1 | 1 |
2 | ssinh.sa 3.1 12/10/90 2 | ssinh.sa 3.1 12/10/90
3 | 3 |
4 | The entry point sSinh computes the hyp 4 | The entry point sSinh computes the hyperbolic sine of
5 | an input argument; sSinhd does the sam 5 | an input argument; sSinhd does the same except for denormalized
6 | input. 6 | input.
7 | 7 |
8 | Input: Double-extended number X in loc 8 | Input: Double-extended number X in location pointed to
9 | by address register a0. 9 | by address register a0.
10 | 10 |
11 | Output: The value sinh(X) returned in 11 | Output: The value sinh(X) returned in floating-point register Fp0.
12 | 12 |
13 | Accuracy and Monotonicity: The returne 13 | Accuracy and Monotonicity: The returned result is within 3 ulps in
14 | 64 significant bit, i.e. withi 14 | 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
15 | result is subsequently rounded 15 | result is subsequently rounded to double precision. The
16 | result is provably monotonic i 16 | result is provably monotonic in double precision.
17 | 17 |
18 | Speed: The program sSINH takes approxi 18 | Speed: The program sSINH takes approximately 280 cycles.
19 | 19 |
20 | Algorithm: 20 | Algorithm:
21 | 21 |
22 | SINH 22 | SINH
23 | 1. If |X| > 16380 log2, go to 3. 23 | 1. If |X| > 16380 log2, go to 3.
24 | 24 |
25 | 2. (|X| <= 16380 log2) Sinh(X) is obta 25 | 2. (|X| <= 16380 log2) Sinh(X) is obtained by the formulae
26 | y = |X|, sgn = sign(X), and z 26 | y = |X|, sgn = sign(X), and z = expm1(Y),
27 | sinh(X) = sgn*(1/2)*( z + z/(1 27 | sinh(X) = sgn*(1/2)*( z + z/(1+z) ).
28 | Exit. 28 | Exit.
29 | 29 |
30 | 3. If |X| > 16480 log2, go to 5. 30 | 3. If |X| > 16480 log2, go to 5.
31 | 31 |
32 | 4. (16380 log2 < |X| <= 16480 log2) 32 | 4. (16380 log2 < |X| <= 16480 log2)
33 | sinh(X) = sign(X) * exp(|X|)/2 33 | sinh(X) = sign(X) * exp(|X|)/2.
34 | However, invoking exp(|X|) may caus 34 | However, invoking exp(|X|) may cause premature overflow.
35 | Thus, we calculate sinh(X) as follo 35 | Thus, we calculate sinh(X) as follows:
36 | Y := |X| 36 | Y := |X|
37 | sgn := sign(X) 37 | sgn := sign(X)
38 | sgnFact := sgn * 2**(16380) 38 | sgnFact := sgn * 2**(16380)
39 | Y' := Y - 16381 log2 39 | Y' := Y - 16381 log2
40 | sinh(X) := sgnFact * exp(Y'). 40 | sinh(X) := sgnFact * exp(Y').
41 | Exit. 41 | Exit.
42 | 42 |
43 | 5. (|X| > 16480 log2) sinh(X) must ove 43 | 5. (|X| > 16480 log2) sinh(X) must overflow. Return
44 | sign(X)*Huge*Huge to generate overf 44 | sign(X)*Huge*Huge to generate overflow and an infinity with
45 | the appropriate sign. Huge is the l 45 | the appropriate sign. Huge is the largest finite number in
46 | extended format. Exit. 46 | extended format. Exit.
47 | 47 |
48 48
49 | Copyright (C) Motorola, Inc. 1 49 | Copyright (C) Motorola, Inc. 1990
50 | All Rights Reserved 50 | All Rights Reserved
51 | 51 |
52 | For details on the license for this fi 52 | For details on the license for this file, please see the
53 | file, README, in this same directory. 53 | file, README, in this same directory.
