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683 lines
19 KiB
683 lines
19 KiB
.file "acosf.s"
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// Copyright (c) 2000, 2001, Intel Corporation
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// All rights reserved.
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//
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// Contributed 2/2/2000 by John Harrison, Ted Kubaska, Bob Norin, Shane Story,
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// and Ping Tak Peter Tang of the Computational Software Lab, Intel Corporation.
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//
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// WARRANTY DISCLAIMER
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//
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
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// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
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// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
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// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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//
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// Intel Corporation is the author of this code, and requests that all
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// problem reports or change requests be submitted to it directly at
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// http://developer.intel.com/opensource.
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// History
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//==============================================================
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// 2/02/00 Initial version
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// 6/28/00 Improved speed
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// 6/31/00 Changed register allocation because of some duplicate macros
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// moved nan exit bundle up to gain a cycle.
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// 8/15/00 Bundle added after call to __libm_error_support to properly
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// set [the previously overwritten] GR_Parameter_RESULT.
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// 8/17/00 Changed predicate register macro-usage to direct predicate
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// names due to an assembler bug.
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// 10/17/00 Improved speed of x=0 and x=1 paths, set D flag if x denormal.
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// 3/13/01 Corrected sign of imm1 value in dep instruction.
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// Description
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//=========================================
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// The acosf function computes the principle value of the arc sine of x.
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// A doman error occurs for arguments not in the range [-1,+1].
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// The acosf function returns the arc cosine in the range [0, +pi] radians.
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// acos(1) returns +0
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// acos(x) returns a Nan and raises the invalid exception for |x| >1
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// |x| <= sqrt(2)/2. get Ax and Bx
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// poly_p1 = x p1
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// poly_p3 = x2 p4 + p3
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// poly_p1 = x2 (poly_p1) + x = x2(x p1) + x
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// poly_p2 = x2( poly_p3) + p2 = x2(x2 p4 + p3) + p2
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// poly_Ax = x5(x2( poly_p3) + p2) + x2(x p1) + x
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// = x5(x2(x2 p4 + p3) + p2) + x2(x p1) + x
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// poly_p7 = x2 p8 + p7
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// poly_p5 = x2 p6 + p5
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// poly_p7 = x4 p9 + (x2 p8 + p7)
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// poly_Bx = x4 (x4 p9 + (x2 p8 + p7)) + x2 p6 + p5
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// sinf1 = x11(x4 (x4 p9 + (x2 p8 + p7)) + x2 p6 + p5) + x5(x2(x2 p4 + p3) + p2) + x2(x p1) + x
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// = x19 p9 + x17 p8 + x15 p7 x13 p6 + x11 p5 + x9 p4 + x7 p3 + x5 p2 + x3 p1 + x
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// answer1 = pi/2 - sinf1
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// |x| > sqrt(2)/2
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// Get z = sqrt(1-x2)
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// Get polynomial in t = 1-x2
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// t2 = t t
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// t4 = t2 t2
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// poly_p4 = t p5 + p4
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// poly_p1 = t p1 + 1
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// poly_p6 = t p7 + p6
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// poly_p2 = t p3 + p2
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// poly_p8 = t p9 + p8
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// poly_p4 = t2 poly_p6 + poly_p4
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// = t2 (t p7 + p6) + (t p5 + p4)
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// poly_p2 = t2 poly_p2 + poly_p1
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// = t2 (t p3 + p2) + (t p1 + 1)
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// poly_p4 = t4 poly_p8 + poly_p4
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// = t4 (t p9 + p8) + (t2 (t p7 + p6) + (t p5 + p4))
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// P(t) = poly_p2 + t4 poly_p8
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// = t2 (t p3 + p2) + (t p1 + 1) + t4 (t4 (t p9 + p8) + (t2 (t p7 + p6) + (t p5 + p4)))
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// = t3 p3 + t2 p2 + t p1 + 1 + t9 p9 + t8 p8 + t7 p7 + t6 p6 + t5 p5 + t4 p4
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// answer2 = sign(x) z P(t) if x>0
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// = sign(x) z P(t) + pi if x<0
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//
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// Assembly macros
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//=========================================
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// predicate registers
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//acosf_pred_LEsqrt2by2 = p7
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//acosf_pred_GTsqrt2by2 = p8
