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|
|       ssinh.sa 3.1 12/10/90
|
|       The entry point sSinh computes the hyperbolic sine of
|       an input argument; sSinhd does the same except for denormalized
|       input.
|
|       Input: Double-extended number X in location pointed to
|               by address register a0.
|
|       Output: The value sinh(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 sSINH takes approximately 280 cycles.
|
|       Algorithm:
|
|       SINH
|       1. If |X| > 16380 log2, go to 3.
|
|       2. (|X| <= 16380 log2) Sinh(X) is obtained by the formulae
|               y = |X|, sgn = sign(X), and z = expm1(Y),
|               sinh(X) = sgn*(1/2)*( z + z/(1+z) ).
|          Exit.
|
|       3. If |X| > 16480 log2, go to 5.
|
|       4. (16380 log2 < |X| <= 16480 log2)
|               sinh(X) = sign(X) * exp(|X|)/2.
|          However, invoking exp(|X|) may cause premature overflow.
|          Thus, we calculate sinh(X) as follows:
|             Y       := |X|
|             sgn     := sign(X)
|             sgnFact := sgn * 2**(16380)
|             Y'      := Y - 16381 log2
|             sinh(X) := sgnFact * exp(Y').
|          Exit.
|
|       5. (|X| > 16480 log2) sinh(X) must overflow. Return
|          sign(X)*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|       THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA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.
 
|SSINH  idnt    2,1 | Motorola 040 Floating Point Software Package
 
        |section        8
 
T1:     .long 0x40C62D38,0xD3D64634 | ... 16381 LOG2 LEAD
T2:     .long 0x3D6F90AE,0xB1E75CC7 | ... 16381 LOG2 TRAIL
 
        |xref   t_frcinx
        |xref   t_ovfl
        |xref   t_extdnrm
        |xref   setox
        |xref   setoxm1
 
        .global ssinhd
ssinhd:
|--SINH(X) = X FOR DENORMALIZED X
 
        bra     t_extdnrm
 
        .global ssinh
ssinh:
        fmovex  (%a0),%fp0      | ...LOAD INPUT
 
        movel   (%a0),%d0
        movew   4(%a0),%d0
        movel   %d0,%a1         | save a copy of original (compacted) operand
        andl    #0x7FFFFFFF,%d0
        cmpl    #0x400CB167,%d0
        bgts    SINHBIG
 
|--THIS IS THE USUAL CASE, |X| < 16380 LOG2
|--Y = |X|, Z = EXPM1(Y), SINH(X) = SIGN(X)*(1/2)*( Z + Z/(1+Z) )
 
        fabsx   %fp0            | ...Y = |X|
 
        moveml  %a1/%d1,-(%sp)
        fmovemx %fp0-%fp0,(%a0)
        clrl    %d1
        bsr     setoxm1         | ...FP0 IS Z = EXPM1(Y)
        fmovel  #0,%fpcr
        moveml  (%sp)+,%a1/%d1
 
        fmovex  %fp0,%fp1
        fadds   #0x3F800000,%fp1        | ...1+Z
        fmovex  %fp0,-(%sp)
        fdivx   %fp1,%fp0               | ...Z/(1+Z)
        movel   %a1,%d0
        andl    #0x80000000,%d0
        orl     #0x3F000000,%d0
        faddx   (%sp)+,%fp0
        movel   %d0,-(%sp)
 
        fmovel  %d1,%fpcr
        fmuls   (%sp)+,%fp0     |last fp inst - possible exceptions set
 
        bra     t_frcinx
 
SINHBIG:
        cmpl    #0x400CB2B3,%d0
        bgt     t_ovfl
        fabsx   %fp0
        fsubd   T1(%pc),%fp0    | ...(|X|-16381LOG2_LEAD)
        movel   #0,-(%sp)
        movel   #0x80000000,-(%sp)
        movel   %a1,%d0
        andl    #0x80000000,%d0
        orl     #0x7FFB0000,%d0
        movel   %d0,-(%sp)      | ...EXTENDED FMT
        fsubd   T2(%pc),%fp0    | ...|X| - 16381 LOG2, ACCURATE
 
        movel   %d1,-(%sp)
        clrl    %d1
        fmovemx %fp0-%fp0,(%a0)
        bsr     setox
        fmovel  (%sp)+,%fpcr
 
        fmulx   (%sp)+,%fp0     |possible exception
        bra     t_frcinx
 
        |end

Line No.	Rev	Author	Line
1	1623	jcastillo	`\|`
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)HugeHuge 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
60			`T1: .long 0x40C62D38,0xD3D64634 \| ... 16381 LOG2 LEAD`
61			`T2: .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`
70			`ssinhd:`
71			`\|--SINH(X) = X FOR DENORMALIZED X`
72
73			`bra t_extdnrm`
74
75			`.global ssinh`
76			`ssinh:`
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
113			`SINHBIG:`
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`

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