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-rw-r--r--sysdeps/ia64/fpu/e_acos.S1499
1 files changed, 729 insertions, 770 deletions
diff --git a/sysdeps/ia64/fpu/e_acos.S b/sysdeps/ia64/fpu/e_acos.S
index 7e83811727..c2b31ab85e 100644
--- a/sysdeps/ia64/fpu/e_acos.S
+++ b/sysdeps/ia64/fpu/e_acos.S
@@ -1,10 +1,10 @@
.file "acos.s"
-// Copyright (C) 2000, 2001, Intel Corporation
+
+// Copyright (c) 2000 - 2003 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.
+// 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
@@ -20,9 +20,7 @@
// * The name of Intel Corporation may not be used to endorse or promote
// products derived from this software without specific prior written
// permission.
-//
-// WARRANTY DISCLAIMER
-//
+
// 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
@@ -37,838 +35,801 @@
//
// 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.
+// http://www.intel.com/software/products/opensource/libraries/num.htm.
// History
//==============================================================
-// 2/02/00 Initial version
-// 8/17/00 New and much faster algorithm.
-// 8/30/00 Avoided bank conflicts on loads, shortened |x|=1 and x=0 paths,
+// 02/02/00 Initial version
+// 08/17/00 New and much faster algorithm.
+// 08/30/00 Avoided bank conflicts on loads, shortened |x|=1 and x=0 paths,
// fixed mfb split issue stalls.
+// 05/20/02 Cleaned up namespace and sf0 syntax
+// 08/02/02 New and much faster algorithm II
+// 02/06/03 Reordered header: .section, .global, .proc, .align
// Description
//=========================================
-// The acos function computes the principle value of the arc sine of x.
+// The acos function computes the principal value of the arc cosine of x.
+// acos(0) returns Pi/2, acos(1) returns 0, acos(-1) returns Pi.
// A doman error occurs for arguments not in the range [-1,+1].
+//
+// The acos function returns the arc cosine in the range [0, Pi] radians.
+//
+// There are 8 paths:
+// 1. x = +/-0.0
+// Return acos(x) = Pi/2 + x
+//
+// 2. 0.0 < |x| < 0.625
+// Return acos(x) = Pi/2 - x - x^3 *PolA(x^2)
+// where PolA(x^2) = A3 + A5*x^2 + A7*x^4 +...+ A35*x^32
+//
+// 3. 0.625 <=|x| < 1.0
+// Return acos(x) = Pi/2 - asin(x) =
+// = Pi/2 - sign(x) * ( Pi/2 - sqrt(R) * PolB(R))
+// Where R = 1 - |x|,
+// PolB(R) = B0 + B1*R + B2*R^2 +...+B12*R^12
+//
+// sqrt(R) is approximated using the following sequence:
+// y0 = (1 + eps)/sqrt(R) - initial approximation by frsqrta,
+// |eps| < 2^(-8)
+// Then 3 iterations are used to refine the result:
+// H0 = 0.5*y0
+// S0 = R*y0
+//
+// d0 = 0.5 - H0*S0
+// H1 = H0 + d0*H0
+// S1 = S0 + d0*S0
+//
+// d1 = 0.5 - H1*S1
+// H2 = H1 + d0*H1
+// S2 = S1 + d0*S1
+//
+// d2 = 0.5 - H2*S2
+// S3 = S3 + d2*S3
+//
+// S3 approximates sqrt(R) with enough accuracy for this algorithm
+//
+// So, the result should be reconstracted as follows:
+// acos(x) = Pi/2 - sign(x) * (Pi/2 - S3*PolB(R))
+//
+// But for optimization purposes the reconstruction step is slightly
+// changed:
+// acos(x) = Cpi + sign(x)*PolB(R)*S2 - sign(x)*d2*S2*PolB(R)
+// where Cpi = 0 if x > 0 and Cpi = Pi if x < 0
+//
+// 4. |x| = 1.0
+// Return acos(1.0) = 0.0, acos(-1.0) = Pi
+//
+// 5. 1.0 < |x| <= +INF
+// A doman error occurs for arguments not in the range [-1,+1]
+//
+// 6. x = [S,Q]NaN
+// Return acos(x) = QNaN
+//
+// 7. x is denormal
+// Return acos(x) = Pi/2 - x,
+//
+// 8. x is unnormal
+// Normalize input in f8 and return to the very beginning of the function
+//
+// Registers used
+//==============================================================
+// Floating Point registers used:
+// f8, input, output
+// f6, f7, f9 -> f15, f32 -> f64
-// The acos function returns the arc cosine in the range [0, +pi] radians.
-// acos(1) returns +0, acos(-1) returns pi, acos(0) returns pi/2.
-// acos(x) returns a Nan and raises the invalid exception for |x| >1
+// General registers used:
+// r3, r21 -> r31, r32 -> r38
-// The acos function is just like asin except that pi/2 is added at the end.
