1// RUN: mlir-opt %s -test-math-polynomial-approximation | FileCheck %s
2
3// Check that all math functions lowered to approximations built from
4// standard operations (add, mul, fma, shift, etc...).
5
6// CHECK-LABEL:   func @exp_scalar(
7// CHECK-SAME:                     %[[VAL_0:.*]]: f32) -> f32 {
8// CHECK-DAG:           %[[VAL_1:.*]] = constant 0.693147182 : f32
9// CHECK-DAG:           %[[VAL_2:.*]] = constant 1.44269502 : f32
10// CHECK-DAG:           %[[VAL_3:.*]] = constant 1.000000e+00 : f32
11// CHECK-DAG:           %[[VAL_4:.*]] = constant 0.499705136 : f32
12// CHECK-DAG:           %[[VAL_5:.*]] = constant 0.168738902 : f32
13// CHECK-DAG:           %[[VAL_6:.*]] = constant 0.0366896503 : f32
14// CHECK-DAG:           %[[VAL_7:.*]] = constant 1.314350e-02 : f32
15// CHECK-DAG:           %[[VAL_8:.*]] = constant 23 : i32
16// CHECK-DAG:           %[[VAL_9:.*]] = constant 0.000000e+00 : f32
17// CHECK-DAG:           %[[VAL_10:.*]] = constant 0x7F800000 : f32
18// CHECK-DAG:           %[[VAL_11:.*]] = constant 0xFF800000 : f32
19// CHECK-DAG:           %[[VAL_12:.*]] = constant 1.17549435E-38 : f32
20// CHECK-DAG:           %[[VAL_13:.*]] = constant 127 : i32
21// CHECK-DAG:           %[[VAL_14:.*]] = constant -127 : i32
22// CHECK:           %[[VAL_15:.*]] = mulf %[[VAL_0]], %[[VAL_2]] : f32
23// CHECK:           %[[VAL_16:.*]] = floorf %[[VAL_15]] : f32
24// CHECK:           %[[VAL_17:.*]] = mulf %[[VAL_16]], %[[VAL_1]] : f32
25// CHECK:           %[[VAL_18:.*]] = subf %[[VAL_0]], %[[VAL_17]] : f32
26// CHECK:           %[[VAL_19:.*]] = mulf %[[VAL_18]], %[[VAL_18]] : f32
27// CHECK:           %[[VAL_20:.*]] = mulf %[[VAL_19]], %[[VAL_19]] : f32
28// CHECK:           %[[VAL_21:.*]] = fmaf %[[VAL_3]], %[[VAL_18]], %[[VAL_3]] : f32
29// CHECK:           %[[VAL_22:.*]] = fmaf %[[VAL_5]], %[[VAL_18]], %[[VAL_4]] : f32
30// CHECK:           %[[VAL_23:.*]] = fmaf %[[VAL_7]], %[[VAL_18]], %[[VAL_6]] : f32
31// CHECK:           %[[VAL_24:.*]] = fmaf %[[VAL_22]], %[[VAL_19]], %[[VAL_21]] : f32
32// CHECK:           %[[VAL_25:.*]] = fmaf %[[VAL_23]], %[[VAL_20]], %[[VAL_24]] : f32
33// CHECK:           %[[VAL_26:.*]] = fptosi %[[VAL_16]] : f32 to i32
34// CHECK:           %[[VAL_27:.*]] = addi %[[VAL_26]], %[[VAL_13]] : i32
35// CHECK:           %[[VAL_28:.*]] = shift_left %[[VAL_27]], %[[VAL_8]] : i32
36// CHECK:           %[[VAL_29:.*]] = bitcast %[[VAL_28]] : i32 to f32
37// CHECK:           %[[VAL_30:.*]] = mulf %[[VAL_25]], %[[VAL_29]] : f32
38// CHECK:           %[[VAL_31:.*]] = cmpi sle, %[[VAL_26]], %[[VAL_13]] : i32
39// CHECK:           %[[VAL_32:.*]] = cmpi sge, %[[VAL_26]], %[[VAL_14]] : i32
40// CHECK:           %[[VAL_33:.*]] = cmpf oeq, %[[VAL_0]], %[[VAL_11]] : f32
41// CHECK:           %[[VAL_34:.*]] = cmpf ogt, %[[VAL_0]], %[[VAL_9]] : f32
42// CHECK:           %[[VAL_35:.*]] = and %[[VAL_31]], %[[VAL_32]] : i1
