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+.file "remainder.s"
+
+
+// Copyright (c) 2000 - 2003, Intel Corporation
+// All rights reserved.
+//
+// Contributed 2000 by the Intel Numerics Group, Intel Corporation
+//
+// 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
+// 07/21/00 Fixed quotient=2^{24*m+23}*1.q1...q23 1 bug
+// 08/15/00 Bundle added after call to __libm_error_support to properly
+//          set [the previously overwritten] GR_Parameter_RESULT.
+// 11/29/00 Set FR_Y to f9
+// 05/20/02 Cleaned up namespace and sf0 syntax
+// 02/10/03 Reordered header: .section, .global, .proc, .align
+//
+// API
+//====================================================================
+// double remainder(double,double);
+//
+// Overview of operation
+//====================================================================
+//  remainder(a,b)=a-i*b,
+//  where i is an integer such that, if b!=0 and a is finite,
+//  |a/b-i|<=1/2. If |a/b-i|=1/2, i is even.
+//
+// Algorithm
+//====================================================================
+// a). eliminate special cases
+// b). if |a/b|<0.25 (first quotient estimate), return a
+// c). use single precision divide algorithm to get quotient q
+//     rounded to 24 bits of precision
+// d). calculate partial remainders (using both q and q-ulp);
+//     select one and RZ(a/b) based on the sign of |a|-|b|*q
+// e). if the exponent difference (exponent(a)-exponent(b))
+//     is less than 24 (quotient estimate<2^{24}-2), use RZ(a/b)
+//     and sticky bits to round to integer; exit loop and
+//     calculate final remainder
+// f). if exponent(a)-exponent(b)>=24, select new value of a as
+//     the partial remainder calculated using RZ(a/b);
+//     repeat from c).
+//
+// Special cases
+//====================================================================
+// a=+/- Inf, or b=+/-0: return NaN, call libm_error_support
+// a=NaN or b=NaN: return NaN
+
+// Registers used
+//====================================================================
+// Predicate registers: p6-p14
+// General registers:   r2,r3,r28,r29,r32 (ar.pfs), r33-r39
+// Floating point registers: f6-f15,f32
+
+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(remainder)
+
+// inputs in f8, f9
+// result in f8
+
+{ .mfi
+  alloc r32=ar.pfs,1,4,4,0
+  // f13=|a|
+  fmerge.s f13=f0,f8
+  nop.i 0
+}
+  {.mfi
+  nop.m 0
+  // f14=|b|
+  fmerge.s f14=f0,f9
+  nop.i 0;;
+}
+ {.mlx
+  mov r28=0x2ffdd
+  // r2=2^{23}
+  movl r3=0x4b000000;;
+}
+
+// Y +-NAN, +-inf, +-0?     p11
+{ .mfi
+	  setf.exp f32=r28
+      fclass.m.unc  p11,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;;
+}
+
+{.mfi
+  nop.m 0
+  mov f12=f0
+  nop.i 0
+}
+{ .mfi
+  // set p7=1
+  cmp.eq.unc p7,p0=r0,r0
+  // Step (1)
+  // y0 = 1 / b in f10
+  frcpa.s1 f10,p6=f13,f14
+  nop.i 0;;
+}
+
+{.bbb
+  (p9) br.cond.spnt FREM_X_NAN_INF
+  (p11) br.cond.spnt FREM_Y_NAN_INF_ZERO
+  nop.b 0
+}  {.mfi
+   nop.m 0
+   // set D flag if a (f8) is denormal
+   fnma.s0 f6=f8,f1,f8
+   nop.i 0;;
+}
+
+
+remloop24:
+  { .mfi
+  nop.m 0
+  // Step (2)
+  // q0 = a * y0 in f12
+  (p6) fma.s1 f12=f13,f10,f0
+  nop.i 0