+// Predicate registers used:
+// p0, p6 -> p14
//
// Assembly macros
//=========================================
-
-#include "libm_support.h"
-
-// predicate registers
-//acos_pred_LEsqrt2by2 = p7
-//acos_pred_GTsqrt2by2 = p8
-
-// integer registers
-ASIN_Addr1 = r33
-ASIN_Addr2 = r34
-ASIN_FFFE = r35
-
-GR_SAVE_B0 = r36
-GR_SAVE_PFS = r37
-GR_SAVE_GP = r38
-
-GR_Parameter_X = r39
-GR_Parameter_Y = r40
-GR_Parameter_RESULT = r41
-GR_Parameter_Tag = r42
-
-// floating point registers
-acos_coeff_P1 = f32
-acos_coeff_P2 = f33
-acos_coeff_P3 = f34
-acos_coeff_P4 = f35
-
-acos_coeff_P5 = f36
-acos_coeff_P6 = f37
-acos_coeff_P7 = f38
-acos_coeff_P8 = f39
-acos_coeff_P9 = f40
-
-acos_coeff_P10 = f41
-acos_coeff_P11 = f42
-acos_coeff_P12 = f43
-acos_coeff_P13 = f44
-acos_coeff_P14 = f45
-
-acos_coeff_P15 = f46
-acos_coeff_P16 = f47
-acos_coeff_P17 = f48
-acos_coeff_P18 = f49
-acos_coeff_P19 = f50
-
-acos_coeff_P20 = f51
-acos_coeff_P21 = f52
-acos_const_sqrt2by2 = f53
-acos_const_piby2 = f54
-acos_abs_x = f55
-
-acos_tx = f56
-acos_tx2 = f57
-acos_tx3 = f58
-acos_tx4 = f59
-acos_tx8 = f60
-
-acos_tx11 = f61
-acos_1poly_p8 = f62
-acos_1poly_p19 = f63
-acos_1poly_p4 = f64
-acos_1poly_p15 = f65
-
-acos_1poly_p6 = f66
-acos_1poly_p17 = f67
-acos_1poly_p0 = f68
-acos_1poly_p11 = f69
-acos_1poly_p2 = f70
-
-acos_1poly_p13 = f71
-acos_series_tx = f72
-acos_t = f73
-acos_t2 = f74
-acos_t3 = f75
-
-acos_t4 = f76
-acos_t8 = f77
-acos_t11 = f78
-acos_poly_p8 = f79
-acos_poly_p19 = f80
-
-acos_poly_p4 = f81
-acos_poly_p15 = f82
-acos_poly_p6 = f83
-acos_poly_p17 = f84
-acos_poly_p0 = f85
-
-acos_poly_p11 = f86
-acos_poly_p2 = f87
-acos_poly_p13 = f88
-acos_series_t = f89
-acos_1by2 = f90
-
-acos_3by2 = f91
-acos_5by2 = f92
-acos_11by4 = f93
-acos_35by8 = f94
-acos_63by8 = f95
-
-acos_231by16 = f96
-acos_y0 = f97
-acos_H0 = f98
-acos_S0 = f99
-acos_d = f100
-
-acos_l1 = f101
-acos_d2 = f102
-acos_T0 = f103
-acos_d1 = f104
-acos_e0 = f105
-
-acos_l2 = f106
-acos_d3 = f107
-acos_T3 = f108
-acos_S1 = f109
-acos_e1 = f110
-
-acos_z = f111
-answer2 = f112
-acos_sgn_x = f113
-acos_429by16 = f114
-acos_18by4 = f115
-
-acos_3by4 = f116
-acos_l3 = f117
-acos_T6 = f118
-acos_const_add = f119
+// integer registers used
+// scratch
+rTblAddr = r3
+
+rPiBy2Ptr = r21
+rTmpPtr3 = r22
+rDenoBound = r23
+rOne = r24
+rAbsXBits = r25
+rHalf = r26
+r0625 = r27
+rSign = r28
+rXBits = r29
+rTmpPtr2 = r30
+rTmpPtr1 = r31
+
+// stacked
+GR_SAVE_PFS = r32
+GR_SAVE_B0 = r33
+GR_SAVE_GP = r34
+GR_Parameter_X = r35
+GR_Parameter_Y = r36
+GR_Parameter_RESULT = r37
+GR_Parameter_TAG = r38
+
+// floating point registers used
+FR_X = f10
+FR_Y = f1
+FR_RESULT = f8
+
+
+// scratch
+fXSqr = f6
+fXCube = f7
+fXQuadr = f9
+f1pX = f10
+f1mX = f11
+f1pXRcp = f12
+f1mXRcp = f13
+fH = f14
+fS = f15
