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// Constants
8DATA coshrodataL23<>+0(SB)/8, $0.231904681384629956E-16
9DATA coshrodataL23<>+8(SB)/8, $0.693147180559945286E+00
10DATA coshrodataL23<>+16(SB)/8, $0.144269504088896339E+01
11DATA coshrodataL23<>+24(SB)/8, $704.E0
12GLOBL coshrodataL23<>+0(SB), RODATA, $32
13DATA coshxinf<>+0(SB)/8, $0x7FF0000000000000
14GLOBL coshxinf<>+0(SB), RODATA, $8
15DATA coshxlim1<>+0(SB)/8, $800.E0
16GLOBL coshxlim1<>+0(SB), RODATA, $8
17DATA coshxaddhy<>+0(SB)/8, $0xc2f0000100003fdf
18GLOBL coshxaddhy<>+0(SB), RODATA, $8
19DATA coshx4ff<>+0(SB)/8, $0x4ff0000000000000
20GLOBL coshx4ff<>+0(SB), RODATA, $8
21DATA coshe1<>+0(SB)/8, $0x3ff000000000000a
22GLOBL coshe1<>+0(SB), RODATA, $8
23
24// Log multiplier table
25DATA coshtab<>+0(SB)/8, $0.442737824274138381E-01
26DATA coshtab<>+8(SB)/8, $0.263602189790660309E-01
27DATA coshtab<>+16(SB)/8, $0.122565642281703586E-01
28DATA coshtab<>+24(SB)/8, $0.143757052860721398E-02
29DATA coshtab<>+32(SB)/8, $-.651375034121276075E-02
30DATA coshtab<>+40(SB)/8, $-.119317678849450159E-01
31DATA coshtab<>+48(SB)/8, $-.150868749549871069E-01
32DATA coshtab<>+56(SB)/8, $-.161992609578469234E-01
33DATA coshtab<>+64(SB)/8, $-.154492360403337917E-01
34DATA coshtab<>+72(SB)/8, $-.129850717389178721E-01
35DATA coshtab<>+80(SB)/8, $-.892902649276657891E-02
36DATA coshtab<>+88(SB)/8, $-.338202636596794887E-02
37DATA coshtab<>+96(SB)/8, $0.357266307045684762E-02
38DATA coshtab<>+104(SB)/8, $0.118665304327406698E-01
39DATA coshtab<>+112(SB)/8, $0.214434994118118914E-01
40DATA coshtab<>+120(SB)/8, $0.322580645161290314E-01
41GLOBL coshtab<>+0(SB), RODATA, $128
42
43// Minimax polynomial approximations
44DATA coshe2<>+0(SB)/8, $0.500000000000004237e+00
45GLOBL coshe2<>+0(SB), RODATA, $8
46DATA coshe3<>+0(SB)/8, $0.166666666630345592e+00
47GLOBL coshe3<>+0(SB), RODATA, $8
48DATA coshe4<>+0(SB)/8, $0.416666664838056960e-01
49GLOBL coshe4<>+0(SB), RODATA, $8
50DATA coshe5<>+0(SB)/8, $0.833349307718286047e-02
51GLOBL coshe5<>+0(SB), RODATA, $8
52DATA coshe6<>+0(SB)/8, $0.138926439368309441e-02
53GLOBL coshe6<>+0(SB), RODATA, $8
54
55// Cosh returns the hyperbolic cosine of x.
56//
57// Special cases are:
58//      Cosh(±0) = 1
59//      Cosh(±Inf) = +Inf
60//      Cosh(NaN) = NaN
61// The algorithm used is minimax polynomial approximation
62// with coefficients determined with a Remez exchange algorithm.
