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//
//      $Id: stanh.S,v 1.2 2001-09-27 12:01:22 chris Exp $
//
//      stanh.sa 3.1 12/10/90
//
//      The entry point sTanh computes the hyperbolic tangent of
//      an input argument; sTanhd does the same except for denormalized
//      input.
//
//      Input: Double-extended number X in location pointed to
//              by address register a0.
//
//      Output: The value tanh(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 stanh takes approximately 270 cycles.
//
//      Algorithm:
//
//      TANH
//      1. If |X| >= (5/2) log2 or |X| <= 2**(-40), go to 3.
//
//      2. (2**(-40) < |X| < (5/2) log2) Calculate tanh(X) by
//              sgn := sign(X), y := 2|X|, z := expm1(Y), and
//              tanh(X) = sgn*( z/(2+z) ).
//              Exit.
//
//      3. (|X| <= 2**(-40) or |X| >= (5/2) log2). If |X| < 1,
//              go to 7.
//
//      4. (|X| >= (5/2) log2) If |X| >= 50 log2, go to 6.
//
//      5. ((5/2) log2 <= |X| < 50 log2) Calculate tanh(X) by
//              sgn := sign(X), y := 2|X|, z := exp(Y),
//              tanh(X) = sgn - [ sgn*2/(1+z) ].
//              Exit.
//
//      6. (|X| >= 50 log2) Tanh(X) = +-1 (round to nearest). Thus, we
//              calculate Tanh(X) by
//              sgn := sign(X), Tiny := 2**(-126),
//              tanh(X) := sgn - sgn*Tiny.
//              Exit.
//
//      7. (|X| < 2**(-40)). Tanh(X) = X.       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//      THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA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.
 
//STANH idnt    2,1 | Motorola 040 Floating Point Software Package
 
        |section        8
 
#include "fpsp.defs"
 
        .set    X,FP_SCR5
        .set    XDCARE,X+2
        .set    XFRAC,X+4
 
        .set    SGN,L_SCR3
 
        .set    V,FP_SCR6
 
BOUNDS1:        .long 0x3FD78000,0x3FFFDDCE // ... 2^(-40), (5/2)LOG2
 
        |xref   t_frcinx
        |xref   t_extdnrm
        |xref   setox
        |xref   setoxm1
 
        .global stanhd
stanhd:
//--TANH(X) = X FOR DENORMALIZED X
 
        bra             t_extdnrm
 
        .global stanh
stanh:
        fmovex          (%a0),%fp0      // ...LOAD INPUT
 
        fmovex          %fp0,X(%a6)
        movel           (%a0),%d0
        movew           4(%a0),%d0
        movel           %d0,X(%a6)
        andl            #0x7FFFFFFF,%d0
        cmp2l           BOUNDS1(%pc),%d0        // ...2**(-40) < |X| < (5/2)LOG2 ?
        bcss            TANHBORS
 
//--THIS IS THE USUAL CASE
//--Y = 2|X|, Z = EXPM1(Y), TANH(X) = SIGN(X) * Z / (Z+2).
 
        movel           X(%a6),%d0
        movel           %d0,SGN(%a6)
        andl            #0x7FFF0000,%d0
        addl            #0x00010000,%d0 // ...EXPONENT OF 2|X|
        movel           %d0,X(%a6)
        andl            #0x80000000,SGN(%a6)
        fmovex          X(%a6),%fp0             // ...FP0 IS Y = 2|X|
 
        movel           %d1,-(%a7)
        clrl            %d1
        fmovemx %fp0-%fp0,(%a0)
        bsr             setoxm1         // ...FP0 IS Z = EXPM1(Y)
        movel           (%a7)+,%d1
 
        fmovex          %fp0,%fp1
        fadds           #0x40000000,%fp1        // ...Z+2
        movel           SGN(%a6),%d0
        fmovex          %fp1,V(%a6)
        eorl            %d0,V(%a6)
 
        fmovel          %d1,%FPCR               //restore users exceptions
        fdivx           V(%a6),%fp0
        bra             t_frcinx
 
TANHBORS:
        cmpl            #0x3FFF8000,%d0
        blt             TANHSM
 
        cmpl            #0x40048AA1,%d0
        bgt             TANHHUGE
 
//-- (5/2) LOG2 < |X| < 50 LOG2,
//--TANH(X) = 1 - (2/[EXP(2X)+1]). LET Y = 2|X|, SGN = SIGN(X),
//--TANH(X) = SGN -     SGN*2/[EXP(Y)+1].
 
