.file "sqrt.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 // 04/04/00 Unwind support added // 08/15/00 Bundle added after call to __libm_error_support to properly // set [the previously overwritten] GR_Parameter_RESULT. // 02/10/03 Reordered header: .section, .global, .proc, .align // //******************************************************************** // // Function: Combined sqrt(x), where // _ // sqrt(x) = |x, for double precision x values // //******************************************************************** // // Accuracy: Correctly Rounded // //******************************************************************** // // Resources Used: // // Floating-Point Registers: f8 (Input and Return Value) // f7 -f14 // // General Purpose Registers: // r32-r36 (Locals) // r37-r40 (Used to pass arguments to error handling routine) // // Predicate Registers: p6, p7, p8 // //********************************************************************* // // IEEE Special Conditions: // // All faults and exceptions should be raised correctly. // sqrt(QNaN) = QNaN // sqrt(SNaN) = QNaN // sqrt(+/-0) = +/-0 // sqrt(negative) = QNaN and error handling is called // //********************************************************************* // // Implementation: // // Modified Newton-Raphson Algorithm // //********************************************************************* GR_SAVE_PFS = r33 GR_SAVE_B0 = r34 GR_SAVE_GP = r35 GR_Parameter_X = r37 GR_Parameter_Y = r38 GR_Parameter_RESULT = r39 .section .text GLOBAL_IEEE754_ENTRY(sqrt) { .mfi alloc r32= ar.pfs,0,5,4,0 frsqrta.s0 f7,p6=f8 nop.i 0 } { .mlx // BEGIN DOUBLE PRECISION MINIMUM LATENCY SQUARE ROOT ALGORITHM nop.m 0 // exponent of +1/2 in r2 movl r2 = 0x0fffe;; } { .mmi // +1/2 in f9 setf.exp f9 = r2 nop.m 0 nop.i 0 } { .mlx nop.m 0 // 3/2 in r3 movl r3=0x3fc00000;; } { .mfi setf.s f10=r3 // Step (1) // y0 = 1/sqrt(a) in f7 fclass.m.unc p7,p8 = f8,0x3A nop.i 0;; } { .mlx nop.m 0 // 5/2 in r2 movl r2 = 0x40200000 } { .mlx nop.m 0 // 63/8 in r3 movl r3 = 0x40fc0000;; } { .mfi setf.s f11=r2 // Step (2) // h = +1/2 * y0 in f6 (p6) fma.s1 f6=f9,f7,f0 nop.i 0 } { .mfi setf.s f12=r3 // Step (3) // g = a * y0 in f7 (p6) fma.s1 f7=f8,f7,f0 nop.i 0 } { .mfi nop.m 0 mov f15 = f8 nop.i 0;; } { .mlx nop.m 0 // 231/16 in r2 movl r2 = 0x41670000;; } { .mfi setf.s f13=r2 // Step (4) // e = 1/2 - g * h in f9 (p6) fnma.s1 f9=f7,f6,f9 nop.i 0 } { .mlx nop.m 0 // 35/8 in r3 movl r3 = 0x408c0000;; } { .mfi setf.s f14=r3 // Step (5) // S = 3/2 + 5/2 * e in f10 (p6) fma.s1 f10=f11,f9,f10 nop.i 0 } { .mfi nop.m 0 // Step (6) // e2 = e * e in f11 (p6) fma.s1 f11=f9,f9,f0 nop.i 0;; } { .mfi nop.m 0 // Step (7) // t = 63/8 + 231/16 * e in f12 (p6) fma.s1 f12=f13,f9,f12 nop.i 0;; } { .mfi nop.m 0 // Step (8) // S1 = e + e2 * S in f10 (p6) fma.s1 f10=f11,f10,f9 nop.i 0 } { .mfi nop.m 0 // Step (9) // e4 = e2 * e2 in f11 (p6) fma.s1 f11=f11,f11,f0 nop.i 0;; } { .mfi nop.m 0 // Step (10) // t1 = 35/8 + e * t in f9 (p6) fma.s1 f9=f9,f12,f14 nop.i 0;; } { .mfi nop.m 0 // Step (11) // G = g + S1 * g in f12 (p6) fma.s1 f12=f10,f7,f7 nop.i 0 } { .mfi nop.m 0 // Step (12) // E = g * e4 in f7 (p6) fma.s1 f7=f7,f11,f0 nop.i 0;; } { .mfi nop.m 0 // Step (13) // u = S1 + e4 * t1 in f10 (p6) fma.s1 f10=f11,f9,f10 nop.i 0;; } { .mfi nop.m 0 // Step (14) // g1 = G + t1 * E in f7 (p6) fma.d.s1 f7=f9,f7,f12 nop.i 0;; } { .mfi nop.m 0 // Step (15) // h1 = h + u * h in f6 (p6) fma.s1 f6=f10,f6,f6 nop.i 0;; } { .mfi nop.m 0 // Step (16) // d = a - g1 * g1 in f9 (p6) fnma.s1 f9=f7,f7,f8 nop.i 0;; } { .mfb nop.m 0 // Step (17) // g2 = g1 + d * h1 in f7 (p6) fma.d.s0 f8=f9,f6,f7 (p6) br.ret.sptk b0 ;; } { .mfb nop.m 0 mov f8 = f7 (p8) br.ret.sptk b0 ;; } { .mfb (p7) mov r40 = 49 nop.f 0 (p7) br.cond.sptk __libm_error_region ;; } // END DOUBLE PRECISION MINIMUM LATENCY SQUARE ROOT ALGORITHM GLOBAL_IEEE754_END(sqrt) // Stack operations when calling error support. // (1) (2) (3) (call) (4) // sp -> + 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) // // This branch includes all those special values that are not negative, // with the result equal to frcpa(x) // .prologue // We are distinguishing between over(under)flow and letting // __libm_error_support set ERANGE or do anything else needed. // (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 stfd [GR_Parameter_Y] = f0,16 // 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 stfd [GR_Parameter_X] = f15 // STORE Parameter 1 on stack add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address nop.b 0 } { .mib stfd [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 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#