4 // Copyright (c) 2000 - 2003, Intel Corporation
5 // All rights reserved.
7 // Contributed 2000 by the Intel Numerics Group, Intel Corporation
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41 //====================================================================
42 // 02/02/00 Initial version
43 // 03/02/00 New algorithm
44 // 04/04/00 Unwind support added
45 // 07/21/00 Fixed quotient=2^{24*m+23}*1.q1...q23 1 bug
46 // 08/15/00 Bundle added after call to __libm_error_support to properly
47 // set [the previously overwritten] GR_Parameter_RESULT.
48 // 11/29/00 Set FR_Y to f9
49 // 05/20/02 Cleaned up namespace and sf0 syntax
50 // 02/10/03 Reordered header: .section, .global, .proc, .align
53 //====================================================================
54 // long double remainderl(long double,long double);
56 // Overview of operation
57 //====================================================================
58 // remainder(a,b)=a-i*b,
59 // where i is an integer such that, if b!=0 and a is finite,
60 // |a/b-i|<=1/2. If |a/b-i|=1/2, i is even.
63 //====================================================================
64 // a). eliminate special cases
65 // b). if |a/b|<0.25 (first quotient estimate), return a
66 // c). use single precision divide algorithm to get quotient q
67 // rounded to 24 bits of precision
68 // d). calculate partial remainders (using both q and q-ulp);
69 // select one and RZ(a/b) based on the sign of |a|-|b|*q
70 // e). if the exponent difference (exponent(a)-exponent(b))
71 // is less than 24 (quotient estimate<2^{24}-2), use RZ(a/b)
72 // and sticky bits to round to integer; exit loop and
73 // calculate final remainder
74 // f). if exponent(a)-exponent(b)>=24, select new value of a as
75 // the partial remainder calculated using RZ(a/b);
79 //====================================================================
80 // a=+/- Inf, or b=+/-0: return NaN, call libm_error_support
81 // a=NaN or b=NaN: return NaN
84 //====================================================================
85 // Predicate registers: p6-p14
86 // General registers: r2,r3,r28,r29,r32 (ar.pfs), r33-r39
87 // Floating point registers: f6-f15,f32
97 GR_Parameter_RESULT = r39
98 GR_Parameter_TAG = r40
106 GLOBAL_IEEE754_ENTRY(remainderl)
112 alloc r32=ar.pfs,1,4,4,0
134 cmp.eq p11,p10=r29,r0;;
137 // Y +-NAN, +-inf, +-0? p11
140 (p10) fclass.m p11,p10 = f9, 0xe7
143 // qnan snan inf norm unorm 0 -+
146 // X +-NAN, +-inf, ? p9
149 fclass.m.unc p9,p8 = f8, 0xe3
160 cmp.eq.unc p7,p0=r0,r0
163 frcpa.s1 f10,p6=f13,f14
166 // Y +-NAN, +-inf, +-0? p11
170 (p10) fclass.nm p11,p0 = f9, 0xff
174 // qnan snan inf norm unorm 0 -+
177 // X +-NAN, +-inf, ? p9
181 (p8) fclass.nm p9,p0 = f8, 0xff
186 (p9) br.cond.spnt FREM_X_NAN_INF
187 (p11) br.cond.spnt FREM_Y_NAN_INF_ZERO
191 // set D flag if a (f8) is denormal
200 // q0 = a * y0 in f15
201 (p6) fma.s1 f12=f13,f10,f0
206 // e0 = 1 - b * y0 in f7
207 (p6) fnma.s1 f7=f14,f10,f1
218 (p6) fma.s1 f15=f12,f7,f12
224 // e1 = e0 * e0 + E in f7
225 (p6) fma.s1 f7=f7,f7,f32
229 (p7) getf.exp r29=f12
238 // q2 = q1 + e1 * q1 in f11
239 (p6) fma.s.s1 f11=f7,f15,f15
244 // q2 = q1 + e1 * q1 in f6
245 (p6) fma.s1 f6=f7,f15,f15
252 // q<1/4 ? (i.e. expon< -2)
253 (p7) cmp.gt p7,p0=r28,r29
260 // if |a/b|<1/4, set D flag before returning
261 (p7) fma.s0 f9=f9,f0,f8
266 // can be combined with bundle above if sign of 0 or
267 // FTZ enabled are not important
268 (p7) fmerge.s f8=f8,f9
