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1|
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|
52| THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA
53| The copyright notice above does not evidence any
54| actual or intended publication of such source code.
55
56|SSINH idnt 2,1 | Motorola 040 Floating Point Software Package
57
58 |section 8
59
60T1: .long 0x40C62D38,0xD3D64634 | ... 16381 LOG2 LEAD
61T2: .long 0x3D6F90AE,0xB1E75CC7 | ... 16381 LOG2 TRAIL
62
63 |xref t_frcinx
64 |xref t_ovfl
65 |xref t_extdnrm
66 |xref setox
67 |xref setoxm1
68
69 .global ssinhd
70ssinhd:
71|--SINH(X) = X FOR DENORMALIZED X
72
73 bra t_extdnrm
74
75 .global ssinh
76ssinh:
77 fmovex (%a0),%fp0 | ...LOAD INPUT
78
79 movel (%a0),%d0
80 movew 4(%a0),%d0
81 movel %d0,%a1 | save a copy of original (compacted) operand
82 andl #0x7FFFFFFF,%d0
83 cmpl #0x400CB167,%d0
84 bgts SINHBIG
85
86|--THIS IS THE USUAL CASE, |X| < 16380 LOG2
87|--Y = |X|, Z = EXPM1(Y), SINH(X) = SIGN(X)*(1/2)*( Z + Z/(1+Z) )
88
89 fabsx %fp0 | ...Y = |X|
90
91 moveml %a1/%d1,-(%sp)
92 fmovemx %fp0-%fp0,(%a0)
93 clrl %d1
94 bsr setoxm1 | ...FP0 IS Z = EXPM1(Y)
95 fmovel #0,%fpcr
96 moveml (%sp)+,%a1/%d1
97
98 fmovex %fp0,%fp1
99 fadds #0x3F800000,%fp1 | ...1+Z
100 fmovex %fp0,-(%sp)
101 fdivx %fp1,%fp0 | ...Z/(1+Z)
102 movel %a1,%d0
103 andl #0x80000000,%d0
104 orl #0x3F000000,%d0
105 faddx (%sp)+,%fp0
106 movel %d0,-(%sp)
107
108 fmovel %d1,%fpcr
109 fmuls (%sp)+,%fp0 |last fp inst - possible exceptions set
110
111 bra t_frcinx
112
113SINHBIG:
114 cmpl #0x400CB2B3,%d0
115 bgt t_ovfl
116 fabsx %fp0
117 fsubd T1(%pc),%fp0 | ...(|X|-16381LOG2_LEAD)
118 movel #0,-(%sp)
119 movel #0x80000000,-(%sp)
120 movel %a1,%d0
121 andl #0x80000000,%d0
122 orl #0x7FFB0000,%d0
123 movel %d0,-(%sp) | ...EXTENDED FMT
124 fsubd T2(%pc),%fp0 | ...|X| - 16381 LOG2, ACCURATE
125
126 movel %d1,-(%sp)
127 clrl %d1
128 fmovemx %fp0-%fp0,(%a0)
129 bsr setox
130 fmovel (%sp)+,%fpcr
131
132 fmulx (%sp)+,%fp0 |possible exception
133 bra t_frcinx
134
135 |end