patch-1.3.94 linux/arch/m68k/fpsp040/stanh.S

• Lines: 186
• Date: Sat Feb 24 22:58:44 1996
• Orig file: v1.3.93/linux/arch/m68k/fpsp040/stanh.S
• Orig date: Thu Jan 1 02:00:00 1970

diff -u --recursive --new-file v1.3.93/linux/arch/m68k/fpsp040/stanh.S linux/arch/m68k/fpsp040/stanh.S
@@ -0,0 +1,185 @@
+|
+|	stanh.sa 3.1 12/10/90
+|
+|	The entry point sTanh computes the hyperbolic tangent of
+|	an input argument; sTanhd does the same except for denormalized
+|	input.
+|
+|	Input: Double-extended number X in location pointed to
+|		by address register a0.
+|
+|	Output: The value tanh(X) returned in floating-point register Fp0.
+|
+|	Accuracy and Monotonicity: The returned result is within 3 ulps in
+|		64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
+|		result is subsequently rounded to double precision. The
+|		result is provably monotonic in double precision.
+|
+|	Speed: The program stanh takes approximately 270 cycles.
+|
+|	Algorithm:
+|
+|	TANH
+|	1. If |X| >= (5/2) log2 or |X| <= 2**(-40), go to 3.
+|
+|	2. (2**(-40) < |X| < (5/2) log2) Calculate tanh(X) by
+|		sgn := sign(X), y := 2|X|, z := expm1(Y), and
+|		tanh(X) = sgn*( z/(2+z) ).
+|		Exit.
+|
+|	3. (|X| <= 2**(-40) or |X| >= (5/2) log2). If |X| < 1,
+|		go to 7.
+|
+|	4. (|X| >= (5/2) log2) If |X| >= 50 log2, go to 6.
+|
+|	5. ((5/2) log2 <= |X| < 50 log2) Calculate tanh(X) by
+|		sgn := sign(X), y := 2|X|, z := exp(Y),
+|		tanh(X) = sgn - [ sgn*2/(1+z) ].
+|		Exit.
+|
+|	6. (|X| >= 50 log2) Tanh(X) = +-1 (round to nearest). Thus, we
+|		calculate Tanh(X) by
+|		sgn := sign(X), Tiny := 2**(-126),
+|		tanh(X) := sgn - sgn*Tiny.
+|		Exit.
+|
+|	7. (|X| < 2**(-40)). Tanh(X) = X.	Exit.
+|
+
+|		Copyright (C) Motorola, Inc. 1990
+|			All Rights Reserved
+|
+|	THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA 
+|	The copyright notice above does not evidence any  
+|	actual or intended publication of such source code.
+
+|STANH	idnt	2,1 | Motorola 040 Floating Point Software Package
+
+	|section	8
+	
+	.include "fpsp.h"
+
+	.set	X,FP_SCR5
+	.set	XDCARE,X+2
+	.set	XFRAC,X+4
+
+	.set	SGN,L_SCR3
+
+	.set	V,FP_SCR6
+
+BOUNDS1:	.long 0x3FD78000,0x3FFFDDCE | ... 2^(-40), (5/2)LOG2
+
+	|xref	t_frcinx
+	|xref	t_extdnrm
+	|xref	setox
+	|xref	setoxm1
+
+	.global	stanhd
+stanhd:
+|--TANH(X) = X FOR DENORMALIZED X
+
+	bra		t_extdnrm
+
+	.global	stanh
+stanh:
+	fmovex		(%a0),%fp0	| ...LOAD INPUT
+
+	fmovex		%fp0,X(%a6)
+	movel		(%a0),%d0
+	movew		4(%a0),%d0
+	movel		%d0,X(%a6)
+	andl		#0x7FFFFFFF,%d0
+	cmp2l		BOUNDS1(%pc),%d0	| ...2**(-40) < |X| < (5/2)LOG2 ?
