stanh.S

  1|
  2|	stanh.sa 3.1 12/10/90
  3|
  4|	The entry point sTanh computes the hyperbolic tangent of
  5|	an input argument; sTanhd 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 tanh(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 stanh takes approximately 270 cycles.
 19|
 20|	Algorithm:
 21|
 22|	TANH
 23|	1. If |X| >= (5/2) log2 or |X| <= 2**(-40), go to 3.
 24|
 25|	2. (2**(-40) < |X| < (5/2) log2) Calculate tanh(X) by
 26|		sgn := sign(X), y := 2|X|, z := expm1(Y), and
 27|		tanh(X) = sgn*( z/(2+z) ).
 28|		Exit.
 29|
 30|	3. (|X| <= 2**(-40) or |X| >= (5/2) log2). If |X| < 1,
 31|		go to 7.
 32|
 33|	4. (|X| >= (5/2) log2) If |X| >= 50 log2, go to 6.
 34|
 35|	5. ((5/2) log2 <= |X| < 50 log2) Calculate tanh(X) by
 36|		sgn := sign(X), y := 2|X|, z := exp(Y),
 37|		tanh(X) = sgn - [ sgn*2/(1+z) ].
 38|		Exit.
 39|
 40|	6. (|X| >= 50 log2) Tanh(X) = +-1 (round to nearest). Thus, we
 41|		calculate Tanh(X) by
 42|		sgn := sign(X), Tiny := 2**(-126),
 43|		tanh(X) := sgn - sgn*Tiny.
 44|		Exit.
 45|
 46|	7. (|X| < 2**(-40)). Tanh(X) = X.	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|STANH	idnt	2,1 | Motorola 040 Floating Point Software Package
 56
 57	|section	8
 58
 59#include "fpsp.h"
 60
 61	.set	X,FP_SCR5
 62	.set	XDCARE,X+2
 63	.set	XFRAC,X+4
 64
 65	.set	SGN,L_SCR3
 66
 67	.set	V,FP_SCR6
 68
 69BOUNDS1:	.long 0x3FD78000,0x3FFFDDCE | ... 2^(-40), (5/2)LOG2
 70
 71	|xref	t_frcinx
 72	|xref	t_extdnrm
 73	|xref	setox
 74	|xref	setoxm1
 75
 76	.global	stanhd
 77stanhd:
 78|--TANH(X) = X FOR DENORMALIZED X
 79
 80	bra		t_extdnrm
 81
 82	.global	stanh
 83stanh:
 84	fmovex		(%a0),%fp0	| ...LOAD INPUT
 85
 86	fmovex		%fp0,X(%a6)
 87	movel		(%a0),%d0
 88	movew		4(%a0),%d0
 89	movel		%d0,X(%a6)
 90	andl		#0x7FFFFFFF,%d0
 91	cmp2l		BOUNDS1(%pc),%d0	| ...2**(-40) < |X| < (5/2)LOG2 ?
 92	bcss		TANHBORS
 93
 94|--THIS IS THE USUAL CASE
 95|--Y = 2|X|, Z = EXPM1(Y), TANH(X) = SIGN(X) * Z / (Z+2).
 96
 97	movel		X(%a6),%d0
 98	movel		%d0,SGN(%a6)
 99	andl		#0x7FFF0000,%d0
100	addl		#0x00010000,%d0	| ...EXPONENT OF 2|X|
101	movel		%d0,X(%a6)
102	andl		#0x80000000,SGN(%a6)
103	fmovex		X(%a6),%fp0		| ...FP0 IS Y = 2|X|
104
105	movel		%d1,-(%a7)
106	clrl		%d1
107	fmovemx	%fp0-%fp0,(%a0)
108	bsr		setoxm1		| ...FP0 IS Z = EXPM1(Y)
109	movel		(%a7)+,%d1
110
111	fmovex		%fp0,%fp1
112	fadds		#0x40000000,%fp1	| ...Z+2
113	movel		SGN(%a6),%d0
114	fmovex		%fp1,V(%a6)
115	eorl		%d0,V(%a6)
116
117	fmovel		%d1,%FPCR		|restore users exceptions
118	fdivx		V(%a6),%fp0
119	bra		t_frcinx
120
121TANHBORS:
122	cmpl		#0x3FFF8000,%d0
123	blt		TANHSM
124
125	cmpl		#0x40048AA1,%d0
126	bgt		TANHHUGE
127
128|-- (5/2) LOG2 < |X| < 50 LOG2,
129|--TANH(X) = 1 - (2/[EXP(2X)+1]). LET Y = 2|X|, SGN = SIGN(X),
130|--TANH(X) = SGN -	SGN*2/[EXP(Y)+1].
131
132	movel		X(%a6),%d0
133	movel		%d0,SGN(%a6)
134	andl		#0x7FFF0000,%d0
135	addl		#0x00010000,%d0	| ...EXPO OF 2|X|
136	movel		%d0,X(%a6)		| ...Y = 2|X|
137	andl		#0x80000000,SGN(%a6)
138	movel		SGN(%a6),%d0
139	fmovex		X(%a6),%fp0		| ...Y = 2|X|
140
141	movel		%d1,-(%a7)
142	clrl		%d1
143	fmovemx	%fp0-%fp0,(%a0)
144	bsr		setox		| ...FP0 IS EXP(Y)
145	movel		(%a7)+,%d1
146	movel		SGN(%a6),%d0
147	fadds		#0x3F800000,%fp0	| ...EXP(Y)+1
148
149	eorl		#0xC0000000,%d0	| ...-SIGN(X)*2
150	fmoves		%d0,%fp1		| ...-SIGN(X)*2 IN SGL FMT
151	fdivx		%fp0,%fp1		| ...-SIGN(X)2 / [EXP(Y)+1 ]
152
153	movel		SGN(%a6),%d0
154	orl		#0x3F800000,%d0	| ...SGN
155	fmoves		%d0,%fp0		| ...SGN IN SGL FMT
156
157	fmovel		%d1,%FPCR		|restore users exceptions
158	faddx		%fp1,%fp0
159
160	bra		t_frcinx
161
162TANHSM:
163	movew		#0x0000,XDCARE(%a6)
164
165	fmovel		%d1,%FPCR		|restore users exceptions
166	fmovex		X(%a6),%fp0		|last inst - possible exception set
167
168	bra		t_frcinx
169
170TANHHUGE:
171|---RETURN SGN(X) - SGN(X)EPS
172	movel		X(%a6),%d0
173	andl		#0x80000000,%d0
174	orl		#0x3F800000,%d0
175	fmoves		%d0,%fp0
176	andl		#0x80000000,%d0
177	eorl		#0x80800000,%d0	| ...-SIGN(X)*EPS
178
179	fmovel		%d1,%FPCR		|restore users exceptions
180	fadds		%d0,%fp0
181
182	bra		t_frcinx
183
184	|end