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Diffstat (limited to 'sysdeps/ia64/fpu/e_remainder.S')
| -rw-r--r-- | sysdeps/ia64/fpu/e_remainder.S | 588 |
1 files changed, 588 insertions, 0 deletions
diff --git a/sysdeps/ia64/fpu/e_remainder.S b/sysdeps/ia64/fpu/e_remainder.S new file mode 100644 index 0000000..3e06517 --- /dev/null +++ b/sysdeps/ia64/fpu/e_remainder.S @@ -0,0 +1,588 @@ +.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# |