+// stacked
+fA3 = f32
+fB1 = f32
+fA5 = f33
+fB2 = f33
+fA7 = f34
+fPiBy2 = f34
+fA9 = f35
+fA11 = f36
+fB10 = f35
+fB11 = f36
+fA13 = f37
+fA15 = f38
+fB4 = f37
+fB5 = f38
+fA17 = f39
+fA19 = f40
+fB6 = f39
+fB7 = f40
+fA21 = f41
+fA23 = f42
+fB3 = f41
+fB8 = f42
+fA25 = f43
+fA27 = f44
+fB9 = f43
+fB12 = f44
+fA29 = f45
+fA31 = f46
+fA33 = f47
+fA35 = f48
+fBaseP = f49
+fB0 = f50
+fSignedS = f51
+fD = f52
+fHalf = f53
+fR = f54
+fCloseTo1Pol = f55
+fSignX = f56
+fDenoBound = f57
+fNormX = f58
+fX8 = f59
+fRSqr = f60
+fRQuadr = f61
+fR8 = f62
+fX16 = f63
+fCpi = f64
// Data tables
//==============================================================
-
-#ifdef _LIBC
-.rodata
-#else
-.data
-#endif
-
+RODATA
.align 16
-
-acos_coeff_1_table:
-ASM_TYPE_DIRECTIVE(acos_coeff_1_table,@object)
-data8 0xE4E7E0A423A21249 , 0x00003FF8 //P7
-data8 0xC2F7EE0200FCE2A5 , 0x0000C003 //P18
-data8 0xB745D7F6C65C20E0 , 0x00003FF9 //P5
-data8 0xF75E381A323D4D94 , 0x0000C002 //P16
-data8 0x8959C2629C1024C0 , 0x0000C002 //P20
-data8 0xAFF68E7D241292C5 , 0x00003FF8 //P9
-data8 0xB6DB6DB7260AC30D , 0x00003FFA //P3
-data8 0xD0417CE2B41CB7BF , 0x0000C000 //P14
-data8 0x81D570FEA724E3E4 , 0x0000BFFD //P12
-data8 0xAAAAAAAAAAAAC277 , 0x00003FFC //P1
-data8 0xF534912FF3E7B76F , 0x00003FFF //P21
-data8 0xc90fdaa22168c235 , 0x00003fff // pi/2
-data8 0x0000000000000000 , 0x00000000 // pad to avoid bank conflicts
-ASM_SIZE_DIRECTIVE(acos_coeff_1_table)
-
-
-acos_coeff_2_table:
-ASM_TYPE_DIRECTIVE(acos_coeff_2_table,@object)
-data8 0x8E26AF5F29B39A2A , 0x00003FF9 //P6
-data8 0xB4F118A4B1015470 , 0x00004003 //P17
-data8 0xF8E38E10C25990E0 , 0x00003FF9 //P4
-data8 0x80F50489AEF1CAC6 , 0x00004002 //P15
-data8 0x92728015172CFE1C , 0x00004003 //P19
-data8 0xBBC3D831D4595971 , 0x00003FF8 //P8
-data8 0x999999999952A5C3 , 0x00003FFB //P2
-data8 0x855576BE6F0975EC , 0x00003FFF //P13
-data8 0xF12420E778077D89 , 0x00003FFA //P11
-data8 0xB6590FF4D23DE003 , 0x00003FF3 //P10
-data8 0xb504f333f9de6484 , 0x00003ffe // sqrt(2)/2
-ASM_SIZE_DIRECTIVE(acos_coeff_2_table)
-
-
-.align 32
-.global acos
-ASM_TYPE_DIRECTIVE(acos,@function)
+LOCAL_OBJECT_START(acos_base_range_table)
+// Ai: Polynomial coefficients for the acos(x), |x| < .625000
+// Bi: Polynomial coefficients for the acos(x), |x| > .625000
+data8 0xBFDAAB56C01AE468 //A29
+data8 0x3FE1C470B76A5B2B //A31
+data8 0xBFDC5FF82A0C4205 //A33
+data8 0x3FC71FD88BFE93F0 //A35
+data8 0xB504F333F9DE6487, 0x00003FFF //B0
+data8 0xAAAAAAAAAAAAFC18, 0x00003FFC //A3
+data8 0x3F9F1C71BC4A7823 //A9
+data8 0x3F96E8BBAAB216B2 //A11
+data8 0x3F91C4CA1F9F8A98 //A13
+data8 0x3F8C9DDCEDEBE7A6 //A15
+data8 0x3F877784442B1516 //A17
+data8 0x3F859C0491802BA2 //A19
+data8 0x9999999998C88B8F, 0x00003FFB //A5
+data8 0x3F6BD7A9A660BF5E //A21
+data8 0x3F9FC1659340419D //A23