43// CHECK:           %[[VAL_36:.*]] = select %[[VAL_33]], %[[VAL_9]], %[[VAL_12]] : f32
44// CHECK:           %[[VAL_37:.*]] = select %[[VAL_34]], %[[VAL_10]], %[[VAL_36]] : f32
45// CHECK:           %[[VAL_38:.*]] = select %[[VAL_35]], %[[VAL_30]], %[[VAL_37]] : f32
46// CHECK:           return %[[VAL_38]] : f32
47// CHECK:         }
48func @exp_scalar(%arg0: f32) -> f32 {
49  %0 = math.exp %arg0 : f32
50  return %0 : f32
51}
52
53// CHECK-LABEL:   func @exp_vector(
54// CHECK-SAME:                     %[[VAL_0:.*]]: vector<8xf32>) -> vector<8xf32> {
55// CHECK:           %[[VAL_1:.*]] = constant dense<0.693147182> : vector<8xf32>
56// CHECK-NOT:       exp
57// CHECK-COUNT-2:   select
58// CHECK:           %[[VAL_38:.*]] = select
59// CHECK:           return %[[VAL_38]] : vector<8xf32>
60// CHECK:         }
61func @exp_vector(%arg0: vector<8xf32>) -> vector<8xf32> {
62  %0 = math.exp %arg0 : vector<8xf32>
63  return %0 : vector<8xf32>
64}
65
66// CHECK-LABEL:   func @expm1_scalar(
67// CHECK-SAME:                       %[[X:.*]]: f32) -> f32 {
68// CHECK-DAG:           %[[CST_MINUSONE:.*]] = constant -1.000000e+00 : f32
69// CHECK-DAG:           %[[CST_LOG2E:.*]] = constant 1.44269502 : f32
70// CHECK-DAG:           %[[CST_ONE:.*]] = constant 1.000000e+00 : f32
71// CHECK:           %[[BEGIN_EXP_X:.*]] = mulf %[[X]], %[[CST_LOG2E]] : f32
72// CHECK-NOT:       exp
73// CHECK-COUNT-2:   select
74// CHECK:           %[[EXP_X:.*]] = select
75// CHECK:           %[[VAL_58:.*]] = cmpf oeq, %[[EXP_X]], %[[CST_ONE]] : f32
76// CHECK:           %[[VAL_59:.*]] = subf %[[EXP_X]], %[[CST_ONE]] : f32
77// CHECK:           %[[VAL_60:.*]] = cmpf oeq, %[[VAL_59]], %[[CST_MINUSONE]] : f32
78// CHECK-NOT:       log
79// CHECK-COUNT-5:   select
80// CHECK:           %[[LOG_U:.*]] = select
81// CHECK:           %[[VAL_104:.*]] = cmpf oeq, %[[LOG_U]], %[[EXP_X]] : f32
82// CHECK:           %[[VAL_105:.*]] = divf %[[X]], %[[LOG_U]] : f32
83// CHECK:           %[[VAL_106:.*]] = mulf %[[VAL_59]], %[[VAL_105]] : f32
84// CHECK:           %[[VAL_107:.*]] = select %[[VAL_104]], %[[EXP_X]], %[[VAL_106]] : f32
85// CHECK:           %[[VAL_108:.*]] = select %[[VAL_60]], %[[CST_MINUSONE]], %[[VAL_107]] : f32
86// CHECK:           %[[VAL_109:.*]] = select %[[VAL_58]], %[[X]], %[[VAL_108]] : f32
87// CHECK:           return %[[VAL_109]] : f32
88// CHECK:         }
89func @expm1_scalar(%arg0: f32) -> f32 {
90  %0 = math.expm1 %arg0 : f32
91  return %0 : f32
92}
93
94// CHECK-LABEL:   func @expm1_vector(
95// CHECK-SAME:                       %[[VAL_0:.*]]: vector<8xf32>) -> vector<8xf32> {
96// CHECK:           %[[VAL_1:.*]] = constant dense<-1.000000e+00> : vector<8xf32>
97// CHECK-NOT:       exp
98// CHECK-COUNT-3:   select
99// CHECK-NOT:       log
100// CHECK-COUNT-5:   select
101// CHECK-NOT:       expm1
