s_cosf.s

glibc 2.9,最新版的C语言库函数

.file "sincosf.s"


// Copyright (c) 2000 - 2005, 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
// 04/02/00 Unwind support added.
// 06/16/00 Updated tables to enforce symmetry
// 08/31/00 Saved 2 cycles in main path, and 9 in other paths.
// 09/20/00 The updated tables regressed to an old version, so reinstated them
// 10/18/00 Changed one table entry to ensure symmetry
// 01/03/01 Improved speed, fixed flag settings for small arguments.
// 02/18/02 Large arguments processing routine excluded
// 05/20/02 Cleaned up namespace and sf0 syntax
// 06/03/02 Insure inexact flag set for large arg result
// 09/05/02 Single precision version is made using double precision one as base
// 02/10/03 Reordered header: .section, .global, .proc, .align
// 03/31/05 Reformatted delimiters between data tables
//
// API
//==============================================================
// float sinf( float x);
// float cosf( float x);
//
// Overview of operation
//==============================================================
//
// Step 1
// ======
// Reduce x to region -1/2*pi/2^k ===== 0 ===== +1/2*pi/2^k  where k=4
//    divide x by pi/2^k.
//    Multiply by 2^k/pi.
//    nfloat = Round result to integer (round-to-nearest)
//
// r = x -  nfloat * pi/2^k
//    Do this as (x -  nfloat * HIGH(pi/2^k)) - nfloat * LOW(pi/2^k) 

//    for increased accuracy.
//    pi/2^k is stored as two numbers that when added make pi/2^k.
//       pi/2^k = HIGH(pi/2^k) + LOW(pi/2^k)
//    HIGH part is rounded to zero, LOW - to nearest
//
// x = (nfloat * pi/2^k) + r
//    r is small enough that we can use a polynomial approximation
//    and is referred to as the reduced argument.
//
// Step 3
// ======
// Take the unreduced part and remove the multiples of 2pi.
// So nfloat = nfloat (with lower k+1 bits cleared) + lower k+1 bits
//
//    nfloat (with lower k+1 bits cleared) is a multiple of 2^(k+1)
//    N * 2^(k+1)
//    nfloat * pi/2^k = N * 2^(k+1) * pi/2^k + (lower k+1 bits) * pi/2^k
//    nfloat * pi/2^k = N * 2 * pi + (lower k+1 bits) * pi/2^k
//    nfloat * pi/2^k = N2pi + M * pi/2^k
//
//
// Sin(x) = Sin((nfloat * pi/2^k) + r)
//        = Sin(nfloat * pi/2^k) * Cos(r) + Cos(nfloat * pi/2^k) * Sin(r)
//
//          Sin(nfloat * pi/2^k) = Sin(N2pi + Mpi/2^k)
//                               = Sin(N2pi)Cos(Mpi/2^k) + Cos(N2pi)Sin(Mpi/2^k)
//                               = Sin(Mpi/2^k)
//
//          Cos(nfloat * pi/2^k) = Cos(N2pi + Mpi/2^k)
//                               = Cos(N2pi)Cos(Mpi/2^k) + Sin(N2pi)Sin(Mpi/2^k)
//                               = Cos(Mpi/2^k)
//
// Sin(x) = Sin(Mpi/2^k) Cos(r) + Cos(Mpi/2^k) Sin(r)
//
//
// Step 4
// ======
// 0 <= M < 2^(k+1)
// There are 2^(k+1) Sin entries in a table.
// There are 2^(k+1) Cos entries in a table.
//
// Get Sin(Mpi/2^k) and Cos(Mpi/2^k) by table lookup.
//
//
// Step 5
// ======
// Calculate Cos(r) and Sin(r) by polynomial approximation.
//
// Cos(r) = 1 + r^2 q1  + r^4 q2  = Series for Cos
// Sin(r) = r + r^3 p1  + r^5 p2  = Series for Sin
//
// and the coefficients q1, q2 and p1, p2 are stored in a table
//
//
// Calculate
// Sin(x) = Sin(Mpi/2^k) Cos(r) + Cos(Mpi/2^k) Sin(r)
//
// as follows
//
//    S[m] = Sin(Mpi/2^k) and C[m] = Cos(Mpi/2^k)
//    rsq = r*r
//
//
//    P = P1 + r^2*P2
//    Q = Q1 + r^2*Q2
//
//       rcub = r * rsq
//       Sin(r) = r + rcub * P
//              = r + r^3p1  + r^5p2 = Sin(r)
//
//            The coefficients are not exactly these values, but almost.
//
//            p1 = -1/6  = -1/3!
//            p2 = 1/120 =  1/5!
//            p3 = -1/5040 = -1/7!
//            p4 = 1/362889 = 1/9!
//
//       P =  r + r^3 * P
//
//    Answer = S[m] Cos(r) + C[m] P
//
//       Cos(r) = 1 + rsq Q
//       Cos(r) = 1 + r^2 Q
//       Cos(r) = 1 + r^2 (q1 + r^2q2)
//       Cos(r) = 1 + r^2q1 + r^4q2
//
//       S[m] Cos(r) = S[m](1 + rsq Q)
//       S[m] Cos(r) = S[m] + S[m] rsq Q
//       S[m] Cos(r) = S[m] + s_rsq Q
//       Q         = S[m] + s_rsq Q
//
// Then,
//
//    Answer = Q + C[m] P