+data8 0xB6DB6DB798149BDF, 0x00003FFA //A7
+data8 0xBFB3EF18964D3ED3 //A25
+data8 0x3FCD285315542CF2 //A27
+data8 0xF15BEEEFF7D2966A, 0x00003FFB //B1
+data8 0x3EF0DDA376D10FB3 //B10
+data8 0xBEB83CAFE05EBAC9 //B11
+data8 0x3F65FFB67B513644 //B4
+data8 0x3F5032FBB86A4501 //B5
+data8 0x3F392162276C7CBA //B6
+data8 0x3F2435949FD98BDF //B7
+data8 0xD93923D7FA08341C, 0x00003FF9 //B2
+data8 0x3F802995B6D90BDB //B3
+data8 0x3F10DF86B341A63F //B8
+data8 0xC90FDAA22168C235, 0x00003FFF // Pi/2
+data8 0x3EFA3EBD6B0ECB9D //B9
+data8 0x3EDE18BA080E9098 //B12
+LOCAL_OBJECT_END(acos_base_range_table)
.section .text
-.proc acos
-.align 32
-
-
-acos:
-
-{ .mfi
- alloc r32 = ar.pfs,1,6,4,0
- fma.s1 acos_tx = f8,f8,f0
- addl ASIN_Addr2 = @ltoff(acos_coeff_2_table),gp
-}
-{ .mfi
- mov ASIN_FFFE = 0xFFFE
- fnma.s1 acos_t = f8,f8,f1
- addl ASIN_Addr1 = @ltoff(acos_coeff_1_table),gp
+GLOBAL_LIBM_ENTRY(acos)
+acos_unnormal_back:
+{ .mfi
+ getf.d rXBits = f8 // grab bits of input value
+ // set p12 = 1 if x is a NaN, denormal, or zero
+ fclass.m p12, p0 = f8, 0xcf
+ adds rSign = 1, r0
+}
+{ .mfi
+ addl rTblAddr = @ltoff(acos_base_range_table),gp
+ // 1 - x = 1 - |x| for positive x
+ fms.s1 f1mX = f1, f1, f8
+ addl rHalf = 0xFFFE, r0 // exponent of 1/2
}
;;
-
-
-{ .mfi
- setf.exp acos_1by2 = ASIN_FFFE
- fmerge.s acos_abs_x = f1,f8
- nop.i 999 ;;
-}
-
-
-{ .mmf
- ld8 ASIN_Addr1 = [ASIN_Addr1]
- ld8 ASIN_Addr2 = [ASIN_Addr2]
- fmerge.s acos_sgn_x = f8,f1
-}
-;;
-
-
-{ .mfi
- nop.m 999
- fcmp.lt.s1 p11,p12 = f8, f0
- nop.i 999 ;;
-}
-
-
-{ .mfi
- ldfe acos_coeff_P7 = [ASIN_Addr1],16
- fma.s1 acos_tx2 = acos_tx,acos_tx,f0
- nop.i 999
-}
-{ .mfi
- ldfe acos_coeff_P6 = [ASIN_Addr2],16
- fma.s1 acos_t2 = acos_t,acos_t,f0
- nop.i 999;;
+{ .mfi
+ addl r0625 = 0x3FE4, r0 // high 16 bits of 0.625
+ // set p8 = 1 if x < 0
+ fcmp.lt.s1 p8, p9 = f8, f0
+ shl rSign = rSign, 63 // sign bit
+}
+{ .mfi
+ // point to the beginning of the table
+ ld8 rTblAddr = [rTblAddr]
+ // 1 + x = 1 - |x| for negative x
+ fma.s1 f1pX = f1, f1, f8
+ adds rOne = 0x3FF, r0
}
-
-
-{ .mmf
- ldfe acos_coeff_P18 = [ASIN_Addr1],16
- ldfe acos_coeff_P17 = [ASIN_Addr2],16
- fclass.m.unc p8,p0 = f8, 0xc3 //@qnan |@snan
-}
;;
-
-
-{ .mmf
- ldfe acos_coeff_P5 = [ASIN_Addr1],16
- ldfe acos_coeff_P4 = [ASIN_Addr2],16
- frsqrta.s1 acos_y0,p0 = acos_t
-}
+{ .mfi
+ andcm rAbsXBits = rXBits, rSign // bits of |x|
+ fmerge.s fSignX = f8, f1 // signum(x)
+ shl r0625 = r0625, 48 // bits of DP representation of 0.625
+}
+{ .mfb
+ setf.exp fHalf = rHalf // load A2 to FP reg
+ fma.s1 fXSqr = f8, f8, f0 // x^2
+ // branch on special path if x is a NaN, denormal, or zero
+(p12) br.cond.spnt acos_special
+}
;;
-
-
-{ .mfi
- ldfe acos_coeff_P16 = [ASIN_Addr1],16
- fcmp.gt.s1 p9,p0 = acos_abs_x,f1
- nop.i 999
-}
-{ .mfb
