.file "nexttoward.s" // Copyright (c) 2001 - 2004, Intel Corporation // All rights reserved. // // Contributed 2001 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 //============================================================== // 08/15/01 Initial version // 08/23/01 Corrected error tag number // 05/20/02 Cleaned up namespace and sf0 syntax // 02/10/03 Reordered header: .section, .global, .proc, .align // 12/14/04 Added error handling on underflow. // // API //============================================================== // double nexttoward( double x, long double y ); // input floating point f8, f9 // output floating point f8 // // Registers used //============================================================== GR_max_pexp = r14 GR_min_pexp = r15 GR_exp = r16 GR_sig = r17 GR_lnorm_sig = r18 GR_sign_mask = r19 GR_exp_mask = r20 GR_sden_sig = r21 GR_new_sig = r22 GR_new_exp = r23 GR_lden_sig = r24 GR_snorm_sig = r25 GR_exp1 = r26 GR_x_exp = r27 GR_min_den_rexp = r28 // 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 GR_Parameter_TAG = r39 FR_lnorm_sig = f10 FR_lnorm_exp = f11 FR_lnorm = f12 FR_sden_sig = f13 FR_sden_exp = f14 FR_sden = f15 FR_save_f8 = f33 FR_new_exp = f34 FR_new_sig = f35 FR_lden_sig = f36 FR_snorm_sig = f37 FR_exp1 = f38 FR_tmp = f39 // // Overview of operation //============================================================== // nexttoward determines the next representable value // after x in the direction of y. .section .text GLOBAL_LIBM_ENTRY(nexttoward) // Extract signexp from x // Is x < y ? p10 if yes, p11 if no // Form smallest denormal significand = ulp size { .mfi getf.exp GR_exp = f8 fcmp.lt.s1 p10,p11 = f8, f9 addl GR_sden_sig = 0x800, r0 } // Form largest normal significand 0xfffffffffffff800 // Form smallest normal exponent { .mfi addl GR_lnorm_sig = -0x800,r0 nop.f 999 addl GR_min_pexp = 0x0fc01, r0 ;; } // Extract significand from x // Is x=y? // Form largest normal exponent { .mfi getf.sig GR_sig = f8 fcmp.eq.s0 p6,p0 = f8, f9 addl GR_max_pexp = 0x103fe, r0 } // Move largest normal significand to fp reg for special cases { .mfi setf.sig FR_lnorm_sig = GR_lnorm_sig nop.f 999 addl GR_sign_mask = 0x20000, r0 ;; } // Move smallest denormal significand and signexp 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 FR_sden_sig = GR_sden_sig fclass.m p8,p0 = f8, 0xc3 (p10) cmp.lt p12,p13 = GR_exp, GR_sign_mask } { .mfi setf.exp FR_sden_exp = GR_min_pexp (p11) cmp.ge p12,p13 = GR_exp, 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 GR_new_sig = GR_sig, GR_sden_sig (p6) fnorm.d.s0 f8=f9 //Normalise dep.z GR_snorm_sig = 1,63,1 // 0x8000000000000000 } { .mlx (p13) sub GR_new_sig = GR_sig, GR_sden_sig movl GR_lden_sig = 0x7ffffffffffff800 ;; } // 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 FR_new_exp = GR_exp fclass.m p9,p0 = f9, 0xc3 (p12) add GR_exp1 = 1, GR_exp } { .mib setf.sig FR_new_sig = GR_new_sig (p13) add GR_exp1 = -1, 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 FR_lnorm_exp = GR_max_pexp fclass.m p7,p0 = f8, 0x7 nop.i 999 } { .mfb nop.m 999 (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 FR_exp1 = GR_exp1 fclass.m p6,p0 = f8, 0x23 addl GR_exp_mask = 0x1ffff, r0 } { .mfb setf.sig FR_snorm_sig = 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 FR_lden_sig = GR_lden_sig mov FR_save_f8 = f8 (p7) br.cond.spnt NEXT_ZERO ;; // Exit if x=0 } // Mask off the sign to get x_exp { .mfb and GR_x_exp = GR_exp_mask, GR_exp nop.f 999 (p6) br.cond.spnt NEXT_INF ;; // Exit if x=inf } // Check 6 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 // 6 sig size decr, x_sig=min_sig, x_exp < min_exp // Set p14, result is zero, sign of x, signal underflow and inexact // // Form exponent of smallest double denormal (if normalized register format) { .mmi adds GR_min_den_rexp = -52, GR_min_pexp (p12) cmp.eq.unc p6,p0 = GR_new_sig, r0 (p13) cmp.eq.unc p8,p10 = GR_new_sig, GR_lden_sig ;; } { .mmi (p6) cmp.lt.unc p6,p7 = GR_x_exp, GR_max_pexp (p8) cmp.gt.unc p8,p9 = GR_x_exp, GR_min_pexp (p10) cmp.eq.unc p10,p0 = GR_new_sig, r0 ;; } // Create small normal in case need to generate underflow flag { .mfi (p10) cmp.le.unc p10,p0 = GR_x_exp, GR_min_pexp fmerge.se FR_tmp = FR_sden_exp, FR_lnorm_sig (p9) cmp.gt.unc p9,p14 = GR_x_exp, GR_min_den_rexp } // Branch if cases 1, 2, 3 { .bbb (p6) br.cond.spnt NEXT_EXPUP (p7) br.cond.spnt NEXT_OVERFLOW (p8) br.cond.spnt NEXT_EXPDOWN ;; } // Branch if cases 4, 5, 6 { .bbb (p9) br.cond.spnt NEXT_NORM_TO_DENORM (p10) br.cond.spnt NEXT_UNDERFLOW_TO_ZERO (p14) br.cond.spnt NEXT_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