.file "asinl.s" // Copyright (C) 2000, 2001, 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. // // 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://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. // // API //============================================================== // long double = asinl(long double) // input floating point f8 // output floating point f8 // // Registers used //============================================================== // // predicate registers used: // p6 -> p12 // // floating-point registers used: // f8 has input, then output // f32 -> f87, f8 -> f13, f32 -> f87 // // general registers used: // r32 -> r47 // // Overview of operation //============================================================== // There are three paths // 1. |x| < 2^-40 ASIN_TINY // 2. 2^-40 <= |x| < 1/4 ASIN_POLY // 3. 1/4 <= |x| < 1 ASIN_ATAN #include "libm_support.h" // Assembly macros //============================================================== FR_RESULT = f10 FR_X = f8 FR_Y = f1 asin_P79 = f32 asin_P59 = f33 asin_P39 = f34 asin_P19 = f35 asin_P810 = f36 asin_P610 = f37 asin_P410 = f38 asin_P210 = f39 asin_A1 = f41 asin_A2 = f42 asin_A3 = f43 asin_A4 = f44 asin_A5 = f45 asin_A6 = f46 asin_A7 = f47 asin_A8 = f48 asin_A9 = f49 asin_A10 = f50 asin_X2 = f51 asin_X4 = f52 asin_B = f53 asin_Bb = f54 asin_C = f55 asin_Cc = f56 asin_D = f57 asin_W = f58 asin_Ww = f59 asin_y0 = f60 asin_y1 = f61 asin_y2 = f62 asin_H = f63 asin_Hh = f64 asin_t1 = f65 asin_t2 = f66 asin_t3 = f67 asin_t4 = f68 asin_t5 = f69 asin_Pseries = f70 asin_NORM_f8 = f71 asin_ABS_NORM_f8 = f72 asin_2m100 = f73 asin_P1P2 = f74 asin_HALF = f75 asin_1mD = f76 asin_1mB = f77 asin_1mBmC = f78 asin_S = f79 asin_BmWW = f80 asin_BmWWpb = f81 asin_2W = f82 asin_1d2W = f83 asin_Dd = f84 asin_XWw = f85 asin_low = f86 asin_pi_by_2 = f87 asin_pi_by_2_lo = f88 asin_GR_17_ones = r33 asin_GR_16_ones = r34 asin_GR_signexp_f8 = r35 asin_GR_exp = r36 asin_GR_true_exp = r37 asin_GR_ff9b = r38 GR_SAVE_B0 = r39 GR_SAVE_SP = r40 GR_SAVE_PFS = r33 // r33 can be used safely. // r40 is address of table of coefficients // Later it is used to save sp across calls GR_SAVE_GP = r41 asin_GR_fffe = r42 asin_GR_retval = r43 GR_Parameter_X = r44 GR_Parameter_Y = r45 GR_Parameter_RESULT = r46 GR_Parameter_TAG = r47 // 2^-40: // A true exponent of -40 is // : -40 + register_bias // : -28 + ffff = ffd7 // A true exponent of -100 is // : -100 + register_bias // : -64 + ffff = ff9b // Data tables //============================================================== #ifdef _LIBC .rodata #else .data #endif .align 16 asin_coefficients: ASM_TYPE_DIRECTIVE(asin_coefficients,@object) data8 0xBB08911F2013961E, 0x00003FF8 // A10 data8 0x981F1095A23A87D3, 0x00003FF8 // A9 data8 0xBDF09C6C4177BCC6, 0x00003FF8 // A8 data8 0xE4C3A60B049ACCEA, 0x00003FF8 // A7 data8 0x8E2789F4E8A8F1AD, 0x00003FF9 // A6 data8 0xB745D09B2B0E850B, 0x00003FF9 // A5 data8 0xF8E38E3BC4C50920, 0x00003FF9 // A4 data8 0xB6DB6DB6D89FCD81, 0x00003FFA // A3 data8 0x99999999999AF376, 0x00003FFB // A2 data8 0xAAAAAAAAAAAAAA71, 0x00003FFC // A1 data8 0xc90fdaa22168c234, 0x00003FFF // pi_by_2_hi data8 0xc4c6628b80dc1cd1, 0x00003FBF // pi_by_2_lo ASM_SIZE_DIRECTIVE(asin_coefficients) .align 32 .global asinl# .section .text .proc asinl# .align 32 asinl: { .mfi alloc r32 = ar.pfs,1,11,4,0 (p0) fnorm asin_NORM_f8 = f8 (p0) mov asin_GR_17_ones = 0x1ffff } { .mii (p0) mov asin_GR_16_ones = 0xffff (p0) mov asin_GR_ff9b = 0xff9b ;; nop.i 999 } { .mmi (p0) setf.exp asin_2m100 = asin_GR_ff9b (p0) addl r40 = @ltoff(asin_coefficients), gp nop.i 999 } ;; { .mmi ld8 r40 = [r40] nop.m 999 nop.i 999 } ;; // Load the constants { .mmi (p0) ldfe asin_A10 = [r40],16 ;; (p0) ldfe asin_A9 = [r40],16 nop.i 999 ;; } { .mmi (p0) ldfe asin_A8 = [r40],16 ;; (p0) ldfe asin_A7 = [r40],16 nop.i 999 ;; } { .mmi (p0) ldfe asin_A6 = [r40],16 ;; (p0) getf.exp asin_GR_signexp_f8 = asin_NORM_f8 nop.i 999 } { .mmi (p0) ldfe asin_A5 = [r40],16 ;; (p0) ldfe asin_A4 = [r40],16 nop.i 999 ;; } { .mfi nop.m 999 (p0) fmerge.s asin_ABS_NORM_f8 = f0, asin_NORM_f8 (p0) and asin_GR_exp = asin_GR_signexp_f8, asin_GR_17_ones ;; } // case 1: |x| < 2^-40 ==> p6 (includes x = +-0) // case 2: 2^-40 <= |x| < 2^-2 ==> p8 // case 3: 2^-2 <= |x| < 1 ==> p9 // case 4: 1 <= |x| ==> p11 // In case 4, we pick up the special case x = +-1 and return +-pi/2 { .mii (p0) ldfe asin_A3 = [r40],16 (p0) sub asin_GR_true_exp = asin_GR_exp, asin_GR_16_ones ;; (p0) cmp.ge.unc p6, p7 = -41, asin_GR_true_exp ;; } { .mii (p0) ldfe asin_A2 = [r40],16 (p7) cmp.ge.unc p8, p9 = -3, asin_GR_true_exp ;; (p9) cmp.ge.unc p10, p11 = -1, asin_GR_true_exp } { .mmi (p0) ldfe asin_A1 = [r40],16 ;; (p0) ldfe asin_pi_by_2 = [r40],16 nop.i 999 } // case 4: |x| >= 1 { .mib nop.m 999 nop.i 999 (p11) br.spnt L(ASIN_ERROR_RETURN) ;; } // case 1: |x| < 2^-40 { .mfb nop.m 999 (p6) fma.s0 f8 = asin_2m100,f8,f8 (p6) br.ret.spnt b0 ;; } // case 2: 2^-40 <= |x| < 2^-2 ==> p8 { .mfi nop.m 999 (p8) fma.s1 asin_X2 = f8,f8, f0 nop.i 999 ;; } { .mfi nop.m 999 (p8) fma.s1 asin_X4 = asin_X2,asin_X2, f0 nop.i 999 ;; } { .mfi nop.m 999 (p8) fma.s1 asin_P810 = asin_X4, asin_A10, asin_A8 nop.i 999 } { .mfi nop.m 999 (p8) fma.s1 asin_P79 = asin_X4, asin_A9, asin_A7 nop.i 999 ;; } { .mfi nop.m 999 (p8) fma.s1 asin_P610 = asin_X4, asin_P810, asin_A6 nop.i 999 } { .mfi nop.m 999 (p8) fma.s1 asin_P59 = asin_X4, asin_P79, asin_A5 nop.i 999 ;; } { .mfi nop.m 999 (p8) fma.s1 asin_P410 = asin_X4, asin_P610, asin_A4 nop.i 999 } { .mfi nop.m 999 (p8) fma.s1 asin_P39 = asin_X4, asin_P59, asin_A3 nop.i 999 ;; } { .mfi nop.m 999 (p8) fma.s1 asin_P210 = asin_X4, asin_P410, asin_A2 nop.i 