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 // 08/15/00 Bundle added after call to __libm_error_support to properly
46 // set [the previously overwritten] GR_Parameter_RESULT.
47 // 11/28/00 Set FR_Y to f9
48 // 03/11/02 Fixed flags for fmod(qnan,zero)
49 // 05/20/02 Cleaned up namespace and sf0 syntax
50 // 02/10/03 Reordered header: .section, .global, .proc, .align
51 // 04/28/03 Fix: fmod(sNaN,0) no longer sets errno
54 //====================================================================
55 // double fmod(double,double);
57 // Overview of operation
58 //====================================================================
60 // where i is an integer such that, if b!=0,
61 // |i|<|a/b| and |a/b-i|<1
64 //====================================================================
65 // a). if |a|<|b|, return a
66 // b). get quotient and reciprocal overestimates accurate to
68 // c). if the exponent difference (exponent(a)-exponent(b))
69 // is less than 32, truncate quotient to integer and
70 // finish in one iteration
71 // d). if exponent(a)-exponent(b)>=32 (q2>=2^32)
72 // round quotient estimate to single precision (k=RN(q2)),
73 // calculate partial remainder (a'=a-k*b),
74 // get quotient estimate (a'*y2), and repeat from c).
77 //====================================================================
78 // b=+/-0: return NaN, call libm_error_support
79 // a=+/-Inf, a=NaN or b=NaN: return NaN
82 //====================================================================
83 // Predicate registers: p6-p11
84 // General registers: r2,r29,r32 (ar.pfs), r33-r39
85 // Floating point registers: f6-f15
94 GR_Parameter_RESULT = r39
95 GR_Parameter_TAG = r40
103 GLOBAL_IEEE754_ENTRY(fmod)
109 alloc r32=ar.pfs,1,4,4,0
124 frcpa.s1 f10,p6=f6,f7
128 // Y +-NAN, +-inf, +-0? p7
131 fclass.m.unc p7,p0 = f9, 0xe7
135 // qnan snan inf norm unorm 0 -+
138 // X +-NAN, +-inf, ? p9
142 fclass.m.unc p9,p0 = f8, 0xe3
146 // |x| < |y|? Return x p8
149 fcmp.lt.unc.s1 p8,p0 = f6,f7
155 // normalize y (if |x|<|y|)
156 (p8) fma.s0 f9=f9,f1,f0
163 (p6) fma.s1 f13=f6,f10,f0
168 // (3) e0 = 1 - b * y0
169 (p6) fnma.s1 f12=f7,f10,f1
175 // normalize x (if |x|<|y|)
176 (p8) fma.d.s0 f8=f8,f1,f0
180 (p9) br.cond.spnt FMOD_X_NAN_INF
181 (p7) br.cond.spnt FMOD_Y_NAN_INF_ZERO
182 // if |x|<|y|, return
183 (p8) br.ret.spnt b0;;
203 (p6) fma.s1 f13=f12,f13,f13
208 // (5) e1 = e0 * e0 + 2^-34
209 (p6) fma.s1 f14=f12,f12,f11
218 // (6) y1 = y0 + e0 * y0
219 (p6) fma.s1 f10=f12,f10,f10
223 // set f12=1.25*2^{-24}
226 (p6) fma.s1 f13=f13,f14,f13
236 // (8) y2 = y1 + e1 * y1
237 (p6) fma.s1 f10=f14,f10,f10
239 cmp.ne.and p6,p10=r0,r0;;
247 fcmp.lt.unc.s1 p8,p7=f13,f15
252 // will truncate quotient to integer, if exponent<32 (in advance)
253 fcvt.fx.trunc.s1 f11=f13
258 // if exponent>32, round quotient to single precision (perform in advance)
259 fma.s.s1 f13=f13,f1,f0
265 (p8) fmerge.s f12=f8,f1
270 // normalize truncated quotient
276 // calculate remainder (assuming f13=RZ(Q))
277 (p7) fnma.s1 f14=f13,f7,f6
282 // also if exponent>32, round quotient to single precision
283 // and subtract 1 ulp: q=q-q*(1.25*2^{-24})
284 (p7) fnma.s.s1 f11=f13,f12,f13
290 // (p8) calculate remainder (82-bit format)
291 (p8) fnma.s1 f11=f13,f7,f6
296 // (p7) calculate remainder (assuming f11=RZ(Q))
297 (p7) fnma.s1 f6=f11,f7,f6
304 // Final iteration (p8): is f6 the correct remainder (quotient was not overestimated) ?