+	bcss		TANHBORS
+
+|--THIS IS THE USUAL CASE
+|--Y = 2|X|, Z = EXPM1(Y), TANH(X) = SIGN(X) * Z / (Z+2).
+
+	movel		X(%a6),%d0
+	movel		%d0,SGN(%a6)
+	andl		#0x7FFF0000,%d0
+	addl		#0x00010000,%d0	| ...EXPONENT OF 2|X|
+	movel		%d0,X(%a6)
+	andl		#0x80000000,SGN(%a6)
+	fmovex		X(%a6),%fp0		| ...FP0 IS Y = 2|X|
+
+	movel		%d1,-(%a7)
+	clrl		%d1
+	fmovemx	%fp0-%fp0,(%a0)
+	bsr		setoxm1	 	| ...FP0 IS Z = EXPM1(Y)
+	movel		(%a7)+,%d1
+
+	fmovex		%fp0,%fp1
+	fadds		#0x40000000,%fp1	| ...Z+2
+	movel		SGN(%a6),%d0
+	fmovex		%fp1,V(%a6)
+	eorl		%d0,V(%a6)
+
+	fmovel		%d1,%FPCR		|restore users exceptions
+	fdivx		V(%a6),%fp0
+	bra		t_frcinx
+
+TANHBORS:
+	cmpl		#0x3FFF8000,%d0
+	blt		TANHSM
+
+	cmpl		#0x40048AA1,%d0
+	bgt		TANHHUGE
+
+|-- (5/2) LOG2 < |X| < 50 LOG2,
+|--TANH(X) = 1 - (2/[EXP(2X)+1]). LET Y = 2|X|, SGN = SIGN(X),
+|--TANH(X) = SGN -	SGN*2/[EXP(Y)+1].
+
+	movel		X(%a6),%d0
+	movel		%d0,SGN(%a6)
+	andl		#0x7FFF0000,%d0
+	addl		#0x00010000,%d0	| ...EXPO OF 2|X|
+	movel		%d0,X(%a6)		| ...Y = 2|X|
+	andl		#0x80000000,SGN(%a6)
+	movel		SGN(%a6),%d0
+	fmovex		X(%a6),%fp0		| ...Y = 2|X|
+
+	movel		%d1,-(%a7)
+	clrl		%d1
+	fmovemx	%fp0-%fp0,(%a0)
+	bsr		setox		| ...FP0 IS EXP(Y)
+	movel		(%a7)+,%d1
+	movel		SGN(%a6),%d0
+	fadds		#0x3F800000,%fp0	| ...EXP(Y)+1
+
+	eorl		#0xC0000000,%d0	| ...-SIGN(X)*2
+	fmoves		%d0,%fp1		| ...-SIGN(X)*2 IN SGL FMT
+	fdivx		%fp0,%fp1	 	| ...-SIGN(X)2 / [EXP(Y)+1 ]
+
+	movel		SGN(%a6),%d0
+	orl		#0x3F800000,%d0	| ...SGN
+	fmoves		%d0,%fp0		| ...SGN IN SGL FMT
+
+	fmovel		%d1,%FPCR		|restore users exceptions
+	faddx		%fp1,%fp0
+
+	bra		t_frcinx
+
+TANHSM:
+	movew		#0x0000,XDCARE(%a6)
+
+	fmovel		%d1,%FPCR		|restore users exceptions
+	fmovex		X(%a6),%fp0		|last inst - possible exception set
+
+	bra		t_frcinx
+
+TANHHUGE:
+|---RETURN SGN(X) - SGN(X)EPS
+	movel		X(%a6),%d0
+	andl		#0x80000000,%d0
+	orl		#0x3F800000,%d0
+	fmoves		%d0,%fp0
+	andl		#0x80000000,%d0
+	eorl		#0x80800000,%d0	| ...-SIGN(X)*EPS
+
+	fmovel		%d1,%FPCR		|restore users exceptions
+	fadds		%d0,%fp0
+
+	bra		t_frcinx
+
+	|end