GNU Linux-libre 4.9.284-gnu1
[releases.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 |       For details on the license for this file, please see the
53 |       file, README, in this same directory.
54
55 |SSINH  idnt    2,1 | Motorola 040 Floating Point Software Package
56
57         |section        8
58
59 T1:     .long 0x40C62D38,0xD3D64634 | ... 16381 LOG2 LEAD
60 T2:     .long 0x3D6F90AE,0xB1E75CC7 | ... 16381 LOG2 TRAIL
61
62         |xref   t_frcinx
63         |xref   t_ovfl
64         |xref   t_extdnrm
65         |xref   setox
66         |xref   setoxm1
67
68         .global ssinhd
69 ssinhd:
70 |--SINH(X) = X FOR DENORMALIZED X
71
72         bra     t_extdnrm
73
74         .global ssinh
75 ssinh:
76         fmovex  (%a0),%fp0      | ...LOAD INPUT
77
78         movel   (%a0),%d0
79         movew   4(%a0),%d0
80         movel   %d0,%a1         | save a copy of original (compacted) operand
81         andl    #0x7FFFFFFF,%d0
82         cmpl    #0x400CB167,%d0
83         bgts    SINHBIG
84
85 |--THIS IS THE USUAL CASE, |X| < 16380 LOG2
86 |--Y = |X|, Z = EXPM1(Y), SINH(X) = SIGN(X)*(1/2)*( Z + Z/(1+Z) )
87
88         fabsx   %fp0            | ...Y = |X|
89
90         moveml  %a1/%d1,-(%sp)
91         fmovemx %fp0-%fp0,(%a0)
92         clrl    %d1
93         bsr     setoxm1         | ...FP0 IS Z = EXPM1(Y)
94         fmovel  #0,%fpcr
95         moveml  (%sp)+,%a1/%d1
96
97         fmovex  %fp0,%fp1
98         fadds   #0x3F800000,%fp1        | ...1+Z
99         fmovex  %fp0,-(%sp)
100         fdivx   %fp1,%fp0               | ...Z/(1+Z)
101         movel   %a1,%d0
102         andl    #0x80000000,%d0
103         orl     #0x3F000000,%d0
104         faddx   (%sp)+,%fp0
105         movel   %d0,-(%sp)
106
107         fmovel  %d1,%fpcr
108         fmuls   (%sp)+,%fp0     |last fp inst - possible exceptions set
109
110         bra     t_frcinx
111
112 SINHBIG:
113         cmpl    #0x400CB2B3,%d0
114         bgt     t_ovfl
115         fabsx   %fp0
116         fsubd   T1(%pc),%fp0    | ...(|X|-16381LOG2_LEAD)
117         movel   #0,-(%sp)
118         movel   #0x80000000,-(%sp)
119         movel   %a1,%d0
120         andl    #0x80000000,%d0
121         orl     #0x7FFB0000,%d0
122         movel   %d0,-(%sp)      | ...EXTENDED FMT
123         fsubd   T2(%pc),%fp0    | ...|X| - 16381 LOG2, ACCURATE
124
125         movel   %d1,-(%sp)
126         clrl    %d1
127         fmovemx %fp0-%fp0,(%a0)
128         bsr     setox
129         fmovel  (%sp)+,%fpcr
130
131         fmulx   (%sp)+,%fp0     |possible exception
132         bra     t_frcinx
133
134         |end