| .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# |
| |
| |