63
64TEXT ·coshAsm(SB),NOSPLIT,$0-16
65	FMOVD   x+0(FP), F0
66	MOVD    $coshrodataL23<>+0(SB), R9
67	LTDBR	F0, F0
68	MOVD    $0x4086000000000000, R2
69	MOVD    $0x4086000000000000, R3
70	BLTU    L19
71	FMOVD   F0, F4
72L2:
73	WORD    $0xED409018     //cdb %f4,.L24-.L23(%r9)
74	BYTE    $0x00
75	BYTE    $0x19
76	BGE     L14     //jnl   .L14
77	BVS     L14
78	WFCEDBS V4, V4, V2
79	BEQ     L20
80L1:
81	FMOVD   F0, ret+8(FP)
82	RET
83
84L14:
85	WFCEDBS V4, V4, V2
86	BVS     L1
87	MOVD    $coshxlim1<>+0(SB), R1
88	FMOVD   0(R1), F2
89	WFCHEDBS        V4, V2, V2
90	BEQ     L21
91	MOVD    $coshxaddhy<>+0(SB), R1
92	FMOVD   coshrodataL23<>+16(SB), F5
93	FMOVD   0(R1), F2
94	WFMSDB  V0, V5, V2, V5
95	FMOVD   coshrodataL23<>+8(SB), F3
96	FADD    F5, F2
97	MOVD    $coshe6<>+0(SB), R1
98	WFMSDB  V2, V3, V0, V3
99	FMOVD   0(R1), F6
100	WFMDB   V3, V3, V1
101	MOVD    $coshe4<>+0(SB), R1
102	FMOVD   coshrodataL23<>+0(SB), F7
103	WFMADB  V2, V7, V3, V2
104	FMOVD   0(R1), F3
105	MOVD    $coshe5<>+0(SB), R1
106	WFMADB  V1, V6, V3, V6
107	FMOVD   0(R1), F7
108	MOVD    $coshe3<>+0(SB), R1
109	FMOVD   0(R1), F3
110	WFMADB  V1, V7, V3, V7
111	FNEG    F2, F3
112	LGDR    F5, R1
113	MOVD    $coshe2<>+0(SB), R3
114	WFCEDBS V4, V0, V0
115	FMOVD   0(R3), F5
116	MOVD    $coshe1<>+0(SB), R3
117	WFMADB  V1, V6, V5, V6
118	FMOVD   0(R3), F5
119	RISBGN	$0, $15, $48, R1, R2
120	WFMADB  V1, V7, V5, V1
121	BVS     L22
122	RISBGZ	$57, $60, $3, R1, R4
123	MOVD    $coshtab<>+0(SB), R3
124	WFMADB  V3, V6, V1, V6
125	WORD    $0x68043000     //ld    %f0,0(%r4,%r3)
126	FMSUB   F0, F3, F2
127	WORD    $0xA71AF000     //ahi   %r1,-4096
128	WFMADB  V2, V6, V0, V6
129L17:
130	RISBGN	$0, $15, $48, R1, R2
131	LDGR    R2, F2
132	FMADD   F2, F6, F2
133	MOVD    $coshx4ff<>+0(SB), R1
134	FMOVD   0(R1), F0
135	FMUL    F2, F0
136	FMOVD   F0, ret+8(FP)
137	RET
138
139L19:
140	FNEG    F0, F4
141	BR      L2
142L20:
143	MOVD    $coshxaddhy<>+0(SB), R1
144	FMOVD   coshrodataL23<>+16(SB), F3
145	FMOVD   0(R1), F2
146	WFMSDB  V0, V3, V2, V3
147	FMOVD   coshrodataL23<>+8(SB), F4
148	FADD    F3, F2
149	MOVD    $coshe6<>+0(SB), R1
150	FMSUB   F4, F2, F0
151	FMOVD   0(R1), F6
152	WFMDB   V0, V0, V1
153	MOVD    $coshe4<>+0(SB), R1
154	FMOVD   0(R1), F4
155	MOVD    $coshe5<>+0(SB), R1
156	FMOVD   coshrodataL23<>+0(SB), F5
157	WFMADB  V1, V6, V4, V6
158	FMADD   F5, F2, F0
159	FMOVD   0(R1), F2
160	MOVD    $coshe3<>+0(SB), R1
161	FMOVD   0(R1), F4
162	WFMADB  V1, V2, V4, V2
163	MOVD    $coshe2<>+0(SB), R1
164	FMOVD   0(R1), F5
165	FNEG    F0, F4
166	WFMADB  V1, V6, V5, V6
167	MOVD    $coshe1<>+0(SB), R1
168	FMOVD   0(R1), F5
169	WFMADB  V1, V2, V5, V1
170	LGDR    F3, R1
171	MOVD    $coshtab<>+0(SB), R5
172	WFMADB  V4, V6, V1, V3
173	RISBGZ	$57, $60, $3, R1, R4
174	WFMSDB  V4, V6, V1, V6
175	WORD    $0x68145000     //ld %f1,0(%r4,%r5)
176	WFMSDB  V4, V1, V0, V2
177	WORD    $0xA7487FBE     //lhi %r4,32702
178	FMADD   F3, F2, F1
179	SUBW    R1, R4
180	RISBGZ	$57, $60, $3, R4, R12
181	WORD    $0x682C5000     //ld %f2,0(%r12,%r5)
182	FMSUB   F2, F4, F0
183	RISBGN	$0, $15, $48, R1, R2
184	WFMADB  V0, V6, V2, V6
185	RISBGN	$0, $15, $48, R4, R3
186	LDGR    R2, F2
187	LDGR    R3, F0
188	FMADD   F2, F1, F2
189	FMADD   F0, F6, F0
190	FADD    F2, F0
191	FMOVD   F0, ret+8(FP)
192	RET
193
194L22:
195	WORD    $0xA7387FBE     //lhi %r3,32702
196	MOVD    $coshtab<>+0(SB), R4
197	SUBW    R1, R3
198	WFMSDB  V3, V6, V1, V6
199	RISBGZ	$57, $60, $3, R3, R3
200	WORD    $0x68034000     //ld %f0,0(%r3,%r4)
201	FMSUB   F0, F3, F2
202	WORD    $0xA7386FBE     //lhi %r3,28606
203	WFMADB  V2, V6, V0, V6
204	SUBW    R1, R3, R1
205	BR      L17
206L21:
207	MOVD    $coshxinf<>+0(SB), R1
208	FMOVD   0(R1), F0
209	FMOVD   F0, ret+8(FP)
210	RET
211
212