4 // Copyright (c) 2000 - 2003, Intel Corporation
5 // All rights reserved.
7 // Contributed 2000 by the Intel Numerics Group, Intel Corporation
9 // Redistribution and use in source and binary forms, with or without
10 // modification, are permitted provided that the following conditions are
13 // * Redistributions of source code must retain the above copyright
14 // notice, this list of conditions and the following disclaimer.
16 // * Redistributions in binary form must reproduce the above copyright
17 // notice, this list of conditions and the following disclaimer in the
18 // documentation and/or other materials provided with the distribution.
20 // * The name of Intel Corporation may not be used to endorse or promote
21 // products derived from this software without specific prior written
24 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
25 // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
26 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
27 // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
28 // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
29 // EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
30 // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
31 // PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
32 // OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
33 // NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
34 // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
36 // Intel Corporation is the author of this code, and requests that all
37 // problem reports or change requests be submitted to it directly at
38 // http://www.intel.com/software/products/opensource/libraries/num.htm.
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} 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 // float remainderf(float,float);
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-p12
86 // General registers: r2,r3,r28,r29,r32 (ar.pfs), r33-r39
87 // Floating point registers: f6-f15
97 GR_Parameter_RESULT = r39
98 GR_Parameter_TAG = r40
106 GLOBAL_IEEE754_ENTRY(remainderf)
112 alloc r32=ar.pfs,1,4,4,0
129 // Y +-NAN, +-inf, +-0? p11
132 fclass.m.unc p11,p0 = f9, 0xe7
135 // qnan snan inf norm unorm 0 -+
138 // X +-NAN, +-inf, ? p9
141 fclass.m.unc p9,p0 = f8, 0xe3
152 cmp.eq.unc p7,p0=r0,r0
155 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
175 // q0 = a * y0 in f15
176 (p6) fma.s1 f15=f13,f10,f0
182 // e0 = 1 - b * y0 in f7
183 (p6) fnma.s1 f7=f14,f10,f1
194 // q1 = q0 + e0 * q0 in f6
195 (p6) fma.s1 f6=f7,f15,f15
201 // e1 = e0 * e0 in f7
202 (p6) fma.s1 f7=f7,f7,f0
206 (p7) getf.exp r29=f15
215 // q2 = q1 + e1 * q1 in f6
216 (p6) fma.s1 f6=f7,f6,f6
222 // e2 = e1 * e1 in f7
223 (p6) fma.s1 f7=f7,f7,f0
228 // q<1/4 ? (i.e. expon< -2)
229 (p7) cmp.gt.unc p7,p0=r28,r29
238 // if |a/b|<1/4, set D flag before returning
239 (p7) fma.s.s0 f9=f9,f0,f8
244 // can be combined with bundle above if sign of 0 or
245 // FTZ enabled are not important
246 (p7) fmerge.s f8=f8,f9
247 // return if |a|<4*|b| (estimated quotient < 1/4)
248 (p7) br.ret.spnt b0;;
252 // set f8 to current a value | sign
254 // r2=2^{-24}+2^{-48} (double prec.)
