.file "acosf.s"
// Copyright (c) 2000 - 2003, 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
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// 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
// 06/28/00 Improved speed
// 06/31/00 Changed register allocation because of some duplicate macros
// moved nan exit bundle up to gain a cycle.
// 08/15/00 Bundle added after call to __libm_error_support to properly
// set [the previously overwritten] GR_Parameter_RESULT.
// 08/17/00 Changed predicate register macro-usage to direct predicate
// names due to an assembler bug.
// 10/17/00 Improved speed of x=0 and x=1 paths, set D flag if x denormal.
// 03/13/01 Corrected sign of imm1 value in dep instruction.
// 05/20/02 Cleaned up namespace and sf0 syntax
// 02/06/03 Reordered header: .section, .global, .proc, .align
// 04/17/03 Moved mutex after label
// Description
//=========================================
// The acosf function computes the principle value of the arc sine of x.
// A doman error occurs for arguments not in the range [-1,+1].
// The acosf function returns the arc cosine in the range [0, +pi] radians.
// acos(1) returns +0
// acos(x) returns a Nan and raises the invalid exception for |x| >1
// |x| <= sqrt(2)/2. get Ax and Bx
// poly_p1 = x p1
// poly_p3 = x2 p4 + p3
// poly_p1 = x2 (poly_p1) + x = x2(x p1) + x
// poly_p2 = x2( poly_p3) + p2 = x2(x2 p4 + p3) + p2
// poly_Ax = x5(x2( poly_p3) + p2) + x2(x p1) + x
// = x5(x2(x2 p4 + p3) + p2) + x2(x p1) + x
// poly_p7 = x2 p8 + p7
// poly_p5 = x2 p6 + p5
// poly_p7 = x4 p9 + (x2 p8 + p7)
// poly_Bx = x4 (x4 p9 + (x2 p8 + p7)) + x2 p6 + p5
// sinf1 = x11(x4 (x4 p9 + (x2 p8 + p7)) + x2 p6 + p5) + x5(x2(x2 p4 + p3) + p2) + x2(x p1) + x
// = x19 p9 + x17 p8 + x15 p7 x13 p6 + x11 p5 + x9 p4 + x7 p3 + x5 p2 + x3 p1 + x
// answer1 = pi/2 - sinf1
// |x| > sqrt(2)/2
// Get z = sqrt(1-x2)
// Get polynomial in t = 1-x2
// t2 = t t
// t4 = t2 t2
// poly_p4 = t p5 + p4
// poly_p1 = t p1 + 1
// poly_p6 = t p7 + p6
// poly_p2 = t p3 + p2
// poly_p8 = t p9 + p8
// poly_p4 = t2 poly_p6 + poly_p4
// = t2 (t p7 + p6) + (t p5 + p4)
// poly_p2 = t2 poly_p2 + poly_p1
// = t2 (t p3 + p2) + (t p1 + 1)
// poly_p4 = t4 poly_p8 + poly_p4
// = t4 (t p9 + p8) + (t2 (t p7 + p6) + (t p5 + p4))
// P(t) = poly_p2 + t4 poly_p8
// = t2 (t p3 + p2) + (t p1 + 1) + t4 (t4 (t p9 + p8) + (t2 (t p7 + p6) + (t p5 + p4)))
// = t3 p3 + t2 p2 + t p1 + 1 + t9 p9 + t8 p8 + t7 p7 + t6 p6 + t5 p5 + t4 p4
// answer2 = sign(x) z P(t) if x>0
// = sign(x) z P(t) + pi if x<0
//
// Assembly macros
//=========================================
// predicate registers
//acosf_pred_LEsqrt2by2 = p7
//acosf_pred_GTsqrt2by2 = p8
// integer registers
ACOSF_Addr1 = r33
ACOSF_Addr2 = r34
ACOSF_GR_1by2 = r35
ACOSF_GR_3by2 = r36
ACOSF_GR_5by2 = r37
GR_SAVE_B0 = r38
GR_SAVE_PFS = r39
GR_SAVE_GP = r40
GR_Parameter_X = r41
GR_Parameter_Y = r42
GR_Parameter_RESULT = r43
GR_Parameter_TAG = r44
// floating point registers
acosf_y = f32
acosf_abs_x = f33
acosf_x2 = f34
acosf_sgn_x = f35
acosf_1by2 = f36
acosf_3by2 = f37
acosf_5by2 = f38
acosf_coeff_P3 = f39
acosf_coeff_P8 = f40
acosf_coeff_P1 = f41
acosf_coeff_P4 = f42
acosf_coeff_P5 = f43
acosf_coeff_P2 = f44
