/* $NetBSD: n_cbrt.S,v 1.9 2024/05/07 15:15:31 riastradh Exp $ */ /* * Copyright (c) 1985, 1993 * The Regents of the University of California. All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * 3. Neither the name of the University nor the names of its contributors * may be used to endorse or promote products derived from this software * without specific prior written permission. * * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF * SUCH DAMAGE. * * @(#)cbrt.s 8.1 (Berkeley) 6/4/93 */ #include <machine/asm.h> /* * double cbrt(double arg) * W. Kahan, 10/13/80. revised 1/13/84 for keeping sign symmetry * error check by E LeBlanc, 8/18/82 * Revised and tested by K.C. Ng, 5/2/85 * Max error less than 0.667 ulps (unit in the last places) */ ENTRY(cbrtf, 0) cvtfd 4(%ap),-(%sp) calls $2,_C_LABEL(cbrt) cvtdf %r0,%r0 ret END(cbrtf) #ifdef WEAK_ALIAS WEAK_ALIAS(cbrtl, cbrt) #endif STRONG_ALIAS(cbrt, d_cbrt) ENTRY(d_cbrt, 0x00c0) # save %r6 & %r7 movq 4(%ap),%r0 # %r0 = argument x jbr dcbrt2 END(d_cbrt) ENTRY(dcbrt_, 0x00c0) # save %r6 & %r7 movq *4(%ap),%r0 # %r0 = argument x dcbrt2: bicw3 $0x807f,%r0,%r2 # biased exponent of x jeql return # dcbrt(0)=0 dcbrt(res)=res. operand bicw3 $0x7fff,%r0,%ap # ap has sign(x) xorw2 %ap,%r0 # %r0 is abs(x) movl %r0,%r2 # %r2 has abs(x) rotl $16,%r2,%r2 # %r2 = |x| with bits unscrambled divl2 $3,%r2 # rough dcbrt with bias/3 addl2 B,%r2 # restore bias, diminish fraction rotl $16,%r2,%r2 # %r2=|q|=|dcbrt| to 5 bits mulf3 %r2,%r2,%r3 # %r3 =qq divf2 %r0,%r3 # %r3 = qq/x mulf2 %r2,%r3 addf2 C,%r3 # %r3 = s = C + qqq/x divf3 %r3,D,%r4 # %r4 = D/s addf2 E,%r4 addf2 %r4,%r3 # %r3 = s + E + D/s divf3 %r3,F,%r3 # %r3 = F / (s + E + D/s) addf2 G,%r3 # %r3 = G + F / (s + E + D/s) mulf2 %r3,%r2 # %r2 = q%r3 = new q to 23 bits clrl %r3 # %r2:%r3 = q as double float muld3 %r2,%r2,%r4 # %r4:%r5 = qq exactly divd2 %r4,%r0 # %r0:%r1 = x/(q*q) rounded subd3 %r2,%r0,%r6 # %r6:%r7 = x/(q*q) - q exactly movq %r2,%r4 # %r4:%r5 = q addw2 $0x80,%r4 # %r4:%r5 = 2 * q addd2 %r0,%r4 # %r4:%r5 = 2*q + x/(q*q) divd2 %r4,%r6 # %r6:%r7 = (x/(q*q)-q)/(2*q+x/(q*q)) muld2 %r2,%r6 # %r6:%r7 = q*(x/(q*q)-q)/(2*q+x/(q*q)) addd3 %r6,%r2,%r0 # %r0:%r1 = q + %r6:%r7 bisw2 %ap,%r0 # restore the sign bit return: ret # error less than 0.667 ulps END(dcbrt_) _ALIGN_TEXT B : .long 721142941 # (86-0.03306235651)*(2^23) C : .float 0f0.5428571429 # 19/35 D : .float 0f-0.7053061224 # -864/1225 E : .float 0f1.414285714 # 99/70 F : .float 0f1.607142857 # 45/28 G : .float 0f0.3571428571 # 5/14