+} { .mfi
+  nop.m 0
+  // Step (3)
+  // e0 = 1 - b * y0 in f7
+  (p6) fnma.s1 f7=f14,f10,f1
+  nop.i 0;;
+}  {.mlx
+  nop.m 0
+  // r2=1.25*2^{-24}
+  movl r2=0x33a00000;;
+}
+
+{.mfi
+  nop.m 0
+  // q1=q0*(1+e0)
+  (p6) fma.s1 f15=f12,f7,f12
+  nop.i 0
+}
+{ .mfi
+  nop.m 0
+  // Step (4)
+  // e1 = e0 * e0 + E in f7
+  (p6) fma.s1 f7=f7,f7,f32
+  nop.i 0;;
+}
+ {.mii
+  (p7) getf.exp r29=f12
+  (p7) mov r28=0xfffd
+  nop.i 0;;
+}
+ { .mfi
+  // f12=2^{23}
+  setf.s f12=r3
+  // Step (5)
+  // q2 = q1 + e1 * q1 in f11
+  (p6) fma.s.s1 f11=f7,f15,f15
+  nop.i 0
+} { .mfi
+   nop.m 0
+  // Step (6)
+  // q2 = q1 + e1 * q1 in f6
+  (p6) fma.s1 f6=f7,f15,f15
+  nop.i 0;;
+}
+
+ {.mmi
+  // f15=1.25*2^{-24}
+  setf.s f15=r2
+  // q<1/4 ? (i.e. expon< -2)
+  (p7) cmp.gt p7,p0=r28,r29
+  nop.i 0;;
+}
+
+{.mfb
+  // r29= -32+bias
+  mov r29=0xffdf
+ // if |a/b|<1/4, set D flag before returning
+ (p7) fma.d.s0 f9=f9,f0,f8
+  nop.b 0;;
+}
+ {.mfb
+ nop.m 0
+ // can be combined with bundle above if sign of 0 or
+ // FTZ enabled are not important
+ (p7) fmerge.s f8=f8,f9
+ // return if |a|<4*|b| (estimated quotient < 1/4)
+ (p7) br.ret.spnt b0;;
+}
+  {.mfi
+  // f7=2^{-32}
+  setf.exp f7=r29
+  // set f8 to current a value | sign
+  fmerge.s f8=f8,f13
+  nop.i 0;;
+}
+
+
+  {.mfi
+  getf.exp r28=f6
+  // last step ? (q<2^{23})
+  fcmp.lt.unc.s1 p0,p12=f6,f12
+  nop.i 0;;
+}
+  {.mfi
+  nop.m 0
+  // r=a-b*q
+  fnma.s1 f6=f14,f11,f13
+  nop.i 0
+} {.mfi
+  // r2=23+bias
+  mov r2=0xffff+23
+  // q'=q-q*(1.25*2^{-24})   (q'=q-ulp)
+  fnma.s.s1 f15=f11,f15,f11
+  nop.i 0;;
+}
+  {.mmi
+  nop.m 0
+  cmp.eq p11,p14=r2,r28
+  nop.i 0;;
+}
+
+.pred.rel "mutex",p11,p14
+  {.mfi
+  nop.m 0
+  // if exp_q=2^23, then r=a-b*2^{23}
+  (p11) fnma.s1 f13=f12,f14,f13
+  nop.i 0
+}
+{.mfi
+  nop.m 0
+  // r2=a-b*q'
+  (p14) fnma.s1 f13=f14,f15,f13
+  nop.i 0;;
+}
+  {.mfi
+  nop.m 0
+  // r>0 iff q=RZ(a/b) and inexact
+  fcmp.gt.unc.s1 p8,p0=f6,f0
+  nop.i 0
+} {.mfi
+  nop.m 0
+  // r<0 iff q'=RZ(a/b) and inexact
+  (p14) fcmp.lt.unc.s1 p9,p10=f6,f0
+  nop.i 0;;
+}
+
+.pred.rel "mutex",p8,p9
+  {.mfi
+   nop.m 0
+  // (p8) Q=q+(last iteration ? sticky bits:0)
+  // i.e. Q=q+q*x  (x=2^{-32} or 0)
+  (p8) fma.s1 f11=f11,f7,f11
+  nop.i 0
+} {.mfi
+  nop.m 0
+  // (p9) Q=q'+(last iteration ? sticky bits:0)
+  // i.e. Q=q'+q'*x  (x=2^{-32} or 0)
+  (p9) fma.s1 f11=f15,f7,f15
+  nop.i 0;;
+}
+
+  {.mfb
+  nop.m 0
+  //  (p9) set r=r2 (new a, if not last iteration)
+  // (p10) new a =r
+  (p10) mov f13=f6
+  (p12) br.cond.sptk remloop24;;
+}
+
+// last iteration
+  {.mfi
+  nop.m 0
+  // set f9=|b|*sgn(a)
+  fmerge.s f9=f8,f9
+  nop.i 0
+}
+  {.mfi
+  nop.m 0
+  // round to integer
+  fcvt.fx.s1 f11=f11
+  nop.i 0;;
+}
+  {.mfi
+  nop.m 0
+  // save sign of a
+  fmerge.s f7=f8,f8
+  nop.i 0
+} {.mfi
+  nop.m 0
+  // normalize
+  fcvt.xf f11=f11
+  nop.i 0;;
+}
+  {.mfi
+  nop.m 0
+  // This can be removed if sign of 0 is not important
+  // get remainder using sf1
+  fnma.d.s1 f12=f9,f11,f8
+  nop.i 0
+}
+  {.mfi
+  nop.m 0
+  // get remainder
+  fnma.d.s0 f8=f9,f11,f8
+  nop.i 0;;
+}
+  {.mfi
+  nop.m 0
+  // f12=0?