acosf_coeff_P7 = f45
acosf_coeff_P6 = f46
acosf_coeff_P9 = f47
acosf_x2 = f48
acosf_x3 = f49
acosf_x4 = f50
acosf_x8 = f51
acosf_x5 = f52
acosf_const_piby2 = f53
acosf_const_sqrt2by2 = f54
acosf_x11 = f55
acosf_poly_p1 = f56
acosf_poly_p3 = f57
acosf_sinf1 = f58
acosf_poly_p2 = f59
acosf_poly_Ax = f60
acosf_poly_p7 = f61
acosf_poly_p5 = f62
acosf_sgnx_t4 = f63
acosf_poly_Bx = f64
acosf_t = f65
acosf_yby2 = f66
acosf_B = f67
acosf_B2 = f68
acosf_Az = f69
acosf_dz = f70
acosf_Sz = f71
acosf_d2z = f72
acosf_Fz = f73
acosf_z = f74
acosf_sgnx_z = f75
acosf_t2 = f76
acosf_2poly_p4 = f77
acosf_2poly_p6 = f78
acosf_2poly_p1 = f79
acosf_2poly_p2 = f80
acosf_2poly_p8 = f81
acosf_t4 = f82
acosf_Pt = f83
acosf_sgnx_2poly_p2 = f84
acosf_sgn_x_piby2 = f85
acosf_poly_p7a = f86
acosf_2poly_p4a = f87
acosf_2poly_p4b = f88
acosf_2poly_p2a = f89
acosf_poly_p1a = f90
// Data tables
//==============================================================
RODATA
.align 16
LOCAL_OBJECT_START(acosf_coeff_1_table)
data8 0x3FC5555607DCF816 // P1
data8 0x3F9CF81AD9BAB2C6 // P4
data8 0x3FC59E0975074DF3 // P7
data8 0xBFA6F4CC2780AA1D // P6
data8 0x3FC2DD45292E93CB // P9
data8 0x3fe6a09e667f3bcd // sqrt(2)/2
LOCAL_OBJECT_END(acosf_coeff_1_table)
LOCAL_OBJECT_START(acosf_coeff_2_table)
data8 0x3FA6F108E31EFBA6 // P3
data8 0xBFCA31BF175D82A0 // P8
data8 0x3FA30C0337F6418B // P5
data8 0x3FB332C9266CB1F9 // P2
data8 0x3ff921fb54442d18 // pi_by_2
LOCAL_OBJECT_END(acosf_coeff_2_table)
.section .text
GLOBAL_LIBM_ENTRY(acosf)
// Load the addresses of the two tables.
// Then, load the coefficients and other constants.
{ .mfi
alloc r32 = ar.pfs,1,8,4,0
fnma.s1 acosf_t = f8,f8,f1
dep.z ACOSF_GR_1by2 = 0x3f,24,8 // 0x3f000000
}
{ .mfi
addl ACOSF_Addr1 = @ltoff(acosf_coeff_1_table),gp
fma.s1 acosf_x2 = f8,f8,f0
addl ACOSF_Addr2 = @ltoff(acosf_coeff_2_table),gp ;;
}
{ .mfi
ld8 ACOSF_Addr1 = [ACOSF_Addr1]
fmerge.s acosf_abs_x = f1,f8
dep ACOSF_GR_3by2 = -1,r0,22,8 // 0x3fc00000
}
{ .mlx
nop.m 999
movl ACOSF_GR_5by2 = 0x40200000;;
}
{ .mfi
setf.s acosf_1by2 = ACOSF_GR_1by2
fmerge.s acosf_sgn_x = f8,f1
nop.i 999
}
{ .mfi
ld8 ACOSF_Addr2 = [ACOSF_Addr2]
nop.f 0
nop.i 999;;
}
{ .mfi
setf.s acosf_5by2 = ACOSF_GR_5by2
fcmp.lt.s1 p11,p12 = f8,f0
nop.i 999;;
}
{ .mmf
ldfpd acosf_coeff_P1,acosf_coeff_P4 = [ACOSF_Addr1],16
setf.s acosf_3by2 = ACOSF_GR_3by2
fclass.m.unc p8,p0 = f8, 0xc3 ;; //@qnan | @snan
}
{ .mfi
ldfpd acosf_coeff_P7,acosf_coeff_P6 = [ACOSF_Addr1],16
fma.s1 acosf_t2 = acosf_t,acosf_t,f0
nop.i 999
}
{ .mfi
ldfpd acosf_coeff_P3,acosf_coeff_P8 = [ACOSF_Addr2],16
fma.s1 acosf_x4 = acosf_x2,acosf_x2,f0
nop.i 999;;
}
{ .mfi
ldfpd acosf_coeff_P9,acosf_const_sqrt2by2 = [ACOSF_Addr1]
fclass.m.unc p10,p0 = f8, 0x07 //@zero
nop.i 999
}
{ .mfi
ldfpd acosf_coeff_P5,acosf_coeff_P2 = [ACOSF_Addr2],16
fma.s1 acosf_x3 = f8,acosf_x2,f0
nop.i 999;;
}
{ .mfi
ldfd acosf_const_piby2 = [ACOSF_Addr2]
frsqrta.s1 acosf_B,p0 = acosf_t
nop.i 999
}
{ .mfb
nop.m 999
(p8) fma.s.s0 f8 = f8,f1,f0
(p8) br.ret.spnt b0 ;; // Exit if x=nan
}
{ .mfb
nop.m 999
fcmp.eq.s1 p6,p0 = acosf_abs_x,f1
(p10) br.cond.spnt ACOSF_ZERO ;; // Branch if x=0
}
{ .mfi
nop.m 999
fcmp.gt.s1 p9,p0 = acosf_abs_x,f1
nop.i 999;;
}
{ .mfi
nop.m 999
