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Annotation of 43BSDTahoe/usr.lib/libm/vax/cbrt.s, revision 1.1

1.1     ! root        1: # Copyright (c) 1985 Regents of the University of California.
        !             2: # All rights reserved.
        !             3: #
        !             4: # Redistribution and use in source and binary forms are permitted
        !             5: # provided that the above copyright notice and this paragraph are
        !             6: # duplicated in all such forms and that any documentation,
        !             7: # advertising materials, and other materials related to such
        !             8: # distribution and use acknowledge that the software was developed
        !             9: # by the University of California, Berkeley.  The name of the
        !            10: # University may not be used to endorse or promote products derived
        !            11: # from this software without specific prior written permission.
        !            12: # THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR
        !            13: # IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
        !            14: # WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE.
        !            15: #
        !            16: # All recipients should regard themselves as participants in an ongoing
        !            17: # research project and hence should feel obligated to report their
        !            18: # experiences (good or bad) with these elementary function codes, using
        !            19: # the sendbug(8) program, to the authors.
        !            20: #
        !            21: #      @(#)cbrt.s      5.3 (Berkeley) 6/30/88
        !            22: #
        !            23:        .data
        !            24:        .align  2
        !            25: _sccsid:
        !            26: .asciz "@(#)cbrt.s     1.1 (Berkeley) 5/23/85; 5.3 (ucb.elefunt) 6/30/88"
        !            27: 
        !            28: # double cbrt(double arg)
        !            29: # W. Kahan, 10/13/80. revised 1/13/84 for keeping sign symmetry
        !            30: # error check by E LeBlanc, 8/18/82
        !            31: # Revised and tested by K.C. Ng, 5/2/85  
        !            32: # Max error less than 0.667 ulps (unit in the last places)
        !            33:        .globl  _cbrt
        !            34:        .globl  _d_cbrt
        !            35:        .globl  _dcbrt_
        !            36:        .text
        !            37:        .align  1
        !            38: 
        !            39: _cbrt:
        !            40: _d_cbrt:
        !            41:        .word   0x00fc          # save r2 to r7
        !            42:        movq    4(ap),r0        # r0 = argument x
        !            43:        jmp     dcbrt2
        !            44: _dcbrt_:
        !            45:        .word   0x00fc          # save r2 to r7
        !            46:        movq    *4(ap),r0       # r0 = argument x
        !            47: 
        !            48: dcbrt2:        bicw3   $0x807f,r0,r2   # biased exponent of x
        !            49:        jeql    return          # dcbrt(0)=0  dcbrt(res)=res. operand
        !            50:        bicw3   $0x7fff,r0,ap   # ap has sign(x)
        !            51:        xorw2   ap,r0           # r0 is abs(x)
        !            52:        movl    r0,r2           # r2 has abs(x)
        !            53:        rotl    $16,r2,r2       # r2 = |x| with bits unscrambled
        !            54:        divl2   $3,r2           # rough dcbrt with bias/3
        !            55:        addl2   B,r2            # restore bias, diminish fraction
        !            56:        rotl    $16,r2,r2       # r2=|q|=|dcbrt| to 5 bits
        !            57:        mulf3   r2,r2,r3        # r3 =qq
        !            58:        divf2   r0,r3           # r3 = qq/x
        !            59:        mulf2   r2,r3
        !            60:        addf2   C,r3            # r3 = s = C + qqq/x
        !            61:        divf3   r3,D,r4         # r4 = D/s
        !            62:        addf2   E,r4
        !            63:        addf2   r4,r3           # r3 = s + E + D/s
        !            64:        divf3   r3,F,r3         # r3 = F / (s + E + D/s)
        !            65:        addf2   G,r3            # r3 = G + F / (s + E + D/s)
        !            66:        mulf2   r3,r2           # r2 = qr3 = new q to 23 bits
        !            67:        clrl    r3              # r2:r3 = q as double float
        !            68:        muld3   r2,r2,r4        # r4:r5 = qq exactly
        !            69:        divd2   r4,r0           # r0:r1 = x/(q*q) rounded
        !            70:        subd3   r2,r0,r6        # r6:r7 = x/(q*q) - q exactly
        !            71:        movq    r2,r4           # r4:r5 = q
        !            72:        addw2   $0x80,r4        # r4:r5 = 2 * q
        !            73:        addd2   r0,r4           # r4:r5 = 2*q + x/(q*q)
        !            74:        divd2   r4,r6           # r6:r7 = (x/(q*q)-q)/(2*q+x/(q*q))
        !            75:        muld2   r2,r6           # r6:r7 = q*(x/(q*q)-q)/(2*q+x/(q*q))
        !            76:        addd3   r6,r2,r0        # r0:r1 = q + r6:r7
        !            77:        bisw2   ap,r0           # restore the sign bit
        !            78: return:
        !            79:        ret                     # error less than 0.667 ulps
        !            80: 
        !            81: .data
        !            82: .align 2
        !            83: B :    .long            721142941              # (86-0.03306235651)*(2^23)
        !            84: C :    .float          0f0.5428571429          # 19/35
        !            85: D :    .float          0f-0.7053061224         # -864/1225
        !            86: E :    .float          0f1.414285714           # 99/70
        !            87: F :    .float          0f1.607142857           # 45/28
        !            88: G :    .float          0f0.3571428571          # 5/14
        !            89: 

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