54 54
55 |SSINH idnt 2,1 | Motorola 040 Floating Po 55 |SSINH idnt 2,1 | Motorola 040 Floating Point Software Package
56 56
57 |section 8 57 |section 8
58 58
59 T1: .long 0x40C62D38,0xD3D64634 | ... 1638 59 T1: .long 0x40C62D38,0xD3D64634 | ... 16381 LOG2 LEAD
60 T2: .long 0x3D6F90AE,0xB1E75CC7 | ... 1638 60 T2: .long 0x3D6F90AE,0xB1E75CC7 | ... 16381 LOG2 TRAIL
61 61
62 |xref t_frcinx 62 |xref t_frcinx
63 |xref t_ovfl 63 |xref t_ovfl
64 |xref t_extdnrm 64 |xref t_extdnrm
65 |xref setox 65 |xref setox
66 |xref setoxm1 66 |xref setoxm1
67 67
68 .global ssinhd 68 .global ssinhd
69 ssinhd: 69 ssinhd:
70 |--SINH(X) = X FOR DENORMALIZED X 70 |--SINH(X) = X FOR DENORMALIZED X
71 71
72 bra t_extdnrm 72 bra t_extdnrm
73 73
74 .global ssinh 74 .global ssinh
75 ssinh: 75 ssinh:
76 fmovex (%a0),%fp0 | ...LOAD INPU 76 fmovex (%a0),%fp0 | ...LOAD INPUT
77 77
78 movel (%a0),%d0 78 movel (%a0),%d0
79 movew 4(%a0),%d0 79 movew 4(%a0),%d0
80 movel %d0,%a1 | save a copy 80 movel %d0,%a1 | save a copy of original (compacted) operand
81 andl #0x7FFFFFFF,%d0 81 andl #0x7FFFFFFF,%d0
82 cmpl #0x400CB167,%d0 82 cmpl #0x400CB167,%d0
83 bgts SINHBIG 83 bgts SINHBIG
84 84
85 |--THIS IS THE USUAL CASE, |X| < 16380 LOG2 85 |--THIS IS THE USUAL CASE, |X| < 16380 LOG2
86 |--Y = |X|, Z = EXPM1(Y), SINH(X) = SIGN(X)*(1 86 |--Y = |X|, Z = EXPM1(Y), SINH(X) = SIGN(X)*(1/2)*( Z + Z/(1+Z) )
87 87
88 fabsx %fp0 | ...Y = |X| 88 fabsx %fp0 | ...Y = |X|
89 89
90 moveml %a1/%d1,-(%sp) 90 moveml %a1/%d1,-(%sp)
91 fmovemx %fp0-%fp0,(%a0) 91 fmovemx %fp0-%fp0,(%a0)
92 clrl %d1 92 clrl %d1
93 bsr setoxm1 | ...FP0 IS Z 93 bsr setoxm1 | ...FP0 IS Z = EXPM1(Y)
94 fmovel #0,%fpcr 94 fmovel #0,%fpcr
95 moveml (%sp)+,%a1/%d1 95 moveml (%sp)+,%a1/%d1
96 96
97 fmovex %fp0,%fp1 97 fmovex %fp0,%fp1
98 fadds #0x3F800000,%fp1 | ...1 98 fadds #0x3F800000,%fp1 | ...1+Z
99 fmovex %fp0,-(%sp) 99 fmovex %fp0,-(%sp)
100 fdivx %fp1,%fp0 | ...Z 100 fdivx %fp1,%fp0 | ...Z/(1+Z)
101 movel %a1,%d0 101 movel %a1,%d0
102 andl #0x80000000,%d0 102 andl #0x80000000,%d0
103 orl #0x3F000000,%d0 103 orl #0x3F000000,%d0
104 faddx (%sp)+,%fp0 104 faddx (%sp)+,%fp0
105 movel %d0,-(%sp) 105 movel %d0,-(%sp)
106 106
107 fmovel %d1,%fpcr 107 fmovel %d1,%fpcr
108 fmuls (%sp)+,%fp0 |last fp inst 108 fmuls (%sp)+,%fp0 |last fp inst - possible exceptions set
109 109
110 bra t_frcinx 110 bra t_frcinx
111 111
112 SINHBIG: 112 SINHBIG:
113 cmpl #0x400CB2B3,%d0 113 cmpl #0x400CB2B3,%d0
114 bgt t_ovfl 114 bgt t_ovfl
115 fabsx %fp0 115 fabsx %fp0
116 fsubd T1(%pc),%fp0 | ...(|X|-1638 116 fsubd T1(%pc),%fp0 | ...(|X|-16381LOG2_LEAD)
117 movel #0,-(%sp) 117 movel #0,-(%sp)
118 movel #0x80000000,-(%sp) 118 movel #0x80000000,-(%sp)
119 movel %a1,%d0 119 movel %a1,%d0
120 andl #0x80000000,%d0 120 andl #0x80000000,%d0
121 orl #0x7FFB0000,%d0 121 orl #0x7FFB0000,%d0
122 movel %d0,-(%sp) | ...EXTENDED 122 movel %d0,-(%sp) | ...EXTENDED FMT
123 fsubd T2(%pc),%fp0 | ...|X| - 163 123 fsubd T2(%pc),%fp0 | ...|X| - 16381 LOG2, ACCURATE
124 124
125 movel %d1,-(%sp) 125 movel %d1,-(%sp)
126 clrl %d1 126 clrl %d1
127 fmovemx %fp0-%fp0,(%a0) 127 fmovemx %fp0-%fp0,(%a0)
128 bsr setox 128 bsr setox
129 fmovel (%sp)+,%fpcr 129 fmovel (%sp)+,%fpcr
130 130
131 fmulx (%sp)+,%fp0 |possible exce 131 fmulx (%sp)+,%fp0 |possible exception
132 bra t_frcinx 132 bra t_frcinx
133 133
134 |end 134 |end
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