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|
|       scosh.sa 3.1 12/10/90
|
|       The entry point sCosh computes the hyperbolic cosine of
|       an input argument; sCoshd does the same except for denormalized
|       input.
|
|       Input: Double-extended number X in location pointed to
|               by address register a0.
|
|       Output: The value cosh(X) returned in floating-point register Fp0.
|
|       Accuracy and Monotonicity: The returned result is within 3 ulps in
|               64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
|               result is subsequently rounded to double precision. The
|               result is provably monotonic in double precision.
|
|       Speed: The program sCOSH takes approximately 250 cycles.
|
|       Algorithm:
|
|       COSH
|       1. If |X| > 16380 log2, go to 3.
|
|       2. (|X| <= 16380 log2) Cosh(X) is obtained by the formulae
|               y = |X|, z = exp(Y), and
|               cosh(X) = (1/2)*( z + 1/z ).
|               Exit.
|
|       3. (|X| > 16380 log2). If |X| > 16480 log2, go to 5.
|
|       4. (16380 log2 < |X| <= 16480 log2)
|               cosh(X) = sign(X) * exp(|X|)/2.
|               However, invoking exp(|X|) may cause premature overflow.
|               Thus, we calculate sinh(X) as follows:
|               Y       := |X|
|               Fact    :=      2**(16380)
|               Y'      := Y - 16381 log2
|               cosh(X) := Fact * exp(Y').
|               Exit.
|
|       5. (|X| > 16480 log2) sinh(X) must overflow. Return
|               Huge*Huge to generate overflow and an infinity with
|               the appropriate sign. Huge is the largest finite number in
|               extended format. Exit.
|
|
 
|               Copyright (C) Motorola, Inc. 1990
|                       All Rights Reserved
|
|       THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA
|       The copyright notice above does not evidence any
|       actual or intended publication of such source code.
 
|SCOSH  idnt    2,1 | Motorola 040 Floating Point Software Package
 
        |section        8
 
        |xref   t_ovfl
        |xref   t_frcinx
        |xref   setox
 
T1:     .long 0x40C62D38,0xD3D64634 | ... 16381 LOG2 LEAD
T2:     .long 0x3D6F90AE,0xB1E75CC7 | ... 16381 LOG2 TRAIL
 
TWO16380: .long 0x7FFB0000,0x80000000,0x00000000,0x00000000
 
        .global scoshd
scoshd:
|--COSH(X) = 1 FOR DENORMALIZED X
 
        fmoves          #0x3F800000,%fp0
 
        fmovel          %d1,%FPCR
        fadds           #0x00800000,%fp0
        bra             t_frcinx
 
        .global scosh
scosh:
        fmovex          (%a0),%fp0      | ...LOAD INPUT
 
        movel           (%a0),%d0
        movew           4(%a0),%d0
        andil           #0x7FFFFFFF,%d0
        cmpil           #0x400CB167,%d0
        bgts            COSHBIG
 
|--THIS IS THE USUAL CASE, |X| < 16380 LOG2
|--COSH(X) = (1/2) * ( EXP(X) + 1/EXP(X) )
 
        fabsx           %fp0            | ...|X|
 
        movel           %d1,-(%sp)
        clrl            %d1
        fmovemx %fp0-%fp0,(%a0) |pass parameter to setox
        bsr             setox           | ...FP0 IS EXP(|X|)
        fmuls           #0x3F000000,%fp0        | ...(1/2)EXP(|X|)
        movel           (%sp)+,%d1
 
        fmoves          #0x3E800000,%fp1        | ...(1/4)
        fdivx           %fp0,%fp1               | ...1/(2 EXP(|X|))
 
        fmovel          %d1,%FPCR
        faddx           %fp1,%fp0
 
        bra             t_frcinx
 
COSHBIG:
        cmpil           #0x400CB2B3,%d0
        bgts            COSHHUGE
 
        fabsx           %fp0
        fsubd           T1(%pc),%fp0            | ...(|X|-16381LOG2_LEAD)
        fsubd           T2(%pc),%fp0            | ...|X| - 16381 LOG2, ACCURATE
 
        movel           %d1,-(%sp)
        clrl            %d1
        fmovemx %fp0-%fp0,(%a0)
        bsr             setox
        fmovel          (%sp)+,%fpcr
 
        fmulx           TWO16380(%pc),%fp0
        bra             t_frcinx
 
COSHHUGE:
        fmovel          #0,%fpsr                |clr N bit if set by source
        bclrb           #7,(%a0)                |always return positive value
        fmovemx (%a0),%fp0-%fp0
        bra             t_ovfl
 