- ldfe acos_coeff_P15 = [ASIN_Addr2],16
-(p8) fma.d f8 = f8,f1,f0
-(p8) br.ret.spnt b0
+{ .mfi
+ adds rPiBy2Ptr = 272, rTblAddr
+ nop.f 0
+ shl rOne = rOne, 52 // bits of 1.0
+}
+{ .mfi
+ adds rTmpPtr1 = 16, rTblAddr
+ nop.f 0
+ // set p6 = 1 if |x| < 0.625
+ cmp.lt p6, p7 = rAbsXBits, r0625
}
;;
-
-
-{ .mmf
- ldfe acos_coeff_P20 = [ASIN_Addr1],16
- ldfe acos_coeff_P19 = [ASIN_Addr2],16
- fclass.m.unc p10,p0 = f8, 0x07 //@zero
-}
+{ .mfi
+ ldfpd fA29, fA31 = [rTblAddr] // A29, fA31
+ // 1 - x = 1 - |x| for positive x
+(p9) fms.s1 fR = f1, f1, f8
+ // point to coefficient of "near 1" polynomial
+(p7) adds rTmpPtr2 = 176, rTblAddr
+}
+{ .mfi
+ ldfpd fA33, fA35 = [rTmpPtr1], 16 // A33, fA35
+ // 1 + x = 1 - |x| for negative x
+(p8) fma.s1 fR = f1, f1, f8
+(p6) adds rTmpPtr2 = 48, rTblAddr
+}
;;
-
-
-{ .mfi
- ldfe acos_coeff_P9 = [ASIN_Addr1],16
- fma.s1 acos_t4 = acos_t2,acos_t2,f0
-(p9) mov GR_Parameter_Tag = 58
-}
-{ .mfi
- ldfe acos_coeff_P8 = [ASIN_Addr2],16
- fma.s1 acos_3by2 = acos_1by2,f1,f1
- nop.i 999;;
+{ .mfi
+ ldfe fB0 = [rTmpPtr1], 16 // B0
+ nop.f 0
+ nop.i 0
}
-
-
-{ .mfi
- ldfe acos_coeff_P2 = [ASIN_Addr2],16
- fma.s1 acos_tx4 = acos_tx2,acos_tx2,f0
- nop.i 999
-}
-{ .mfb
- ldfe acos_coeff_P3 = [ASIN_Addr1],16
- fma.s1 acos_t3 = acos_t,acos_t2,f0
-(p9) br.cond.spnt __libm_error_region
+{ .mib
+ adds rTmpPtr3 = 16, rTmpPtr2
+ // set p10 = 1 if |x| = 1.0
+ cmp.eq p10, p0 = rAbsXBits, rOne
+ // branch on special path for |x| = 1.0
+(p10) br.cond.spnt acos_abs_1
}
;;
-
-
-{ .mfi
- ldfe acos_coeff_P13 = [ASIN_Addr2],16
- fma.s1 acos_H0 = acos_y0,acos_1by2,f0
- nop.i 999
-}
-{ .mfi
- ldfe acos_coeff_P14 = [ASIN_Addr1],16
- fma.s1 acos_S0 = acos_y0,acos_t,f0
- nop.i 999;;
+{ .mfi
+ ldfe fA3 = [rTmpPtr2], 48 // A3 or B1
+ nop.f 0
+ adds rTmpPtr1 = 64, rTmpPtr3
}
-
-
-{ .mfi
- ldfe acos_coeff_P11 = [ASIN_Addr2],16
- fcmp.eq.s1 p6,p0 = acos_abs_x, f1
- nop.i 999
-}
-{ .mfi
- ldfe acos_coeff_P12 = [ASIN_Addr1],16
- fma.s1 acos_tx3 = acos_tx,acos_tx2,f0
- nop.i 999
+{ .mib
+ ldfpd fA9, fA11 = [rTmpPtr3], 16 // A9, A11 or B10, B11
+ // set p11 = 1 if |x| > 1.0
+ cmp.gt p11, p0 = rAbsXBits, rOne
+ // branch on special path for |x| > 1.0
+(p11) br.cond.spnt acos_abs_gt_1
}
;;
-
-
-{ .mfi
- ldfe acos_coeff_P10 = [ASIN_Addr2],16
- fma.s1 acos_1poly_p6 = acos_tx,acos_coeff_P7,acos_coeff_P6
- nop.i 999
-}
-{ .mfi
- ldfe acos_coeff_P1 = [ASIN_Addr1],16
- fma.s1 acos_poly_p6 = acos_t,acos_coeff_P7,acos_coeff_P6
- nop.i 999;;
+{ .mfi
+ ldfpd fA17, fA19 = [rTmpPtr2], 16 // A17, A19 or B6, B7
+ // initial approximation of 1 / sqrt(1 - x)
+ frsqrta.s1 f1mXRcp, p0 = f1mX
+ nop.i 0
}
-
-
-{ .mfi
- ldfe acos_const_sqrt2by2 = [ASIN_Addr2],16
- fma.s1 acos_5by2 = acos_3by2,f1,f1
- nop.i 999
-}
-{ .mfi
- ldfe acos_coeff_P21 = [ASIN_Addr1],16
- fma.s1 acos_11by4 = acos_3by2,acos_3by2,acos_1by2