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// integer registers
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ACOSF_Addr1 = r33
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ACOSF_Addr2 = r34
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ACOSF_GR_1by2 = r35
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ACOSF_GR_3by2 = r36
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ACOSF_GR_5by2 = r37
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GR_SAVE_B0 = r38
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GR_SAVE_PFS = r39
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GR_SAVE_GP = r40
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GR_Parameter_X = r41
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GR_Parameter_Y = r42
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GR_Parameter_RESULT = r43
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GR_Parameter_TAG = r44
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// floating point registers
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acosf_y = f32
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acosf_abs_x = f33
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acosf_x2 = f34
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acosf_sgn_x = f35
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acosf_1by2 = f36
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acosf_3by2 = f37
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acosf_5by2 = f38
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acosf_coeff_P3 = f39
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acosf_coeff_P8 = f40
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acosf_coeff_P1 = f41
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acosf_coeff_P4 = f42
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acosf_coeff_P5 = f43
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acosf_coeff_P2 = f44
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acosf_coeff_P7 = f45
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acosf_coeff_P6 = f46
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acosf_coeff_P9 = f47
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acosf_x2 = f48
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acosf_x3 = f49
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acosf_x4 = f50
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acosf_x8 = f51
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acosf_x5 = f52
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acosf_const_piby2 = f53
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acosf_const_sqrt2by2 = f54
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acosf_x11 = f55
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acosf_poly_p1 = f56
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acosf_poly_p3 = f57
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acosf_sinf1 = f58
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acosf_poly_p2 = f59
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acosf_poly_Ax = f60
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acosf_poly_p7 = f61
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acosf_poly_p5 = f62
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acosf_sgnx_t4 = f63
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acosf_poly_Bx = f64
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acosf_t = f65
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acosf_yby2 = f66
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acosf_B = f67
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acosf_B2 = f68
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acosf_Az = f69
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acosf_dz = f70
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acosf_Sz = f71
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acosf_d2z = f72
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acosf_Fz = f73
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acosf_z = f74
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acosf_sgnx_z = f75
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acosf_t2 = f76
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acosf_2poly_p4 = f77
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acosf_2poly_p6 = f78
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acosf_2poly_p1 = f79
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acosf_2poly_p2 = f80
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acosf_2poly_p8 = f81
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acosf_t4 = f82
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acosf_Pt = f83
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acosf_sgnx_2poly_p2 = f84
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acosf_sgn_x_piby2 = f85
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acosf_poly_p7a = f86
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acosf_2poly_p4a = f87
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acosf_2poly_p4b = f88
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acosf_2poly_p2a = f89
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acosf_poly_p1a = f90
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// Data tables
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//==============================================================
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.data
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.align 16
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acosf_coeff_1_table:
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data8 0x3FC5555607DCF816 // P1
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data8 0x3F9CF81AD9BAB2C6 // P4
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data8 0x3FC59E0975074DF3 // P7
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data8 0xBFA6F4CC2780AA1D // P6
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data8 0x3FC2DD45292E93CB // P9
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data8 0x3fe6a09e667f3bcd // sqrt(2)/2
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acosf_coeff_2_table:
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data8 0x3FA6F108E31EFBA6 // P3
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data8 0xBFCA31BF175D82A0 // P8
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data8 0x3FA30C0337F6418B // P5
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data8 0x3FB332C9266CB1F9 // P2
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data8 0x3ff921fb54442d18 // pi_by_2
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.align 32
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.global acosf
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.section .text
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.proc acosf
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.align 32
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acosf:
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// Load the addresses of the two tables.
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// Then, load the coefficients and other constants.
