/
mathimpl.py
453 lines (361 loc) · 15.1 KB
/
mathimpl.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
"""
Provide math calls that uses intrinsics or libc math functions.
"""
import math
import operator
import sys
import numpy as np
import llvmlite.ir
from llvmlite.ir import Constant
from numba.core.imputils import Registry, impl_ret_untracked
from numba import typeof
from numba.core import types, utils, config, cgutils
from numba.core.extending import overload
from numba.core.typing import signature
from numba.cpython.unsafe.numbers import trailing_zeros
registry = Registry('mathimpl')
lower = registry.lower
# Helpers, shared with cmathimpl.
_NP_FLT_FINFO = np.finfo(np.dtype('float32'))
FLT_MAX = _NP_FLT_FINFO.max
FLT_MIN = _NP_FLT_FINFO.tiny
_NP_DBL_FINFO = np.finfo(np.dtype('float64'))
DBL_MAX = _NP_DBL_FINFO.max
DBL_MIN = _NP_DBL_FINFO.tiny
FLOAT_ABS_MASK = 0x7fffffff
FLOAT_SIGN_MASK = 0x80000000
DOUBLE_ABS_MASK = 0x7fffffffffffffff
DOUBLE_SIGN_MASK = 0x8000000000000000
def is_nan(builder, val):
"""
Return a condition testing whether *val* is a NaN.
"""
return builder.fcmp_unordered('uno', val, val)
def is_inf(builder, val):
"""
Return a condition testing whether *val* is an infinite.
"""
pos_inf = Constant(val.type, float("+inf"))
neg_inf = Constant(val.type, float("-inf"))
isposinf = builder.fcmp_ordered('==', val, pos_inf)
isneginf = builder.fcmp_ordered('==', val, neg_inf)
return builder.or_(isposinf, isneginf)
def is_finite(builder, val):
"""
Return a condition testing whether *val* is a finite.
"""
# is_finite(x) <=> x - x != NaN
val_minus_val = builder.fsub(val, val)
return builder.fcmp_ordered('ord', val_minus_val, val_minus_val)
def f64_as_int64(builder, val):
"""
Bitcast a double into a 64-bit integer.
"""
assert val.type == llvmlite.ir.DoubleType()
return builder.bitcast(val, llvmlite.ir.IntType(64))
def int64_as_f64(builder, val):
"""
Bitcast a 64-bit integer into a double.
"""
assert val.type == llvmlite.ir.IntType(64)
return builder.bitcast(val, llvmlite.ir.DoubleType())
def f32_as_int32(builder, val):
"""
Bitcast a float into a 32-bit integer.
"""
assert val.type == llvmlite.ir.FloatType()
return builder.bitcast(val, llvmlite.ir.IntType(32))
def int32_as_f32(builder, val):
"""
Bitcast a 32-bit integer into a float.
"""
assert val.type == llvmlite.ir.IntType(32)
return builder.bitcast(val, llvmlite.ir.FloatType())
def negate_real(builder, val):
"""
Negate real number *val*, with proper handling of zeros.
"""
# The negative zero forces LLVM to handle signed zeros properly.
return builder.fsub(Constant(val.type, -0.0), val)
def call_fp_intrinsic(builder, name, args):
"""
Call a LLVM intrinsic floating-point operation.
"""
mod = builder.module
intr = mod.declare_intrinsic(name, [a.type for a in args])
return builder.call(intr, args)
def _unary_int_input_wrapper_impl(wrapped_impl):
"""
Return an implementation factory to convert the single integral input
argument to a float64, then defer to the *wrapped_impl*.
"""
def implementer(context, builder, sig, args):
val, = args
input_type = sig.args[0]
fpval = context.cast(builder, val, input_type, types.float64)
inner_sig = signature(types.float64, types.float64)
res = wrapped_impl(context, builder, inner_sig, (fpval,))
return context.cast(builder, res, types.float64, sig.return_type)
return implementer
def unary_math_int_impl(fn, float_impl):
impl = _unary_int_input_wrapper_impl(float_impl)
lower(fn, types.Integer)(impl)
def unary_math_intr(fn, intrcode):
"""
Implement the math function *fn* using the LLVM intrinsic *intrcode*.