- nop.i 999;;
+{ .mfi
+ ldfpd fA13, fA15 = [rTmpPtr3] // A13, A15 or B4, B5
+ fma.s1 fXCube = fXSqr, f8, f0 // x^3
+ nop.i 0
}
-
-
-{ .mfi
- ldfe acos_const_piby2 = [ASIN_Addr1],16
- fma.s1 acos_poly_p17 = acos_t,acos_coeff_P18,acos_coeff_P17
- nop.i 999
-}
-{ .mfb
- nop.m 999
- fma.s1 acos_3by4 = acos_3by2,acos_1by2,f0
-(p10) br.cond.spnt L(ACOS_ZERO) // Branch to short path if x=0
+;;
+{ .mfi
+ ldfe fA5 = [rTmpPtr2], 48 // A5 or B2
+ // initial approximation of 1 / sqrt(1 + x)
+ frsqrta.s1 f1pXRcp, p0 = f1pX
+ nop.i 0
+}
+{ .mfi
+ ldfpd fA21, fA23 = [rTmpPtr1], 16 // A21, A23 or B3, B8
+ fma.s1 fXQuadr = fXSqr, fXSqr, f0 // x^4
+ nop.i 0
}
;;
-
-
-{ .mfi
- nop.m 999
- fma.s1 acos_poly_p15 = acos_t,acos_coeff_P16,acos_coeff_P15
- nop.i 999
-}
-{ .mfb
- nop.m 999
- fnma.s1 acos_d = acos_S0,acos_H0,acos_1by2
-(p6) br.cond.spnt L(ACOS_ABS_ONE) // Branch to short path if |x|=1
+{ .mfi
+ ldfe fA7 = [rTmpPtr1] // A7 or Pi/2
+ fma.s1 fRSqr = fR, fR, f0 // R^2
+ nop.i 0
+}
+{ .mfb
+ ldfpd fA25, fA27 = [rTmpPtr2] // A25, A27 or B9, B12
+ nop.f 0
+(p6) br.cond.spnt acos_base_range;
}
;;
-
-{ .mfi
- nop.m 999
- fma.s1 acos_poly_p19 = acos_t,acos_coeff_P20,acos_coeff_P19
- nop.i 999
-}
-{ .mfi
- nop.m 999
- fma.s1 acos_poly_p4 = acos_t,acos_coeff_P5,acos_coeff_P4
- nop.i 999;;
+{ .mfi
+ nop.m 0
+(p9) fma.s1 fH = fHalf, f1mXRcp, f0 // H0 for x > 0
+ nop.i 0
}
-
-
-{ .mfi
- nop.m 999
- fma.s1 acos_1poly_p17 = acos_tx,acos_coeff_P18,acos_coeff_P17
- nop.i 999
-}
-{ .mfi
- nop.m 999
- fma.s1 acos_poly_p8 = acos_t,acos_coeff_P9,acos_coeff_P8
- nop.i 999;;
+{ .mfi
+ nop.m 0
+(p9) fma.s1 fS = f1mX, f1mXRcp, f0 // S0 for x > 0
+ nop.i 0
}
-
-
-{ .mfi
- nop.m 999
- fms.s1 acos_35by8 = acos_5by2,acos_11by4,acos_5by2
- nop.i 999
-}
-{ .mfi
- nop.m 999
- fma.s1 acos_63by8 = acos_5by2,acos_11by4,f1
- nop.i 999;;
+;;
+{ .mfi
+ nop.m 0
+(p8) fma.s1 fH = fHalf, f1pXRcp, f0 // H0 for x < 0
+ nop.i 0
}
-
-
-{ .mfi
- nop.m 999
- fma.s1 acos_poly_p13 = acos_t,acos_coeff_P14,acos_coeff_P13
- nop.i 999
-}
-{ .mfi
- nop.m 999
- fma.s1 acos_18by4 = acos_3by2,acos_5by2,acos_3by4
- nop.i 999;;
+{ .mfi
+ nop.m 0
+(p8) fma.s1 fS = f1pX, f1pXRcp, f0 // S0 for x > 0
+ nop.i 0
}
-
-
-{ .mfi
- nop.m 999
- fma.s1 acos_l1 = acos_5by2,acos_d,acos_3by2
- nop.i 999
-}
-{ .mfi
- nop.m 999
- fma.s1 acos_d2 = acos_d,acos_d,f0
- nop.i 999;;
+;;
+{ .mfi
+ nop.m 0
+ fma.s1 fRQuadr = fRSqr, fRSqr, f0 // R^4
+ nop.i 0
}
-
-
-{ .mfi
- nop.m 999
- fma.s1 acos_poly_p15 = acos_t2,acos_poly_p17,acos_poly_p15
- nop.i 999
-}
-{ .mfi
- nop.m 999
- fma.s1 acos_T0 = acos_d,acos_S0,f0
- nop.i 999;;
+;;
+{ .mfi
+ nop.m 0
+ fma.s1 fB11 = fB11, fR, fB10
+ nop.i 0
}
-
-
-{ .mfi
- nop.m 999
- fma.s1 acos_poly_p19 = acos_t2,acos_coeff_P21,acos_poly_p19
- nop.i 999
-}
-{ .mfi
- nop.m 999