// Registers used
//==============================================================
// general input registers:
// r14 -> r19
// r32 -> r45

// predicate registers used:
// p6 -> p14

// floating-point registers used
// f9 -> f15
// f32 -> f61

// Assembly macros
//==============================================================
sincosf_NORM_f8                 = f9
sincosf_W                       = f10
sincosf_int_Nfloat              = f11
sincosf_Nfloat                  = f12

sincosf_r                       = f13
sincosf_rsq                     = f14
sincosf_rcub                    = f15
sincosf_save_tmp                = f15

sincosf_Inv_Pi_by_16            = f32
sincosf_Pi_by_16_1              = f33
sincosf_Pi_by_16_2              = f34

sincosf_Inv_Pi_by_64            = f35

sincosf_Pi_by_16_3              = f36

sincosf_r_exact                 = f37

sincosf_Sm                      = f38
sincosf_Cm                      = f39

sincosf_P1                      = f40
sincosf_Q1                      = f41
sincosf_P2                      = f42
sincosf_Q2                      = f43
sincosf_P3                      = f44
sincosf_Q3                      = f45
sincosf_P4                      = f46
sincosf_Q4                      = f47

sincosf_P_temp1                 = f48
sincosf_P_temp2                 = f49

sincosf_Q_temp1                 = f50
sincosf_Q_temp2                 = f51

sincosf_P                       = f52
sincosf_Q                       = f53

sincosf_srsq                    = f54

sincosf_SIG_INV_PI_BY_16_2TO61  = f55
sincosf_RSHF_2TO61              = f56
sincosf_RSHF                    = f57
sincosf_2TOM61                  = f58
sincosf_NFLOAT                  = f59
sincosf_W_2TO61_RSH             = f60

fp_tmp                          = f61

/////////////////////////////////////////////////////////////

sincosf_AD_1                    = r33
sincosf_AD_2                    = r34
sincosf_exp_limit               = r35
sincosf_r_signexp               = r36
sincosf_AD_beta_table           = r37
sincosf_r_sincos                = r38

sincosf_r_exp                   = r39
sincosf_r_17_ones               = r40

sincosf_GR_sig_inv_pi_by_16     = r14
sincosf_GR_rshf_2to61           = r15
sincosf_GR_rshf                 = r16
sincosf_GR_exp_2tom61           = r17
sincosf_GR_n                    = r18
sincosf_GR_m                    = r19
sincosf_GR_32m                  = r19
sincosf_GR_all_ones             = r19

gr_tmp                          = r41
GR_SAVE_PFS                     = r41
GR_SAVE_B0                      = r42
GR_SAVE_GP                      = r43

RODATA
.align 16

// Pi/16 parts
LOCAL_OBJECT_START(double_sincosf_pi)
   data8 0xC90FDAA22168C234, 0x00003FFC // pi/16 1st part
   data8 0xC4C6628B80DC1CD1, 0x00003FBC // pi/16 2nd part
LOCAL_OBJECT_END(double_sincosf_pi)

// Coefficients for polynomials
LOCAL_OBJECT_START(double_sincosf_pq_k4)
   data8 0x3F810FABB668E9A2 // P2
   data8 0x3FA552E3D6DE75C9 // Q2
   data8 0xBFC555554447BC7F // P1
   data8 0xBFDFFFFFC447610A // Q1
LOCAL_OBJECT_END(double_sincosf_pq_k4)