        movel           X(%a6),%d0
        movel           %d0,SGN(%a6)
        andl            #0x7FFF0000,%d0
        addl            #0x00010000,%d0 // ...EXPO OF 2|X|
        movel           %d0,X(%a6)              // ...Y = 2|X|
        andl            #0x80000000,SGN(%a6)
        movel           SGN(%a6),%d0
        fmovex          X(%a6),%fp0             // ...Y = 2|X|
 
        movel           %d1,-(%a7)
        clrl            %d1
        fmovemx %fp0-%fp0,(%a0)
        bsr             setox           // ...FP0 IS EXP(Y)
        movel           (%a7)+,%d1
        movel           SGN(%a6),%d0
        fadds           #0x3F800000,%fp0        // ...EXP(Y)+1
 
        eorl            #0xC0000000,%d0 // ...-SIGN(X)*2
        fmoves          %d0,%fp1                // ...-SIGN(X)*2 IN SGL FMT
        fdivx           %fp0,%fp1               // ...-SIGN(X)2 / [EXP(Y)+1 ]
 
        movel           SGN(%a6),%d0
        orl             #0x3F800000,%d0 // ...SGN
        fmoves          %d0,%fp0                // ...SGN IN SGL FMT
 
        fmovel          %d1,%FPCR               //restore users exceptions
        faddx           %fp1,%fp0
 
        bra             t_frcinx
 
TANHSM:
        movew           #0x0000,XDCARE(%a6)
 
        fmovel          %d1,%FPCR               //restore users exceptions
        fmovex          X(%a6),%fp0             //last inst - possible exception set
 
        bra             t_frcinx
 
TANHHUGE:
//---RETURN SGN(X) - SGN(X)EPS
        movel           X(%a6),%d0
        andl            #0x80000000,%d0
        orl             #0x3F800000,%d0
        fmoves          %d0,%fp0
        andl            #0x80000000,%d0
        eorl            #0x80800000,%d0 // ...-SIGN(X)*EPS
 
        fmovel          %d1,%FPCR               //restore users exceptions
        fadds           %d0,%fp0
 
