.file "sqrtf.s" // Copyright (c) 2000, Intel Corporation // All rights reserved. // // Contributed 2/2/2000 by John Harrison, Ted Kubaska, Bob Norin, Shane Story, // and Ping Tak Peter Tang of the Computational Software Lab, Intel Corporation. // // WARRANTY DISCLAIMER // // 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://developer.intel.com/opensource. // //********************************************************************* // History: // // 2/02/00 Initial version // 4/04/00 Unwind support added // 8/15/00 Bundle added after call to __libm_error_support to properly // set [the previously overwritten] GR_Parameter_RESULT. // //********************************************************************* // // 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 .proc sqrtf# .global sqrtf# .align 64 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 (p0) 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) // .endp sqrtf .proc __libm_error_region __libm_error_region: .prologue { .mii add GR_Parameter_Y=-32,sp // Parameter 2 value (p0) 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 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 };; .endp __libm_error_region .type __libm_error_support#,@function .global __libm_error_support#