
  Path: `ivy/functional/frontends/paddle/fft.py`
  Content:
  ```
  1 # global
  2 import ivy
  3 from ivy.func_wrapper import with_supported_dtypes
  4 from ivy.functional.frontends.paddle.func_wrapper import (
  5     to_ivy_arrays_and_back,
  6 )
  7 
  8 
  9 @with_supported_dtypes(
  10     {"2.5.1 and below": ("complex64", "complex128")},
  11     "paddle",
  12 )
  13 @to_ivy_arrays_and_back
  14 def fft(x, n=None, axis=-1.0, norm="backward", name=None):
  15     ret = ivy.fft(ivy.astype(x, "complex128"), axis, norm=norm, n=n)
  16     return ivy.astype(ret, x.dtype)
  17 
  18 
  19 @with_supported_dtypes(
  20     {
  21         "2.5.1 and below": (
  22             "int32",
  23             "int64",
  24             "float32",
  25             "float64",
  26             "complex64",
  27             "complex128",
  28         )
  29     },
  30     "paddle",
  31 )
  32 @to_ivy_arrays_and_back
  33 def fftshift(x, axes=None, name=None):
  34     shape = x.shape
  35 
  36     if axes is None:
  37         axes = tuple(range(x.ndim))
  38         shifts = [(dim // 2) for dim in shape]
  39     elif isinstance(axes, int):
  40         shifts = shape[axes] // 2
  41     else:
  42         shifts = ivy.concat([shape[ax] // 2 for ax in axes])
  43 
  44     roll = ivy.roll(x, shifts, axis=axes)
  45 
  46     return roll
  47 
  48 
  49 @with_supported_dtypes(
  50     {"2.5.1 and below": ("complex64", "complex128")},
  51     "paddle",
  52 )
  53 @to_ivy_arrays_and_back
  54 def hfft(x, n=None, axis=-1, norm="backward", name=None):
  55     """Compute the FFT of a signal that has Hermitian symmetry, resulting in a real
  56     spectrum."""
  57     # Determine the input shape and axis length
  58     input_shape = x.shape
  59     input_len = input_shape[axis]
  60 
  61     # Calculate n if not provided
  62     if n is None:
  63         n = 2 * (input_len - 1)
  64 
  65     # Perform the FFT along the specified axis
  66     result = ivy.fft(x, axis, n=n, norm=norm)
  67 
  68     return ivy.real(result)
  69 
  70 
  71 @with_supported_dtypes(
  72     {"2.5.1 and below": ("complex64", "complex128")},
  73     "paddle",
  74 )
  75 @to_ivy_arrays_and_back
  76 def ifft(x, n=None, axis=-1.0, norm="backward", name=None):
  77     ret = ivy.ifft(ivy.astype(x, "complex128"), axis, norm=norm, n=n)
  78     return ivy.astype(ret, x.dtype)
  79 
  80 
  81 @with_supported_dtypes(
  82     {
  83         "2.5.1 and below": (
  84             "int32",
  85             "int64",
  86             "float32",
  87             "float64",
  88         )
  89     },
  90     "paddle",
  91 )
  92 @to_ivy_arrays_and_back
  93 def ifftshift(x, axes=None, name=None):
  94     shape = x.shape
  95 
  96     if axes is None:
  97         axes = tuple(range(x.ndim))
  98         shifts = [-(dim // 2) for dim in shape]
  99     elif isinstance(axes, int):
  100         shifts = -(shape[axes] // 2)
  101     else:
  102         shifts = ivy.concat([-shape[ax] // 2 for ax in axes])
  103 
  104     roll = ivy.roll(x, shifts, axis=axes)
  105 
  106     return roll
  107 
  108 
  109 @with_supported_dtypes(
  110     {"2.5.1 and below": ("complex64", "complex128")},
  111     "paddle",
  112 )
  113 @to_ivy_arrays_and_back
  114 def irfft(x, n=None, axis=-1.0, norm="backward", name=None):
  115     if n is None:
  116         n = 2 * (x.shape[axis] - 1)
  117 
  118     pos_freq_terms = ivy.take_along_axis(x, range(n // 2 + 1), axis)
  119     neg_freq_terms = ivy.conj(pos_freq_terms[1:-1][::-1])
  120     combined_freq_terms = ivy.concat((pos_freq_terms, neg_freq_terms), axis=axis)
  121     time_domain = ivy.ifft(combined_freq_terms, axis, norm=norm, n=n)
  122     if ivy.isreal(x):
  123         time_domain = ivy.real(time_domain)
  124     return time_domain
  125
  ```
  --- END FILES ---
  
  Please first localize the bug based on the issue statement, and then generate a patch according to the `git diff` format fenced by three backticks.