fma.s1 acosf_x8 = acosf_x4,acosf_x4,f0
nop.i 999
}
{ .mfb
nop.m 999
fma.s1 acosf_t4 = acosf_t2,acosf_t2,f0
(p6) br.cond.spnt ACOSF_ABS_ONE ;; // Branch if |x|=1
}
{ .mfi
nop.m 999
fma.s1 acosf_x5 = acosf_x2,acosf_x3,f0
nop.i 999
}
{ .mfb
(p9) mov GR_Parameter_TAG = 59
fma.s1 acosf_yby2 = acosf_t,acosf_1by2,f0
(p9) br.cond.spnt __libm_error_region ;; // Branch if |x|>1
}
{ .mfi
nop.m 999
fma.s1 acosf_Az = acosf_t,acosf_B,f0
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 acosf_B2 = acosf_B,acosf_B,f0
nop.i 999;;
}
{ .mfi
nop.m 999
fma.s1 acosf_poly_p1 = f8,acosf_coeff_P1,f0
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 acosf_2poly_p1 = acosf_coeff_P1,acosf_t,f1
nop.i 999;;
}
{ .mfi
nop.m 999
fma.s1 acosf_poly_p3 = acosf_coeff_P4,acosf_x2,acosf_coeff_P3
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 acosf_2poly_p6 = acosf_coeff_P7,acosf_t,acosf_coeff_P6
nop.i 999;;
}
{ .mfi
nop.m 999
fma.s1 acosf_poly_p7 = acosf_x2,acosf_coeff_P8,acosf_coeff_P7
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 acosf_2poly_p2 = acosf_coeff_P3,acosf_t,acosf_coeff_P2
nop.i 999;;
}
{ .mfi
nop.m 999
fma.s1 acosf_poly_p5 = acosf_x2,acosf_coeff_P6,acosf_coeff_P5
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 acosf_2poly_p4 = acosf_coeff_P5,acosf_t,acosf_coeff_P4
nop.i 999;;
}
{ .mfi
nop.m 999
fma.s1 acosf_x11 = acosf_x8,acosf_x3,f0
nop.i 999
}
{ .mfi
nop.m 999
fnma.s1 acosf_dz = acosf_B2,acosf_yby2,acosf_1by2
nop.i 999;;
}
{ .mfi
nop.m 999
fma.s1 acosf_poly_p1a = acosf_x2,acosf_poly_p1,f8
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 acosf_2poly_p8 = acosf_coeff_P9,acosf_t,acosf_coeff_P8
nop.i 999;;
}
// Get the absolute value of x and determine the region in which x lies
{ .mfi
nop.m 999
fcmp.le.s1 p7,p8 = acosf_abs_x,acosf_const_sqrt2by2
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 acosf_poly_p2 = acosf_x2,acosf_poly_p3,acosf_coeff_P2
nop.i 999;;
}
{ .mfi
nop.m 999
fma.s1 acosf_poly_p7a = acosf_x4,acosf_coeff_P9,acosf_poly_p7
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 acosf_2poly_p2a = acosf_2poly_p2,acosf_t2,acosf_2poly_p1
nop.i 999;;
}
{ .mfi
nop.m 999
(p8) fma.s1 acosf_sgnx_t4 = acosf_sgn_x,acosf_t4,f0
nop.i 999
}
{ .mfi
nop.m 999
(p8) fma.s1 acosf_2poly_p4a = acosf_2poly_p6,acosf_t2,acosf_2poly_p4
nop.i 999;;
}
{ .mfi
nop.m 999
(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.s0 f8 = acosf_z,acosf_Pt,acosf_sgn_x_piby2
nop.i 999
}
{ .mfb
nop.m 999
(p7) fms.s.s0 f8 = acosf_const_piby2,f1,acosf_sinf1
br.ret.sptk b0 ;;
}
ACOSF_ZERO:
// Here if x=0
{ .mfb
nop.m 999
fma.s.s0 f8 = acosf_const_piby2,f1,f0 // acosf(0)=pi/2
br.ret.sptk b0 ;;
}
ACOSF_ABS_ONE:
.pred.rel "mutex",p11,p12
// Here if |x|=1
{ .mfi
nop.m 999
(p11) fma.s.s0 f8 = acosf_const_piby2,f1,acosf_const_piby2 // acosf(-1)=pi
nop.i 999
}
{ .mfb
nop.m 999
(p12) fma.s.s0 f8 = f1,f0,f0 // acosf(1)=0
br.ret.sptk b0 ;;
}
GLOBAL_LIBM_END(acosf)
libm_alias_float_other (acos, acos)
// 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
LOCAL_LIBM_ENTRY(__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 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
};;
LOCAL_LIBM_END(__libm_error_region)
.type __libm_error_support#,@function
.global __libm_error_support#