stanh.S

|
|	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
|
|       For details on the license for this file, please see the
|       file, README, in this same directory.

|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