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 // double remainder(double,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
96 GR_Parameter_RESULT = r39
97 GR_Parameter_TAG = r40
105 GLOBAL_IEEE754_ENTRY(remainder)
111 alloc r32=ar.pfs,1,4,4,0
128 // Y +-NAN, +-inf, +-0? p11
131 fclass.m.unc p11,p0 = f9, 0xe7
134 // qnan snan inf norm unorm 0 -+
137 // X +-NAN, +-inf, ? p9
140 fclass.m.unc p9,p0 = f8, 0xe3
151 cmp.eq.unc p7,p0=r0,r0
154 frcpa.s1 f10,p6=f13,f14
159 (p9) br.cond.spnt FREM_X_NAN_INF
160 (p11) br.cond.spnt FREM_Y_NAN_INF_ZERO
164 // set D flag if a (f8) is denormal
174 // q0 = a * y0 in f12
175 (p6) fma.s1 f12=f13,f10,f0
180 // e0 = 1 - b * y0 in f7
181 (p6) fnma.s1 f7=f14,f10,f1
192 (p6) fma.s1 f15=f12,f7,f12
198 // e1 = e0 * e0 + E in f7
199 (p6) fma.s1 f7=f7,f7,f32
203 (p7) getf.exp r29=f12
211 // q2 = q1 + e1 * q1 in f11
212 (p6) fma.s.s1 f11=f7,f15,f15
217 // q2 = q1 + e1 * q1 in f6
218 (p6) fma.s1 f6=f7,f15,f15
225 // q<1/4 ? (i.e. expon< -2)
226 (p7) cmp.gt p7,p0=r28,r29
233 // if |a/b|<1/4, set D flag before returning
234 (p7) fma.d.s0 f9=f9,f0,f8
239 // can be combined with bundle above if sign of 0 or
240 // FTZ enabled are not important
241 (p7) fmerge.s f8=f8,f9
242 // return if |a|<4*|b| (estimated quotient < 1/4)
243 (p7) br.ret.spnt b0;;
248 // set f8 to current a value | sign
256 // last step ? (q<2^{23})
257 fcmp.lt.unc.s1 p0,p12=f6,f12
263 fnma.s1 f6=f14,f11,f13
268 // q'=q-q*(1.25*2^{-24}) (q'=q-ulp)
269 fnma.s.s1 f15=f11,f15,f11
274 cmp.eq p11,p14=r2,r28
278 .pred.rel "mutex",p11,p14
281 // if exp_q=2^23, then r=a-b*2^{23}
282 (p11) fnma.s1 f13=f12,f14,f13
288 (p14) fnma.s1 f13=f14,f15,f13
293 // r>0 iff q=RZ(a/b) and inexact
294 fcmp.gt.unc.s1 p8,p0=f6,f0
298 // r<0 iff q'=RZ(a/b) and inexact
299 (p14) fcmp.lt.unc.s1 p9,p10=f6,f0
303 .pred.rel "mutex",p8,p9
306 // (p8) Q=q+(last iteration ? sticky bits:0)
307 // i.e. Q=q+q*x (x=2^{-32} or 0)
308 (p8) fma.s1 f11=f11,f7,f11
312 // (p9) Q=q'+(last iteration ? sticky bits:0)
313 // i.e. Q=q'+q'*x (x=2^{-32} or 0)
314 (p9) fma.s1 f11=f15,f7,f15
320 // (p9) set r=r2 (new a, if not last iteration)
323 (p12) br.cond.sptk remloop24;;
352 // This can be removed if sign of 0 is not important
353 // get remainder using sf1
354 fnma.d.s1 f12=f9,f11,f8
360 fnma.d.s0 f8=f9,f11,f8
366 // This can be removed if sign of 0 is not important
367 fcmp.eq.unc.s1 p8,p0=f12,f0
372 // if f8=0, set sign correctly
373 // This can be removed if sign of 0 is not important
374 (p8) fmerge.s f8=f7,f8
390 fcmp.eq.unc.s1 p11,p0=f10,f0
397 (p11) br.cond.spnt FREM_Y_ZERO;;
400 // X infinity? Return QNAN indefinite
403 fclass.m.unc p8,p0 = f8, 0x23
406 // X infinity? Return QNAN indefinite
409 fclass.m.unc p11,p0 = f8, 0x23
415 (p8) fclass.m.unc p0,p8=f9,0xc3
420 // also set Denormal flag if necessary
421 (p8) fma.s0 f9=f9,f1,f0
426 (p8) frcpa.s0 f8,p7 = f8,f8
437 (p8) fma.d.s0 f8=f8,f1,f0
444 (p11) br.cond.spnt EXP_ERROR_RETURN;;
458 fclass.m.unc p7,p0 = f9, 0x23
464 (p7) fma.d.s0 f8=f8,f1,f0
465 (p7) br.ret.spnt b0 ;;
471 fclass.m.unc p9,p0 = f9, 0xc3
477 (p9) fma.d.s0 f8=f9,f1,f0
478 (p9) br.ret.spnt b0 ;;
482 // Y zero? Must be zero at this point
483 // because it is the only choice left.
484 // Return QNAN indefinite
489 fclass.m.unc p9,p10 = f8, 0xc3
494 (p10) fclass.nm p9,p10 = f8, 0xff
500 (p9) frcpa.s0 f11,p7=f8,f0
506 (p10) frcpa.s0 f11,p7 = f0,f0
512 fmerge.s f10 = f8, f8
518 fma.d.s0 f8=f11,f1,f0
526 mov GR_Parameter_TAG = 124
528 br.sptk __libm_error_region;;
531 GLOBAL_IEEE754_END(remainder)
535 LOCAL_LIBM_ENTRY(__libm_error_region)
538 add GR_Parameter_Y=-32,sp // Parameter 2 value
540 .save ar.pfs,GR_SAVE_PFS
541 mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
545 add sp=-64,sp // Create new stack
547 mov GR_SAVE_GP=gp // Save gp
550 stfd [GR_Parameter_Y] = FR_Y,16 // Save Parameter 2 on stack
551 add GR_Parameter_X = 16,sp // Parameter 1 address
553 mov GR_SAVE_B0=b0 // Save b0
557 stfd [GR_Parameter_X] = FR_X // Store Parameter 1 on stack
558 add GR_Parameter_RESULT = 0,GR_Parameter_Y
559 nop.b 0 // Parameter 3 address
562 stfd [GR_Parameter_Y] = FR_RESULT // Store Parameter 3 on stack
563 add GR_Parameter_Y = -16,GR_Parameter_Y
564 br.call.sptk b0=__libm_error_support# // Call error handling function
569 add GR_Parameter_RESULT = 48,sp
572 ldfd f8 = [GR_Parameter_RESULT] // Get return result off stack
574 add sp = 64,sp // Restore stack pointer
575 mov b0 = GR_SAVE_B0 // Restore return address
578 mov gp = GR_SAVE_GP // Restore gp
579 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
580 br.ret.sptk b0 // Return
583 LOCAL_LIBM_END(__libm_error_region)
587 .type __libm_error_support#,@function
588 .global __libm_error_support#