102// CHECK-COUNT-3:   select
103// CHECK:           %[[VAL_115:.*]] = select
104// CHECK:           return %[[VAL_115]] : vector<8xf32>
105// CHECK:         }
106func @expm1_vector(%arg0: vector<8xf32>) -> vector<8xf32> {
107  %0 = math.expm1 %arg0 : vector<8xf32>
108  return %0 : vector<8xf32>
109}
110
111// CHECK-LABEL:   func @log_scalar(
112// CHECK-SAME:                             %[[X:.*]]: f32) -> f32 {
113// CHECK:           %[[VAL_1:.*]] = constant 0.000000e+00 : f32
114// CHECK:           %[[VAL_2:.*]] = constant 1.000000e+00 : f32
115// CHECK:           %[[VAL_3:.*]] = constant -5.000000e-01 : f32
116// CHECK:           %[[VAL_4:.*]] = constant 1.17549435E-38 : f32
117// CHECK:           %[[VAL_5:.*]] = constant 0xFF800000 : f32
118// CHECK:           %[[VAL_6:.*]] = constant 0x7F800000 : f32
119// CHECK:           %[[VAL_7:.*]] = constant 0x7FC00000 : f32
120// CHECK:           %[[VAL_8:.*]] = constant 0.707106769 : f32
121// CHECK:           %[[VAL_9:.*]] = constant 0.0703768358 : f32
122// CHECK:           %[[VAL_10:.*]] = constant -0.115146101 : f32
123// CHECK:           %[[VAL_11:.*]] = constant 0.116769984 : f32
124// CHECK:           %[[VAL_12:.*]] = constant -0.12420141 : f32
125// CHECK:           %[[VAL_13:.*]] = constant 0.142493233 : f32
126// CHECK:           %[[VAL_14:.*]] = constant -0.166680574 : f32
127// CHECK:           %[[VAL_15:.*]] = constant 0.200007141 : f32
128// CHECK:           %[[VAL_16:.*]] = constant -0.24999994 : f32
129// CHECK:           %[[VAL_17:.*]] = constant 0.333333313 : f32
130// CHECK:           %[[VAL_18:.*]] = constant 1.260000e+02 : f32
131// CHECK:           %[[VAL_19:.*]] = constant -2139095041 : i32
132// CHECK:           %[[VAL_20:.*]] = constant 1056964608 : i32
133// CHECK:           %[[VAL_21:.*]] = constant 23 : i32
134// CHECK:           %[[VAL_22:.*]] = constant 0.693147182 : f32
135// CHECK:           %[[VAL_23:.*]] = cmpf ogt, %[[X]], %[[VAL_4]] : f32
136// CHECK:           %[[VAL_24:.*]] = select %[[VAL_23]], %[[X]], %[[VAL_4]] : f32
137// CHECK-NOT:       frexp
138// CHECK:           %[[VAL_25:.*]] = bitcast %[[VAL_24]] : f32 to i32
139// CHECK:           %[[VAL_26:.*]] = and %[[VAL_25]], %[[VAL_19]] : i32
140// CHECK:           %[[VAL_27:.*]] = or %[[VAL_26]], %[[VAL_20]] : i32
141// CHECK:           %[[VAL_28:.*]] = bitcast %[[VAL_27]] : i32 to f32
142// CHECK:           %[[VAL_29:.*]] = bitcast %[[VAL_24]] : f32 to i32
143// CHECK:           %[[VAL_30:.*]] = shift_right_unsigned %[[VAL_29]], %[[VAL_21]] : i32
144// CHECK:           %[[VAL_31:.*]] = sitofp %[[VAL_30]] : i32 to f32
145// CHECK:           %[[VAL_32:.*]] = subf %[[VAL_31]], %[[VAL_18]] : f32
146// CHECK:           %[[VAL_33:.*]] = cmpf olt, %[[VAL_28]], %[[VAL_8]] : f32
147// CHECK:           %[[VAL_34:.*]] = select %[[VAL_33]], %[[VAL_28]], %[[VAL_1]] : f32
