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-.file "fmod.s"
-
-
-// Copyright (c) 2000 - 2003, Intel Corporation
-// All rights reserved.
-//
-//
-// Redistribution and use in source and binary forms, with or without
-// modification, are permitted provided that the following conditions are
-// met:
-//
-// * Redistributions of source code must retain the above copyright
-// notice, this list of conditions and the following disclaimer.
-//
-// * 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.
-//
-// * The name of Intel Corporation may not be used to endorse or promote
-// products derived from this software without specific prior written
-// permission.
-
-// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS 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 INTEL OR ITS
-// 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.
-//
-// Intel Corporation is the author of this code, and requests that all
-// problem reports or change requests be submitted to it directly at
-// http://www.intel.com/software/products/opensource/libraries/num.htm.
-//
-// History
-//====================================================================
-// 02/02/00 Initial version
-// 03/02/00 New Algorithm
-// 04/04/00 Unwind support added
-// 08/15/00 Bundle added after call to __libm_error_support to properly
-// set [the previously overwritten] GR_Parameter_RESULT.
-// 11/28/00 Set FR_Y to f9
-// 03/11/02 Fixed flags for fmod(qnan,zero)
-// 05/20/02 Cleaned up namespace and sf0 syntax
-// 02/10/03 Reordered header: .section, .global, .proc, .align
-// 04/28/03 Fix: fmod(sNaN,0) no longer sets errno
-//
-// API
-//====================================================================
-// double fmod(double,double);
-//
-// Overview of operation
-//====================================================================
-// fmod(a,b)=a-i*b,
-// where i is an integer such that, if b!=0,
-// |i|<|a/b| and |a/b-i|<1
-//
-// Algorithm
-//====================================================================
-// a). if |a|<|b|, return a
-// b). get quotient and reciprocal overestimates accurate to
-// 33 bits (q2,y2)
-// c). if the exponent difference (exponent(a)-exponent(b))
-// is less than 32, truncate quotient to integer and
-// finish in one iteration
-// d). if exponent(a)-exponent(b)>=32 (q2>=2^32)
-// round quotient estimate to single precision (k=RN(q2)),
-// calculate partial remainder (a'=a-k*b),
-// get quotient estimate (a'*y2), and repeat from c).
-//
-// Special cases
-//====================================================================
-// b=+/-0: return NaN, call libm_error_support
-// a=+/-Inf, a=NaN or b=NaN: return NaN
-//
-// Registers used
-//====================================================================
-// Predicate registers: p6-p11
-// General registers: r2,r29,r32 (ar.pfs), r33-r39
-// Floating point registers: f6-f15
-
-GR_SAVE_B0 = r33
-GR_SAVE_PFS = r34
-GR_SAVE_GP = r35
-GR_SAVE_SP = r36
-
-GR_Parameter_X = r37
-GR_Parameter_Y = r38
-GR_Parameter_RESULT = r39
-GR_Parameter_TAG = r40
-
-FR_X = f10
-FR_Y = f9
-FR_RESULT = f8
