1// Copyright 2016 The Go Authors. All rights reserved.
2// Use of this source code is governed by a BSD-style
3// license that can be found in the LICENSE file.
4
5#include "textflag.h"
6
7// Minimax polynomial approximations
8DATA tanhrodataL18<>+0(SB)/8, $-1.0
9DATA tanhrodataL18<>+8(SB)/8, $-2.0
10DATA tanhrodataL18<>+16(SB)/8, $1.0
11DATA tanhrodataL18<>+24(SB)/8, $2.0
12DATA tanhrodataL18<>+32(SB)/8, $0.20000000000000011868E+01
13DATA tanhrodataL18<>+40(SB)/8, $0.13333333333333341256E+01
14DATA tanhrodataL18<>+48(SB)/8, $0.26666666663549111502E+00
15DATA tanhrodataL18<>+56(SB)/8, $0.66666666658721844678E+00
16DATA tanhrodataL18<>+64(SB)/8, $0.88890217768964374821E-01
17DATA tanhrodataL18<>+72(SB)/8, $0.25397199429103821138E-01
18DATA tanhrodataL18<>+80(SB)/8, $-.346573590279972643E+00
19DATA tanhrodataL18<>+88(SB)/8, $20.E0
20GLOBL tanhrodataL18<>+0(SB), RODATA, $96
21
22// Constants
23DATA tanhrlog2<>+0(SB)/8, $0x4007154760000000
24GLOBL tanhrlog2<>+0(SB), RODATA, $8
25DATA tanhxadd<>+0(SB)/8, $0xc2f0000100003ff0
26GLOBL tanhxadd<>+0(SB), RODATA, $8
27DATA tanhxmone<>+0(SB)/8, $-1.0
28GLOBL tanhxmone<>+0(SB), RODATA, $8
29DATA tanhxzero<>+0(SB)/8, $0
30GLOBL tanhxzero<>+0(SB), RODATA, $8
31
32// Polynomial coefficients
33DATA tanhtab<>+0(SB)/8, $0.000000000000000000E+00
34DATA tanhtab<>+8(SB)/8, $-.171540871271399150E-01
35DATA tanhtab<>+16(SB)/8, $-.306597931864376363E-01
36DATA tanhtab<>+24(SB)/8, $-.410200970469965021E-01
37DATA tanhtab<>+32(SB)/8, $-.486343079978231466E-01
38DATA tanhtab<>+40(SB)/8, $-.538226193725835820E-01
39DATA tanhtab<>+48(SB)/8, $-.568439602538111520E-01
40DATA tanhtab<>+56(SB)/8, $-.579091847395528847E-01
41DATA tanhtab<>+64(SB)/8, $-.571909584179366341E-01
42DATA tanhtab<>+72(SB)/8, $-.548312665987204407E-01
43DATA tanhtab<>+80(SB)/8, $-.509471843643441085E-01
44DATA tanhtab<>+88(SB)/8, $-.456353588448863359E-01
45DATA tanhtab<>+96(SB)/8, $-.389755254243262365E-01
46DATA tanhtab<>+104(SB)/8, $-.310332908285244231E-01
47DATA tanhtab<>+112(SB)/8, $-.218623539150173528E-01
48DATA tanhtab<>+120(SB)/8, $-.115062908917949451E-01
49GLOBL tanhtab<>+0(SB), RODATA, $128
50
51// Tanh returns the hyperbolic tangent of the argument.
52//
53// Special cases are:
54//      Tanh(±0) = ±0
55//      Tanh(±Inf) = ±1
56//      Tanh(NaN) = NaN
57// The algorithm used is minimax polynomial approximation using a table of
58// polynomial coefficients determined with a Remez exchange algorithm.
