| .file "sqrtf.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. |
| // 05/20/02 Cleaned up namespace and sf0 syntax |
| // 02/10/03 Reordered header: .section, .global, .proc, .align |
| // |
| //********************************************************************* |
| // |
| // Function: Combined sqrtf(x), where |
| // _ |
| // sqrtf(x) = |x, for single 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. |
| // sqrtf(QNaN) = QNaN |
| // sqrtf(SNaN) = QNaN |
| // sqrtf(+/-0) = +/-0 |
| // sqrtf(negative) = QNaN and error handling is called |
| // |
| //******************************************************************** |
| // |
| // Implementation: |
| // |
| // Modified Newton-Raphson Algorithm |
| // |
| //******************************************************************** |
| |
| |
| GR_SAVE_B0 = r34 |
| GR_SAVE_PFS = r33 |
| GR_SAVE_GP = r35 |
| |
| GR_Parameter_X = r37 |
| GR_Parameter_Y = r38 |
| GR_Parameter_RESULT = r39 |
| GR_Parameter_TAG = r40 |
| |
| FR_X = f13 |
| FR_Y = f0 |
| FR_RESULT = f8 |
| |
| |
| .section .text |
| GLOBAL_IEEE754_ENTRY(sqrtf) |
| { .mlx |
| // BEGIN SINGLE PRECISION MINIMUM LATENCY SQUARE ROOT ALGORITHM |
| alloc r32= ar.pfs,0,5,4,0 |
| // exponent of +1/2 in r2 |
| movl r2 = 0x0fffe |
| } { .mfi |
| // +1/2 in f12 |
| nop.m 0 |
| frsqrta.s0 f7,p6=f8 |
| nop.i 0;; |
| } { .mfi |
| setf.exp f12 = r2 |
| // Step (1) |
| // y0 = 1/sqrt(a) in f7 |
| fclass.m.unc p7,p8 = f8,0x3A |
| nop.i 0 |
| } { .mfi |
| nop.m 0 |
| // Make a copy of x just in case |
| mov f13 = f8 |
| nop.i 0;; |
| } { .mfi |
| nop.m 0 |
| // Step (2) |
| // H0 = 1/2 * y0 in f9 |
| (p6) fma.s1 f9=f12,f7,f0 |
| nop.i 0 |
| } { .mfi |
| nop.m 0 |
| // Step (3) |
| // S0 = a * y0 in f7 |
| (p6) fma.s1 f7=f8,f7,f0 |
| nop.i 0;; |
| } { .mfi |
| nop.m 0 |
| // Step (4) |
| // d = 1/2 - S0 * H0 in f10 |
| (p6) fnma.s1 f10=f7,f9,f12 |
| nop.i 0 |
| } { .mfi |
| nop.m 0 |
| // Step (0'') |
| // 3/2 = 1 + 1/2 in f12 |
| (p6) fma.s1 f12=f12,f1,f1 |
| nop.i 0;; |
| } { .mfi |
| nop.m 0 |
| // Step (5) |
| // e = 1 + 3/2 * d in f12 |
| (p6) fma.s1 f12=f12,f10,f1 |
| nop.i 0 |
| } { .mfi |
| nop.m 0 |
| // Step (6) |
| // T0 = d * S0 in f11 |
| (p6) fma.s1 f11=f10,f7,f0 |
| nop.i 0;; |
| } { .mfi |
| nop.m 0 |
| // Step (7) |
| // G0 = d * H0 in f10 |
| (p6) fma.s1 f10=f10,f9,f0 |
| nop.i 0;; |
| } { .mfi |
| nop.m 0 |
| // Step (8) |
| // S1 = S0 + e * T0 in f7 |
| (p6) fma.s.s1 f7=f12,f11,f7 |
| nop.i 0;; |
| } { .mfi |
| nop.m 0 |
| // Step (9) |
| // H1 = H0 + e * G0 in f12 |
| (p6) fma.s1 f12=f12,f10,f9 |
| nop.i 0;; |
| } { .mfi |
| nop.m 0 |
| // Step (10) |
| // d1 = a - S1 * S1 in f9 |
| (p6) fnma.s1 f9=f7,f7,f8 |
| nop.i 0;; |
| } { .mfb |
| nop.m 0 |
| // Step (11) |
| // S = S1 + d1 * H1 in f7 |
| (p6) fma.s.s0 f8=f9,f12,f7 |
| (p6) br.ret.sptk b0 ;; |
| // END SINGLE PRECISION MINIMUM LATENCY SQUARE ROOT ALGORITHM |
| } { .mfb |
| nop.m 0 |
| mov f8 = f7 |
| (p8) br.ret.sptk b0 ;; |
| } |
| // |
| // This branch includes all those special values that are not negative, |
| // with the result equal to frcpa(x) |
| // |
| GLOBAL_IEEE754_END(sqrtf) |
| |
| |
| LOCAL_LIBM_ENTRY(__libm_error_region) |
| .prologue |
| { .mii |
| add GR_Parameter_Y=-32,sp // Parameter 2 value |
| mov GR_Parameter_TAG = 50 |
| .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 |
| stfs [GR_Parameter_Y] = FR_Y,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 |
| { .mib |
| stfs [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 |
| stfs [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 |
| ldfs 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# |