148// CHECK:           %[[VAL_35:.*]] = subf %[[VAL_28]], %[[VAL_2]] : f32
149// CHECK:           %[[VAL_36:.*]] = select %[[VAL_33]], %[[VAL_2]], %[[VAL_1]] : f32
150// CHECK:           %[[VAL_37:.*]] = subf %[[VAL_32]], %[[VAL_36]] : f32
151// CHECK:           %[[VAL_38:.*]] = addf %[[VAL_35]], %[[VAL_34]] : f32
152// CHECK:           %[[VAL_39:.*]] = mulf %[[VAL_38]], %[[VAL_38]] : f32
153// CHECK:           %[[VAL_40:.*]] = mulf %[[VAL_39]], %[[VAL_38]] : f32
154// CHECK:           %[[VAL_41:.*]] = fmaf %[[VAL_9]], %[[VAL_38]], %[[VAL_10]] : f32
155// CHECK:           %[[VAL_42:.*]] = fmaf %[[VAL_12]], %[[VAL_38]], %[[VAL_13]] : f32
156// CHECK:           %[[VAL_43:.*]] = fmaf %[[VAL_15]], %[[VAL_38]], %[[VAL_16]] : f32
157// CHECK:           %[[VAL_44:.*]] = fmaf %[[VAL_41]], %[[VAL_38]], %[[VAL_11]] : f32
158// CHECK:           %[[VAL_45:.*]] = fmaf %[[VAL_42]], %[[VAL_38]], %[[VAL_14]] : f32
159// CHECK:           %[[VAL_46:.*]] = fmaf %[[VAL_43]], %[[VAL_38]], %[[VAL_17]] : f32
160// CHECK:           %[[VAL_47:.*]] = fmaf %[[VAL_44]], %[[VAL_40]], %[[VAL_45]] : f32
161// CHECK:           %[[VAL_48:.*]] = fmaf %[[VAL_47]], %[[VAL_40]], %[[VAL_46]] : f32
162// CHECK:           %[[VAL_49:.*]] = mulf %[[VAL_48]], %[[VAL_40]] : f32
163// CHECK:           %[[VAL_50:.*]] = fmaf %[[VAL_3]], %[[VAL_39]], %[[VAL_49]] : f32
164// CHECK:           %[[VAL_51:.*]] = addf %[[VAL_38]], %[[VAL_50]] : f32
165// CHECK:           %[[VAL_52:.*]] = fmaf %[[VAL_37]], %[[VAL_22]], %[[VAL_51]] : f32
166// CHECK:           %[[VAL_53:.*]] = cmpf ult, %[[X]], %[[VAL_1]] : f32
167// CHECK:           %[[VAL_54:.*]] = cmpf oeq, %[[X]], %[[VAL_1]] : f32
168// CHECK:           %[[VAL_55:.*]] = cmpf oeq, %[[X]], %[[VAL_6]] : f32
169// CHECK:           %[[VAL_56:.*]] = select %[[VAL_55]], %[[VAL_6]], %[[VAL_52]] : f32
170// CHECK:           %[[VAL_57:.*]] = select %[[VAL_53]], %[[VAL_7]], %[[VAL_56]] : f32
171// CHECK:           %[[VAL_58:.*]] = select %[[VAL_54]], %[[VAL_5]], %[[VAL_57]] : f32
172// CHECK:           return %[[VAL_58]] : f32
173// CHECK:         }
174func @log_scalar(%arg0: f32) -> f32 {
175  %0 = math.log %arg0 : f32
176  return %0 : f32
177}
178
179// CHECK-LABEL:   func @log_vector(
180// CHECK-SAME:                     %[[VAL_0:.*]]: vector<8xf32>) -> vector<8xf32> {
181// CHECK:           %[[CST_LN2:.*]] = constant dense<0.693147182> : vector<8xf32>
182// CHECK-COUNT-5:   select
183// CHECK:           %[[VAL_71:.*]] = select
184// CHECK:           return %[[VAL_71]] : vector<8xf32>
185// CHECK:         }
186func @log_vector(%arg0: vector<8xf32>) -> vector<8xf32> {
187  %0 = math.log %arg0 : vector<8xf32>
188  return %0 : vector<8xf32>
189}
190
191// CHECK-LABEL:   func @log2_scalar(
192// CHECK-SAME:                      %[[VAL_0:.*]]: f32) -> f32 {
193// CHECK:           %[[CST_LOG2E:.*]] = constant 1.44269502 : f32
