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533 lines
11 KiB
533 lines
11 KiB
.file "fmod.s"
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// Copyright (c) 2000, 2001, Intel Corporation
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// All rights reserved.
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//
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// Contributed 2/2/2000 by John Harrison, Cristina Iordache, Ted Kubaska,
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// Bob Norin, Shane Story, and Ping Tak Peter Tang of the Computational
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// Software Lab, Intel Corporation.
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//
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// WARRANTY DISCLAIMER
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//
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
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// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
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// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
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// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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//
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// Intel Corporation is the author of this code, and requests that all
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// problem reports or change requests be submitted to it directly at
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// http://developer.intel.com/opensource.
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//
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// History
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//====================================================================
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// 2/02/00 Initial version
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// 3/02/00 New Algorithm
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// 4/04/00 Unwind support added
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// 8/15/00 Bundle added after call to __libm_error_support to properly
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// set [the previously overwritten] GR_Parameter_RESULT.
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//11/28/00 Set FR_Y to f9
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//
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// API
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//====================================================================
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// double fmod(double,double);
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//
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// Overview of operation
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//====================================================================
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// fmod(a,b)=a-i*b,
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// where i is an integer such that, if b!=0,
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// |i|<|a/b| and |a/b-i|<1
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//
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// Algorithm
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//====================================================================
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// a). if |a|<|b|, return a
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// b). get quotient and reciprocal overestimates accurate to
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// 33 bits (q2,y2)
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// c). if the exponent difference (exponent(a)-exponent(b))
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// is less than 32, truncate quotient to integer and
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// finish in one iteration
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// d). if exponent(a)-exponent(b)>=32 (q2>=2^32)
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// round quotient estimate to single precision (k=RN(q2)),
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// calculate partial remainder (a'=a-k*b),
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// get quotient estimate (a'*y2), and repeat from c).
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//
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// Special cases
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//====================================================================
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// b=+/-0: return NaN, call libm_error_support
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// a=+/-Inf, a=NaN or b=NaN: return NaN
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//
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// Registers used
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//====================================================================
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// Predicate registers: p6-p11
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// General registers: r2,r29,r32 (ar.pfs), r33-r39
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// Floating point registers: f6-f15
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.section .text
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GR_SAVE_B0 = r33
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GR_SAVE_PFS = r34
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GR_SAVE_GP = r35
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GR_SAVE_SP = r36
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GR_Parameter_X = r37
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GR_Parameter_Y = r38
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GR_Parameter_RESULT = r39
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GR_Parameter_TAG = r40
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FR_X = f10
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FR_Y = f9
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FR_RESULT = f8
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.proc fmod#
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.align 32
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.global fmod#
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.align 32
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fmod:
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// inputs in f8, f9
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// result in f8
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{ .mfi
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alloc r32=ar.pfs,1,4,4,0
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// f6=|a|
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fmerge.s f6=f0,f8
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mov r2 = 0x0ffdd
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}
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{.mfi
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nop.m 0
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// f7=|b|
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fmerge.s f7=f0,f9
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nop.i 0;;
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}
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{ .mfi
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setf.exp f11 = r2
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// (1) y0
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frcpa.s1 f10,p6=f6,f7
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nop.i 0
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}
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// Y +-NAN, +-inf, +-0? p7
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{ .mfi
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nop.m 999
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fclass.m.unc p7,p0 = f9, 0xe7
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nop.i 999;;
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}
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// qnan snan inf norm unorm 0 -+
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// 1 1 1 0 0 0 11
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// e 3
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// X +-NAN, +-inf, ? p9
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{ .mfi
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nop.m 999
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fclass.m.unc p9,p0 = f8, 0xe3
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nop.i 999
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}
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// |x| < |y|? Return x p8
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{ .mfi
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nop.m 999
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fcmp.lt.unc.s1 p8,p0 = f6,f7
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nop.i 999 ;;
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}
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{ .mfi
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nop.m 0
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// normalize y (if |x|<|y|)
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(p8) fma.s0 f9=f9,f1,f0
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nop.i 0;;
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}
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{ .mfi
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mov r2=0x1001f
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// (2) q0=a*y0
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(p6) fma.s1 f13=f6,f10,f0
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nop.i 0
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}
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{ .mfi
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nop.m 0
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// (3) e0 = 1 - b * y0
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(p6) fnma.s1 f12=f7,f10,f1
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nop.i 0;;
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}
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{.mfi
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nop.m 0
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// normalize x (if |x|<|y|)
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(p8) fma.d.s0 f8=f8,f1,f0
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nop.i 0
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}
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{.bbb
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(p9) br.cond.spnt FMOD_X_NAN_INF
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(p7) br.cond.spnt FMOD_Y_NAN_INF_ZERO
