usr/src/lib/libm/vax/sqrt.s

/*
 * Copyright (c) 1985 Regents of the University of California.
 *
 * Use and reproduction of this software are granted  in  accordance  with
 * the terms and conditions specified in  the  Berkeley  Software  License
 * Agreement (in particular, this entails acknowledgement of the programs'
 * source, and inclusion of this notice) with the additional understanding
 * that  all  recipients  should regard themselves as participants  in  an
 * ongoing  research  project and hence should  feel  obligated  to report
 * their  experiences (good or bad) with these elementary function  codes,
 * using "sendbug 4bsd-bugs@BERKELEY", to the authors.
 *
 *
 * @(#)sqrt.s   1.1 (Berkeley) 8/21/85; 1.2 (ucb.elefunt) %G%
 *
 * double sqrt(arg)   revised August 15,1982
 * double arg;
 * if(arg<0.0) { _errno = EDOM; return(<a reserved operand>); }
 * if arg is a reserved operand it is returned as it is
 * W. Kahan's magic square root
 * coded by Heidi Stettner and revised by Emile LeBlanc 8/18/82
 *
 * entry points:_d_sqrt         address of double arg is on the stack
 *              _sqrt           double arg is on the stack
 */
        .text
        .align  1
        .globl  _sqrt
        .globl  _d_sqrt
        .globl  libm$dsqrt_r5
        .set    EDOM,33

_d_sqrt:
        .word   0x003c          # save r5,r4,r3,r2
        movq    *4(ap),r0
        jmp     dsqrt2
_sqrt:
        .word   0x003c          # save r5,r4,r3,r2
        movq    4(ap),r0
dsqrt2: bicw3   $0x807f,r0,r2   # check exponent of input
        jeql    noexp           # biased exponent is zero -> 0.0 or reserved
        bsbb    libm$dsqrt_r5
noexp:  ret

/* **************************** internal procedure */

libm$dsqrt_r5:                  # ENTRY POINT FOR cdabs and cdsqrt
                                # returns double square root scaled by
                                # 2^r6

        movd    r0,r4
        jleq    nonpos          # argument is not positive
        movzwl  r4,r2
        ashl    $-1,r2,r0
        addw2   $0x203c,r0      # r0 has magic initial approximation
/*
 * Do two steps of Heron's rule
 * ((arg/guess) + guess) / 2 = better guess
 */
        divf3   r0,r4,r2
        addf2   r2,r0
        subw2   $0x80,r0        # divide by two

        divf3   r0,r4,r2
        addf2   r2,r0
        subw2   $0x80,r0        # divide by two

/* Scale argument and approximation to prevent over/underflow */

        bicw3   $0x807f,r4,r1
        subw2   $0x4080,r1              # r1 contains scaling factor
        subw2   r1,r4
        movl    r0,r2
        subw2   r1,r2

/* Cubic step
 *
 * b = a + 2*a*(n-a*a)/(n+3*a*a) where b is better approximation,
 * a is approximation, and n is the original argument.
 * (let s be scale factor in the following comments)
 */
        clrl    r1
        clrl    r3
        muld2   r0,r2                   # r2:r3 = a*a/s
        subd2   r2,r4                   # r4:r5 = n/s - a*a/s
        addw2   $0x100,r2               # r2:r3 = 4*a*a/s
        addd2   r4,r2                   # r2:r3 = n/s + 3*a*a/s
        muld2   r0,r4                   # r4:r5 = a*n/s - a*a*a/s
        divd2   r2,r4                   # r4:r5 = a*(n-a*a)/(n+3*a*a)
        addw2   $0x80,r4                # r4:r5 = 2*a*(n-a*a)/(n+3*a*a)
        addd2   r4,r0                   # r0:r1 = a + 2*a*(n-a*a)/(n+3*a*a)
        rsb                             # DONE!
nonpos:
        jneq    negarg
        ret                     # argument and root are zero
negarg:
        pushl   $EDOM
        calls   $1,_infnan      # generate the reserved op fault
        ret