59
60TEXT ·tanhAsm(SB),NOSPLIT,$0-16
61	FMOVD   x+0(FP), F0
62	// special case Tanh(±0) = ±0
63	FMOVD   $(0.0), F1
64	FCMPU   F0, F1
65	BEQ     tanhIsZero
66	MOVD    $tanhrodataL18<>+0(SB), R5
67	LTDBR	F0, F0
68	MOVD    $0x4034000000000000, R1
69	BLTU    L15
70	FMOVD   F0, F1
71L2:
72	MOVD    $tanhxadd<>+0(SB), R2
73	FMOVD   0(R2), F2
74	MOVD    tanhrlog2<>+0(SB), R2
75	LDGR    R2, F4
76	WFMSDB  V0, V4, V2, V4
77	MOVD    $tanhtab<>+0(SB), R3
78	LGDR    F4, R2
79	RISBGZ	$57, $60, $3, R2, R4
80	WORD    $0xED105058     //cdb %f1,.L19-.L18(%r5)
81	BYTE    $0x00
82	BYTE    $0x19
83	RISBGN	$0, $15, $48, R2, R1
84	WORD    $0x68543000     //ld %f5,0(%r4,%r3)
85	LDGR    R1, F6
86	BLT     L3
87	MOVD    $tanhxzero<>+0(SB), R1
88	FMOVD   0(R1), F2
89	WFCHDBS V0, V2, V4
90	BEQ     L9
91	WFCHDBS V2, V0, V2
92	BNE     L1
93	MOVD    $tanhxmone<>+0(SB), R1
94	FMOVD   0(R1), F0
95	FMOVD   F0, ret+8(FP)
96	RET
97
98L3:
99	FADD    F4, F2
100	FMOVD   tanhrodataL18<>+80(SB), F4
101	FMADD   F4, F2, F0
102	FMOVD   tanhrodataL18<>+72(SB), F1
103	WFMDB   V0, V0, V3
104	FMOVD   tanhrodataL18<>+64(SB), F2
105	WFMADB  V0, V1, V2, V1
106	FMOVD   tanhrodataL18<>+56(SB), F4
107	FMOVD   tanhrodataL18<>+48(SB), F2
108	WFMADB  V1, V3, V4, V1
109	FMOVD   tanhrodataL18<>+40(SB), F4
110	WFMADB  V3, V2, V4, V2
111	FMOVD   tanhrodataL18<>+32(SB), F4
112	WORD    $0xB9270022     //lhr %r2,%r2
113	WFMADB  V3, V1, V4, V1
114	FMOVD   tanhrodataL18<>+24(SB), F4
115	WFMADB  V3, V2, V4, V3
116	WFMADB  V0, V5, V0, V2
117	WFMADB  V0, V1, V3, V0
118	WORD    $0xA7183ECF     //lhi %r1,16079
119	WFMADB  V0, V2, V5, V2
120	FMUL    F6, F2
121	MOVW    R2, R10
122	MOVW    R1, R11
123	CMPBLE  R10, R11, L16
124	FMOVD   F6, F0
125	WORD    $0xED005010     //adb %f0,.L28-.L18(%r5)
126	BYTE    $0x00
127	BYTE    $0x1A
128	WORD    $0xA7184330     //lhi %r1,17200
129	FADD    F2, F0
130	MOVW    R2, R10
131	MOVW    R1, R11
132	CMPBGT  R10, R11, L17
133	WORD    $0xED605010     //sdb %f6,.L28-.L18(%r5)
134	BYTE    $0x00
135	BYTE    $0x1B
136	FADD    F6, F2
137	WFDDB   V0, V2, V0
138	FMOVD   F0, ret+8(FP)
139	RET
140
141L9:
142	FMOVD   tanhrodataL18<>+16(SB), F0
143L1:
144	FMOVD   F0, ret+8(FP)
145	RET
146
147L15:
148	FNEG    F0, F1
149	BR      L2
150L16:
151	FADD    F6, F2
152	FMOVD   tanhrodataL18<>+8(SB), F0
153	FMADD   F4, F2, F0
154	FMOVD   tanhrodataL18<>+0(SB), F4
155	FNEG    F0, F0
156	WFMADB  V0, V2, V4, V0
157	FMOVD   F0, ret+8(FP)
158	RET
159
160L17:
161	WFDDB   V0, V4, V0
162	FMOVD   tanhrodataL18<>+16(SB), F2
163	WFSDB   V0, V2, V0
164	FMOVD   F0, ret+8(FP)
165	RET
166
167tanhIsZero:      //return ±0
168	FMOVD   F0, ret+8(FP)
169	RET
170