blob: 8a560edc7653e903580c74490b0f4d69a2f43f2a [file] [log] [blame]
Linus Torvalds1da177e2005-04-16 15:20:36 -07001|
2| ssinh.sa 3.1 12/10/90
3|
4| The entry point sSinh computes the hyperbolic sine of
5| an input argument; sSinhd does the same except for denormalized
6| input.
7|
8| Input: Double-extended number X in location pointed to
9| by address register a0.
10|
11| Output: The value sinh(X) returned in floating-point register Fp0.
12|
13| Accuracy and Monotonicity: The returned result is within 3 ulps in
14| 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
15| result is subsequently rounded to double precision. The
16| result is provably monotonic in double precision.
17|
18| Speed: The program sSINH takes approximately 280 cycles.
19|
20| Algorithm:
21|
22| SINH
23| 1. If |X| > 16380 log2, go to 3.
24|
25| 2. (|X| <= 16380 log2) Sinh(X) is obtained by the formulae
26| y = |X|, sgn = sign(X), and z = expm1(Y),
27| sinh(X) = sgn*(1/2)*( z + z/(1+z) ).
28| Exit.
29|
30| 3. If |X| > 16480 log2, go to 5.
31|
32| 4. (16380 log2 < |X| <= 16480 log2)
33| sinh(X) = sign(X) * exp(|X|)/2.
34| However, invoking exp(|X|) may cause premature overflow.
35| Thus, we calculate sinh(X) as follows:
36| Y := |X|
37| sgn := sign(X)
38| sgnFact := sgn * 2**(16380)
39| Y' := Y - 16381 log2
40| sinh(X) := sgnFact * exp(Y').
41| Exit.
42|
43| 5. (|X| > 16480 log2) sinh(X) must overflow. Return
44| sign(X)*Huge*Huge to generate overflow and an infinity with
45| the appropriate sign. Huge is the largest finite number in
46| extended format. Exit.
47|
48
49| Copyright (C) Motorola, Inc. 1990
50| All Rights Reserved
51|
Matt Waddele00d82d2006-02-11 17:55:48 -080052| For details on the license for this file, please see the
53| file, README, in this same directory.
Linus Torvalds1da177e2005-04-16 15:20:36 -070054
55|SSINH idnt 2,1 | Motorola 040 Floating Point Software Package
56
57 |section 8
58
59T1: .long 0x40C62D38,0xD3D64634 | ... 16381 LOG2 LEAD
60T2: .long 0x3D6F90AE,0xB1E75CC7 | ... 16381 LOG2 TRAIL
61
62 |xref t_frcinx
63 |xref t_ovfl
64 |xref t_extdnrm
65 |xref setox
66 |xref setoxm1
67
68 .global ssinhd
69ssinhd:
70|--SINH(X) = X FOR DENORMALIZED X
71
72 bra t_extdnrm
73
74 .global ssinh
75ssinh:
76 fmovex (%a0),%fp0 | ...LOAD INPUT
77
78 movel (%a0),%d0
79 movew 4(%a0),%d0
80 movel %d0,%a1 | save a copy of original (compacted) operand
81 andl #0x7FFFFFFF,%d0
82 cmpl #0x400CB167,%d0
83 bgts SINHBIG
84
85|--THIS IS THE USUAL CASE, |X| < 16380 LOG2
86|--Y = |X|, Z = EXPM1(Y), SINH(X) = SIGN(X)*(1/2)*( Z + Z/(1+Z) )
87
88 fabsx %fp0 | ...Y = |X|
89
90 moveml %a1/%d1,-(%sp)
91 fmovemx %fp0-%fp0,(%a0)
92 clrl %d1
93 bsr setoxm1 | ...FP0 IS Z = EXPM1(Y)
94 fmovel #0,%fpcr
95 moveml (%sp)+,%a1/%d1
96
97 fmovex %fp0,%fp1
98 fadds #0x3F800000,%fp1 | ...1+Z
99 fmovex %fp0,-(%sp)
100 fdivx %fp1,%fp0 | ...Z/(1+Z)
101 movel %a1,%d0
102 andl #0x80000000,%d0
103 orl #0x3F000000,%d0
104 faddx (%sp)+,%fp0
105 movel %d0,-(%sp)
106
107 fmovel %d1,%fpcr
108 fmuls (%sp)+,%fp0 |last fp inst - possible exceptions set
109
110 bra t_frcinx
111
112SINHBIG:
113 cmpl #0x400CB2B3,%d0
114 bgt t_ovfl
115 fabsx %fp0
116 fsubd T1(%pc),%fp0 | ...(|X|-16381LOG2_LEAD)
117 movel #0,-(%sp)
118 movel #0x80000000,-(%sp)
119 movel %a1,%d0
120 andl #0x80000000,%d0
121 orl #0x7FFB0000,%d0
122 movel %d0,-(%sp) | ...EXTENDED FMT
123 fsubd T2(%pc),%fp0 | ...|X| - 16381 LOG2, ACCURATE
124
125 movel %d1,-(%sp)
126 clrl %d1
127 fmovemx %fp0-%fp0,(%a0)
128 bsr setox
129 fmovel (%sp)+,%fpcr
130
131 fmulx (%sp)+,%fp0 |possible exception
132 bra t_frcinx
133
134 |end