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