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|
|
| 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
|
