c8b3308bb1438f2ccec917137957563fffe8d9c3
[linux-3.10.git] / arch / m68k / fpsp040 / ssinh.S
1 |
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)*Huge*Huge 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52 |       THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA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