194// CHECK-COUNT-5:   select
195// CHECK:           %[[VAL_65:.*]] = select
196// CHECK:           return %[[VAL_65]] : f32
197// CHECK:         }
198func @log2_scalar(%arg0: f32) -> f32 {
199  %0 = math.log2 %arg0 : f32
200  return %0 : f32
201}
202
203// CHECK-LABEL:   func @log2_vector(
204// CHECK-SAME:                      %[[VAL_0:.*]]: vector<8xf32>) -> vector<8xf32> {
205// CHECK:           %[[CST_LOG2E:.*]] = constant dense<1.44269502> : vector<8xf32>
206// CHECK-COUNT-5:   select
207// CHECK:           %[[VAL_71:.*]] = select
208// CHECK:           return %[[VAL_71]] : vector<8xf32>
209// CHECK:         }
210func @log2_vector(%arg0: vector<8xf32>) -> vector<8xf32> {
211  %0 = math.log2 %arg0 : vector<8xf32>
212  return %0 : vector<8xf32>
213}
214
215// CHECK-LABEL:   func @log1p_scalar(
216// CHECK-SAME:                       %[[X:.*]]: f32) -> f32 {
217// CHECK:           %[[CST_ONE:.*]] = constant 1.000000e+00 : f32
218// CHECK:           %[[U:.*]] = addf %[[X]], %[[CST_ONE]] : f32
219// CHECK:           %[[U_SMALL:.*]] = cmpf oeq, %[[U]], %[[CST_ONE]] : f32
220// CHECK-NOT:       log
221// CHECK-COUNT-5:   select
222// CHECK:           %[[LOG_U:.*]] = select
223// CHECK:           %[[U_INF:.*]] = cmpf oeq, %[[U]], %[[LOG_U]] : f32
224// CHECK:           %[[VAL_69:.*]] = subf %[[U]], %[[CST_ONE]] : f32
225// CHECK:           %[[VAL_70:.*]] = divf %[[LOG_U]], %[[VAL_69]] : f32
226// CHECK:           %[[LOG_LARGE:.*]] = mulf %[[X]], %[[VAL_70]] : f32
227// CHECK:           %[[VAL_72:.*]] = or %[[U_SMALL]], %[[U_INF]]  : i1
228// CHECK:           %[[APPROX:.*]] = select %[[VAL_72]], %[[X]], %[[LOG_LARGE]] : f32
229// CHECK:           return %[[APPROX]] : f32
230// CHECK:         }
231func @log1p_scalar(%arg0: f32) -> f32 {
232  %0 = math.log1p %arg0 : f32
233  return %0 : f32
234}
235
236// CHECK-LABEL:   func @log1p_vector(
237// CHECK-SAME:                       %[[VAL_0:.*]]: vector<8xf32>) -> vector<8xf32> {
238// CHECK:           %[[CST_ONE:.*]] = constant dense<1.000000e+00> : vector<8xf32>
239// CHECK-COUNT-6:   select
240// CHECK:           %[[VAL_79:.*]] = select
241// CHECK:           return %[[VAL_79]] : vector<8xf32>
242// CHECK:         }
243func @log1p_vector(%arg0: vector<8xf32>) -> vector<8xf32> {
244  %0 = math.log1p %arg0 : vector<8xf32>
245  return %0 : vector<8xf32>
246}
247
248
249// CHECK-LABEL:   func @tanh_scalar(
250// CHECK-SAME:                      %[[VAL_0:.*]]: f32) -> f32 {
251// CHECK:           %[[VAL_1:.*]] = constant -7.90531111 : f32
252// CHECK:           %[[VAL_2:.*]] = constant 7.90531111 : f32
253// CHECK:           %[[VAL_3:.*]] = constant 4.000000e-04 : f32
254// CHECK:           %[[VAL_4:.*]] = constant 0.00489352457 : f32
255// CHECK:           %[[VAL_5:.*]] = constant 6.37261954E-4 : f32
256// CHECK:           %[[VAL_6:.*]] = constant 1.48572235E-5 : f32
