.file "sincosf.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 revision // 4/02/00 Unwind support added. // 5/10/00 Improved speed with new algorithm. // 8/08/00 Improved speed by avoiding SIR flush. // 8/17/00 Changed predicate register macro-usage to direct predicate // names due to an assembler bug. // 8/30/00 Put sin_of_r before sin_tbl_S_cos_of_r to gain a cycle // 1/02/00 Fixed flag settings, improved speed. // // API //============================================================== // float sinf( float x); // float cosf( float x); // #include "libm_support.h" // Assembly macros //============================================================== // SIN_Sin_Flag = p6 // SIN_Cos_Flag = p7 // integer registers used SIN_AD_PQ_1 = r33 SIN_AD_PQ_2 = r33 sin_GR_sincos_flag = r34 sin_GR_Mint = r35 sin_GR_index = r36 gr_tmp = r37 GR_SAVE_B0 = r37 GR_SAVE_GP = r38 GR_SAVE_PFS = r39 // floating point registers used sin_coeff_P1 = f32 sin_coeff_P2 = f33 sin_coeff_Q1 = f34 sin_coeff_Q2 = f35 sin_coeff_P4 = f36 sin_coeff_P5 = f37 sin_coeff_Q3 = f38 sin_coeff_Q4 = f39 sin_Mx = f40 sin_Mfloat = f41 sin_tbl_S = f42 sin_tbl_C = f43 sin_r = f44 sin_rcube = f45 sin_tsq = f46 sin_r7 = f47 sin_t = f48 sin_poly_p2 = f49 sin_poly_p1 = f50 fp_tmp = f51 sin_poly_p3 = f52 sin_poly_p4 = f53 sin_of_r = f54 sin_S_t = f55 sin_poly_q2 = f56 sin_poly_q1 = f57 sin_S_tcube = f58 sin_poly_q3 = f59 sin_poly_q4 = f60 sin_tbl_S_tcube = f61 sin_tbl_S_cos_of_r = f62 sin_coeff_Q5 = f63 sin_coeff_Q6 = f64 sin_coeff_P3 = f65 sin_poly_q5 = f66 sin_poly_q12 = f67 sin_poly_q3456 = f68 fp_tmp2 = f69 SIN_NORM_f8 = f70 #ifdef _LIBC .rodata #else .data #endif .align 16 sin_coeff_1_table: ASM_TYPE_DIRECTIVE(sin_coeff_1_table,@object) data8 0xBF56C16C16BF6462 // q3 data8 0x3EFA01A0128B9EBC // q4 data8 0xBE927E42FDF33FFE // q5 data8 0x3E21DA5C72A446F3 // q6 data8 0x3EC71DD1D5E421A4 // p4 data8 0xBE5AC5C9D0ACF95A // p5 data8 0xBFC55555555554CA // p1 data8 0x3F811111110F2395 // p2 data8 0xBFE0000000000000 // q1 data8 0x3FA55555555554EF // q2 data8 0xBF2A01A011232913 // p3 data8 0x0000000000000000 // pad ///////////////////////////////////////// data8 0xBFE1A54991426566 //sin(-32) data8 0x3FEAB1F5305DE8E5 //cos(-32) data8 0x3FD9DBC0B640FC81 //sin(-31) data8 0x3FED4591C3E12A20 //cos(-31) data8 0x3FEF9DF47F1C903D //sin(-30) data8 0x3FC3BE82F2505A52 //cos(-30) data8 0x3FE53C7D20A6C9E7 //sin(-29) data8 0xBFE7F01658314E47 //cos(-29) data8 0xBFD156853B4514D6 //sin(-28) data8 0xBFEECDAAD1582500 //cos(-28) data8 0xBFEE9AA1B0E5BA30 //sin(-27) data8 