# Copyright (c) 2024 Graphcore Ltd. All rights reserved.
import fractions
import numpy as np
[docs]def float_pow2str(v: float, min_exponent: float = -np.inf) -> str:
"""
Render floating point values as exact fractions times a power of two.
Example: float_pow2str(127.0) is "127/64*2^6",
That is (a significand between 1 and 2) times (a power of two).
If `min_exponent` is supplied, then values with exponent below `min_exponent`,
are printed as fractions less than 1, with exponent set to `min_exponent`.
This is typically used to represent subnormal values.
"""
if not np.isfinite(v):
return str(v)
signstr = "-" if np.signbit(v) else ""
x = np.abs(v)
e = int(np.floor(np.log2(x)))
sig = np.ldexp(x, -e)
if e < min_exponent:
sig = np.ldexp(sig, e - min_exponent)
e = int(min_exponent)
pow2str = f"2^{e:d}"
significand = fractions.Fraction(sig)
if significand == 1:
return signstr + pow2str
else:
return signstr + f"{significand}*{pow2str}"
[docs]def float_tilde_unless_roundtrip_str(v: float, width: int = 14, d: int = 8) -> str:
"""
Return a string representation of :paramref:`v`, in base 10,
with maximum width :paramref:`width` and decimal digits :paramref:`d`
"""
# valstr: string representation of value in base 10
# If the representation does not roundtrip to the value,
# it is preceded by a "~" to indicate "approximately equal to"
s = f"{v}"
if len(s) > width:
if abs(v) < 1 and "e" not in s:
s = f"{v:.{d}f}"
else:
s = f"{v:.{d}}"
if np.isfinite(v) and float(s) != v:
s = "~" + s
return s