.file "nextafterl.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 // 03/03/00 Modified to conform to C9X, and improve speed of main path // 03/14/00 Fixed case where x is a power of 2, and x > y, improved speed // 04/04/00 Unwind support added // 05/12/00 Fixed erroneous denormal flag setting for exponent change cases 1,3 // 08/15/00 Bundle added after call to __libm_error_support to properly // set [the previously overwritten] GR_Parameter_RESULT. // 09/09/00 Updated fcmp so that qnans do not raise invalid. // 12/15/00 Fixed case of smallest long double normal to largest denormal, // now adhere to C99 for two zero args, and fixed flag settings // for several cases // 05/20/02 Cleaned up namespace and sf0 syntax // 02/10/03 Reordered header: .section, .global, .proc, .align // // API //============================================================== // long double nextafterl( long double x, long double y ); // input floating point f8, f9 // output floating point f8 // // Registers used //============================================================== nextafter_GR_max_pexp = r14 nextafter_GR_min_pexp = r15 nextafter_GR_exp = r16 nextafter_GR_sig = r17 nextafter_GR_lnorm_sig = r18 nextafter_GR_sign_mask = r19 nextafter_GR_exp_mask = r20 nextafter_GR_sden_sig = r21 nextafter_GR_new_sig = r22 nextafter_GR_new_exp = r23 nextafter_GR_lden_sig = r24 nextafter_GR_snorm_sig = r25 nextafter_GR_exp1 = r26 nextafter_GR_x_exp = r27 // r36-39 parameters for libm_error_support GR_SAVE_B0 = r34 GR_SAVE_GP = r35 GR_SAVE_PFS = r32 GR_Parameter_X = r36 GR_Parameter_Y = r37 GR_Parameter_RESULT = r38 NEXTAFTER_lnorm_sig = f10 NEXTAFTER_lnorm_exp = f11 NEXTAFTER_lnorm = f12 NEXTAFTER_sden_sig = f13 NEXTAFTER_den_exp = f14 NEXTAFTER_sden = f15 NEXTAFTER_snorm_exp = f32 NEXTAFTER_save_f8 = f33 NEXTAFTER_new_exp = f34 NEXTAFTER_new_sig = f35 NEXTAFTER_lden_sig = f36 NEXTAFTER_snorm_sig = f37 NEXTAFTER_exp1 = f38 NEXTAFTER_tmp = f39 // // Overview of operation //============================================================== // nextafterl determines the next representable value // after x in the direction of y. .section .text GLOBAL_LIBM_ENTRY(nextafterl) // Extract signexp from x // Is x < y ? p10 if yes, p11 if no // Form smallest denormal significand = ulp size { .mfi getf.exp nextafter_GR_exp = f8 fcmp.lt.s1 p10,p11 = f8, f9 addl nextafter_GR_sden_sig = 0x1, r0 } // Form largest normal significand 0xffffffffffffffff // Form smallest normal exponent { .mfi addl nextafter_GR_lnorm_sig = -0x1,r0 nop.f 999 addl nextafter_GR_min_pexp = 0x0c001, r0 ;; } // Extract significand from x // Is x=y? This fcmp also sets Invalid and Denormal if required // Form largest normal exponent { .mfi getf.sig nextafter_GR_sig = f8 fcmp.eq.s0 p6,p0 = f8, f9 addl nextafter_GR_max_pexp = 0x13ffe, r0 } // Move largest normal significand to fp reg for special cases { .mfi setf.sig NEXTAFTER_lnorm_sig = nextafter_GR_lnorm_sig nop.f 999 addl nextafter_GR_sign_mask = 0x20000, r0 ;; } // Move smallest denormal significand and exp to fp regs // Is x=nan? // Set p12 and p13 based on whether significand increases or decreases // It increases (p12 set) if x=0 or if x>y and x<0 // It decreases (p13 set) if xy and x>=0 { .mfi setf.sig NEXTAFTER_sden_sig = nextafter_GR_sden_sig fclass.m p8,p0 = f8, 0xc3 (p10) cmp.lt p12,p13 = nextafter_GR_exp, nextafter_GR_sign_mask } // Move smallest normal exp to fp regs { .mfi setf.exp NEXTAFTER_snorm_exp = nextafter_GR_min_pexp nop.f 999 (p11) cmp.ge p12,p13 = nextafter_GR_exp, nextafter_GR_sign_mask ;; } .pred.rel "mutex",p12,p13 // Form expected new significand, adding or subtracting 1 ulp increment // If x=y set result to y // Form smallest normal significand and largest denormal significand { .mfi (p12) add nextafter_GR_new_sig = nextafter_GR_sig, nextafter_GR_sden_sig (p6) fmerge.s f8=f9,f9 dep.z nextafter_GR_snorm_sig = 1,63,1 // 0x8000000000000000 } { .mlx (p13) sub nextafter_GR_new_sig = nextafter_GR_sig, nextafter_GR_sden_sig movl nextafter_GR_lden_sig = 0x7fffffffffffffff ;; } // Move expected result significand and signexp to fp regs // Is y=nan? // Form new exponent in case result exponent needs incrementing or decrementing { .mfi setf.exp NEXTAFTER_new_exp = nextafter_GR_exp fclass.m p9,p0 = f9, 0xc3 (p12) add nextafter_GR_exp1 = 1, nextafter_GR_exp } { .mib setf.sig NEXTAFTER_new_sig = nextafter_GR_new_sig (p13) add nextafter_GR_exp1 = -1, nextafter_GR_exp (p6) br.ret.spnt b0 ;; // Exit if x=y } // Move largest normal signexp to fp reg for special cases // Is x=zero? { .mfi setf.exp NEXTAFTER_lnorm_exp = nextafter_GR_max_pexp fclass.m p7,p0 = f8, 0x7 nop.i 999 } { .mfb setf.exp NEXTAFTER_den_exp = nextafter_GR_min_pexp (p8) fma.s0 f8 = f8,f1,f9 (p8) br.ret.spnt b0 ;; // Exit if x=nan } // Move exp+-1 and smallest normal significand to fp regs for special cases // Is x=inf? { .mfi setf.exp NEXTAFTER_exp1 = nextafter_GR_exp1 fclass.m p6,p0 = f8, 0x23 addl nextafter_GR_exp_mask = 0x1ffff, r0 } { .mfb setf.sig NEXTAFTER_snorm_sig = nextafter_GR_snorm_sig (p9) fma.s0 f8 = f8,f1,f9 (p9) br.ret.spnt b0 ;; // Exit if y=nan } // Move largest denormal significand to fp regs for special cases // Save x { .mfb setf.sig NEXTAFTER_lden_sig = nextafter_GR_lden_sig mov NEXTAFTER_save_f8 = f8 (p7) br.cond.spnt NEXTAFTER_ZERO ;; // Exit if x=0 } // Mask off the sign to get x_exp { .mfb and nextafter_GR_x_exp = nextafter_GR_exp_mask, nextafter_GR_exp nop.f 999 (p6) br.cond.spnt NEXTAFTER_INF ;; // Exit if x=inf } // Check 5 special cases when significand rolls over: // 1 sig size incr, x_sig=max_sig, x_exp < max_exp // Set p6, result is sig=min_sig, exp++ // 2 sig size incr, x_sig=max_sig, x_exp >= max_exp // Set p7, result is inf, signal overflow // 3 sig size decr, x_sig=min_sig, x_exp > min_exp // Set p8, result is sig=max_sig, exp-- // 4 sig size decr, x_sig=min_sig, x_exp = min_exp // Set p9, result is sig=max_den_sig, exp same, signal underflow and inexact // 5 sig size decr, x_sig=min_den_sig, x_exp = min_exp // Set p10, result is zero, sign of x, signal underflow and inexact // { .mmi (p12) cmp.eq.unc p6,p0 = nextafter_GR_new_sig, r0 (p13) cmp.eq.unc p9,p10 = nextafter_GR_new_sig, nextafter_GR_lden_sig nop.i 999 ;; } { .mmi (p6) cmp.lt.unc p6,p7 = nextafter_GR_x_exp, nextafter_GR_max_pexp (p10) cmp.eq.unc p10,p0 = nextafter_GR_new_sig, r0 (p9) cmp.le.unc p9,p8 = nextafter_GR_x_exp, nextafter_GR_min_pexp ;; } // Create small normal in case need to generate underflow flag { .mfi nop.m 999 fmerge.se NEXTAFTER_tmp = NEXTAFTER_snorm_exp, NEXTAFTER_lnorm_sig nop.i 999 } // Branch if cases 1, 2, 3 { .bbb (p6) br.cond.spnt NEXTAFTER_EXPUP (p7) br.cond.spnt NEXTAFTER_OVERFLOW (p8) br.cond.spnt NEXTAFTER_EXPDOWN ;; } // Branch if cases 4, 5 { .mbb nop.m 999 (p9) br.cond.spnt NEXTAFTER_NORM_TO_DENORM (p10) br.cond.spnt NEXTAFTER_UNDERFLOW_TO_ZERO ;; } // Here if no special cases // Set p6 if result will be a denormal, so can force underflow flag // Case 1: x_exp=min_exp, x_sig=unnormalized // Case 2: x_exp + psp -> + psp -> + sp -> + // | | | | // | | <- GR_Y R3 ->| <- GR_RESULT | -> f8 // | | | | // | <-GR_Y Y2->| Y2 ->| <- GR_Y | // | | | | // | | <- GR_X X1 ->| | // | | | | // sp-64 -> + sp -> + sp -> + + // save ar.pfs save b0 restore gp // save gp restore ar.pfs LOCAL_LIBM_ENTRY(__libm_error_region) NEXTAFTER_OVERFLOW: // Here if f8 is finite, but result will be infinite // Use frcpa to generate infinity of correct sign // Call error support to report possible range error .prologue { .mfi alloc r32=ar.pfs,2,2,4,0 frcpa.s1 f8,p6 = NEXTAFTER_save_f8, f0 nop.i 999 ;; } // Create largest long double { .mfi nop.m 999 fmerge.se NEXTAFTER_lnorm = NEXTAFTER_lnorm_exp,NEXTAFTER_lnorm_sig nop.i 999 ;; } // Force overflow and inexact flags to be set { .mfi mov r39 = 153 // Error code fma.s0 NEXTAFTER_tmp = NEXTAFTER_lnorm,NEXTAFTER_lnorm,f0 nop.i 999 } ;; // (1) { .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 };; // (2) { .mmi stfe [GR_Parameter_Y] = f9,16 // STORE 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 // (3) { .mib stfe [GR_Parameter_X] = NEXTAFTER_save_f8 // STORE Parameter 1 on stack add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address nop.b 0 } { .mib stfe [GR_Parameter_Y] = f8 // 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 };; // (4) { .mmi ldfe 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#