257// CHECK:           %[[VAL_7:.*]] = constant 5.12229725E-8 : f32
258// CHECK:           %[[VAL_8:.*]] = constant -8.60467184E-11 : f32
259// CHECK:           %[[VAL_9:.*]] = constant 2.00018794E-13 : f32
260// CHECK:           %[[VAL_10:.*]] = constant -2.76076837E-16 : f32
261// CHECK:           %[[VAL_11:.*]] = constant 0.00489352504 : f32
262// CHECK:           %[[VAL_12:.*]] = constant 0.00226843474 : f32
263// CHECK:           %[[VAL_13:.*]] = constant 1.18534706E-4 : f32
264// CHECK:           %[[VAL_14:.*]] = constant 1.19825836E-6 : f32
265// CHECK:           %[[VAL_15:.*]] = cmpf olt, %[[VAL_0]], %[[VAL_2]] : f32
266// CHECK:           %[[VAL_16:.*]] = select %[[VAL_15]], %[[VAL_0]], %[[VAL_2]] : f32
267// CHECK:           %[[VAL_17:.*]] = cmpf ogt, %[[VAL_16]], %[[VAL_1]] : f32
268// CHECK:           %[[VAL_18:.*]] = select %[[VAL_17]], %[[VAL_16]], %[[VAL_1]] : f32
269// CHECK:           %[[VAL_19:.*]] = absf %[[VAL_0]] : f32
270// CHECK:           %[[VAL_20:.*]] = cmpf olt, %[[VAL_19]], %[[VAL_3]] : f32
271// CHECK:           %[[VAL_21:.*]] = mulf %[[VAL_18]], %[[VAL_18]] : f32
272// CHECK:           %[[VAL_22:.*]] = fmaf %[[VAL_21]], %[[VAL_10]], %[[VAL_9]] : f32
273// CHECK:           %[[VAL_23:.*]] = fmaf %[[VAL_21]], %[[VAL_22]], %[[VAL_8]] : f32
274// CHECK:           %[[VAL_24:.*]] = fmaf %[[VAL_21]], %[[VAL_23]], %[[VAL_7]] : f32
275// CHECK:           %[[VAL_25:.*]] = fmaf %[[VAL_21]], %[[VAL_24]], %[[VAL_6]] : f32
276// CHECK:           %[[VAL_26:.*]] = fmaf %[[VAL_21]], %[[VAL_25]], %[[VAL_5]] : f32
277// CHECK:           %[[VAL_27:.*]] = fmaf %[[VAL_21]], %[[VAL_26]], %[[VAL_4]] : f32
278// CHECK:           %[[VAL_28:.*]] = mulf %[[VAL_18]], %[[VAL_27]] : f32
279// CHECK:           %[[VAL_29:.*]] = fmaf %[[VAL_21]], %[[VAL_14]], %[[VAL_13]] : f32
280// CHECK:           %[[VAL_30:.*]] = fmaf %[[VAL_21]], %[[VAL_29]], %[[VAL_12]] : f32
281// CHECK:           %[[VAL_31:.*]] = fmaf %[[VAL_21]], %[[VAL_30]], %[[VAL_11]] : f32
282// CHECK:           %[[VAL_32:.*]] = divf %[[VAL_28]], %[[VAL_31]] : f32
283// CHECK:           %[[VAL_33:.*]] = select %[[VAL_20]], %[[VAL_18]], %[[VAL_32]] : f32
284// CHECK:           return %[[VAL_33]] : f32
285// CHECK:         }
286func @tanh_scalar(%arg0: f32) -> f32 {
287  %0 = math.tanh %arg0 : f32
288  return %0 : f32
289}
290
291// CHECK-LABEL:   func @tanh_vector(
292// CHECK-SAME:                      %[[VAL_0:.*]]: vector<8xf32>) -> vector<8xf32> {
293// CHECK:           %[[VAL_1:.*]] = constant dense<-7.90531111> : vector<8xf32>
294// CHECK-NOT:       tanh
295// CHECK-COUNT-2:   select
296// CHECK:           %[[VAL_33:.*]] = select
297// CHECK:           return %[[VAL_33]] : vector<8xf32>
298// CHECK:         }
299func @tanh_vector(%arg0: vector<8xf32>) -> vector<8xf32> {
300  %0 = math.tanh %arg0 : vector<8xf32>
301  return %0 : vector<8xf32>
302}
303