269 // return if |a|<4*|b| (estimated quotient < 1/4)
270 (p7) br.ret.spnt b0;;
275 // set f8 to current a value | sign
281 // last step ? (q<2^{23})
282 fcmp.lt.unc.s1 p0,p12=f6,f12
288 fnma.s1 f6=f14,f11,f13
293 // q'=q-q*(1.25*2^{-24}) (q'=q-ulp)
294 fnma.s.s1 f15=f11,f15,f11
299 cmp.eq p11,p14=r2,r28
303 .pred.rel "mutex",p11,p14
306 // if exp_q=2^23, then r=a-b*2^{23}
307 (p11) fnma.s1 f13=f12,f14,f13
313 (p14) fnma.s1 f13=f14,f15,f13
318 // r>0 iff q=RZ(a/b) and inexact
319 fcmp.gt.unc.s1 p8,p0=f6,f0
323 // r<0 iff q'=RZ(a/b) and inexact
324 (p14) fcmp.lt.unc.s1 p9,p10=f6,f0
328 .pred.rel "mutex",p8,p9
331 // (p8) Q=q+(last iteration ? sticky bits:0)
332 // i.e. Q=q+q*x (x=2^{-32} or 0)
333 (p8) fma.s1 f11=f11,f7,f11
337 // (p9) Q=q'+(last iteration ? sticky bits:0)
338 // i.e. Q=q'+q'*x (x=2^{-32} or 0)
339 (p9) fma.s1 f11=f15,f7,f15
345 // (p9) set r=r2 (new a, if not last iteration)
348 (p12) br.cond.sptk remloop24;;
377 // This can be removed if sign of 0 is not important
378 // get remainder using sf1
379 fnma.s1 f12=f9,f11,f8
391 // This can be removed if sign of 0 is not important
392 fcmp.eq.unc.s1 p8,p0=f12,f0
397 // if f8=0, set sign correctly
398 // This can be removed if sign of 0 is not important
399 (p8) fmerge.s f8=f7,f8
416 fcmp.eq.unc.s1 p11,p0=f10,f0
423 (p11) br.cond.spnt FREM_Y_ZERO;;
426 // X infinity? Return QNAN indefinite
429 fclass.m.unc p8,p0 = f8, 0x23
432 // X infinity? Return QNAN indefinite
435 fclass.m.unc p11,p0 = f8, 0x23
441 (p8) fclass.m.unc p0,p8=f9,0xc3
446 // also set Denormal flag if necessary
447 (p8) fnma.s0 f9=f9,f1,f9
452 (p8) frcpa.s0 f8,p7 = f8,f8
463 (p8) fma.s0 f8=f8,f1,f0
470 (p11) br.cond.spnt EXP_ERROR_RETURN;;
483 fclass.m.unc p7,p0 = f9, 0x23
489 (p7) fma.s0 f8=f8,f1,f0
490 (p7) br.ret.spnt b0 ;;
496 fclass.m.unc p9,p10 = f9, 0xc3
501 (p10) fclass.nm p9,p0 = f9, 0xff
507 (p9) fma.s0 f8=f9,f1,f0
508 (p9) br.ret.spnt b0 ;;
512 // Y zero? Must be zero at this point
513 // because it is the only choice left.
514 // Return QNAN indefinite
519 fclass.m.unc p9,p10 = f8, 0xc3
524 (p10) fclass.nm p9,p10 = f8, 0xff
530 (p9) frcpa.s0 f11,p7=f8,f0
535 (p10) frcpa.s0 f11,p7 = f0,f0
541 fmerge.s f10 = f8, f8
554 mov GR_Parameter_TAG = 123
556 br.sptk __libm_error_region;;
559 GLOBAL_IEEE754_END(remainderl)
561 LOCAL_LIBM_ENTRY(__libm_error_region)
564 add GR_Parameter_Y=-32,sp // Parameter 2 value
566 .save ar.pfs,GR_SAVE_PFS
567 mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
571 add sp=-64,sp // Create new stack
573 mov GR_SAVE_GP=gp // Save gp
576 stfe [GR_Parameter_Y] = FR_Y,16 // Save Parameter 2 on stack
577 add GR_Parameter_X = 16,sp // Parameter 1 address
579 mov GR_SAVE_B0=b0 // Save b0
583 stfe [GR_Parameter_X] = FR_X // Store Parameter 1 on stack
584 add GR_Parameter_RESULT = 0,GR_Parameter_Y
585 nop.b 0 // Parameter 3 address
588 stfe [GR_Parameter_Y] = FR_RESULT // Store Parameter 3 on stack
589 add GR_Parameter_Y = -16,GR_Parameter_Y
590 br.call.sptk b0=__libm_error_support# // Call error handling function
595 add GR_Parameter_RESULT = 48,sp
598 ldfe f8 = [GR_Parameter_RESULT] // Get return result off stack
600 add sp = 64,sp // Restore stack pointer
601 mov b0 = GR_SAVE_B0 // Restore return address
604 mov gp = GR_SAVE_GP // Restore gp
605 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
606 br.ret.sptk b0 // Return
609 LOCAL_LIBM_END(__libm_error_region)
612 .type __libm_error_support#,@function
613 .global __libm_error_support#