0xBFD2B266F959DED5 //cos(-27) data8 0xBFE866E0FAC32583 //sin(-26) data8 0x3FE4B3902691A9ED //cos(-26) data8 0x3FC0F0E6F31E809D //sin(-25) data8 0x3FEFB7EEF59504FF //cos(-25) data8 0x3FECFA7F7919140F //sin(-24) data8 0x3FDB25BFB50A609A //cos(-24) data8 0x3FEB143CD0247D02 //sin(-23) data8 0xBFE10CF7D591F272 //cos(-23) data8 0x3F8220A29F6EB9F4 //sin(-22) data8 0xBFEFFFADD8D4ACDA //cos(-22) data8 0xBFEAC5E20BB0D7ED //sin(-21) data8 0xBFE186FF83773759 //cos(-21) data8 0xBFED36D8F55D3CE0 //sin(-20) data8 0x3FDA1E043964A83F //cos(-20) data8 0xBFC32F2D28F584CF //sin(-19) data8 0x3FEFA377DE108258 //cos(-19) data8 0x3FE8081668131E26 //sin(-18) data8 0x3FE52150815D2470 //cos(-18) data8 0x3FEEC3C4AC42882B //sin(-17) data8 0xBFD19C46B07F58E7 //cos(-17) data8 0x3FD26D02085F20F8 //sin(-16) data8 0xBFEEA5257E962F74 //cos(-16) data8 0xBFE4CF2871CEC2E8 //sin(-15) data8 0xBFE84F5D069CA4F3 //cos(-15) data8 0xBFEFB30E327C5E45 //sin(-14) data8 0x3FC1809AEC2CA0ED //cos(-14) data8 0xBFDAE4044881C506 //sin(-13) data8 0x3FED09CDD5260CB7 //cos(-13) data8 0x3FE12B9AF7D765A5 //sin(-12) data8 0x3FEB00DA046B65E3 //cos(-12) data8 0x3FEFFFEB762E93EB //sin(-11) data8 0x3F7220AE41EE2FDF //cos(-11) data8 0x3FE1689EF5F34F52 //sin(-10) data8 0xBFEAD9AC890C6B1F //cos(-10) data8 0xBFDA6026360C2F91 //sin( -9) data8 0xBFED27FAA6A6196B //cos( -9) data8 0xBFEFA8D2A028CF7B //sin( -8) data8 0xBFC29FBEBF632F94 //cos( -8) data8 0xBFE50608C26D0A08 //sin( -7) data8 0x3FE81FF79ED92017 //cos( -7) data8 0x3FD1E1F18AB0A2C0 //sin( -6) data8 0x3FEEB9B7097822F5 //cos( -6) data8 0x3FEEAF81F5E09933 //sin( -5) data8 0x3FD22785706B4AD9 //cos( -5) data8 0x3FE837B9DDDC1EAE //sin( -4) data8 0xBFE4EAA606DB24C1 //cos( -4) data8 0xBFC210386DB6D55B //sin( -3) data8 0xBFEFAE04BE85E5D2 //cos( -3) data8 0xBFED18F6EAD1B446 //sin( -2) data8 0xBFDAA22657537205 //cos( -2) data8 0xBFEAED548F090CEE //sin( -1) data8 0x3FE14A280FB5068C //cos( -1) data8 0x0000000000000000 //sin( 0) data8 0x3FF0000000000000 //cos( 0) data8 0x3FEAED548F090CEE //sin( 1) data8 0x3FE14A280FB5068C //cos( 1) data8 0x3FED18F6EAD1B446 //sin( 2) data8 0xBFDAA22657537205 //cos( 2) data8 0x3FC210386DB6D55B //sin( 3) data8 0xBFEFAE04BE85E5D2 //cos( 3) data8 0xBFE837B9DDDC1EAE //sin( 4) data8 0xBFE4EAA606DB24C1 //cos( 4) data8 0xBFEEAF81F5E09933 //sin( 5) data8 0x3FD22785706B4AD9 //cos( 5) data8 0xBFD1E1F18AB0A2C0 //sin( 6) data8 0x3FEEB9B7097822F5 //cos( 6) data8 0x3FE50608C26D0A08 //sin( 7) data8 0x3FE81FF79ED92017 //cos( 7) data8 0x3FEFA8D2A028CF7B //sin( 8) data8 0xBFC29FBEBF632F94 //cos( 