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{ .mfi
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alloc r32 = ar.pfs,1,8,4,0
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fnma.s1 acosf_t = f8,f8,f1
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dep.z ACOSF_GR_1by2 = 0x3f,24,8 // 0x3f000000
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}
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{ .mfi
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addl ACOSF_Addr1 = @ltoff(acosf_coeff_1_table),gp
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fma.s1 acosf_x2 = f8,f8,f0
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addl ACOSF_Addr2 = @ltoff(acosf_coeff_2_table),gp ;;
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}
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{ .mfi
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ld8 ACOSF_Addr1 = [ACOSF_Addr1]
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fmerge.s acosf_abs_x = f1,f8
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dep ACOSF_GR_3by2 = -1,r0,22,8 // 0x3fc00000
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}
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{ .mlx
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nop.m 999
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movl ACOSF_GR_5by2 = 0x40200000;;
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}
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{ .mfi
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setf.s acosf_1by2 = ACOSF_GR_1by2
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fmerge.s acosf_sgn_x = f8,f1
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nop.i 999
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}
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{ .mfi
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ld8 ACOSF_Addr2 = [ACOSF_Addr2]
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nop.f 0
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nop.i 999;;
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}
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{ .mfi
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setf.s acosf_5by2 = ACOSF_GR_5by2
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fcmp.lt.s1 p11,p12 = f8,f0
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nop.i 999;;
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}
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{ .mmf
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ldfpd acosf_coeff_P1,acosf_coeff_P4 = [ACOSF_Addr1],16
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setf.s acosf_3by2 = ACOSF_GR_3by2
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fclass.m.unc p8,p0 = f8, 0xc3 ;; //@qnan | @snan
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}
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{ .mfi
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ldfpd acosf_coeff_P7,acosf_coeff_P6 = [ACOSF_Addr1],16
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fma.s1 acosf_t2 = acosf_t,acosf_t,f0
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nop.i 999
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}
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{ .mfi
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ldfpd acosf_coeff_P3,acosf_coeff_P8 = [ACOSF_Addr2],16
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fma.s1 acosf_x4 = acosf_x2,acosf_x2,f0
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nop.i 999;;
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}
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{ .mfi
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ldfpd acosf_coeff_P9,acosf_const_sqrt2by2 = [ACOSF_Addr1]
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fclass.m.unc p10,p0 = f8, 0x07 //@zero
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nop.i 999
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}
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{ .mfi
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ldfpd acosf_coeff_P5,acosf_coeff_P2 = [ACOSF_Addr2],16
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fma.s1 acosf_x3 = f8,acosf_x2,f0
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nop.i 999;;
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}
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{ .mfi
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ldfd acosf_const_piby2 = [ACOSF_Addr2]
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frsqrta.s1 acosf_B,p0 = acosf_t
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nop.i 999
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}
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{ .mfb
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nop.m 999
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(p8) fma.s f8 = f8,f1,f0
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(p8) br.ret.spnt b0 ;; // Exit if x=nan
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}
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{ .mfb
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nop.m 999
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fcmp.eq.s1 p6,p0 = acosf_abs_x,f1
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(p10) br.cond.spnt ACOSF_ZERO ;; // Branch if x=0
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}
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{ .mfi
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nop.m 999
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fcmp.gt.s1 p9,p0 = acosf_abs_x,f1
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nop.i 999;;
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}
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{ .mfi
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nop.m 999
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fma.s1 acosf_x8 = acosf_x4,acosf_x4,f0
