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
59T1:	.long 0x40C62D38,0xD3D64634 | ... 16381 LOG2 LEAD
60T2:	.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
69ssinhd:
70|--SINH(X) = X FOR DENORMALIZED X
71
72	bra	t_extdnrm
73
74	.global	ssinh
75ssinh:
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
112SINHBIG:
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
135