8) data8 0x3FDA6026360C2F91 //sin( 9) data8 0xBFED27FAA6A6196B //cos( 9) data8 0xBFE1689EF5F34F52 //sin( 10) data8 0xBFEAD9AC890C6B1F //cos( 10) data8 0xBFEFFFEB762E93EB //sin( 11) data8 0x3F7220AE41EE2FDF //cos( 11) data8 0xBFE12B9AF7D765A5 //sin( 12) data8 0x3FEB00DA046B65E3 //cos( 12) data8 0x3FDAE4044881C506 //sin( 13) data8 0x3FED09CDD5260CB7 //cos( 13) data8 0x3FEFB30E327C5E45 //sin( 14) data8 0x3FC1809AEC2CA0ED //cos( 14) data8 0x3FE4CF2871CEC2E8 //sin( 15) data8 0xBFE84F5D069CA4F3 //cos( 15) data8 0xBFD26D02085F20F8 //sin( 16) data8 0xBFEEA5257E962F74 //cos( 16) data8 0xBFEEC3C4AC42882B //sin( 17) data8 0xBFD19C46B07F58E7 //cos( 17) data8 0xBFE8081668131E26 //sin( 18) data8 0x3FE52150815D2470 //cos( 18) data8 0x3FC32F2D28F584CF //sin( 19) data8 0x3FEFA377DE108258 //cos( 19) data8 0x3FED36D8F55D3CE0 //sin( 20) data8 0x3FDA1E043964A83F //cos( 20) data8 0x3FEAC5E20BB0D7ED //sin( 21) data8 0xBFE186FF83773759 //cos( 21) data8 0xBF8220A29F6EB9F4 //sin( 22) data8 0xBFEFFFADD8D4ACDA //cos( 22) data8 0xBFEB143CD0247D02 //sin( 23) data8 0xBFE10CF7D591F272 //cos( 23) data8 0xBFECFA7F7919140F //sin( 24) data8 0x3FDB25BFB50A609A //cos( 24) data8 0xBFC0F0E6F31E809D //sin( 25) data8 0x3FEFB7EEF59504FF //cos( 25) data8 0x3FE866E0FAC32583 //sin( 26) data8 0x3FE4B3902691A9ED //cos( 26) data8 0x3FEE9AA1B0E5BA30 //sin( 27) data8 0xBFD2B266F959DED5 //cos( 27) data8 0x3FD156853B4514D6 //sin( 28) data8 0xBFEECDAAD1582500 //cos( 28) data8 0xBFE53C7D20A6C9E7 //sin( 29) data8 0xBFE7F01658314E47 //cos( 29) data8 0xBFEF9DF47F1C903D //sin( 30) data8 0x3FC3BE82F2505A52 //cos( 30) data8 0xBFD9DBC0B640FC81 //sin( 31) data8 0x3FED4591C3E12A20 //cos( 31) data8 0x3FE1A54991426566 //sin( 32) data8 0x3FEAB1F5305DE8E5 //cos( 32) ASM_SIZE_DIRECTIVE(sin_coeff_1_table) ////////////////////////////////////////// .global sinf .global cosf #ifdef _LIBC .global __sinf .global __cosf #endif .text .proc cosf #ifdef _LIBC .proc __cosf #endif .align 32 cosf: #ifdef _LIBC __cosf: #endif { .mfi alloc r32 = ar.pfs,1,7,0,0 fcvt.fx.s1 sin_Mx = f8 cmp.ne p6,p7 = r0,r0 // p7 set if cos } { .mfi addl SIN_AD_PQ_1 = @ltoff(sin_coeff_1_table),gp fnorm.s0 SIN_NORM_f8 = f8 // Sets denormal or invalid mov sin_GR_sincos_flag = 0x0 } ;; { .mfi ld8 SIN_AD_PQ_1 = [SIN_AD_PQ_1] fclass.m.unc p9,p0 = f8, 0x07 cmp.ne p8,p0 = r0,r0 } { .mfb nop.m 999 nop.f 999 br.sptk L(SINCOSF_COMMON) } ;; .endp cosf ASM_SIZE_DIRECTIVE(cosf) .text .proc sinf #ifdef _LIBC .proc __sinf #endif .align 32 sinf: #ifdef _LIBC __sinf: #endif { .mfi alloc r32 = ar.pfs,1,7,0,0 