999 } { .mfi nop.m 999 (p8) fma.s1 asin_P19 = asin_X4, asin_P39, asin_A1 nop.i 999 ;; } { .mfi nop.m 999 (p8) fma.s1 asin_P1P2 = asin_X2, asin_P210, asin_P19 nop.i 999 ;; } { .mfi nop.m 999 (p8) fma.s1 asin_P1P2 = asin_X2, asin_P1P2, f0 nop.i 999 ;; } { .mfb nop.m 999 (p8) fma.s0 f8 = asin_NORM_f8, asin_P1P2, asin_NORM_f8 (p8) br.ret.spnt b0 ;; } // case 3: 2^-2 <= |x| < 1 // 1- X*X is computed as B + b // Step 1.1: Get B and b // atan2 will return // f8 = Z_hi // f10 = Z_lo // f11 = s_lo { .mfi (p0) mov asin_GR_fffe = 0xfffe (p0) fmerge.se f8 = asin_ABS_NORM_f8, asin_ABS_NORM_f8 nop.i 0 };; { .mmf nop.m 0 (p0) setf.exp asin_HALF = asin_GR_fffe (p0) fmerge.se f12 = asin_NORM_f8, asin_NORM_f8 ;; } { .mfi nop.m 999 (p0) fcmp.lt.unc.s1 p6,p7 = asin_ABS_NORM_f8, asin_HALF nop.i 999 ;; } { .mfi nop.m 999 (p7) fma.s1 asin_D = f1,f1,asin_ABS_NORM_f8 nop.i 999 } { .mfi nop.m 999 (p7) fms.s1 asin_C = f1,f1,asin_ABS_NORM_f8 nop.i 999 ;; } { .mfi nop.m 999 (p7) fma.s1 asin_B = asin_C, asin_D, f0 nop.i 999 } { .mfi nop.m 999 (p7) fms.s1 asin_1mD = f1,f1,asin_D nop.i 999 ;; } { .mfi nop.m 999 (p7) fma.s1 asin_Dd = asin_1mD,f1, asin_ABS_NORM_f8 nop.i 999 } { .mfi nop.m 999 (p7) fms.s1 asin_Bb = asin_C, asin_D, asin_B nop.i 999 ;; } { .mfi nop.m 999 (p7) fma.s1 asin_Bb = asin_C, asin_Dd, asin_Bb nop.i 999 } { .mfi nop.m 999 (p6) fma.s1 asin_C = asin_ABS_NORM_f8, asin_ABS_NORM_f8, f0 nop.i 999 ;; } { .mfi nop.m 999 (p6) fms.s1 asin_B = f1, f1, asin_C nop.i 999 } { .mfi nop.m 999 (p6) fms.s1 asin_Cc = asin_ABS_NORM_f8, asin_ABS_NORM_f8, asin_C nop.i 999 ;; } { .mfi nop.m 999 (p0) fma.s1 asin_Hh = asin_HALF, asin_B, f0 nop.i 999 } { .mfi nop.m 999 (p6) fms.s1 asin_1mB = f1, f1, asin_B nop.i 999 ;; } // Step 1.2: // sqrt(B + b) is computed as W + w // Get W { .mfi nop.m 999 (p0) frsqrta.s1 asin_y0,p8 = asin_B nop.i 999 ;; } { .mfi nop.m 999 (p6) fms.s1 asin_1mBmC = asin_1mB, f1, asin_C nop.i 999 ;; } { .mfi nop.m 999 (p0) fma.s1 asin_t1 = asin_y0, asin_y0, f0 nop.i 999 ;; } { .mfi nop.m 999 (p6) fms.s1 asin_Bb = asin_1mBmC, f1, asin_Cc nop.i 999 ;; } { .mfi nop.m 999 (p0) fnma.s1 asin_t2 = asin_t1, asin_Hh, asin_HALF nop.i 999 ;; } { .mfi nop.m 999 (p0) fma.s1 asin_y1 = asin_t2, asin_y0, asin_y0 nop.i 999 ;; } { .mfi nop.m 999 (p0) fma.s1 asin_t3 = asin_y1, asin_Hh, f0 nop.i 999 ;; } { .mfi nop.m 999 (p0) fnma.s1 asin_t4 = asin_t3, asin_y1, asin_HALF nop.i 999 ;; } { .mfi nop.m 999 (p0) fma.s1 asin_y2 = asin_t4, asin_y1, asin_y1 nop.i 999 ;; } { .mfi nop.m 999 (p0) fma.s1 asin_S = asin_B, asin_y2, f0 nop.i 999 } { .mfi nop.m 999 (p0) fma.s1 asin_H = asin_y2, asin_HALF, f0 nop.i 999 ;; } { .mfi nop.m 999 (p0) fma.s1 asin_t5 = asin_Hh, asin_y2, f0 nop.i 999 ;; } { .mfi nop.m 999 (p0) fnma.s1 asin_Dd = asin_S, asin_S, asin_B nop.i 999 ;; } { .mfi nop.m 999 (p0) fma.s1 asin_W = asin_Dd, asin_H, asin_S