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// if |x|<|y|, return
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(p8) br.ret.spnt b0;;
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}
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{.mfi
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nop.m 0
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// normalize x
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fma.s0 f6=f6,f1,f0
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nop.i 0
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}
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{.mfi
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nop.m 0
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// normalize y
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fma.s0 f7=f7,f1,f0
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nop.i 0;;
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}
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{.mfi
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// f15=2^32
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setf.exp f15=r2
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// (4) q1=q0+e0*q0
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(p6) fma.s1 f13=f12,f13,f13
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nop.i 0
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}
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{ .mfi
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nop.m 0
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// (5) e1 = e0 * e0 + 2^-34
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(p6) fma.s1 f14=f12,f12,f11
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nop.i 0;;
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}
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{.mlx
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nop.m 0
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movl r2=0x33a00000;;
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}
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{ .mfi
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nop.m 0
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// (6) y1 = y0 + e0 * y0
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(p6) fma.s1 f10=f12,f10,f10
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nop.i 0;;
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}
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{.mfi
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// set f12=1.25*2^{-24}
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setf.s f12=r2
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// (7) q2=q1+e1*q1
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(p6) fma.s1 f13=f13,f14,f13
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nop.i 0;;
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}
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{.mfi
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nop.m 0
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fmerge.s f9=f8,f9
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nop.i 0
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}
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{ .mfi
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nop.m 0
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// (8) y2 = y1 + e1 * y1
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(p6) fma.s1 f10=f14,f10,f10
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// set p6=0, p10=0
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cmp.ne.and p6,p10=r0,r0;;
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}
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.align 32
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loop53:
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{.mfi
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nop.m 0
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// compare q2, 2^32
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fcmp.lt.unc.s1 p8,p7=f13,f15
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nop.i 0
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}
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{.mfi
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nop.m 0
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// will truncate quotient to integer, if exponent<32 (in advance)
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fcvt.fx.trunc.s1 f11=f13
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nop.i 0;;
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}
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{.mfi
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nop.m 0
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// if exponent>32, round quotient to single precision (perform in advance)
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fma.s.s1 f13=f13,f1,f0
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nop.i 0;;
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}
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{.mfi
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nop.m 0
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// set f12=sgn(a)
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(p8) fmerge.s f12=f8,f1
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nop.i 0
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}
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{.mfi
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nop.m 0
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// normalize truncated quotient
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(p8) fcvt.xf f13=f11
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nop.i 0;;
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}
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{ .mfi
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nop.m 0
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// calculate remainder (assuming f13=RZ(Q))
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(p7) fnma.s1 f14=f13,f7,f6
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nop.i 0
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}
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{.mfi
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nop.m 0
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// also if exponent>32, round quotient to single precision
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// and subtract 1 ulp: q=q-q*(1.25*2^{-24})
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(p7) fnma.s.s1 f11=f13,f12,f13
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nop.i 0;;
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}
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{.mfi
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nop.m 0
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// (p8) calculate remainder (82-bit format)
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(p8) fnma.s1 f11=f13,f7,f6
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nop.i 0
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}
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{.mfi
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nop.m 0
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// (p7) calculate remainder (assuming f11=RZ(Q))
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(p7) fnma.s1 f6=f11,f7,f6
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nop.i 0;;
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}
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{.mfi
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nop.m 0
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// Final iteration (p8): is f6 the correct remainder (quotient was not overestimated) ?
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(p8) fcmp.lt.unc.s1 p6,p10=f11,f0
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nop.i 0;;
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}
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{.mfi
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nop.m 0
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// get new quotient estimation: a'*y2
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(p7) fma.s1 f13=f14,f10,f0
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nop.i 0
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}
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{.mfb
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nop.m 0
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// was f14=RZ(Q) ? (then new remainder f14>=0)
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(p7) fcmp.lt.unc.s1 p7,p9=f14,f0
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nop.b 0;;
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}
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.pred.rel "mutex",p6,p10
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{.mfb
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nop.m 0
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// add b to estimated remainder (to cover the case when the quotient was overestimated)
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// also set correct sign by using f9=|b|*sgn(a), f12=sgn(a)
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(p6) fma.d.s0 f8=f11,f12,f9
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nop.b 0
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}
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{.mfb
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nop.m 0
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// calculate remainder (single precision)
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// set correct sign of result before returning
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(p10) fma.d.s0 f8=f11,f12,f0
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(p8) br.ret.sptk b0;;
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}
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{.mfi
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nop.m 0
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// if f13!=RZ(Q), get alternative quotient estimation: a''*y2
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(p7) fma.s1 f13=f6,f10,f0
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nop.i 0
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}
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{.mfb
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nop.m 0
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// if f14 was RZ(Q), set remainder to f14
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(p9) mov f6=f14
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br.cond.sptk loop53;;
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}
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FMOD_X_NAN_INF:
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// Y zero ?