fcvt.fx.s1 sin_Mx = f8 cmp.eq p6,p7 = r0,r0 // p6 set if sin } { .mfi addl SIN_AD_PQ_1 = @ltoff(sin_coeff_1_table),gp fnorm.s0 SIN_NORM_f8 = f8 // Sets denormal or invalid mov sin_GR_sincos_flag = 0x1 } ;; { .mfi ld8 SIN_AD_PQ_1 = [SIN_AD_PQ_1] fclass.m.unc p8,p0 = f8, 0x07 cmp.ne p9,p0 = r0,r0 } { .mfb nop.m 999 nop.f 999 br.sptk L(SINCOSF_COMMON) } ;; L(SINCOSF_COMMON): // Here with p6 if sin, p7 if cos, p8 if sin(0), p9 if cos(0) { .mmf ldfpd sin_coeff_Q3, sin_coeff_Q4 = [SIN_AD_PQ_1], 16 nop.m 999 fclass.m.unc p11,p0 = f8, 0x23 // Test for x=inf } ;; { .mfb ldfpd sin_coeff_Q5, sin_coeff_Q6 = [SIN_AD_PQ_1], 16 fclass.m.unc p10,p0 = f8, 0xc3 // Test for x=nan (p8) br.ret.spnt b0 // Exit for sin(0) } { .mfb nop.m 999 (p9) fma.s f8 = f1,f1,f0 (p9) br.ret.spnt b0 // Exit for cos(0) } ;; { .mmf ldfpd sin_coeff_P4, sin_coeff_P5 = [SIN_AD_PQ_1], 16 addl gr_tmp = -1,r0 fcvt.xf sin_Mfloat = sin_Mx } ;; { .mfi getf.sig sin_GR_Mint = sin_Mx (p11) frcpa.s0 f8,p13 = f0,f0 // qnan indef if x=inf nop.i 999 } { .mfb ldfpd sin_coeff_P1, sin_coeff_P2 = [SIN_AD_PQ_1], 16 nop.f 999 (p11) br.ret.spnt b0 // Exit for x=inf } ;; { .mfi ldfpd sin_coeff_Q1, sin_coeff_Q2 = [SIN_AD_PQ_1], 16 nop.f 999 cmp.ge p8,p9 = -33,sin_GR_Mint } { .mfb add sin_GR_index = 32,sin_GR_Mint (p10) fma.s f8 = f8,f1,f0 // Force qnan if x=nan (p10) br.ret.spnt b0 // Exit for x=nan } ;; { .mmi ldfd sin_coeff_P3 = [SIN_AD_PQ_1], 16 (p9) cmp.le p8,p0 = 33, sin_GR_Mint shl sin_GR_index = sin_GR_index,4 } ;; { .mfi setf.sig fp_tmp = gr_tmp // Create constant such that fmpy sets inexact fnma.s1 sin_r = f1,sin_Mfloat,SIN_NORM_f8 (p8) cmp.eq.unc p11,p12=sin_GR_sincos_flag,r0 // p11 if must call dbl cos // p12 if must call dbl sin } { .mbb add SIN_AD_PQ_2 = sin_GR_index,SIN_AD_PQ_1 (p11) br.cond.spnt COS_DOUBLE (p12) br.cond.spnt SIN_DOUBLE } ;; .pred.rel "mutex",p6,p7 //SIN_Sin_Flag, SIN_Cos_Flag { .mmi (p6) ldfpd sin_tbl_S,sin_tbl_C = [SIN_AD_PQ_2] (p7) ldfpd sin_tbl_C,sin_tbl_S = [SIN_AD_PQ_2] nop.i 999 } ;; { .mfi nop.m 999 (p6) fclass.m.unc p8,p0 = f8, 0x0b // If sin, note denormal input to set uflow nop.i 999 } { .mfi nop.m 999 fma.s1 sin_t = sin_r,sin_r,f0 nop.i 999 } ;; { .mfi nop.m 999 fma.s1 sin_rcube = sin_t,sin_r,f0 nop.i 999 } { .mfi nop.m 999 fma.s1 sin_tsq = sin_t,sin_t,f0 nop.i 999 } ;; { .mfi nop.m 999 fma.s1 sin_poly_q3 = sin_t,sin_coeff_Q4,sin_coeff_Q3 nop.i 999 } { .mfi nop.m 999 fma.s1 sin_poly_q5 = sin_t,sin_coeff_Q6,sin_coeff_Q5 nop.i 999 } ;; { .mfi nop.m 999 fma.s1 sin_poly_p1 = sin_t,sin_coeff_P5,sin_coeff_P4 