        |end

Line No.	Rev	Author	Line
1	1623	jcastillo	`\|`
2			`\| scosh.sa 3.1 12/10/90`
3			`\|`
4			`\| The entry point sCosh computes the hyperbolic cosine of`
5			`\| an input argument; sCoshd 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 cosh(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 sCOSH takes approximately 250 cycles.`
19			`\|`
20			`\| Algorithm:`
21			`\|`
22			`\| COSH`
23			`\| 1. If \|X\| > 16380 log2, go to 3.`
24			`\|`
25			`\| 2. (\|X\| <= 16380 log2) Cosh(X) is obtained by the formulae`
26			`\| y = \|X\|, z = exp(Y), and`
27			`\| cosh(X) = (1/2)*( z + 1/z ).`
28			`\| Exit.`
29			`\|`
30			`\| 3. (\|X\| > 16380 log2). If \|X\| > 16480 log2, go to 5.`
31			`\|`
32			`\| 4. (16380 log2 < \|X\| <= 16480 log2)`
33			`\| cosh(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			`\| Fact := 2**(16380)`
38			`\| Y' := Y - 16381 log2`
39			`\| cosh(X) := Fact * exp(Y').`
40			`\| Exit.`
41			`\|`
42			`\| 5. (\|X\| > 16480 log2) sinh(X) must overflow. Return`
43			`\| Huge*Huge to generate overflow and an infinity with`
44			`\| the appropriate sign. Huge is the largest finite number in`
45			`\| extended format. Exit.`
46			`\|`
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			`\|SCOSH idnt 2,1 \| Motorola 040 Floating Point Software Package`
57
58			`\|section 8`
59
60			`\|xref t_ovfl`
61			`\|xref t_frcinx`
62			`\|xref setox`
63
64			`T1: .long 0x40C62D38,0xD3D64634 \| ... 16381 LOG2 LEAD`
65			`T2: .long 0x3D6F90AE,0xB1E75CC7 \| ... 16381 LOG2 TRAIL`
66
67			`TWO16380: .long 0x7FFB0000,0x80000000,0x00000000,0x00000000`
68
69			`.global scoshd`
70			`scoshd:`
71			`\|--COSH(X) = 1 FOR DENORMALIZED X`
72
73			`fmoves #0x3F800000,%fp0`
74
75			`fmovel %d1,%FPCR`
76			`fadds #0x00800000,%fp0`
77			`bra t_frcinx`
78
79			`.global scosh`
80			`scosh:`
81			`fmovex (%a0),%fp0 \| ...LOAD INPUT`
82
83			`movel (%a0),%d0`
84			`movew 4(%a0),%d0`
85			`andil #0x7FFFFFFF,%d0`
86			`cmpil #0x400CB167,%d0`
87			`bgts COSHBIG`
88
89			`\|--THIS IS THE USUAL CASE, \|X\| < 16380 LOG2`
90			`\|--COSH(X) = (1/2) * ( EXP(X) + 1/EXP(X) )`
91
92			`fabsx %fp0 \| ...\|X\|`
93
94			`movel %d1,-(%sp)`
95			`clrl %d1`
96			`fmovemx %fp0-%fp0,(%a0) \|pass parameter to setox`
97			`bsr setox \| ...FP0 IS EXP(\|X\|)`
98			`fmuls #0x3F000000,%fp0 \| ...(1/2)EXP(\|X\|)`
99			`movel (%sp)+,%d1`
100
101			`fmoves #0x3E800000,%fp1 \| ...(1/4)`
102			`fdivx %fp0,%fp1 \| ...1/(2 EXP(\|X\|))`
103
104			`fmovel %d1,%FPCR`
105			`faddx %fp1,%fp0`
106
107			`bra t_frcinx`
108
109			`COSHBIG:`
110			`cmpil #0x400CB2B3,%d0`
111			`bgts COSHHUGE`
112
113			`fabsx %fp0`
114			`fsubd T1(%pc),%fp0 \| ...(\|X\|-16381LOG2_LEAD)`
115			`fsubd T2(%pc),%fp0 \| ...\|X\| - 16381 LOG2, ACCURATE`
116
117			`movel %d1,-(%sp)`
118			`clrl %d1`
119			`fmovemx %fp0-%fp0,(%a0)`
120			`bsr setox`
121			`fmovel (%sp)+,%fpcr`
122
123			`fmulx TWO16380(%pc),%fp0`
124			`bra t_frcinx`
125
126			`COSHHUGE:`
127			`fmovel #0,%fpsr \|clr N bit if set by source`
128			`bclrb #7,(%a0) \|always return positive value`
129			`fmovemx (%a0),%fp0-%fp0`
130			`bra t_ovfl`
131
132			`\|end`

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