- fma.s1 acos_poly_p4 = acos_t2,acos_poly_p6,acos_poly_p4
- nop.i 999;;
+{ .mfi
+ nop.m 0
+ fma.s1 fB1 = fB1, fR, fB0
+ nop.i 0
}
-
-
-{ .mfi
- nop.m 999
- fma.s1 acos_d1 = acos_35by8,acos_d,f0
- nop.i 999
-}
-{ .mfi
- nop.m 999
- fma.s1 acos_231by16 = acos_3by2,acos_35by8,acos_63by8
- nop.i 999;;
+;;
+{ .mfi
+ nop.m 0
+ fma.s1 fB5 = fB5, fR, fB4
+ nop.i 0
}
-
-
-{ .mfi
- nop.m 999
- fma.s1 acos_poly_p2 = acos_t,acos_coeff_P3,acos_coeff_P2
- nop.i 999
-}
-{ .mfi
- nop.m 999
- fma.s1 acos_poly_p8 = acos_t2,acos_coeff_P10,acos_poly_p8
- nop.i 999;;
+{ .mfi
+ nop.m 0
+ fma.s1 fB7 = fB7, fR, fB6
+ nop.i 0
}
-
-
-{ .mfi
- nop.m 999
- fma.s1 acos_poly_p11 = acos_t,acos_coeff_P12,acos_coeff_P11
- nop.i 999
-}
-{ .mfi
- nop.m 999
- fma.s1 acos_e0 = acos_d2,acos_l1,acos_d
- nop.i 999;;
+;;
+{ .mfi
+ nop.m 0
+ fma.s1 fB3 = fB3, fR, fB2
+ nop.i 0
}
-
-
-{ .mfi
- nop.m 999
- fma.s1 acos_1poly_p15 = acos_tx,acos_coeff_P16,acos_coeff_P15
- nop.i 999
-}
-{ .mfi
- nop.m 999
- fma.s1 acos_poly_p0 = acos_t,acos_coeff_P1,f1
- nop.i 999;;
+;;
+{ .mfi
+ nop.m 0
+ fnma.s1 fD = fH, fS, fHalf // d0 = 1/2 - H0*S0
+ nop.i 0
}
-
-
-{ .mfi
- nop.m 999
- fma.s1 acos_1poly_p19 = acos_tx,acos_coeff_P20,acos_coeff_P19
- nop.i 999
-}
-{ .mfi
- nop.m 999
- fma.s1 acos_1poly_p4 = acos_tx,acos_coeff_P5,acos_coeff_P4
- nop.i 999;;
+;;
+{ .mfi
+ nop.m 0
+ fma.s1 fR8 = fRQuadr, fRQuadr, f0 // R^4
+ nop.i 0
}
-
-
-{ .mfi
- nop.m 999
- fma.s1 acos_1poly_p8 = acos_tx,acos_coeff_P9,acos_coeff_P8
- nop.i 999
-}
-{ .mfi
- nop.m 999
- fma.s1 acos_l2 = acos_231by16,acos_d,acos_63by8
- nop.i 999;;
+{ .mfi
+ nop.m 0
+ fma.s1 fB9 = fB9, fR, fB8
+ nop.i 0
}
-
-
-{ .mfi
- nop.m 999
- fma.s1 acos_d3 = acos_d2,acos_d,f0
- nop.i 999
-}
-{ .mfi
- nop.m 999
- fma.s1 acos_T3 = acos_d2,acos_T0,f0
- nop.i 999;;
+;;
+{.mfi
+ nop.m 0
+ fma.s1 fB12 = fB12, fRSqr, fB11
+ nop.i 0
}
-
-
-{ .mfi
- nop.m 999
- fma.s1 acos_429by16 = acos_18by4,acos_11by4,acos_231by16
- nop.i 999
-}
-{ .mfi
- nop.m 999
- fma.s1 acos_S1 = acos_e0,acos_S0,acos_S0
- nop.i 999;;
+{.mfi
+ nop.m 0
+ fma.s1 fB7 = fB7, fRSqr, fB5
+ nop.i 0
}
-
-
-{ .mfi
- nop.m 999
- fma.s1 acos_poly_p4 = acos_t4,acos_poly_p8,acos_poly_p4
- nop.i 999
-}
-{ .mfi
- nop.m 999
- fma.s1 acos_poly_p15 = acos_t4,acos_poly_p19,acos_poly_p15
- nop.i 999;;
+;;
+{.mfi
+ nop.m 0
+ fma.s1 fB3 = fB3, fRSqr, fB1
+ nop.i 0
}
-
-
-{ .mfi
- nop.m 999
- fma.s1 acos_poly_p0 = acos_t2,acos_poly_p2,acos_poly_p0
- nop.i 999
-}
-{ .mfi
- nop.m 999
- fma.s1 acos_poly_p11 = acos_t2,acos_poly_p13,acos_poly_p11
- nop.i 999;;
+;;
+{ .mfi
+ nop.m 0
+ fma.s1 fH = fH, fD, fH // H1 = H0 + H0*d0
+ nop.i 0
}
-
-
-{ .mfi
- nop.m 999
- fma.s1 acos_t8 = acos_t4,acos_t4,f0
- nop.i 999
-}
-{ .mfi
- nop.m 999
- fma.s1 acos_e1 = acos_d2,acos_l2,acos_d1
- nop.i 999;;
+{ .mfi
+ nop.m 0
+ fma.s1 fS = fS, fD, fS // S1 = S0 + S0*d0