263 // q3 = q2 + e2 * q2 in f6
264 (p6) fma.d.s1 f6=f7,f6,f6
271 (p6) fma.s.s1 f11=f6,f1,f0
277 // last step ? (q3<2^{24}-2 --> q<2^{24})
278 fcmp.lt.unc.s1 p0,p12=f6,f12
289 fnma.s1 f6=f14,f11,f13
294 // q'=q-q*(1.25*2^{-24}) (q'=q-ulp)
295 fnma.s.s1 f15=f11,f15,f11
302 fnma.s1 f13=f14,f15,f13
307 // r>0 iff q=RZ(a/b) and inexact
308 fcmp.gt.unc.s1 p8,p0=f6,f0
313 // r<0 iff q'=RZ(a/b) and inexact
314 fcmp.lt.unc.s1 p9,p10=f6,f0
317 .pred.rel "mutex",p8,p9
320 // (p8) Q=q+(last iteration ? sticky bits:0)
321 // i.e. Q=q+q*x (x=2^{-32} or 0)
322 (p8) fma.s1 f11=f11,f12,f11
327 // (p9) Q=q'+(last iteration ? sticky bits:0)
328 // i.e. Q=q'+q'*x (x=2^{-24} or 0: if expon. difference=23, want to round back to q)
329 (p9) fma.s1 f11=f15,f7,f15
335 // (p9) set r=r2 (new a, if not last iteration)
338 (p12) br.cond.sptk remloop24;;
368 // This can be removed if sign of 0 is not important
369 // get remainder using sf1
370 fnma.s.s1 f12=f9,f11,f8
376 fnma.s.s0 f8=f9,f11,f8
385 // This can be removed if sign of 0 is not important
386 fcmp.eq.unc.s1 p8,p0=f12,f0
391 // if f8=0, set sign correctly
392 // This can be removed if sign of 0 is not important
393 (p8) fmerge.s f8=f7,f8
409 fcmp.eq.unc.s1 p11,p0=f10,f0
416 (p11) br.cond.spnt FREM_Y_ZERO;;
419 // X infinity? Return QNAN indefinite
422 fclass.m.unc p8,p0 = f8, 0x23
425 // X infinity? Return QNAN indefinite
428 fclass.m.unc p11,p0 = f8, 0x23
434 (p8) fclass.m.unc p0,p8=f9,0xc3
439 // also set Denormal flag if necessary
440 (p8) fma.s0 f9=f9,f1,f0
445 (p8) frcpa.s0 f8,p7 = f8,f8
456 (p8) fma.s.s0 f8=f8,f1,f0
463 (p11) br.cond.spnt EXP_ERROR_RETURN;;
477 fclass.m.unc p7,p0 = f9, 0x23
483 (p7) fma.s.s0 f8=f8,f1,f0
484 (p7) br.ret.spnt b0 ;;
490 fclass.m.unc p9,p0 = f9, 0xc3
496 (p9) fma.s.s0 f8=f9,f1,f0
497 (p9) br.ret.spnt b0 ;;
501 // Y zero? Must be zero at this point
502 // because it is the only choice left.
503 // Return QNAN indefinite
508 fclass.m.unc p9,p10 = f8, 0xc3
513 (p10) fclass.nm p9,p10 = f8, 0xff
519 (p9) frcpa.s0 f11,p7=f8,f0
525 (p10) frcpa.s0 f11,p7 = f0,f0
531 fmerge.s f10 = f8, f8
537 fma.s.s0 f8=f11,f1,f0
545 mov GR_Parameter_TAG = 125
547 br.sptk __libm_error_region;;
550 GLOBAL_IEEE754_END(remainderf)
554 LOCAL_LIBM_ENTRY(__libm_error_region)
557 add GR_Parameter_Y=-32,sp // Parameter 2 value
559 .save ar.pfs,GR_SAVE_PFS
560 mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
564 add sp=-64,sp // Create new stack
566 mov GR_SAVE_GP=gp // Save gp
569 stfs [GR_Parameter_Y] = FR_Y,16 // Save Parameter 2 on stack
570 add GR_Parameter_X = 16,sp // Parameter 1 address
572 mov GR_SAVE_B0=b0 // Save b0
576 stfs [GR_Parameter_X] = FR_X // Store Parameter 1 on stack
577 add GR_Parameter_RESULT = 0,GR_Parameter_Y
578 nop.b 0 // Parameter 3 address
581 stfs [GR_Parameter_Y] = FR_RESULT // Store Parameter 3 on stack
582 add GR_Parameter_Y = -16,GR_Parameter_Y
583 br.call.sptk b0=__libm_error_support#;; // Call error handling function
588 add GR_Parameter_RESULT = 48,sp
591 ldfs f8 = [GR_Parameter_RESULT] // Get return result off stack
593 add sp = 64,sp // Restore stack pointer
594 mov b0 = GR_SAVE_B0 // Restore return address
597 mov gp = GR_SAVE_GP // Restore gp
598 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
599 br.ret.sptk b0 // Return
602 LOCAL_LIBM_END(__libm_error_region)
605 .type __libm_error_support#,@function
606 .global __libm_error_support#