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[/] [or1k/] [trunk/] [linux/] [linux-2.4/] [arch/] [m68k/] [fpsp040/] [stanh.S] - Blame information for rev 1765

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1 1275 phoenix 
|
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|       stanh.sa 3.1 12/10/90
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|
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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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|
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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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|
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|       Output: The value tanh(X) returned in floating-point register Fp0.
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|
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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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|
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|       Speed: The program stanh takes approximately 270 cycles.
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|
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|       Algorithm:
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|
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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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|
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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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|
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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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|
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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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|
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|       7. (|X| < 2**(-40)). Tanh(X) = X.       Exit.
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|
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|               Copyright (C) Motorola, Inc. 1990
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|                       All Rights Reserved
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|
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|       THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA
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|       The copyright notice above does not evidence any
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|       actual or intended publication of such source code.
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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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