.file "fmodl.s"// Copyright (c) 2000 - 2004, 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 fmodl(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// 11/23/04 Reformatted routine and improved speed//// API//====================================================================// long double fmodl(long double, long 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).//// Registers used//====================================================================GR_SMALLBIASEXP     = r2GR_2P32             = r3GR_SMALLBIASEXP     = r20GR_ROUNDCONST       = r21GR_SIG_B            = r22GR_ARPFS            = r23GR_TMP1             = r24GR_TMP2             = r25GR_TMP3             = r26GR_SAVE_B0          = r33GR_SAVE_PFS         = r34GR_SAVE_GP          = r35GR_SAVE_SP          = r36GR_Parameter_X      = r37GR_Parameter_Y      = r38GR_Parameter_RESULT = r39GR_Parameter_TAG    = r40FR_X                = f10FR_Y                = f9FR_RESULT           = f8FR_ABS_A            = f6FR_ABS_B            = f7FR_Y_INV            = f10FR_SMALLBIAS        = f11FR_E0               = f12FR_Q                = f13FR_E1               = f14FR_2P32             = f15FR_TMPX             = f32FR_TMPY             = f33FR_ROUNDCONST       = f34FR_QINT             = f35FR_QRND24           = f36FR_NORM_B           = f37FR_TMP              = f38FR_TMP2             = f39FR_DFLAG            = f40FR_Y_INV0           = f41FR_Y_INV1           = f42FR_Q0               = f43FR_Q1               = f44FR_QINT_Z           = f45FR_QREM             = f46FR_B_SGN_A          = f47.section .textGLOBAL_IEEE754_ENTRY(fmodl)// inputs in f8, f9// result in f8{ .mfi       getf.sig GR_SIG_B = f9       // FR_ABS_A = |a|       fmerge.s FR_ABS_A = f0, f8       mov GR_SMALLBIASEXP = 0x0ffdd}{ .mfi       nop.m 0       // FR_ABS_B = |b|       fmerge.s FR_ABS_B = f0, f9       nop.i 0};;{ .mfi       setf.exp FR_SMALLBIAS = GR_SMALLBIASEXP       // (1) y0       frcpa.s1 FR_Y_INV0, p6 = FR_ABS_A, FR_ABS_B       nop.i 0};;{ .mlx       nop.m 0       movl GR_ROUNDCONST = 0x33a00000};;// eliminate special cases{ .mmi       nop.m 0       nop.m 0       // y pseudo-zero ?       cmp.eq p7, p10 = GR_SIG_B, r0};;// set p7 if b +/-NAN, +/-inf, +/-0{ .mfi       nop.m 0 (p10) fclass.m p7, p10 = f9, 0xe7       nop.i 0};;{ .mfi       mov GR_2P32 = 0x1001f       // (2) q0 = a*y0 (p6)  fma.s1 FR_Q0 = FR_ABS_A, FR_Y_INV0, f0       nop.i 0}{ .mfi       nop.m 0       // (3) e0 = 1 - b * y0 (p6)  fnma.s1 FR_E0 = FR_ABS_B, FR_Y_INV0, f1       nop.i 0};;// set p9 if a +/-NAN, +/-inf{ .mfi       nop.m 0       fclass.m.unc p9, p11 = f8, 0xe3       nop.i 0}       // |a| < |b|? Return a, p8=1{ .mfi       nop.m 0 (p10) fcmp.lt.unc.s1 p8, p0 = FR_ABS_A, FR_ABS_B       nop.i 0};;// set p7 if b +/-NAN, +/-inf, +/-0{ .mfi       nop.m 0       // pseudo-NaN ? (p10) fclass.nm p7, p0 = f9, 0xff       nop.i 0};;// set p9 if a is +/-NaN, +/-Inf{ .mfi       nop.m 0 (p11) fclass.nm p9, p0 = f8, 0xff       nop.i 0}{ .mfi       nop.m 0       // b denormal ? set D flag (if |a|<|b|) (p8)  fnma.s0 FR_DFLAG = f9, f1, f9       nop.i 0};;{ .mfi       // FR_2P32 = 2^32       setf.exp FR_2P32 = GR_2P32       // (4) q1 = q0+e0*q0 (p6)  fma.s1 FR_Q1 = FR_E0, FR_Q0, FR_Q0       nop.i 0}{ .mfi       nop.m 0       // (5) e1 = e0 * e0 + 2^-34 (p6)  fma.s1 FR_E1 = FR_E0, FR_E0, FR_SMALLBIAS       nop.i 0};;{ .mfi       nop.m 0       // normalize a (if |a|<|b|) (p8)  fma.s0 f8 = f8, f1, f0       nop.i 0}{ .bbb (p9) br.cond.spnt FMOD_A_NAN_INF (p7) br.cond.spnt FMOD_B_NAN_INF_ZERO       // if |a|<|b|, return (p8) br.ret.spnt b0};;{ .mfi       nop.m 0       // (6) y1 = y0 + e0 * y0 (p6)  fma.s1 FR_Y_INV1 = FR_E0, FR_Y_INV0, FR_Y_INV0       nop.i 0};;{ .mfi       nop.m 0       // a denormal ? set D flag       // b denormal ? set D flag       fcmp.eq.s0 p12,p0 = FR_ABS_A, FR_ABS_B       nop.i 0}{ .mfi       // set FR_ROUNDCONST = 1.25*2^{-24}       setf.s FR_ROUNDCONST = GR_ROUNDCONST       // (7) q2 = q1+e1*q1 (p6)  fma.s1 FR_Q = FR_Q1, FR_E1, FR_Q1       nop.i 0};;{ .mfi       nop.m 0       fmerge.s FR_B_SGN_A = f8, f9       nop.i 0}{ .mfi       nop.m 0       // (8) y2 = y1 + e1 * y1 (p6)  fma.s1 FR_Y_INV = FR_E1, FR_Y_INV1, FR_Y_INV1       // set p6 = 0, p10 = 0       cmp.ne.and p6, p10 = r0, r0};;//   will compute integer quotient bits (24 bits per iteration).align 32loop64:{ .mfi       nop.m 0       // compare q2, 2^32       fcmp.lt.unc.s1 p8, p7 = FR_Q, FR_2P32       nop.i 0}{ .mfi       nop.m 0       // will truncate quotient to integer, if exponent<32 (in advance)       fcvt.fx.trunc.s1 FR_QINT = FR_Q       nop.i 0};;{ .mfi       nop.m 0       // if exponent>32 round quotient to single precision (perform in advance)       fma.s.s1 FR_QRND24 = FR_Q, f1, f0       nop.i 0};;{ .mfi       nop.m 0       // set FR_ROUNDCONST = sgn(a) (p8)  fmerge.s FR_ROUNDCONST = f8, f1       nop.i 0}{ .mfi       nop.m 0       // normalize truncated quotient (p8)  fcvt.xf FR_QRND24 = FR_QINT       nop.i 0};;{ .mfi       nop.m 0       // calculate remainder (assuming FR_QRND24 = RZ(Q)) (p7)  fnma.s1 FR_E1 = FR_QRND24, FR_ABS_B, FR_ABS_A       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 FR_QINT_Z = FR_QRND24, FR_ROUNDCONST, FR_QRND24       nop.i 0};;{ .mfi       nop.m 0       // (p8) calculate remainder (82-bit format) (p8)  fnma.s1 FR_QREM = FR_QRND24, FR_ABS_B, FR_ABS_A       nop.i 0}{ .mfi       nop.m 0       // (p7) calculate remainder (assuming FR_QINT_Z = RZ(Q)) (p7)  fnma.s1 FR_ABS_A = FR_QINT_Z, FR_ABS_B, FR_ABS_A       nop.i 0};;{ .mfi       nop.m 0       // Final iteration (p8): is FR_ABS_A the correct remainder        // (quotient was not overestimated) ? (p8)  fcmp.lt.unc.s1 p6, p10 = FR_QREM, f0       nop.i 0};;{ .mfi       nop.m 0       // get new quotient estimation: a'*y2 (p7)  fma.s1 FR_Q = FR_E1, FR_Y_INV, f0       nop.i 0}{ .mfb       nop.m 0       // was FR_Q = RZ(Q) ? (then new remainder FR_E1> = 0) (p7)  fcmp.lt.unc.s1 p7, p9 = FR_E1, 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        // FR_B_SGN_A = |b|*sgn(a), FR_ROUNDCONST = sgn(a) (p6)  fma.s0 f8 = FR_QREM, FR_ROUNDCONST, FR_B_SGN_A       nop.b 0}{ .mfb       nop.m 0       // set correct sign of result before returning: FR_ROUNDCONST = sgn(a) (p10) fma.s0 f8 = FR_QREM, FR_ROUNDCONST, f0 (p8)  br.ret.sptk b0};;{ .mfi       nop.m 0       // if f13! = RZ(Q), get alternative quotient estimation: a''*y2 (p7)  fma.s1 FR_Q = FR_ABS_A, FR_Y_INV, f0       nop.i 0}{ .mfb       nop.m 0       // if FR_E1 was RZ(Q), set remainder to FR_E1 (p9)  fma.s1 FR_ABS_A = FR_E1, f1, f0       br.cond.sptk loop64};;FMOD_A_NAN_INF:// b zero ?{ .mfi       nop.m 0       fclass.m p10, p0 = f8, 0xc3 // Test a = nan       nop.i 0}{ .mfi       nop.m 0       fma.s1 FR_NORM_B = 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 = FR_NORM_B, f0 (p10) br.ret.spnt b0 // Exit with result = a if a = nan and b = zero};;{ .mib       nop.m 0       nop.i 0       // if Y zero (p11) br.cond.spnt FMOD_B_ZERO};;// a= infinity? Return QNAN indefinite{ .mfi       // set p7 t0 0       cmp.ne p7, p0 = r0, r0       fclass.m.unc p8, p9 = f8, 0x23       nop.i 0};;// b NaN ?{ .mfi       nop.m 0 (p8)  fclass.m p9, p8 = f9, 0xc3       nop.i 0};;// b not pseudo-zero ? (GR_SIG_B holds significand){ .mii       nop.m 0 (p8)  cmp.ne p7, p0 = GR_SIG_B, r0       nop.i 0};;{ .mfi       nop.m 0 (p8)  frcpa.s0 f8, p0 = f8, f8       nop.i 0}{ .mfi       nop.m 0       // also set Denormal flag if necessary (p7)  fnma.s0 f9 = f9, f1, f9       nop.i 0};;{ .mfb       nop.m 0 (p8)  fma.s0 f8 = f8, f1, f0       nop.b 0};;{ .mfb       nop.m 0 (p9)  frcpa.s0 f8, p7 = f8, f9       br.ret.sptk b0};;FMOD_B_NAN_INF_ZERO:// b INF{ .mfi       nop.m 0       fclass.m.unc p7, p0 = f9, 0x23       nop.i 0};;{ .mfb       nop.m 0 (p7)  fma.s0 f8 = f8, f1, f0 (p7)  br.ret.spnt b0};;// b NAN?{ .mfi       nop.m 0       fclass.m.unc p9, p10 = f9, 0xc3       nop.i 0};;{ .mfi       nop.m 0 (p10) fclass.nm p9, p0 = f9, 0xff       nop.i 0};;{ .mfb       nop.m 0 (p9)  fma.s0 f8 = f9, f1, f0 (p9)  br.ret.spnt b0};;FMOD_B_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 FR_TMP, p0 = f0, f0       nop.i 0};;// a NAN?{ .mfi       nop.m 0       fclass.m.unc p9, p10 = f8, 0xc3       nop.i 0};;{ .mfi       alloc GR_ARPFS = ar.pfs, 1, 4, 4, 0 (p10) fclass.nm p9, p10 = f8, 0xff       nop.i 0};;{ .mfi       nop.m 0 (p9)  frcpa.s0 FR_TMP2, p7 = f8, f0       nop.i 0};;{ .mfi       nop.m 0 (p10) frcpa.s0 FR_TMP2, p7 = f9, f9       mov GR_Parameter_TAG = 120};;{ .mfi       nop.m 0       fmerge.s FR_X = f8, f8       nop.i 0}{ .mfb       nop.m 0       fma.s0 f8 = FR_TMP2, f1, f0       br.sptk __libm_error_region};;GLOBAL_IEEE754_END(fmodl)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       stfe [ 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       stfe [ 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       stfe [ 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       ldfe 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#