-
-
-.section .text
-GLOBAL_IEEE754_ENTRY(fmod)
-
-// inputs in f8, f9
-// result in f8
-
-{ .mfi
- alloc r32=ar.pfs,1,4,4,0
- // f6=|a|
- fmerge.s f6=f0,f8
- mov r2 = 0x0ffdd
-}
- {.mfi
- nop.m 0
- // f7=|b|
- fmerge.s f7=f0,f9
- nop.i 0;;
-}
-
-{ .mfi
- setf.exp f11 = r2
- // (1) y0
- frcpa.s1 f10,p6=f6,f7
- nop.i 0
-}
-
-// Y +-NAN, +-inf, +-0? p7
-{ .mfi
- nop.m 999
- fclass.m.unc p7,p0 = f9, 0xe7
- nop.i 999;;
-}
-
-// qnan snan inf norm unorm 0 -+
-// 1 1 1 0 0 0 11
-// e 3
-// X +-NAN, +-inf, ? p9
-
-{ .mfi
- nop.m 999
- fclass.m.unc p9,p0 = f8, 0xe3
- nop.i 999
-}
-
-// |x| < |y|? Return x p8
-{ .mfi
- nop.m 999
- fcmp.lt.unc.s1 p8,p0 = f6,f7
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 0
- // normalize y (if |x|<|y|)
- (p8) fma.s0 f9=f9,f1,f0
- nop.i 0;;
-}
-
- { .mfi
- mov r2=0x1001f
- // (2) q0=a*y0
- (p6) fma.s1 f13=f6,f10,f0
- nop.i 0
-}
-{ .mfi
- nop.m 0
- // (3) e0 = 1 - b * y0
- (p6) fnma.s1 f12=f7,f10,f1
- nop.i 0;;
-}
-
- {.mfi
- nop.m 0
- // normalize x (if |x|<|y|)
- (p8) fma.d.s0 f8=f8,f1,f0
- nop.i 0
-}
-{.bbb
- (p9) br.cond.spnt FMOD_X_NAN_INF
- (p7) br.cond.spnt FMOD_Y_NAN_INF_ZERO
- // if |x|<|y|, return
- (p8) br.ret.spnt b0;;
-}
-
- {.mfi
- nop.m 0
- // normalize x
- fma.s0 f6=f6,f1,f0
- nop.i 0
-}
-{.mfi
- nop.m 0
- // normalize y
- fma.s0 f7=f7,f1,f0
- nop.i 0;;
-}
-
- {.mfi
- // f15=2^32
- setf.exp f15=r2
- // (4) q1=q0+e0*q0
- (p6) fma.s1 f13=f12,f13,f13
- nop.i 0
-}
-{ .mfi
- nop.m 0
- // (5) e1 = e0 * e0 + 2^-34
- (p6) fma.s1 f14=f12,f12,f11
- nop.i 0;;
-}
-{.mlx
- nop.m 0
- movl r2=0x33a00000;;
-}
-{ .mfi
- nop.m 0
- // (6) y1 = y0 + e0 * y0
- (p6) fma.s1 f10=f12,f10,f10
- nop.i 0;;
-}
-{.mfi
- // set f12=1.25*2^{-24}
- setf.s f12=r2
- // (7) q2=q1+e1*q1
- (p6) fma.s1 f13=f13,f14,f13
- nop.i 0;;
-}
-{.mfi
- nop.m 0
- fmerge.s f9=f8,f9
- nop.i 0
-}
-{ .mfi
- nop.m 0
- // (8) y2 = y1 + e1 * y1
- (p6) fma.s1 f10=f14,f10,f10
- // set p6=0, p10=0
- cmp.ne.and p6,p10=r0,r0;;
-}
-
-.align 32
-loop53:
- {.mfi
- nop.m 0
- // compare q2, 2^32
- fcmp.lt.unc.s1 p8,p7=f13,f15
- nop.i 0
-}
- {.mfi
- nop.m 0
- // will truncate quotient to integer, if exponent<32 (in advance)
- fcvt.fx.trunc.s1 f11=f13
- nop.i 0;;
-}
- {.mfi
- nop.m 0
- // if exponent>32, round quotient to single precision (perform in advance)
- fma.s.s1 f13=f13,f1,f0
- nop.i 0;;
-}
- {.mfi
- nop.m 0
- // set f12=sgn(a)
- (p8) fmerge.s f12=f8,f1
- nop.i 0
-}
- {.mfi
- nop.m 0
- // normalize truncated quotient
- (p8) fcvt.xf f13=f11
- nop.i 0;;
-}
- { .mfi
- nop.m 0
- // calculate remainder (assuming f13=RZ(Q))
- (p7) fnma.s1 f14=f13,f7,f6
- nop.i 0
-}
- {.mfi
- nop.m 0
- // also if exponent>32, round quotient to single precision
- // and subtract 1 ulp: q=q-q*(1.25*2^{-24})
- (p7) fnma.s.s1 f11=f13,f12,f13
- nop.i 0;;
-}
-
- {.mfi
- nop.m 0
- // (p8) calculate remainder (82-bit format)
- (p8) fnma.s1 f11=f13,f7,f6
- nop.i 0
-}
- {.mfi
- nop.m 0
- // (p7) calculate remainder (assuming f11=RZ(Q))
- (p7) fnma.s1 f6=f11,f7,f6
- nop.i 0;;
-}
-
-
- {.mfi
- nop.m 0
- // Final iteration (p8): is f6 the correct remainder (quotient was not overestimated) ?
