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|
|       satanh.sa 3.3 12/19/90
|
|       The entry point satanh computes the inverse
|       hyperbolic tangent of
|       an input argument; satanhd does the same except for denormalized
|       input.
|
|       Input: Double-extended number X in location pointed to
|               by address register a0.
|
|       Output: The value arctanh(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 satanh takes approximately 270 cycles.
|
|       Algorithm:
|
|       ATANH
|       1. If |X| >= 1, go to 3.
|
|       2. (|X| < 1) Calculate atanh(X) by
|               sgn := sign(X)
|               y := |X|
|               z := 2y/(1-y)
|               atanh(X) := sgn * (1/2) * logp1(z)
|               Exit.
|
|       3. If |X| > 1, go to 5.
|
|       4. (|X| = 1) Generate infinity with an appropriate sign and
|               divide-by-zero by
|               sgn := sign(X)
|               atan(X) := sgn / (+0).
|               Exit.
|
|       5. (|X| > 1) Generate an invalid operation by 0 * infinity.
|               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|       THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA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.
 
|satanh idnt    2,1 | Motorola 040 Floating Point Software Package
 
        |section        8
 
        |xref   t_dz
        |xref   t_operr
        |xref   t_frcinx
        |xref   t_extdnrm
        |xref   slognp1
 
        .global satanhd
satanhd:
|--ATANH(X) = X FOR DENORMALIZED X
 
        bra             t_extdnrm
 
        .global satanh
satanh:
        movel           (%a0),%d0
        movew           4(%a0),%d0
        andil           #0x7FFFFFFF,%d0
        cmpil           #0x3FFF8000,%d0
        bges            ATANHBIG
 
|--THIS IS THE USUAL CASE, |X| < 1
|--Y = |X|, Z = 2Y/(1-Y), ATANH(X) = SIGN(X) * (1/2) * LOG1P(Z).
 
        fabsx           (%a0),%fp0      | ...Y = |X|
        fmovex          %fp0,%fp1
        fnegx           %fp1            | ...-Y
        faddx           %fp0,%fp0               | ...2Y
        fadds           #0x3F800000,%fp1        | ...1-Y
        fdivx           %fp1,%fp0               | ...2Y/(1-Y)
        movel           (%a0),%d0
        andil           #0x80000000,%d0
        oril            #0x3F000000,%d0 | ...SIGN(X)*HALF
        movel           %d0,-(%sp)
 
        fmovemx %fp0-%fp0,(%a0) | ...overwrite input
        movel           %d1,-(%sp)
        clrl            %d1
        bsr             slognp1         | ...LOG1P(Z)
        fmovel          (%sp)+,%fpcr
        fmuls           (%sp)+,%fp0
        bra             t_frcinx
 
ATANHBIG:
        fabsx           (%a0),%fp0      | ...|X|
        fcmps           #0x3F800000,%fp0
        fbgt            t_operr
        bra             t_dz
 
        |end

Line No.	Rev	Author	Line
1	1623	jcastillo	`\|`
2			`\| satanh.sa 3.3 12/19/90`
3			`\|`
4			`\| The entry point satanh computes the inverse`
5			`\| hyperbolic tangent of`
6			`\| an input argument; satanhd does the same except for denormalized`
7			`\| input.`
8			`\|`
9			`\| Input: Double-extended number X in location pointed to`
10			`\| by address register a0.`
11			`\|`
12			`\| Output: The value arctanh(X) returned in floating-point register Fp0.`
13			`\|`
14			`\| Accuracy and Monotonicity: The returned result is within 3 ulps in`
15			`\| 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the`
16			`\| result is subsequently rounded to double precision. The`
17			`\| result is provably monotonic in double precision.`
18			`\|`
19			`\| Speed: The program satanh takes approximately 270 cycles.`
20			`\|`
21			`\| Algorithm:`
22			`\|`
23			`\| ATANH`
24			`\| 1. If \|X\| >= 1, go to 3.`
25			`\|`
26			`\| 2. (\|X\| < 1) Calculate atanh(X) by`
27			`\| sgn := sign(X)`
28			`\| y := \|X\|`
29			`\| z := 2y/(1-y)`
30			`\| atanh(X) := sgn * (1/2) * logp1(z)`
31			`\| Exit.`
32			`\|`
33			`\| 3. If \|X\| > 1, go to 5.`
34			`\|`
35			`\| 4. (\|X\| = 1) Generate infinity with an appropriate sign and`
36			`\| divide-by-zero by`
37			`\| sgn := sign(X)`
38			`\| atan(X) := sgn / (+0).`
39			`\| Exit.`
40			`\|`
41			`\| 5. (\|X\| > 1) Generate an invalid operation by 0 * infinity.`
42			`\| Exit.`
43			`\|`
44
45			`\| Copyright (C) Motorola, Inc. 1990`
46			`\| All Rights Reserved`
47			`\|`
48			`\| THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA`
49			`\| The copyright notice above does not evidence any`
50			`\| actual or intended publication of such source code.`
51
52			`\|satanh idnt 2,1 \| Motorola 040 Floating Point Software Package`
53
54			`\|section 8`
55
56			`\|xref t_dz`
57			`\|xref t_operr`
58			`\|xref t_frcinx`
59			`\|xref t_extdnrm`
60			`\|xref slognp1`
61
62			`.global satanhd`
63			`satanhd:`
64			`\|--ATANH(X) = X FOR DENORMALIZED X`
65
66			`bra t_extdnrm`
67
68			`.global satanh`
69			`satanh:`
70			`movel (%a0),%d0`
71			`movew 4(%a0),%d0`
72			`andil #0x7FFFFFFF,%d0`
73			`cmpil #0x3FFF8000,%d0`
74			`bges ATANHBIG`
75
76			`\|--THIS IS THE USUAL CASE, \|X\| < 1`
77			`\|--Y = \|X\|, Z = 2Y/(1-Y), ATANH(X) = SIGN(X) * (1/2) * LOG1P(Z).`
78
79			`fabsx (%a0),%fp0 \| ...Y = \|X\|`
80			`fmovex %fp0,%fp1`
81			`fnegx %fp1 \| ...-Y`
82			`faddx %fp0,%fp0 \| ...2Y`
83			`fadds #0x3F800000,%fp1 \| ...1-Y`
84			`fdivx %fp1,%fp0 \| ...2Y/(1-Y)`
85			`movel (%a0),%d0`
86			`andil #0x80000000,%d0`
87			`oril #0x3F000000,%d0 \| ...SIGN(X)*HALF`
88			`movel %d0,-(%sp)`
89
90			`fmovemx %fp0-%fp0,(%a0) \| ...overwrite input`
91			`movel %d1,-(%sp)`
92			`clrl %d1`
93			`bsr slognp1 \| ...LOG1P(Z)`
94			`fmovel (%sp)+,%fpcr`
95			`fmuls (%sp)+,%fp0`
96			`bra t_frcinx`
97
98			`ATANHBIG:`
99			`fabsx (%a0),%fp0 \| ...\|X\|`
100			`fcmps #0x3F800000,%fp0`
101			`fbgt t_operr`
102			`bra t_dz`
103
104			`\|end`

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