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Diffstat (limited to 'sysdeps/ia64/fpu/e_fmod.S')
| -rw-r--r-- | sysdeps/ia64/fpu/e_fmod.S | 555 |
1 files changed, 555 insertions, 0 deletions
diff --git a/sysdeps/ia64/fpu/e_fmod.S b/sysdeps/ia64/fpu/e_fmod.S new file mode 100644 index 0000000..c29056e --- /dev/null +++ b/sysdeps/ia64/fpu/e_fmod.S @@ -0,0 +1,555 @@ +.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# |