+  // This can be removed if sign of 0 is not important
+  fcmp.eq.unc.s1 p8,p0=f12,f0
+  nop.i 0;;
+}
+  {.mfb
+  nop.m 0
+  // if f8=0, set sign correctly
+  // This can be removed if sign of 0 is not important
+  (p8) fmerge.s f8=f7,f8
+  // return
+  br.ret.sptk b0;;
+}
+
+
+FREM_X_NAN_INF:
+
+// Y zero ?
+{.mfi
+  nop.m 0
+  fma.s1 f10=f9,f1,f0
+  nop.i 0;;
+}
+{.mfi
+ nop.m 0
+ fcmp.eq.unc.s1 p11,p0=f10,f0
+ nop.i 0;;
+}
+{.mib
+  nop.m 0
+  nop.i 0
+  // if Y zero
+  (p11) br.cond.spnt FREM_Y_ZERO;;
+}
+
+// X infinity? Return QNAN indefinite
+{ .mfi
+      nop.m 999
+      fclass.m.unc  p8,p0 = f8, 0x23
+      nop.i 999
+}
+// X infinity? Return QNAN indefinite
+{ .mfi
+      nop.m 999
+      fclass.m.unc  p11,p0 = f8, 0x23
+      nop.i 999;;
+}
+// Y NaN ?
+{.mfi
+	 nop.m 999
+(p8) fclass.m.unc p0,p8=f9,0xc3
+	 nop.i 0;;
+}
+{.mfi
+	nop.m 999
+	// also set Denormal flag if necessary
+(p8) fma.s0 f9=f9,f1,f0
+    nop.i 0
+}
+{ .mfi
+      nop.m 999
+(p8)  frcpa.s0 f8,p7 = f8,f8
+      nop.i 999 ;;
+}
+
+{.mfi
+      nop.m 999
+(p11) mov f10=f8
+	  nop.i 0
+}
+{ .mfi
+      nop.m 999
+(p8) fma.d.s0 f8=f8,f1,f0
+	  nop.i 0 ;;
+}
+
+{ .mfb
+      nop.m 999
+      frcpa.s0 f8,p7=f8,f9
+	  (p11) br.cond.spnt EXP_ERROR_RETURN;;
+}
+{ .mib
+	nop.m 0
+	nop.i 0
+	br.ret.spnt    b0 ;;
+}
+
+
+FREM_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 ;;
+}
+
+FREM_Y_ZERO:
+// Y zero? Must be zero at this point
+// because it is the only choice left.
+// Return QNAN indefinite
+
+// 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 = f0,f0
+	  nop.i 999;;
+}
+
+{ .mfi
+      nop.m 999
+      fmerge.s      f10 = f8, f8
+      nop.i 999
+}
+
+{ .mfi
+      nop.m 999
+      fma.d.s0 f8=f11,f1,f0
+      nop.i 999
+}
+
+
+EXP_ERROR_RETURN:
+
+{ .mib
+      mov   GR_Parameter_TAG = 124
+	  nop.i 999
+      br.sptk __libm_error_region;;
+}
+
+GLOBAL_IEEE754_END(remainder)
+
+
+
+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#