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nop.i 999
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}
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{ .mfb
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nop.m 999
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fma.s1 acosf_t4 = acosf_t2,acosf_t2,f0
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(p6) br.cond.spnt ACOSF_ABS_ONE ;; // Branch if |x|=1
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}
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{ .mfi
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nop.m 999
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fma.s1 acosf_x5 = acosf_x2,acosf_x3,f0
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nop.i 999
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}
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{ .mfb
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(p9) mov GR_Parameter_TAG = 59
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fma.s1 acosf_yby2 = acosf_t,acosf_1by2,f0
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(p9) br.cond.spnt __libm_error_region ;; // Branch if |x|>1
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}
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{ .mfi
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nop.m 999
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fma.s1 acosf_Az = acosf_t,acosf_B,f0
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nop.i 999
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}
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{ .mfi
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nop.m 999
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fma.s1 acosf_B2 = acosf_B,acosf_B,f0
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nop.i 999;;
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}
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{ .mfi
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nop.m 999
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fma.s1 acosf_poly_p1 = f8,acosf_coeff_P1,f0
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nop.i 999
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}
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{ .mfi
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nop.m 999
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fma.s1 acosf_2poly_p1 = acosf_coeff_P1,acosf_t,f1
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nop.i 999;;
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}
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{ .mfi
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nop.m 999
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fma.s1 acosf_poly_p3 = acosf_coeff_P4,acosf_x2,acosf_coeff_P3
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nop.i 999
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}
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{ .mfi
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nop.m 999
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fma.s1 acosf_2poly_p6 = acosf_coeff_P7,acosf_t,acosf_coeff_P6
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nop.i 999;;
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}
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{ .mfi
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nop.m 999
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fma.s1 acosf_poly_p7 = acosf_x2,acosf_coeff_P8,acosf_coeff_P7
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nop.i 999
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}
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{ .mfi
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nop.m 999
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fma.s1 acosf_2poly_p2 = acosf_coeff_P3,acosf_t,acosf_coeff_P2
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nop.i 999;;
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}
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{ .mfi
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nop.m 999
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fma.s1 acosf_poly_p5 = acosf_x2,acosf_coeff_P6,acosf_coeff_P5
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nop.i 999
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}
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{ .mfi
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nop.m 999
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fma.s1 acosf_2poly_p4 = acosf_coeff_P5,acosf_t,acosf_coeff_P4
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nop.i 999;;
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}
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{ .mfi
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nop.m 999
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fma.s1 acosf_x11 = acosf_x8,acosf_x3,f0
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nop.i 999
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}
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{ .mfi
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nop.m 999
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fnma.s1 acosf_dz = acosf_B2,acosf_yby2,acosf_1by2
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nop.i 999;;
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}
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{ .mfi
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nop.m 999
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fma.s1 acosf_poly_p1a = acosf_x2,acosf_poly_p1,f8
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nop.i 999
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}
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{ .mfi
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nop.m 999
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fma.s1 acosf_2poly_p8 = acosf_coeff_P9,acosf_t,acosf_coeff_P8
