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+.file "fmod.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
+// 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)
+
+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#