- (p8) fcmp.lt.unc.s1 p6,p10=f11,f0
- nop.i 0;;
-}
- {.mfi
- nop.m 0
- // get new quotient estimation: a'*y2
- (p7) fma.s1 f13=f14,f10,f0
- nop.i 0
-}
- {.mfb
- nop.m 0
- // was f14=RZ(Q) ? (then new remainder f14>=0)
- (p7) fcmp.lt.unc.s1 p7,p9=f14,f0
- nop.b 0;;
-}
-
-
-.pred.rel "mutex",p6,p10
- {.mfb
- nop.m 0
- // add b to estimated remainder (to cover the case when the quotient was overestimated)
- // also set correct sign by using f9=|b|*sgn(a), f12=sgn(a)
- (p6) fma.d.s0 f8=f11,f12,f9
- nop.b 0
-}
- {.mfb
- nop.m 0
- // calculate remainder (single precision)
- // set correct sign of result before returning
- (p10) fma.d.s0 f8=f11,f12,f0
- (p8) br.ret.sptk b0;;
-}
- {.mfi
- nop.m 0
- // if f13!=RZ(Q), get alternative quotient estimation: a''*y2
- (p7) fma.s1 f13=f6,f10,f0
- nop.i 0
-}
- {.mfb
- nop.m 0
- // if f14 was RZ(Q), set remainder to f14
- (p9) mov f6=f14
- br.cond.sptk loop53;;
-}
-
-
-
-FMOD_X_NAN_INF:
-
-// Y zero ?
-{.mfi
- nop.m 0
- fclass.m p10,p0=f8,0xc3 // Test x=nan
- nop.i 0
-}
-{.mfi
- nop.m 0
- fma.s1 f10=f9,f1,f0
- nop.i 0;;
-}
-
-{.mfi
- nop.m 0
- fma.s0 f8=f8,f1,f0
- nop.i 0
-}
-{.mfi
- nop.m 0
-(p10) fclass.m p10,p0=f9,0x07 // Test x=nan, and y=zero
- nop.i 0;;
-}
-
-{.mfb
- nop.m 0
- fcmp.eq.unc.s1 p11,p0=f10,f0
-(p10) br.ret.spnt b0;; // Exit with result=x if x=nan and y=zero
-}
-{.mib
- nop.m 0
- nop.i 0
- // if Y zero
- (p11) br.cond.spnt FMOD_Y_ZERO;;
-}
-
-// X infinity? Return QNAN indefinite
-{ .mfi
- nop.m 999
- fclass.m.unc p8,p9 = f8, 0x23
- nop.i 999;;
-}
-// Y NaN ?
-{.mfi
- nop.m 999
-(p8) fclass.m p9,p8=f9,0xc3
- nop.i 0;;
-}
-{.mfi
- nop.m 999
-(p8) frcpa.s0 f8,p0 = f8,f8
- nop.i 0
-}
-{ .mfi
- nop.m 999
- // also set Denormal flag if necessary
-(p8) fma.s0 f9=f9,f1,f0
- nop.i 999 ;;
-}
-
-{ .mfb
- nop.m 999
-(p8) fma.d.s0 f8=f8,f1,f0
- nop.b 999 ;;
-}
-
-{ .mfb
- nop.m 999
-(p9) frcpa.s0 f8,p7=f8,f9
- br.ret.sptk b0 ;;
-}
-
-
-FMOD_Y_NAN_INF_ZERO:
-
-// Y INF
-{ .mfi
- nop.m 999
- fclass.m.unc p7,p0 = f9, 0x23
- nop.i 999 ;;
-}
-
-{ .mfb
- nop.m 999
-(p7) fma.d.s0 f8=f8,f1,f0
-(p7) br.ret.spnt b0 ;;
-}
-
-// Y NAN?