  
  Here is an example:
  
  ```diff
  diff --git a/examples/server_async.py b/examples/server_async.py
  --- a/examples/server_async.py
  +++ b/examples/server_async.py
  @@ -313,4 +313,4 @@
   
   
   if __name__ == "__main__":
  -    asyncio.run(run_async_server("."), debug=True)
  +    asyncio.run(run_async_server(), debug=True)
  diff --git a/examples/server_sync.py b/examples/server_sync.py
  --- a/examples/server_sync.py
  +++ b/examples/server_sync.py
  @@ -313,5 +313,5 @@
   
   
   if __name__ == "__main__":
  -    server = run_sync_server(".")
  +    server = run_sync_server()
       server.shutdown()
  
  ```
  
golden_diff: diff --git a/ivy/functional/frontends/paddle/fft.py b/ivy/functional/frontends/paddle/fft.py
  --- a/ivy/functional/frontends/paddle/fft.py
  +++ b/ivy/functional/frontends/paddle/fft.py
  @@ -122,3 +122,12 @@
       if ivy.isreal(x):
           time_domain = ivy.real(time_domain)
       return time_domain
  +
  +
  +@to_ivy_arrays_and_back
  +def rfftfreq(n, d=1.0, dtype=None, name=None):
  +    dtype = ivy.default_dtype()
  +    val = 1.0 / (n * d)
  +    pos_max = n // 2 + 1
  +    indices = ivy.arange(0, pos_max, dtype=dtype)
  +    return indices * val
  
verification_info: {"golden_diff": "diff --git a/ivy/functional/frontends/paddle/fft.py b/ivy/functional/frontends/paddle/fft.py\n--- a/ivy/functional/frontends/paddle/fft.py\n+++ b/ivy/functional/frontends/paddle/fft.py\n@@ -122,3 +122,12 @@\n     if ivy.isreal(x):\n         time_domain = ivy.real(time_domain)\n     return time_domain\n+\n+\n+@to_ivy_arrays_and_back\n+def rfftfreq(n, d=1.0, dtype=None, name=None):\n+    dtype = ivy.default_dtype()\n+    val = 1.0 / (n * d)\n+    pos_max = n // 2 + 1\n+    indices = ivy.arange(0, pos_max, dtype=dtype)\n+    return indices * val\n", "issue": "rfftfreq\n\n", "before_files": [{"content": "# global\nimport ivy\nfrom ivy.func_wrapper import with_supported_dtypes\nfrom ivy.functional.frontends.paddle.func_wrapper import (\n    to_ivy_arrays_and_back,\n)\n\n\n@with_supported_dtypes(\n    {\"2.5.1 and below\": (\"complex64\", \"complex128\")},\n    \"paddle\",\n)\n@to_ivy_arrays_and_back\ndef fft(x, n=None, axis=-1.0, norm=\"backward\", name=None):\n    ret = ivy.fft(ivy.astype(x, \"complex128\"), axis, norm=norm, n=n)\n    return ivy.astype(ret, x.dtype)\n\n\n@with_supported_dtypes(\n    {\n        \"2.5.1 and below\": (\n            \"int32\",\n            \"int64\",\n            \"float32\",\n            \"float64\",\n            \"complex64\",\n            \"complex128\",\n        )\n    },\n    \"paddle\",\n)\n@to_ivy_arrays_and_back\ndef fftshift(x, axes=None, name=None):\n    shape = x.shape\n\n    if axes is None:\n        axes = tuple(range(x.ndim))\n        shifts = [(dim // 2) for dim in shape]\n    elif isinstance(axes, int):\n        shifts = shape[axes] // 2\n    else:\n        shifts = ivy.concat([shape[ax] // 2 for ax in axes])\n\n    roll = ivy.roll(x, shifts, axis=axes)\n\n    return roll\n\n\n@with_supported_dtypes(\n    {\"2.5.1 and below\": (\"complex64\", \"complex128\")},\n    \"paddle\",\n)\n@to_ivy_arrays_and_back\ndef hfft(x, n=None, axis=-1, norm=\"backward\", name=None):\n    \"\"\"Compute the FFT of a signal that has Hermitian symmetry, resulting in a real\n    spectrum.