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{.mfi
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nop.m 0
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fma.s1 f10=f9,f1,f0
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nop.i 0;;
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}
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{.mfi
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nop.m 0
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fcmp.eq.unc.s1 p11,p0=f10,f0
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nop.i 0;;
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}
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{.mib
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nop.m 0
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nop.i 0
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// if Y zero
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(p11) br.cond.spnt FMOD_Y_ZERO;;
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}
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// X infinity? Return QNAN indefinite
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{ .mfi
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nop.m 999
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fclass.m.unc p8,p9 = f8, 0x23
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nop.i 999;;
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}
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// Y NaN ?
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{.mfi
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nop.m 999
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(p8) fclass.m p9,p8=f9,0xc3
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nop.i 0;;
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}
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{.mfi
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nop.m 999
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(p8) frcpa.s0 f8,p0 = f8,f8
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nop.i 0
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}
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{ .mfi
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nop.m 999
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// also set Denormal flag if necessary
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(p8) fma.s0 f9=f9,f1,f0
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nop.i 999 ;;
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}
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{ .mfb
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nop.m 999
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(p8) fma.d f8=f8,f1,f0
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nop.b 999 ;;
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}
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{ .mfb
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nop.m 999
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(p9) frcpa.s0 f8,p7=f8,f9
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br.ret.sptk b0 ;;
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}
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FMOD_Y_NAN_INF_ZERO:
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// Y INF
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{ .mfi
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nop.m 999
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fclass.m.unc p7,p0 = f9, 0x23
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nop.i 999 ;;
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}
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{ .mfb
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nop.m 999
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(p7) fma.d f8=f8,f1,f0
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(p7) br.ret.spnt b0 ;;
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}
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// Y NAN?
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{ .mfi
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nop.m 999
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fclass.m.unc p9,p0 = f9, 0xc3
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nop.i 999 ;;
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}
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{ .mfb
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nop.m 999
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(p9) fma.d f8=f9,f1,f0
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(p9) br.ret.spnt b0 ;;
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}
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FMOD_Y_ZERO:
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// Y zero? Must be zero at this point
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// because it is the only choice left.
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// Return QNAN indefinite
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{.mfi
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nop.m 0
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// set Invalid
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frcpa f12,p0=f0,f0
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nop.i 0
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}
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// X NAN?
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{ .mfi
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nop.m 999
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fclass.m.unc p9,p10 = f8, 0xc3
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nop.i 999 ;;
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}
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{ .mfi
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nop.m 999
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(p10) fclass.nm p9,p10 = f8, 0xff
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nop.i 999 ;;
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}
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{.mfi
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nop.m 999
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(p9) frcpa f11,p7=f8,f0
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nop.i 0;;
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}
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{ .mfi
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nop.m 999
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(p10) frcpa f11,p7 = f9,f9
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mov GR_Parameter_TAG = 121 ;;
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}
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{ .mfi
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nop.m 999
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fmerge.s f10 = f8, f8
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nop.i 999
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}
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{ .mfb
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nop.m 999
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fma.d f8=f11,f1,f0
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br.sptk __libm_error_region;;
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}
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.endp fmod
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.proc __libm_error_region
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__libm_error_region:
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.prologue
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{ .mfi
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add GR_Parameter_Y=-32,sp // Parameter 2 value
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nop.f 0
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.save ar.pfs,GR_SAVE_PFS
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mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
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}
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{ .mfi
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.fframe 64
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add sp=-64,sp // Create new stack
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nop.f 0
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mov GR_SAVE_GP=gp // Save gp
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};;
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{ .mmi
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stfd [GR_Parameter_Y] = FR_Y,16 // Save Parameter 2 on stack
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add GR_Parameter_X = 16,sp // Parameter 1 address
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.save b0, GR_SAVE_B0
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mov GR_SAVE_B0=b0 // Save b0
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};;
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.body
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{ .mib
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stfd [GR_Parameter_X] = FR_X // Store Parameter 1 on stack
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add GR_Parameter_RESULT = 0,GR_Parameter_Y
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nop.b 0 // Parameter 3 address
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}
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{ .mib
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stfd [GR_Parameter_Y] = FR_RESULT // Store Parameter 3 on stack
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add GR_Parameter_Y = -16,GR_Parameter_Y
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br.call.sptk b0=__libm_error_support# // Call error handling function
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};;
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{ .mmi
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nop.m 0
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nop.m 0
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add GR_Parameter_RESULT = 48,sp
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};;
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{ .mmi
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ldfd f8 = [GR_Parameter_RESULT] // Get return result off stack
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.restore
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add sp = 64,sp // Restore stack pointer
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mov b0 = GR_SAVE_B0 // Restore return address
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};;
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{ .mib
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mov gp = GR_SAVE_GP // Restore gp
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mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
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br.ret.sptk b0 // Return
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};;
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.endp __libm_error_region
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.type __libm_error_support#,@function
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.global __libm_error_support#
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