305 (p8) fcmp.lt.unc.s1 p6,p10=f11,f0
310 // get new quotient estimation: a'*y2
311 (p7) fma.s1 f13=f14,f10,f0
316 // was f14=RZ(Q) ? (then new remainder f14>=0)
317 (p7) fcmp.lt.unc.s1 p7,p9=f14,f0
322 .pred.rel "mutex",p6,p10
325 // add b to estimated remainder (to cover the case when the quotient was overestimated)
326 // also set correct sign by using f9=|b|*sgn(a), f12=sgn(a)
327 (p6) fma.d.s0 f8=f11,f12,f9
332 // calculate remainder (single precision)
333 // set correct sign of result before returning
334 (p10) fma.d.s0 f8=f11,f12,f0
335 (p8) br.ret.sptk b0;;
339 // if f13!=RZ(Q), get alternative quotient estimation: a''*y2
340 (p7) fma.s1 f13=f6,f10,f0
345 // if f14 was RZ(Q), set remainder to f14
347 br.cond.sptk loop53;;
357 fclass.m p10,p0=f8,0xc3 // Test x=nan
373 (p10) fclass.m p10,p0=f9,0x07 // Test x=nan, and y=zero
379 fcmp.eq.unc.s1 p11,p0=f10,f0
380 (p10) br.ret.spnt b0;; // Exit with result=x if x=nan and y=zero
386 (p11) br.cond.spnt FMOD_Y_ZERO;;
389 // X infinity? Return QNAN indefinite
392 fclass.m.unc p8,p9 = f8, 0x23
398 (p8) fclass.m p9,p8=f9,0xc3
403 (p8) frcpa.s0 f8,p0 = f8,f8
408 // also set Denormal flag if necessary
409 (p8) fma.s0 f9=f9,f1,f0
415 (p8) fma.d.s0 f8=f8,f1,f0
421 (p9) frcpa.s0 f8,p7=f8,f9
431 fclass.m.unc p7,p0 = f9, 0x23
437 (p7) fma.d.s0 f8=f8,f1,f0
438 (p7) br.ret.spnt b0 ;;
444 fclass.m.unc p9,p0 = f9, 0xc3
450 (p9) fma.d.s0 f8=f9,f1,f0
451 (p9) br.ret.spnt b0 ;;
455 // Y zero? Must be zero at this point
456 // because it is the only choice left.
457 // Return QNAN indefinite
462 frcpa.s0 f12,p0=f0,f0
468 fclass.m.unc p9,p10 = f8, 0xc3
473 (p10) fclass.nm p9,p10 = f8, 0xff
479 (p9) frcpa.s0 f11,p7=f8,f0
485 (p10) frcpa.s0 f11,p7 = f9,f9
486 mov GR_Parameter_TAG = 121 ;;
491 fmerge.s f10 = f8, f8
497 fma.d.s0 f8=f11,f1,f0
498 br.sptk __libm_error_region;;
501 GLOBAL_IEEE754_END(fmod)
503 LOCAL_LIBM_ENTRY(__libm_error_region)
506 add GR_Parameter_Y=-32,sp // Parameter 2 value
508 .save ar.pfs,GR_SAVE_PFS
509 mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
513 add sp=-64,sp // Create new stack
515 mov GR_SAVE_GP=gp // Save gp
518 stfd [GR_Parameter_Y] = FR_Y,16 // Save Parameter 2 on stack
519 add GR_Parameter_X = 16,sp // Parameter 1 address
521 mov GR_SAVE_B0=b0 // Save b0
525 stfd [GR_Parameter_X] = FR_X // Store Parameter 1 on stack
526 add GR_Parameter_RESULT = 0,GR_Parameter_Y
527 nop.b 0 // Parameter 3 address
530 stfd [GR_Parameter_Y] = FR_RESULT // Store Parameter 3 on stack
531 add GR_Parameter_Y = -16,GR_Parameter_Y
532 br.call.sptk b0=__libm_error_support# // Call error handling function
537 add GR_Parameter_RESULT = 48,sp
540 ldfd f8 = [GR_Parameter_RESULT] // Get return result off stack
542 add sp = 64,sp // Restore stack pointer
543 mov b0 = GR_SAVE_B0 // Restore return address
546 mov gp = GR_SAVE_GP // Restore gp
547 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
548 br.ret.sptk b0 // Return
551 LOCAL_LIBM_END(__libm_error_region)
554 .type __libm_error_support#,@function
555 .global __libm_error_support#