"""
@lower(fn, types.Float)
def float_impl(context, builder, sig, args):
res = call_fp_intrinsic(builder, intrcode, args)
return impl_ret_untracked(context, builder, sig.return_type, res)
unary_math_int_impl(fn, float_impl)
return float_impl
def unary_math_extern(fn, f32extern, f64extern, int_restype=False):
"""
Register implementations of Python function *fn* using the
external function named *f32extern* and *f64extern* (for float32
and float64 inputs, respectively).
If *int_restype* is true, then the function's return value should be
integral, otherwise floating-point.
"""
f_restype = types.int64 if int_restype else None
def float_impl(context, builder, sig, args):
"""
Implement *fn* for a types.Float input.
"""
[val] = args
mod = builder.module
input_type = sig.args[0]
lty = context.get_value_type(input_type)
func_name = {
types.float32: f32extern,
types.float64: f64extern,
}[input_type]
fnty = llvmlite.ir.FunctionType(lty, [lty])
fn = cgutils.insert_pure_function(builder.module, fnty, name=func_name)
res = builder.call(fn, (val,))
res = context.cast(builder, res, input_type, sig.return_type)
return impl_ret_untracked(context, builder, sig.return_type, res)
lower(fn, types.Float)(float_impl)
# Implement wrapper for integer inputs
unary_math_int_impl(fn, float_impl)
return float_impl
unary_math_intr(math.fabs, 'llvm.fabs')
exp_impl = unary_math_intr(math.exp, 'llvm.exp')
log_impl = unary_math_intr(math.log, 'llvm.log')
log10_impl = unary_math_intr(math.log10, 'llvm.log10')
sin_impl = unary_math_intr(math.sin, 'llvm.sin')
cos_impl = unary_math_intr(math.cos, 'llvm.cos')
log1p_impl = unary_math_extern(math.log1p, "log1pf", "log1p")
expm1_impl = unary_math_extern(math.expm1, "expm1f", "expm1")
erf_impl = unary_math_extern(math.erf, "erff", "erf")
erfc_impl = unary_math_extern(math.erfc, "erfcf", "erfc")
tan_impl = unary_math_extern(math.tan, "tanf", "tan")
asin_impl = unary_math_extern(math.asin, "asinf", "asin")
acos_impl = unary_math_extern(math.acos, "acosf", "acos")
atan_impl = unary_math_extern(math.atan, "atanf", "atan")
asinh_impl = unary_math_extern(math.asinh, "asinhf", "asinh")
acosh_impl = unary_math_extern(math.acosh, "acoshf", "acosh")
atanh_impl = unary_math_extern(math.atanh, "atanhf", "atanh")
sinh_impl = unary_math_extern(math.sinh, "sinhf", "sinh")
cosh_impl = unary_math_extern(math.cosh, "coshf", "cosh")
tanh_impl = unary_math_extern(math.tanh, "tanhf", "tanh")
log2_impl = unary_math_extern(math.log2, "log2f", "log2")
ceil_impl = unary_math_extern(math.ceil, "ceilf", "ceil", True)
floor_impl = unary_math_extern(math.floor, "floorf", "floor", True)
gamma_impl = unary_math_extern(math.gamma, "numba_gammaf", "numba_gamma") # work-around
sqrt_impl = unary_math_extern(math.sqrt, "sqrtf", "sqrt")
trunc_impl = unary_math_extern(math.trunc, "truncf", "trunc", True)
lgamma_impl = unary_math_extern(math.lgamma, "lgammaf", "lgamma")
@lower(math.isnan, types.Float)
def isnan_float_impl(context, builder, sig, args):
[val] = args
res = is_nan(builder, val)
return impl_ret_untracked(context, builder, sig.return_type, res)
@lower(math.isnan, types.Integer)
def isnan_int_impl(context, builder, sig, args):
res = cgutils.false_bit
return impl_ret_untracked(context, builder, sig.return_type, res)
@lower(math.isinf, types.Float)
def isinf_float_impl(context, builder, sig, args):
[val] = args
res = is_inf(builder, val)
return impl_ret_untracked(context, builder, sig.return_type, res)
@lower(math.isinf, types.Integer)
def isinf_int_impl(context, builder, sig, args):