// Sincos table (S[m], C[m])
LOCAL_OBJECT_START(double_sin_cos_beta_k4)
    data8 0x0000000000000000 // sin ( 0 Pi / 16 )
    data8 0x3FF0000000000000 // cos ( 0 Pi / 16 )
//
    data8 0x3FC8F8B83C69A60B // sin ( 1 Pi / 16 )
    data8 0x3FEF6297CFF75CB0 // cos ( 1 Pi / 16 )
//
    data8 0x3FD87DE2A6AEA963 // sin ( 2 Pi / 16 )
    data8 0x3FED906BCF328D46 // cos ( 2 Pi / 16 )
//
    data8 0x3FE1C73B39AE68C8 // sin ( 3 Pi / 16 )
    data8 0x3FEA9B66290EA1A3 // cos ( 3 Pi / 16 )
//
    data8 0x3FE6A09E667F3BCD // sin ( 4 Pi / 16 )
    data8 0x3FE6A09E667F3BCD // cos ( 4 Pi / 16 )
//
    data8 0x3FEA9B66290EA1A3 // sin ( 5 Pi / 16 )
    data8 0x3FE1C73B39AE68C8 // cos ( 5 Pi / 16 )
//
    data8 0x3FED906BCF328D46 // sin ( 6 Pi / 16 )
    data8 0x3FD87DE2A6AEA963 // cos ( 6 Pi / 16 )
//
    data8 0x3FEF6297CFF75CB0 // sin ( 7 Pi / 16 )
    data8 0x3FC8F8B83C69A60B // cos ( 7 Pi / 16 )
//
    data8 0x3FF0000000000000 // sin ( 8 Pi / 16 )
    data8 0x0000000000000000 // cos ( 8 Pi / 16 )
//
    data8 0x3FEF6297CFF75CB0 // sin ( 9 Pi / 16 )
    data8 0xBFC8F8B83C69A60B // cos ( 9 Pi / 16 )
//
    data8 0x3FED906BCF328D46 // sin ( 10 Pi / 16 )
    data8 0xBFD87DE2A6AEA963 // cos ( 10 Pi / 16 )
//
    data8 0x3FEA9B66290EA1A3 // sin ( 11 Pi / 16 )
    data8 0xBFE1C73B39AE68C8 // cos ( 11 Pi / 16 )
//
    data8 0x3FE6A09E667F3BCD // sin ( 12 Pi / 16 )
    data8 0xBFE6A09E667F3BCD // cos ( 12 Pi / 16 )
//
    data8 0x3FE1C73B39AE68C8 // sin ( 13 Pi / 16 )
    data8 0xBFEA9B66290EA1A3 // cos ( 13 Pi / 16 )
//
    data8 0x3FD87DE2A6AEA963 // sin ( 14 Pi / 16 )
    data8 0xBFED906BCF328D46 // cos ( 14 Pi / 16 )
//
    data8 0x3FC8F8B83C69A60B // sin ( 15 Pi / 16 )
    data8 0xBFEF6297CFF75CB0 // cos ( 15 Pi / 16 )
//
    data8 0x0000000000000000 // sin ( 16 Pi / 16 )
    data8 0xBFF0000000000000 // cos ( 16 Pi / 16 )
//
    data8 0xBFC8F8B83C69A60B // sin ( 17 Pi / 16 )
    data8 0xBFEF6297CFF75CB0 // cos ( 17 Pi / 16 )
//
    data8 0xBFD87DE2A6AEA963 // sin ( 18 Pi / 16 )
    data8 0xBFED906BCF328D46 // cos ( 18 Pi / 16 )
//
    data8 0xBFE1C73B39AE68C8 // sin ( 19 Pi / 16 )
    data8 0xBFEA9B66290EA1A3 // cos ( 19 Pi / 16 )
//
    data8 0xBFE6A09E667F3BCD // sin ( 20 Pi / 16 )
    data8 0xBFE6A09E667F3BCD // cos ( 20 Pi / 16 )
//
    data8 0xBFEA9B66290EA1A3 // sin ( 21 Pi / 16 )
    data8 0xBFE1C73B39AE68C8 // cos ( 21 Pi / 16 )
//
    data8 0xBFED906BCF328D46 // sin ( 22 Pi / 16 )
    data8 0xBFD87DE2A6AEA963 // cos ( 22 Pi / 16 )
//
    data8 0xBFEF6297CFF75CB0 // sin ( 23 Pi / 16 )
    data8 0xBFC8F8B83C69A60B // cos ( 23 Pi / 16 )
//
    data8 0xBFF0000000000000 // sin ( 24 Pi / 16 )
    data8 0x0000000000000000 // cos ( 24 Pi / 16 )
//
    data8 0xBFEF6297CFF75CB0 // sin ( 25 Pi / 16 )
    data8 0x3FC8F8B83C69A60B // cos ( 25 Pi / 16 )
//