Annotation of sys/arch/m68k/fpsp/scosh.sa, Revision 1.1.1.1
1.1 nbrk 1: * $OpenBSD: scosh.sa,v 1.2 1996/05/29 21:05:36 niklas Exp $
2: * $NetBSD: scosh.sa,v 1.2 1994/10/26 07:49:39 cgd Exp $
3:
4: * MOTOROLA MICROPROCESSOR & MEMORY TECHNOLOGY GROUP
5: * M68000 Hi-Performance Microprocessor Division
6: * M68040 Software Package
7: *
8: * M68040 Software Package Copyright (c) 1993, 1994 Motorola Inc.
9: * All rights reserved.
10: *
11: * THE SOFTWARE is provided on an "AS IS" basis and without warranty.
12: * To the maximum extent permitted by applicable law,
13: * MOTOROLA DISCLAIMS ALL WARRANTIES WHETHER EXPRESS OR IMPLIED,
14: * INCLUDING IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A
15: * PARTICULAR PURPOSE and any warranty against infringement with
16: * regard to the SOFTWARE (INCLUDING ANY MODIFIED VERSIONS THEREOF)
17: * and any accompanying written materials.
18: *
19: * To the maximum extent permitted by applicable law,
20: * IN NO EVENT SHALL MOTOROLA BE LIABLE FOR ANY DAMAGES WHATSOEVER
21: * (INCLUDING WITHOUT LIMITATION, DAMAGES FOR LOSS OF BUSINESS
22: * PROFITS, BUSINESS INTERRUPTION, LOSS OF BUSINESS INFORMATION, OR
23: * OTHER PECUNIARY LOSS) ARISING OF THE USE OR INABILITY TO USE THE
24: * SOFTWARE. Motorola assumes no responsibility for the maintenance
25: * and support of the SOFTWARE.
26: *
27: * You are hereby granted a copyright license to use, modify, and
28: * distribute the SOFTWARE so long as this entire notice is retained
29: * without alteration in any modified and/or redistributed versions,
30: * and that such modified versions are clearly identified as such.
31: * No licenses are granted by implication, estoppel or otherwise
32: * under any patents or trademarks of Motorola, Inc.
33:
34: *
35: * scosh.sa 3.1 12/10/90
36: *
37: * The entry point sCosh computes the hyperbolic cosine of
38: * an input argument; sCoshd does the same except for denormalized
39: * input.
40: *
41: * Input: Double-extended number X in location pointed to
42: * by address register a0.
43: *
44: * Output: The value cosh(X) returned in floating-point register Fp0.
45: *
46: * Accuracy and Monotonicity: The returned result is within 3 ulps in
47: * 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
48: * result is subsequently rounded to double precision. The
49: * result is provably monotonic in double precision.
50: *
51: * Speed: The program sCOSH takes approximately 250 cycles.
52: *
53: * Algorithm:
54: *
55: * COSH
56: * 1. If |X| > 16380 log2, go to 3.
57: *
58: * 2. (|X| <= 16380 log2) Cosh(X) is obtained by the formulae
59: * y = |X|, z = exp(Y), and
60: * cosh(X) = (1/2)*( z + 1/z ).
61: * Exit.
62: *
63: * 3. (|X| > 16380 log2). If |X| > 16480 log2, go to 5.
64: *
65: * 4. (16380 log2 < |X| <= 16480 log2)
66: * cosh(X) = sign(X) * exp(|X|)/2.
67: * However, invoking exp(|X|) may cause premature overflow.
68: * Thus, we calculate sinh(X) as follows:
69: * Y := |X|
70: * Fact := 2**(16380)
71: * Y' := Y - 16381 log2
72: * cosh(X) := Fact * exp(Y').
73: * Exit.
74: *
75: * 5. (|X| > 16480 log2) sinh(X) must overflow. Return
76: * Huge*Huge to generate overflow and an infinity with
77: * the appropriate sign. Huge is the largest finite number in
78: * extended format. Exit.
79: *
80:
81: SCOSH IDNT 2,1 Motorola 040 Floating Point Software Package
82:
83: section 8
84:
85: xref t_ovfl
86: xref t_frcinx
87: xref setox
88:
89: T1 DC.L $40C62D38,$D3D64634 ... 16381 LOG2 LEAD
90: T2 DC.L $3D6F90AE,$B1E75CC7 ... 16381 LOG2 TRAIL
91:
92: TWO16380 DC.L $7FFB0000,$80000000,$00000000,$00000000
93:
94: xdef scoshd
95: scoshd:
96: *--COSH(X) = 1 FOR DENORMALIZED X
97:
98: FMOVE.S #:3F800000,FP0
99:
100: FMOVE.L d1,FPCR
101: FADD.S #:00800000,FP0
102: bra t_frcinx
103:
104: xdef scosh
105: scosh:
106: FMOVE.X (a0),FP0 ...LOAD INPUT
107:
108: move.l (a0),d0
109: move.w 4(a0),d0
110: ANDI.L #$7FFFFFFF,d0
111: CMPI.L #$400CB167,d0
112: BGT.B COSHBIG
113:
114: *--THIS IS THE USUAL CASE, |X| < 16380 LOG2
115: *--COSH(X) = (1/2) * ( EXP(X) + 1/EXP(X) )
116:
117: FABS.X FP0 ...|X|
118:
119: move.l d1,-(sp)
120: clr.l d1
121: fmovem.x fp0,(a0) ;pass parameter to setox
122: bsr setox ...FP0 IS EXP(|X|)
123: FMUL.S #:3F000000,FP0 ...(1/2)EXP(|X|)
124: move.l (sp)+,d1
125:
126: FMOVE.S #:3E800000,FP1 ...(1/4)
127: FDIV.X FP0,FP1 ...1/(2 EXP(|X|))
128:
129: FMOVE.L d1,FPCR
130: FADD.X fp1,FP0
131:
132: bra t_frcinx
133:
134: COSHBIG:
135: CMPI.L #$400CB2B3,d0
136: BGT.B COSHHUGE
137:
138: FABS.X FP0
139: FSUB.D T1(pc),FP0 ...(|X|-16381LOG2_LEAD)
140: FSUB.D T2(pc),FP0 ...|X| - 16381 LOG2, ACCURATE
141:
142: move.l d1,-(sp)
143: clr.l d1
144: fmovem.x fp0,(a0)
145: bsr setox
146: fmove.l (sp)+,fpcr
147:
148: FMUL.X TWO16380(pc),FP0
149: bra t_frcinx
150:
151: COSHHUGE:
152: fmove.l #0,fpsr ;clr N bit if set by source
153: bclr.b #7,(a0) ;always return positive value
154: fmovem.x (a0),fp0
155: bra t_ovfl
156:
157: end
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