res = cgutils.false_bit
return impl_ret_untracked(context, builder, sig.return_type, res)
@lower(math.isfinite, types.Float)
def isfinite_float_impl(context, builder, sig, args):
[val] = args
res = is_finite(builder, val)
return impl_ret_untracked(context, builder, sig.return_type, res)
@lower(math.isfinite, types.Integer)
def isfinite_int_impl(context, builder, sig, args):
res = cgutils.true_bit
return impl_ret_untracked(context, builder, sig.return_type, res)
@lower(math.copysign, types.Float, types.Float)
def copysign_float_impl(context, builder, sig, args):
lty = args[0].type
mod = builder.module
fn = cgutils.get_or_insert_function(mod, llvmlite.ir.FunctionType(lty, (lty, lty)),
'llvm.copysign.%s' % lty.intrinsic_name)
res = builder.call(fn, args)
return impl_ret_untracked(context, builder, sig.return_type, res)
# -----------------------------------------------------------------------------
@lower(math.frexp, types.Float)
def frexp_impl(context, builder, sig, args):
val, = args
fltty = context.get_data_type(sig.args[0])
intty = context.get_data_type(sig.return_type[1])
expptr = cgutils.alloca_once(builder, intty, name='exp')
fnty = llvmlite.ir.FunctionType(fltty, (fltty, llvmlite.ir.PointerType(intty)))
fname = {
"float": "numba_frexpf",
"double": "numba_frexp",
}[str(fltty)]
fn = cgutils.get_or_insert_function(builder.module, fnty, fname)
res = builder.call(fn, (val, expptr))
res = cgutils.make_anonymous_struct(builder, (res, builder.load(expptr)))
return impl_ret_untracked(context, builder, sig.return_type, res)
@lower(math.ldexp, types.Float, types.intc)
def ldexp_impl(context, builder, sig, args):
val, exp = args
fltty, intty = map(context.get_data_type, sig.args)
fnty = llvmlite.ir.FunctionType(fltty, (fltty, intty))
fname = {
"float": "numba_ldexpf",
"double": "numba_ldexp",
}[str(fltty)]
fn = cgutils.insert_pure_function(builder.module, fnty, name=fname)
res = builder.call(fn, (val, exp))
return impl_ret_untracked(context, builder, sig.return_type, res)
# -----------------------------------------------------------------------------
@lower(math.atan2, types.int64, types.int64)
def atan2_s64_impl(context, builder, sig, args):
[y, x] = args
y = builder.sitofp(y, llvmlite.ir.DoubleType())
x = builder.sitofp(x, llvmlite.ir.DoubleType())
fsig = signature(types.float64, types.float64, types.float64)
return atan2_float_impl(context, builder, fsig, (y, x))
@lower(math.atan2, types.uint64, types.uint64)
def atan2_u64_impl(context, builder, sig, args):
[y, x] = args
y = builder.uitofp(y, llvmlite.ir.DoubleType())
x = builder.uitofp(x, llvmlite.ir.DoubleType())
fsig = signature(types.float64, types.float64, types.float64)
return atan2_float_impl(context, builder, fsig, (y, x))
@lower(math.atan2, types.Float, types.Float)
def atan2_float_impl(context, builder, sig, args):
assert len(args) == 2
mod = builder.module
ty = sig.args[0]
lty = context.get_value_type(ty)
func_name = {
types.float32: "atan2f",
types.float64: "atan2"
}[ty]
fnty = llvmlite.ir.FunctionType(lty, (lty, lty))
fn = cgutils.insert_pure_function(builder.module, fnty, name=func_name)
res = builder.call(fn, args)
return impl_ret_untracked(context, builder, sig.return_type, res)
# -----------------------------------------------------------------------------
@lower(math.hypot, types.int64, types.int64)
def hypot_s64_impl(context, builder, sig, args):
[x, y] = args
y = builder.sitofp(y, llvmlite.ir.DoubleType())
x = builder.sitofp(x, llvmlite.ir.DoubleType())
fsig = signature(types.float64, types.float64, types.float64)