-{ .mfi
- nop.m 999
- fclass.m.unc p9,p0 = f9, 0xc3
- nop.i 999 ;;
-}
-
-{ .mfb
- nop.m 999
-(p9) fma.d.s0 f8=f9,f1,f0
-(p9) br.ret.spnt b0 ;;
-}
-
-FMOD_Y_ZERO:
-// Y zero? Must be zero at this point
-// because it is the only choice left.
-// Return QNAN indefinite
-
-{.mfi
- nop.m 0
- // set Invalid
- frcpa.s0 f12,p0=f0,f0
- nop.i 0
-}
-// X NAN?
-{ .mfi
- nop.m 999
- fclass.m.unc p9,p10 = f8, 0xc3
- nop.i 999 ;;
-}
-{ .mfi
- nop.m 999
-(p10) fclass.nm p9,p10 = f8, 0xff
- nop.i 999 ;;
-}
-
-{.mfi
- nop.m 999
- (p9) frcpa.s0 f11,p7=f8,f0
- nop.i 0;;
-}
-
-{ .mfi
- nop.m 999
-(p10) frcpa.s0 f11,p7 = f9,f9
- mov GR_Parameter_TAG = 121 ;;
-}
-
-{ .mfi
- nop.m 999
- fmerge.s f10 = f8, f8
- nop.i 999
-}
-
-{ .mfb
- nop.m 999
- fma.d.s0 f8=f11,f1,f0
- br.sptk __libm_error_region;;
-}
-
-GLOBAL_IEEE754_END(fmod)
-libm_alias_double_other (__fmod, fmod)
-
-LOCAL_LIBM_ENTRY(__libm_error_region)
-.prologue
-{ .mfi
- add GR_Parameter_Y=-32,sp // Parameter 2 value
- nop.f 0
-.save ar.pfs,GR_SAVE_PFS
- mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
-}
-{ .mfi
-.fframe 64
- add sp=-64,sp // Create new stack
- nop.f 0
- mov GR_SAVE_GP=gp // Save gp
-};;
-{ .mmi
- stfd [GR_Parameter_Y] = FR_Y,16 // Save Parameter 2 on stack
- add GR_Parameter_X = 16,sp // Parameter 1 address
-.save b0, GR_SAVE_B0
- mov GR_SAVE_B0=b0 // Save b0
-};;
-.body
-{ .mib
- stfd [GR_Parameter_X] = FR_X // Store Parameter 1 on stack
- add GR_Parameter_RESULT = 0,GR_Parameter_Y
- nop.b 0 // Parameter 3 address
-}
-{ .mib
- stfd [GR_Parameter_Y] = FR_RESULT // Store Parameter 3 on stack
- add GR_Parameter_Y = -16,GR_Parameter_Y
- br.call.sptk b0=__libm_error_support# // Call error handling function
-};;
-{ .mmi
- nop.m 0
- nop.m 0
- add GR_Parameter_RESULT = 48,sp
-};;
-{ .mmi
- ldfd f8 = [GR_Parameter_RESULT] // Get return result off stack
-.restore sp
- add sp = 64,sp // Restore stack pointer
- mov b0 = GR_SAVE_B0 // Restore return address
-};;
-{ .mib
- mov gp = GR_SAVE_GP // Restore gp
- mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
- br.ret.sptk b0 // Return
-};;
-
-LOCAL_LIBM_END(__libm_error_region)
-
-
-.type __libm_error_support#,@function
-.global __libm_error_support#
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