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nop.i 999;;
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}
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// Get the absolute value of x and determine the region in which x lies
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{ .mfi
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nop.m 999
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fcmp.le.s1 p7,p8 = acosf_abs_x,acosf_const_sqrt2by2
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nop.i 999
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}
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{ .mfi
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nop.m 999
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fma.s1 acosf_poly_p2 = acosf_x2,acosf_poly_p3,acosf_coeff_P2
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nop.i 999;;
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}
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{ .mfi
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nop.m 999
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fma.s1 acosf_poly_p7a = acosf_x4,acosf_coeff_P9,acosf_poly_p7
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nop.i 999
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}
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{ .mfi
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nop.m 999
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fma.s1 acosf_2poly_p2a = acosf_2poly_p2,acosf_t2,acosf_2poly_p1
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nop.i 999;;
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}
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{ .mfi
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nop.m 999
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(p8) fma.s1 acosf_sgnx_t4 = acosf_sgn_x,acosf_t4,f0
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nop.i 999
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}
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{ .mfi
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nop.m 999
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(p8) fma.s1 acosf_2poly_p4a = acosf_2poly_p6,acosf_t2,acosf_2poly_p4
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nop.i 999;;
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}
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{ .mfi
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nop.m 999
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(p8) fma.s1 acosf_Sz = acosf_5by2,acosf_dz,acosf_3by2
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p8) fma.s1 acosf_d2z = acosf_dz,acosf_dz,f0
|
|
nop.i 999;;
|
|
}
|
|
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p8) fnma.d.s1 acosf_sgn_x_piby2 = acosf_sgn_x,acosf_const_piby2,acosf_const_piby2
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p7) fma.s1 acosf_poly_Ax = acosf_x5,acosf_poly_p2,acosf_poly_p1a
|
|
nop.i 999;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p7) fma.s1 acosf_poly_Bx = acosf_x4,acosf_poly_p7a,acosf_poly_p5
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p8) fma.s1 acosf_sgnx_2poly_p2 = acosf_sgn_x,acosf_2poly_p2a,f0
|
|
nop.i 999;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
fcmp.eq.s0 p6,p0 = f8,f0 // Only purpose is to set D if x denormal
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p8) fma.s1 acosf_2poly_p4b = acosf_2poly_p8,acosf_t4,acosf_2poly_p4a
|
|
nop.i 999;;
|
|
}
|
|
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p8) fma.s1 acosf_Fz = acosf_d2z,acosf_Sz,acosf_dz
|
|
nop.i 999;;
|
|
}
|
|
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p8) fma.d.s1 acosf_Pt = acosf_2poly_p4b,acosf_sgnx_t4,acosf_sgnx_2poly_p2
|
|
nop.i 999;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p8) fma.d.s1 acosf_z = acosf_Az,acosf_Fz,acosf_Az
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p7) fma.d.s1 acosf_sinf1 = acosf_x11,acosf_poly_Bx,acosf_poly_Ax
|
|
nop.i 999;;
|
|
}
|
|
|
|
.pred.rel "mutex",p8,p7 //acosf_pred_GTsqrt2by2,acosf_pred_LEsqrt2by2
|
|
{ .mfi
|
|
nop.m 999
|
|
(p8) fma.s f8 = acosf_z,acosf_Pt,acosf_sgn_x_piby2
|
|
nop.i 999
|
|
}
|
|
|
|
{ .mfb
|
|
nop.m 999
|
|
(p7) fms.s f8 = acosf_const_piby2,f1,acosf_sinf1
|
|
br.ret.sptk b0 ;;
|
|
}
|
|
|
|
ACOSF_ZERO:
|
|
// Here if x=0
|
|
{ .mfb
|
|
nop.m 999
|
|
fma.s f8 = acosf_const_piby2,f1,f0 // acosf(0)=pi/2
|
|
br.ret.sptk b0 ;;
|
|
}
|
|
|
|
|
|
.pred.rel "mutex",p11,p12
|
|
ACOSF_ABS_ONE:
|
|
// Here if |x|=1
|
|
{ .mfi
|
|
nop.m 999
|
|
(p11) fma.s f8 = acosf_const_piby2,f1,acosf_const_piby2 // acosf(-1)=pi
|
|
nop.i 999
|
|
}
|
|
{ .mfb
|
|
nop.m 999
|
|
(p12) fma.s f8 = f1,f0,f0 // acosf(1)=0
|
|
br.ret.sptk b0 ;;
|
|
}
|
|
|
|
.endp acosf
|
|
|
|
|
|
// Stack operations when calling error support.
|
|
// (1) (2)
|
|
// sp -> + psp -> +
|
|
// | |
|
|
// | | <- GR_Y
|
|
// | |
|
|
// | <-GR_Y Y2->|
|
|
// | |
|
|
// | | <- GR_X
|
|
// | |
|
|
// sp-64 -> + sp -> +
|
|
// save ar.pfs save b0
|
|
// save gp
|
|
|
|
|
|
// Stack operations when calling error support.
|
|
// (3) (call) (4)
|
|
// psp -> + sp -> +
|
|
// | |
|
|
// R3 ->| <- GR_RESULT | -> f8
|
|
// | |
|
|
// Y2 ->| <- GR_Y |
|
|
// | |
|
|
// X1 ->| |
|
|
// | |
|
|
// sp -> + +
|
|
// restore gp
|
|
// restore ar.pfs
|
|
|
|
|
|
.proc __libm_error_region
|
|
__libm_error_region:
|
|
.prologue
|
|
{ .mfi
|
|
add GR_Parameter_Y=-32,sp // Parameter 2 value
|
|
nop.f 999
|
|
.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] = f1,16 // 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
|
|
{ .mfi
|
|
nop.m 0
|
|
frcpa.s0 f9,p0 = f0,f0
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mib
|
|
stfs [GR_Parameter_X] = f8 // Store Parameter 1 on stack
|
|
add GR_Parameter_RESULT = 0,GR_Parameter_Y
|
|
nop.b 0 // Parameter 3 address
|
|
}
|
|
{ .mib
|
|
stfs [GR_Parameter_Y] = f9 // 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#
|