| .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# |