nop.i 999 ;; } { .mfi nop.m 999 (p0) fma.s1 asin_2W = asin_W, f1, asin_W nop.i 999 } // Step 1.3 // Get w { .mfi nop.m 999 (p0) fnma.s1 asin_BmWW = asin_W, asin_W, asin_B nop.i 999 ;; } // Step 2 // asin(x) = atan2(X,sqrt(1-X*X)) // = atan2(X, W) -Xw // corr = Xw // asin(x) = Z_hi + (s_lo*Z_lo - corr) // Call atan2(X, W) // Save W in f9 // Save X in f12 // Save w in f13 { .mfi nop.m 999 (p0) fmerge.se f9 = asin_W, asin_W nop.i 999 ;; } { .mfi nop.m 999 (p0) fma.s1 asin_BmWWpb = asin_BmWW, f1, asin_Bb nop.i 999 ;; } { .mfi nop.m 999 (p0) frcpa.s1 asin_1d2W,p9 = f1, asin_2W nop.i 999 ;; } { .mfi nop.m 999 (p0) fma.s1 asin_Ww = asin_BmWWpb, asin_1d2W, f0 nop.i 999 ;; } .endp asinl ASM_SIZE_DIRECTIVE(asinl) .proc __libm_callout __libm_callout: .prologue { .mfi nop.m 0 nop.f 0 .save ar.pfs,GR_SAVE_PFS mov GR_SAVE_PFS=ar.pfs // Save ar.pfs };; { .mfi mov GR_SAVE_GP=gp // Save gp nop.f 0 .save b0, GR_SAVE_B0 mov GR_SAVE_B0=b0 // Save b0 } .body {.mfb nop.m 0 (p0) fmerge.se f13 = asin_Ww, asin_Ww (p0) br.call.sptk.many b0=__libm_atan2_reg# };; { .mfi mov gp = GR_SAVE_GP // Restore gp (p0) fma.s1 asin_XWw = asin_ABS_NORM_f8,f13,f0 mov b0 = GR_SAVE_B0 // Restore return address };; // asin_XWw = Xw = corr // asin_low = (s_lo * Z_lo - corr) // f8 = Z_hi + (s_lo * Z_lo - corr) { .mfi nop.m 999 (p0) fms.s1 asin_low = f11, f10, asin_XWw mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs };; { .mfi nop.m 999 (p0) fma.s0 f8 = f8, f1, asin_low nop.i 999 ;; } { .mfb nop.m 999 (p0) fmerge.s f8 = f12,f8 (p0) br.ret.sptk b0 ;; } .endp __libm_callout ASM_SIZE_DIRECTIVE(__libm_callout) .proc SPECIAL SPECIAL: L(ASIN_ERROR_RETURN): // If X is 1, return (sign of X)pi/2 { .mfi nop.m 999 (p0) fcmp.eq.unc p6,p7 = asin_ABS_NORM_f8,f1 nop.i 999 ;; } { .mfb (p6) ldfe asin_pi_by_2_lo = [r40] (p6) fmerge.s asin_pi_by_2 = f8,asin_pi_by_2 nop.b 0;; } // If X is a NAN, leave // qnan snan inf norm unorm 0 -+ // 1 1 0 0 0 0 11 { .mfb nop.m 999 (p6) fma.s0 f8 = f8,asin_pi_by_2_lo,asin_pi_by_2 (p6) br.ret.spnt b0 } { .mfi nop.m 999 (p0) fclass.m.unc p12,p0 = f8, 0xc3 nop.i 999 ;; } { .mfb nop.m 999 (p12) fma.s0 f8 = f8,f1,f0 (p12) br.ret.spnt b0 ;; } { .mfi (p0) mov GR_Parameter_TAG = 60 (p0) frcpa f10, p6 = f0, f0 nop.i 0 };; .endp SPECIAL ASM_SIZE_DIRECTIVE(SPECIAL) .proc __libm_error_region __libm_error_region: .prologue { .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 };; { .mmi stfe [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 stfe [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 stfe [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 ldfe 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 };; .endp __libm_error_region ASM_SIZE_DIRECTIVE(__libm_error_region) .type __libm_error_support#,@function .global __libm_error_support# .type __libm_atan2_reg#,@function .global __libm_atan2_reg#