nop.i 999 } { .mfi nop.m 999 fma.s1 sin_poly_p2 = sin_t,sin_coeff_P2,sin_coeff_P1 nop.i 999 } ;; { .mfi nop.m 999 fma.s1 sin_poly_q1 = sin_t,sin_coeff_Q2,sin_coeff_Q1 nop.i 999 } { .mfi nop.m 999 fma.s1 sin_S_t = sin_t,sin_tbl_S,f0 nop.i 999 } ;; { .mfi nop.m 999 (p8) fmpy.s.s0 fp_tmp2 = f8,f8 // Dummy mult to set underflow if sin(denormal) nop.i 999 } { .mfi nop.m 999 fma.s1 sin_r7 = sin_rcube,sin_tsq,f0 nop.i 999 } ;; { .mfi nop.m 999 fma.s1 sin_poly_q3456 = sin_tsq,sin_poly_q5,sin_poly_q3 nop.i 999 } ;; { .mfi nop.m 999 fma.s1 sin_poly_p3 = sin_t,sin_poly_p1,sin_coeff_P3 nop.i 999 } { .mfi nop.m 999 fma.s1 sin_poly_p4 = sin_rcube,sin_poly_p2,sin_r nop.i 999 } ;; { .mfi nop.m 999 fma.s1 sin_tbl_S_tcube = sin_S_t,sin_tsq,f0 nop.i 999 } { .mfi nop.m 999 fma.s1 sin_poly_q12 = sin_S_t,sin_poly_q1,sin_tbl_S nop.i 999 } ;; { .mfi nop.m 999 fma.d.s1 sin_of_r = sin_r7,sin_poly_p3,sin_poly_p4 nop.i 999 } ;; { .mfi nop.m 999 fma.d.s1 sin_tbl_S_cos_of_r = sin_tbl_S_tcube,sin_poly_q3456,sin_poly_q12 nop.i 999 } { .mfi nop.m 999 fmpy.s0 fp_tmp = fp_tmp, fp_tmp // Dummy mult to set inexact nop.i 999 } ;; .pred.rel "mutex",p6,p7 //SIN_Sin_Flag, SIN_Cos_Flag { .mfi nop.m 999 //(SIN_Sin_Flag) fma.s f8 = sin_tbl_C,sin_of_r,sin_tbl_S_cos_of_r (p6) fma.s f8 = sin_tbl_C,sin_of_r,sin_tbl_S_cos_of_r nop.i 999 } { .mfb nop.m 999 //(SIN_Cos_Flag) fnma.s f8 = sin_tbl_C,sin_of_r,sin_tbl_S_cos_of_r (p7) fnma.s f8 = sin_tbl_C,sin_of_r,sin_tbl_S_cos_of_r br.ret.sptk b0 } .endp sinf ASM_SIZE_DIRECTIVE(sinf) .proc SIN_DOUBLE SIN_DOUBLE: .prologue { .mfi nop.m 0 nop.f 0 .save ar.pfs,GR_SAVE_PFS mov GR_SAVE_PFS=ar.pfs } ;; { .mfi mov GR_SAVE_GP=gp nop.f 0 .save b0, GR_SAVE_B0 mov GR_SAVE_B0=b0 } .body { .mmb nop.m 999 nop.m 999 br.call.sptk.many b0=sin } ;; { .mfi mov gp = GR_SAVE_GP nop.f 999 mov b0 = GR_SAVE_B0 } ;; { .mfi nop.m 999 fma.s f8 = f8,f1,f0 (p0) mov ar.pfs = GR_SAVE_PFS } { .mib nop.m 999 nop.i 999 (p0) br.ret.sptk b0 } ;; .endp SIN_DOUBLE ASM_SIZE_DIRECTIVE(SIN_DOUBLE) .proc COS_DOUBLE COS_DOUBLE: .prologue { .mfi nop.m 0 nop.f 0 .save ar.pfs,GR_SAVE_PFS mov GR_SAVE_PFS=ar.pfs } ;; { .mfi mov GR_SAVE_GP=gp nop.f 0 .save b0, GR_SAVE_B0 mov GR_SAVE_B0=b0 } .body { .mmb nop.m 999 nop.m 999 br.call.sptk.many b0=cos } ;; { .mfi mov gp = GR_SAVE_GP nop.f 999 mov b0 = GR_SAVE_B0 } ;; { .mfi nop.m 999 fma.s f8 = f8,f1,f0 (p0) mov ar.pfs = GR_SAVE_PFS } { .mib nop.m 999 nop.i 999 (p0) br.ret.sptk b0 } ;; .endp COS_DOUBLE ASM_SIZE_DIRECTIVE(COS_DOUBLE) .type sin,@function .global sin .type cos,@function .global cos