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Diffstat (limited to 'sysdeps/ia64/fpu/e_fmodl.S')
| -rw-r--r-- | sysdeps/ia64/fpu/e_fmodl.S | 672 |
1 files changed, 672 insertions, 0 deletions
diff --git a/sysdeps/ia64/fpu/e_fmodl.S b/sysdeps/ia64/fpu/e_fmodl.S new file mode 100644 index 0000000..258e4ef --- /dev/null +++ b/sysdeps/ia64/fpu/e_fmodl.S @@ -0,0 +1,672 @@ +.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 = r2 +GR_2P32 = r3 +GR_SMALLBIASEXP = r20 +GR_ROUNDCONST = r21 +GR_SIG_B = r22 +GR_ARPFS = r23 +GR_TMP1 = r24 +GR_TMP2 = r25 +GR_TMP3 = r26 + +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 + +FR_ABS_A = f6 +FR_ABS_B = f7 +FR_Y_INV = f10 +FR_SMALLBIAS = f11 +FR_E0 = f12 +FR_Q = f13 +FR_E1 = f14 +FR_2P32 = f15 +FR_TMPX = f32 +FR_TMPY = f33 +FR_ROUNDCONST = f34 +FR_QINT = f35 +FR_QRND24 = f36 +FR_NORM_B = f37 +FR_TMP = f38 +FR_TMP2 = f39 +FR_DFLAG = f40 +FR_Y_INV0 = f41 +FR_Y_INV1 = f42 +FR_Q0 = f43 +FR_Q1 = f44 +FR_QINT_Z = f45 +FR_QREM = f46 +FR_B_SGN_A = f47 + +.section .text +GLOBAL_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 32 +loop64: +{ .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# |