        bra             t_frcinx
 
        |end

Line No.	Rev	Author	Line
1	158	chris	`//`
2	208	chris	`// $Id: stanh.S,v 1.2 2001-09-27 12:01:22 chris Exp $`
3	158	chris	`//`
4			`// stanh.sa 3.1 12/10/90`
5			`//`
6			`// The entry point sTanh computes the hyperbolic tangent of`
7			`// an input argument; sTanhd does the same except for denormalized`
8			`// input.`
9			`//`
10			`// Input: Double-extended number X in location pointed to`
11			`// by address register a0.`
12			`//`
13			`// Output: The value tanh(X) returned in floating-point register Fp0.`
14			`//`
15			`// Accuracy and Monotonicity: The returned result is within 3 ulps in`
16			`// 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the`
17			`// result is subsequently rounded to double precision. The`
18			`// result is provably monotonic in double precision.`
19			`//`
20			`// Speed: The program stanh takes approximately 270 cycles.`
21			`//`
22			`// Algorithm:`
23			`//`
24			`// TANH`
25			`// 1. If \|X\| >= (5/2) log2 or \|X\| <= 2**(-40), go to 3.`
26			`//`
27			`// 2. (2**(-40) < \|X\| < (5/2) log2) Calculate tanh(X) by`
28			`// sgn := sign(X), y := 2\|X\|, z := expm1(Y), and`
29			`// tanh(X) = sgn*( z/(2+z) ).`
30			`// Exit.`
31			`//`
32			`// 3. (\|X\| <= 2**(-40) or \|X\| >= (5/2) log2). If \|X\| < 1,`
33			`// go to 7.`
34			`//`
35			`// 4. (\|X\| >= (5/2) log2) If \|X\| >= 50 log2, go to 6.`
36			`//`
37			`// 5. ((5/2) log2 <= \|X\| < 50 log2) Calculate tanh(X) by`
38			`// sgn := sign(X), y := 2\|X\|, z := exp(Y),`
39			`// tanh(X) = sgn - [ sgn*2/(1+z) ].`
40			`// Exit.`
41			`//`
42			`// 6. (\|X\| >= 50 log2) Tanh(X) = +-1 (round to nearest). Thus, we`
43			`// calculate Tanh(X) by`
44			`// sgn := sign(X), Tiny := 2**(-126),`
45			`// tanh(X) := sgn - sgn*Tiny.`
46			`// Exit.`
47			`//`
48			`// 7. (\|X\| < 2**(-40)). Tanh(X) = X. Exit.`
49			`//`
50
51			`// Copyright (C) Motorola, Inc. 1990`
52			`// All Rights Reserved`
53			`//`
54			`// THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA`
55			`// The copyright notice above does not evidence any`
56			`// actual or intended publication of such source code.`
57
58			`//STANH idnt 2,1 \| Motorola 040 Floating Point Software Package`
59
60			`\|section 8`
61
62			`#include "fpsp.defs"`
63
64			`.set X,FP_SCR5`
65			`.set XDCARE,X+2`
66			`.set XFRAC,X+4`
67
68			`.set SGN,L_SCR3`
69
70			`.set V,FP_SCR6`
71
72			`BOUNDS1: .long 0x3FD78000,0x3FFFDDCE // ... 2^(-40), (5/2)LOG2`
73
74			`\|xref t_frcinx`
75			`\|xref t_extdnrm`
76			`\|xref setox`
77			`\|xref setoxm1`
78
79			`.global stanhd`
80			`stanhd:`
81			`//--TANH(X) = X FOR DENORMALIZED X`
82
83			`bra t_extdnrm`
84
85			`.global stanh`
86			`stanh:`
87			`fmovex (%a0),%fp0 // ...LOAD INPUT`
88
89			`fmovex %fp0,X(%a6)`
90			`movel (%a0),%d0`
91			`movew 4(%a0),%d0`
92			`movel %d0,X(%a6)`
93			`andl #0x7FFFFFFF,%d0`
94			`cmp2l BOUNDS1(%pc),%d0 // ...2**(-40) < \|X\| < (5/2)LOG2 ?`
95			`bcss TANHBORS`
96
97			`//--THIS IS THE USUAL CASE`
98			`//--Y = 2\|X\|, Z = EXPM1(Y), TANH(X) = SIGN(X) * Z / (Z+2).`
99
100			`movel X(%a6),%d0`
101			`movel %d0,SGN(%a6)`
102			`andl #0x7FFF0000,%d0`
103			`addl #0x00010000,%d0 // ...EXPONENT OF 2\|X\|`
104			`movel %d0,X(%a6)`
105			`andl #0x80000000,SGN(%a6)`
106			`fmovex X(%a6),%fp0 // ...FP0 IS Y = 2\|X\|`
107
108			`movel %d1,-(%a7)`
109			`clrl %d1`
110			`fmovemx %fp0-%fp0,(%a0)`
111			`bsr setoxm1 // ...FP0 IS Z = EXPM1(Y)`
112			`movel (%a7)+,%d1`
113
114			`fmovex %fp0,%fp1`
115			`fadds #0x40000000,%fp1 // ...Z+2`
116			`movel SGN(%a6),%d0`
117			`fmovex %fp1,V(%a6)`
118			`eorl %d0,V(%a6)`
119
120			`fmovel %d1,%FPCR //restore users exceptions`
121			`fdivx V(%a6),%fp0`
122			`bra t_frcinx`
123
124			`TANHBORS:`
125			`cmpl #0x3FFF8000,%d0`
126			`blt TANHSM`
127
128			`cmpl #0x40048AA1,%d0`
129			`bgt TANHHUGE`
130
131			`//-- (5/2) LOG2 < \|X\| < 50 LOG2,`
132			`//--TANH(X) = 1 - (2/[EXP(2X)+1]). LET Y = 2\|X\|, SGN = SIGN(X),`
133			`//--TANH(X) = SGN - SGN*2/[EXP(Y)+1].`
134
135			`movel X(%a6),%d0`
136			`movel %d0,SGN(%a6)`
137			`andl #0x7FFF0000,%d0`
138			`addl #0x00010000,%d0 // ...EXPO OF 2\|X\|`
139			`movel %d0,X(%a6) // ...Y = 2\|X\|`
140			`andl #0x80000000,SGN(%a6)`
141			`movel SGN(%a6),%d0`
142			`fmovex X(%a6),%fp0 // ...Y = 2\|X\|`
143
144			`movel %d1,-(%a7)`
145			`clrl %d1`
146			`fmovemx %fp0-%fp0,(%a0)`
147			`bsr setox // ...FP0 IS EXP(Y)`
148			`movel (%a7)+,%d1`
149			`movel SGN(%a6),%d0`
150			`fadds #0x3F800000,%fp0 // ...EXP(Y)+1`
151
152			`eorl #0xC0000000,%d0 // ...-SIGN(X)*2`
153			`fmoves %d0,%fp1 // ...-SIGN(X)*2 IN SGL FMT`
154			`fdivx %fp0,%fp1 // ...-SIGN(X)2 / [EXP(Y)+1 ]`
155
156			`movel SGN(%a6),%d0`
157			`orl #0x3F800000,%d0 // ...SGN`
158			`fmoves %d0,%fp0 // ...SGN IN SGL FMT`
159
160			`fmovel %d1,%FPCR //restore users exceptions`
161			`faddx %fp1,%fp0`
162
163			`bra t_frcinx`
164
165			`TANHSM:`
166			`movew #0x0000,XDCARE(%a6)`
167
168			`fmovel %d1,%FPCR //restore users exceptions`
169			`fmovex X(%a6),%fp0 //last inst - possible exception set`
170
171			`bra t_frcinx`
172
173			`TANHHUGE:`
174			`//---RETURN SGN(X) - SGN(X)EPS`
175			`movel X(%a6),%d0`
176			`andl #0x80000000,%d0`
177			`orl #0x3F800000,%d0`
178			`fmoves %d0,%fp0`
179			`andl #0x80000000,%d0`
180			`eorl #0x80800000,%d0 // ...-SIGN(X)*EPS`
181
182			`fmovel %d1,%FPCR //restore users exceptions`
183			`fadds %d0,%fp0`
184
185			`bra t_frcinx`
186
187			`\|end`

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[/] [or1k/] [trunk/] [rtems/] [c/] [src/] [lib/] [libcpu/] [m68k/] [m68040/] [fpsp/] [stanh.S] - Blame information for rev 1765