res = hypot_float_impl(context, builder, fsig, (x, y))
return impl_ret_untracked(context, builder, sig.return_type, res)
@lower(math.hypot, types.uint64, types.uint64)
def hypot_u64_impl(context, builder, sig, args):
[x, y] = args
y = builder.sitofp(y, llvmlite.ir.DoubleType())
x = builder.sitofp(x, llvmlite.ir.DoubleType())
fsig = signature(types.float64, types.float64, types.float64)
res = hypot_float_impl(context, builder, fsig, (x, y))
return impl_ret_untracked(context, builder, sig.return_type, res)
@lower(math.hypot, types.Float, types.Float)
def hypot_float_impl(context, builder, sig, args):
xty, yty = sig.args
assert xty == yty == sig.return_type
x, y = args
# Windows has alternate names for hypot/hypotf, see
# https://msdn.microsoft.com/fr-fr/library/a9yb3dbt%28v=vs.80%29.aspx
fname = {
types.float32: "_hypotf" if sys.platform == 'win32' else "hypotf",
types.float64: "_hypot" if sys.platform == 'win32' else "hypot",
}[xty]
plat_hypot = types.ExternalFunction(fname, sig)
if sys.platform == 'win32' and config.MACHINE_BITS == 32:
inf = xty(float('inf'))
def hypot_impl(x, y):
if math.isinf(x) or math.isinf(y):
return inf
return plat_hypot(x, y)
else:
def hypot_impl(x, y):
return plat_hypot(x, y)
res = context.compile_internal(builder, hypot_impl, sig, args)
return impl_ret_untracked(context, builder, sig.return_type, res)
# -----------------------------------------------------------------------------
@lower(math.radians, types.Float)
def radians_float_impl(context, builder, sig, args):
[x] = args
coef = context.get_constant(sig.return_type, math.pi / 180)
res = builder.fmul(x, coef)
return impl_ret_untracked(context, builder, sig.return_type, res)
unary_math_int_impl(math.radians, radians_float_impl)
# -----------------------------------------------------------------------------
@lower(math.degrees, types.Float)
def degrees_float_impl(context, builder, sig, args):
[x] = args
coef = context.get_constant(sig.return_type, 180 / math.pi)
res = builder.fmul(x, coef)
return impl_ret_untracked(context, builder, sig.return_type, res)
unary_math_int_impl(math.degrees, degrees_float_impl)
# -----------------------------------------------------------------------------
@lower(math.pow, types.Float, types.Float)
@lower(math.pow, types.Float, types.Integer)
def pow_impl(context, builder, sig, args):
impl = context.get_function(operator.pow, sig)
return impl(builder, args)
# -----------------------------------------------------------------------------
def _unsigned(T):
"""Convert integer to unsigned integer of equivalent width."""
pass
@overload(_unsigned)
def _unsigned_impl(T):
if T in types.unsigned_domain:
return lambda T: T
elif T in types.signed_domain:
newT = getattr(types, 'uint{}'.format(T.bitwidth))
return lambda T: newT(T)
def gcd_impl(context, builder, sig, args):
xty, yty = sig.args
assert xty == yty == sig.return_type
x, y = args
def gcd(a, b):
"""
Stein's algorithm, heavily cribbed from Julia implementation.
"""
T = type(a)
if a == 0: return abs(b)
if b == 0: return abs(a)
za = trailing_zeros(a)
zb = trailing_zeros(b)
k = min(za, zb)
# Uses np.*_shift instead of operators due to return types
u = _unsigned(abs(np.right_shift(a, za)))
v = _unsigned(abs(np.right_shift(b, zb)))
while u != v:
if u > v:
u, v = v, u
v -= u
v = np.right_shift(v, trailing_zeros(v))
r = np.left_shift(T(u), k)
return r
res = context.compile_internal(builder, gcd, sig, args)
return impl_ret_untracked(context, builder, sig.return_type, res)
lower(math.gcd, types.Integer, types.Integer)(gcd_impl)