\"\"\"\n    # Determine the input shape and axis length\n    input_shape = x.shape\n    input_len = input_shape[axis]\n\n    # Calculate n if not provided\n    if n is None:\n        n = 2 * (input_len - 1)\n\n    # Perform the FFT along the specified axis\n    result = ivy.fft(x, axis, n=n, norm=norm)\n\n    return ivy.real(result)\n\n\n@with_supported_dtypes(\n    {\"2.5.1 and below\": (\"complex64\", \"complex128\")},\n    \"paddle\",\n)\n@to_ivy_arrays_and_back\ndef ifft(x, n=None, axis=-1.0, norm=\"backward\", name=None):\n    ret = ivy.ifft(ivy.astype(x, \"complex128\"), axis, norm=norm, n=n)\n    return ivy.astype(ret, x.dtype)\n\n\n@with_supported_dtypes(\n    {\n        \"2.5.1 and below\": (\n            \"int32\",\n            \"int64\",\n            \"float32\",\n            \"float64\",\n        )\n    },\n    \"paddle\",\n)\n@to_ivy_arrays_and_back\ndef ifftshift(x, axes=None, name=None):\n    shape = x.shape\n\n    if axes is None:\n        axes = tuple(range(x.ndim))\n        shifts = [-(dim // 2) for dim in shape]\n    elif isinstance(axes, int):\n        shifts = -(shape[axes] // 2)\n    else:\n        shifts = ivy.concat([-shape[ax] // 2 for ax in axes])\n\n    roll = ivy.roll(x, shifts, axis=axes)\n\n    return roll\n\n\n@with_supported_dtypes(\n    {\"2.5.1 and below\": (\"complex64\", \"complex128\")},\n    \"paddle\",\n)\n@to_ivy_arrays_and_back\ndef irfft(x, n=None, axis=-1.0, norm=\"backward\", name=None):\n    if n is None:\n        n = 2 * (x.shape[axis] - 1)\n\n    pos_freq_terms = ivy.take_along_axis(x, range(n // 2 + 1), axis)\n    neg_freq_terms = ivy.conj(pos_freq_terms[1:-1][::-1])\n    combined_freq_terms = ivy.concat((pos_freq_terms, neg_freq_terms), axis=axis)\n    time_domain = ivy.ifft(combined_freq_terms, axis, norm=norm, n=n)\n    if ivy.isreal(x):\n        time_domain = ivy.real(time_domain)\n    return time_domain\n", "path": "ivy/functional/frontends/paddle/fft.py"}], "after_files": [{"content": "# global\nimport ivy\nfrom ivy.func_wrapper import with_supported_dtypes\nfrom ivy.functional.frontends.paddle.func_wrapper import (\n    to_ivy_arrays_and_back,\n)\n\n\n@with_supported_dtypes(\n    {\"2.5.1 and below\": (\"complex64\", \"complex128\")},\n    \"paddle\",\n)\n@to_ivy_arrays_and_back\ndef fft(x, n=None, axis=-1.0, norm=\"backward\", name=None):\n    ret = ivy.fft(ivy.astype(x, \"complex128\"), axis, norm=norm, n=n)\n    return ivy.astype(ret, x.dtype)\n\n\n@with_supported_dtypes(\n    {\n        \"2.5.1 and below\": (\n            \"int32\",\n            \"int64\",\n            \"float32\",\n            \"float64\",\n            \"complex64\",\n            \"complex128\",\n        )\n    },\n    \"paddle\",\n)\n@to_ivy_arrays_and_back\ndef fftshift(x, axes=None, name=None):\n    shape = x.shape\n\n    if axes is None:\n        axes = tuple(range(x.ndim))\n        shifts = [(dim // 2) for dim in shape]\n    elif isinstance(axes, int):\n        shifts = shape[axes] // 2\n    else:\n        shifts = ivy.concat([shape[ax] // 2 for ax in axes])\n\n    roll = ivy.roll(x, shifts, axis=axes)\n\n    return roll\n\n\n@with_supported_dtypes(\n    {\"2.5.1 and below\": (\"complex64\", \"complex128\")},\n    \"paddle\",\n)\n@to_ivy_arrays_and_back\ndef hfft(x, n=None, axis=-1, norm=\"backward\", name=None):\n    \"\"\"Compute the FFT of a signal that has Hermitian symmetry, resulting in a real\n    spectrum.\"\"\"\n    # Determine the input shape and axis length\n    input_shape = x.shape\n    input_len = input_shape[axis]\n\n    # Calculate n if not provided\n    if n is None:\n        n = 2 * (input_len - 1)\n\n    # Perform the FFT along the specified axis\n    result = ivy.fft(x, axis, n=n, norm=norm)\n\n    return ivy.real(result)\n\n\n@with_supported_dtypes(\n    {\"2.5.1 and below\": (\"complex64\", \"complex128\")},\n    \"paddle\",\n)\n@to_ivy_arrays_and_back\ndef ifft(x, n=None, axis=-1.0, norm=\"backward\", name=None):\n    ret = ivy.ifft(ivy.astype(x, \"complex128\"), axis, norm=norm, n=n)\n    return ivy.astype(ret, x.dtype)\n\n\n@with_supported_dtypes(\n    {\n        \"2.5.1 and below\": (\n            \"int32\",\n            \"int64\",\n            \"float32\",\n            \"float64\",\n        )\n    },\n    \"paddle\",\n)\n@to_ivy_arrays_and_back\ndef ifftshift(x, axes=None, name=None):\n    shape = x.shape\n\n    if axes is None:\n        axes = tuple(range(x.ndim))\n        shifts = [-(dim // 2) for dim in shape]\n    elif isinstance(axes, int):\n        shifts = -(shape[axes] // 2)\n    else:\n        shifts = ivy.concat([-shape[ax] // 2 for ax in axes])\n\n    roll = ivy.roll(x, shifts, axis=axes)\n\n    return roll\n\n\n@with_supported_dtypes(\n    {\"2.5.1 and below\": (\"complex64\", \"complex128\")},\n    \"paddle\",\n)\n@to_ivy_arrays_and_back\ndef irfft(x, n=None, axis=-1.0, norm=\"backward\", name=None):\n    if n is None:\n        n = 2 * (x.shape[axis] - 1)\n\n    pos_freq_terms = ivy.take_along_axis(x, range(n // 2 + 1), axis)\n    neg_freq_terms = ivy.conj(pos_freq_terms[1:-1][::-1])\n    combined_freq_terms = ivy.concat((pos_freq_terms, neg_freq_terms), axis=axis)\n    time_domain = ivy.ifft(combined_freq_terms, axis, norm=norm, n=n)\n    if ivy.isreal(x):\n        time_domain = ivy.real(time_domain)\n    return time_domain\n\n\n@to_ivy_arrays_and_back\ndef rfftfreq(n, d=1.0, dtype=None, name=None):\n    dtype = ivy.default_dtype()\n    val = 1.0 / (n * d)\n    pos_max = n // 2 + 1\n    indices = ivy.arange(0, pos_max, dtype=dtype)\n    return indices * val\n", "path": "ivy/functional/frontends/paddle/fft.py"}]}