1|
  2|	scosh.sa 3.1 12/10/90
  3|
  4|	The entry point sCosh computes the hyperbolic cosine of
  5|	an input argument; sCoshd 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 cosh(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 sCOSH takes approximately 250 cycles.
 19|
 20|	Algorithm:
 21|
 22|	COSH
 23|	1. If |X| > 16380 log2, go to 3.
 24|
 25|	2. (|X| <= 16380 log2) Cosh(X) is obtained by the formulae
 26|		y = |X|, z = exp(Y), and
 27|		cosh(X) = (1/2)*( z + 1/z ).
 28|		Exit.
 29|
 30|	3. (|X| > 16380 log2). If |X| > 16480 log2, go to 5.
 31|
 32|	4. (16380 log2 < |X| <= 16480 log2)
 33|		cosh(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|		Fact	:=	2**(16380)
 38|		Y'	:= Y - 16381 log2
 39|		cosh(X) := Fact * exp(Y').
 40|		Exit.
 41|
 42|	5. (|X| > 16480 log2) sinh(X) must overflow. Return
 43|		Huge*Huge to generate overflow and an infinity with
 44|		the appropriate sign. Huge is the largest finite number in
 45|		extended format. Exit.
 46|
 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|SCOSH	idnt	2,1 | Motorola 040 Floating Point Software Package
 56
 57	|section	8
 58
 59	|xref	t_ovfl
 60	|xref	t_frcinx
 61	|xref	setox
 62
 63T1:	.long 0x40C62D38,0xD3D64634 | ... 16381 LOG2 LEAD
 64T2:	.long 0x3D6F90AE,0xB1E75CC7 | ... 16381 LOG2 TRAIL
 65
 66TWO16380: .long 0x7FFB0000,0x80000000,0x00000000,0x00000000
 67
 68	.global	scoshd
 69scoshd:
 70|--COSH(X) = 1 FOR DENORMALIZED X
 71
 72	fmoves		#0x3F800000,%fp0
 73
 74	fmovel		%d1,%FPCR
 75	fadds		#0x00800000,%fp0
 76	bra		t_frcinx
 77
 78	.global	scosh
 79scosh:
 80	fmovex		(%a0),%fp0	| ...LOAD INPUT
 81
 82	movel		(%a0),%d0
 83	movew		4(%a0),%d0
 84	andil		#0x7FFFFFFF,%d0
 85	cmpil		#0x400CB167,%d0
 86	bgts		COSHBIG
 87
 88|--THIS IS THE USUAL CASE, |X| < 16380 LOG2
 89|--COSH(X) = (1/2) * ( EXP(X) + 1/EXP(X) )
 90
 91	fabsx		%fp0		| ...|X|
 92
 93	movel		%d1,-(%sp)
 94	clrl		%d1
 95	fmovemx	%fp0-%fp0,(%a0)	|pass parameter to setox
 96	bsr		setox		| ...FP0 IS EXP(|X|)
 97	fmuls		#0x3F000000,%fp0	| ...(1/2)EXP(|X|)
 98	movel		(%sp)+,%d1
 99
100	fmoves		#0x3E800000,%fp1	| ...(1/4)
101	fdivx		%fp0,%fp1		| ...1/(2 EXP(|X|))
102
103	fmovel		%d1,%FPCR
104	faddx		%fp1,%fp0
105
106	bra		t_frcinx
107
108COSHBIG:
109	cmpil		#0x400CB2B3,%d0
110	bgts		COSHHUGE
111
112	fabsx		%fp0
113	fsubd		T1(%pc),%fp0		| ...(|X|-16381LOG2_LEAD)
114	fsubd		T2(%pc),%fp0		| ...|X| - 16381 LOG2, ACCURATE
115
116	movel		%d1,-(%sp)
117	clrl		%d1
118	fmovemx	%fp0-%fp0,(%a0)
119	bsr		setox
120	fmovel		(%sp)+,%fpcr
121
122	fmulx		TWO16380(%pc),%fp0
123	bra		t_frcinx
124
125COSHHUGE:
126	fmovel		#0,%fpsr		|clr N bit if set by source
127	bclrb		#7,(%a0)		|always return positive value
128	fmovemx	(%a0),%fp0-%fp0
129	bra		t_ovfl
130
131	|end