def remainder(x1, x2): x1, x2 = _promote_args("remainder", x1, x2) zero = _constant_like(x1, 0) trunc_mod = lax.rem(x1, x2) trunc_mod_not_zero = lax.ne(trunc_mod, zero) do_plus = lax.bitwise_and( lax.ne(lax.lt(trunc_mod, zero), lax.lt(x2, zero)), trunc_mod_not_zero) return lax.select(do_plus, lax.add(trunc_mod, x2), trunc_mod)
def fn(x1, x2): x1, x2 = _promote_args(numpy_fn.__name__, x1, x2) # Comparison on complex types are defined as a lexicographic ordering on # the (real, imag) pair. if dtypes.issubdtype(dtypes.dtype(x1), np.complexfloating): rx = lax.real(x1) ry = lax.real(x2) return lax.select(lax.eq(rx, ry), lax_fn(lax.imag(x1), lax.imag(x2)), lax_fn(rx, ry)) return lax_fn(x1, x2)
def _one_to_one_binop(numpy_fn, lax_fn, promote_to_inexact=False, lax_doc=False): if promote_to_inexact: fn = lambda x1, x2: lax_fn(*_promote_args_inexact(numpy_fn.__name__, x1, x2)) else: fn = lambda x1, x2: lax_fn(*_promote_args(numpy_fn.__name__, x1, x2)) fn = jit(fn, inline=True) if lax_doc: doc = dedent('\n\n'.join(lax_fn.__doc__.split('\n\n')[1:])).strip() return _wraps(numpy_fn, lax_description=doc)(fn) else: return _wraps(numpy_fn)(fn)
def _power(x1, x2): x1, x2 = _promote_args("power", x1, x2) dtype = dtypes.dtype(x1) if not dtypes.issubdtype(dtype, np.integer): return lax.pow(x1, x2) # Integer power => use binary exponentiation. # TODO(phawkins): add integer pow support to XLA. bits = 6 # Anything more would overflow for any x1 > 1 zero = _constant_like(x2, 0) one = _constant_like(x2, 1) # Initialize acc carefully such that pow(0, x2) is zero for x2 != 0 acc = _where(lax.bitwise_and(lax.eq(x1, zero), lax.ne(x2, zero)), zero, one) for _ in range(bits): acc = _where(lax.bitwise_and(x2, one), lax.mul(acc, x1), acc) x1 = lax.mul(x1, x1) x2 = lax.shift_right_logical(x2, one) return acc
def floor_divide(x1, x2): x1, x2 = _promote_args("floor_divide", x1, x2) dtype = dtypes.dtype(x1) if dtypes.issubdtype(dtype, np.integer): quotient = lax.div(x1, x2) select = logical_and(lax.sign(x1) != lax.sign(x2), lax.rem(x1, x2) != 0) # TODO(mattjj): investigate why subtracting a scalar was causing promotion return _where(select, quotient - 1, quotient) elif dtypes.issubdtype(dtype, np.complexfloating): x1r = lax.real(x1) x1i = lax.imag(x1) x2r = lax.real(x2) x2i = lax.imag(x2) which = lax.ge(lax.abs(x2r), lax.abs(x2i)) rat1 = _where(which, lax.full_like(x2i, 1), lax.div(x2r, x2i)) rat2 = _where(which, lax.div(x2i, x2r), _lax_const(x2i, 1)) out = lax.floor(lax.div(lax.add(lax.mul(x1r, rat1), lax.mul(x1i, rat2)), lax.add(lax.mul(x2r, rat1), lax.mul(x2i, rat2)))) return lax.convert_element_type(out, dtype) else: return _float_divmod(x1, x2)[0]
def signbit(x): x, = _promote_args("signbit", x) dtype = dtypes.dtype(x) if dtypes.issubdtype(dtype, np.integer): return lax.lt(x, _constant_like(x, 0)) elif dtypes.issubdtype(dtype, np.bool_): return lax.full_like(x, False, dtype=np.bool_) elif not dtypes.issubdtype(dtype, np.floating): raise ValueError("jax.numpy.signbit is not well defined for %s" % dtype) # TPU supports BF16 but not S16 types, so as a workaround, convert BF16 to # F32. if dtype == dtypes.bfloat16: dtype = np.float32 x = lax.convert_element_type(x, np.float32) info = dtypes.finfo(dtype) if info.bits not in _INT_DTYPES: raise NotImplementedError( "jax.numpy.signbit only supports 16, 32, and 64-bit types.") int_type = _INT_DTYPES[info.bits] x = lax.bitcast_convert_type(x, int_type) return lax.convert_element_type(x >> (info.nexp + info.nmant), np.bool_)
def fn(x1, x2): x1, x2 = _promote_args(numpy_fn.__name__, x1, x2) return lax_fn(x1, x2) if x1.dtype != np.bool_ else bool_lax_fn(x1, x2)
def fmod(x1, x2): _check_arraylike("fmod", x1, x2) if dtypes.issubdtype(dtypes.result_type(x1, x2), np.integer): x2 = _where(x2 == 0, lax_internal._ones(x2), x2) return lax.rem(*_promote_args("fmod", x1, x2))
def divmod(x1, x2): x1, x2 = _promote_args("divmod", x1, x2) if dtypes.issubdtype(dtypes.dtype(x1), np.integer): return floor_divide(x1, x2), remainder(x1, x2) else: return _float_divmod(x1, x2)
def right_shift(x1, x2): x1, x2 = _promote_args(np.right_shift.__name__, x1, x2) lax_fn = lax.shift_right_logical if \ np.issubdtype(x1.dtype, np.unsignedinteger) else lax.shift_right_arithmetic return lax_fn(x1, x2)
def op(*args): zero = lambda x: lax.full_like(x, shape=(), fill_value=0) args = (x if dtypes.issubdtype(dtypes.dtype(x), np.bool_) else lax.ne( x, zero(x)) for x in args) return bitwise_op(*_promote_args(np_op.__name__, *args))