+ nop.i 0
}
-
-
-{ .mfi
- nop.m 999
- fma.s1 acos_1poly_p4 = acos_tx2,acos_1poly_p6,acos_1poly_p4
- nop.i 999
-}
-{ .mfi
- nop.m 999
- fma.s1 acos_1poly_p15 = acos_tx2,acos_1poly_p17,acos_1poly_p15
- nop.i 999;;
+;;
+{.mfi
+ nop.m 0
+(p9) fma.s1 fCpi = f1, f0, f0 // Cpi = 0 if x > 0
+ nop.i 0
}
-
-
-{ .mfi
- nop.m 999
- fma.s1 acos_1poly_p8 = acos_tx2,acos_coeff_P10,acos_1poly_p8
- nop.i 999
-}
-{ .mfi
- nop.m 999
- fma.s1 acos_1poly_p19 = acos_tx2,acos_coeff_P21,acos_1poly_p19
- nop.i 999;;
+{ .mfi
+ nop.m 0
+(p8) fma.s1 fCpi = fPiBy2, f1, fPiBy2 // Cpi = Pi if x < 0
+ nop.i 0
}
-
-
-{ .mfi
- nop.m 999
- fma.s1 acos_1poly_p2 = acos_tx,acos_coeff_P3,acos_coeff_P2
- nop.i 999
-}
-{ .mfi
- nop.m 999
- fma.s1 acos_1poly_p13 = acos_tx,acos_coeff_P14,acos_coeff_P13
- nop.i 999;;
+;;
+{ .mfi
+ nop.m 0
+ fma.s1 fB12 = fB12, fRSqr, fB9
+ nop.i 0
}
-
-
-{ .mfi
- nop.m 999
- fma.s1 acos_1poly_p0 = acos_tx,acos_coeff_P1,f1
- nop.i 999
-}
-{ .mfi
- nop.m 999
- fma.s1 acos_1poly_p11 = acos_tx,acos_coeff_P12,acos_coeff_P11
- nop.i 999;;
+{ .mfi
+ nop.m 0
+ fma.s1 fB7 = fB7, fRQuadr, fB3
+ nop.i 0
}
-
-
-{ .mfi
- nop.m 999
- fma.s1 acos_l3 = acos_429by16,acos_d,f0
- nop.i 999
-}
-{ .mfi
- nop.m 999
- fma.s1 acos_z = acos_e1,acos_T3,acos_S1
- nop.i 999;;
+;;
+{.mfi
+ nop.m 0
+ fnma.s1 fD = fH, fS, fHalf // d1 = 1/2 - H1*S1
+ nop.i 0
}
-
-
-{ .mfi
- nop.m 999
- fma.s1 acos_poly_p11 = acos_t4,acos_poly_p15,acos_poly_p11
- nop.i 999
-}
-{ .mfi
- nop.m 999
- fma.s1 acos_T6 = acos_T3,acos_d3,f0
- nop.i 999;;
+{ .mfi
+ nop.m 0
+ fnma.s1 fSignedS = fSignX, fS, f0 // -signum(x)*S1
+ nop.i 0
}
-
-
-{ .mfi
- nop.m 999
- fma.s1 acos_t11 = acos_t8,acos_t3,f0
- nop.i 999
-}
-{ .mfi
- nop.m 999
- fma.s1 acos_poly_p0 = acos_t4,acos_poly_p4,acos_poly_p0
- nop.i 999;;
+;;
+{ .mfi
+ nop.m 0
+ fma.s1 fCloseTo1Pol = fB12, fR8, fB7
+ nop.i 0
}
-
-
-{ .mfi
- nop.m 999
- fma.s1 acos_1poly_p4 = acos_tx4,acos_1poly_p8,acos_1poly_p4
- nop.i 999
-}
-{ .mfi
- nop.m 999
- fma.s1 acos_1poly_p15 = acos_tx4,acos_1poly_p19,acos_1poly_p15
- nop.i 999;;
+;;
+{ .mfi
+ nop.m 0
+ fma.s1 fH = fH, fD, fH // H2 = H1 + H1*d1
+ nop.i 0
}
-
-
-{ .mfi
- nop.m 999
- fma.s1 acos_1poly_p0 = acos_tx2,acos_1poly_p2,acos_1poly_p0
- nop.i 999
-}
-{ .mfi
- nop.m 999
- fma.s1 acos_1poly_p11 = acos_tx2,acos_1poly_p13,acos_1poly_p11
- nop.i 999;;
+{ .mfi
+ nop.m 0
+ fma.s1 fS = fS, fD, fS // S2 = S1 + S1*d1
+ nop.i 0
}
-
-
-{ .mfi
- nop.m 999
-// fcmp.le.s1 acos_pred_LEsqrt2by2,acos_pred_GTsqrt2by2 = acos_abs_x,acos_const_sqrt2by2
- fcmp.le.s1 p7,p8 = acos_abs_x,acos_const_sqrt2by2
- nop.i 999
-}
-{ .mfi
- nop.m 999
- fma.s1 acos_tx8 = acos_tx4,acos_tx4,f0
- nop.i 999;;
+;;
+{ .mfi
+ nop.m 0
+ // -signum(x)* S2 = -signum(x)*(S1 + S1*d1)
+ fma.s1 fSignedS = fSignedS, fD, fSignedS
+ nop.i 0
}
-
-
-{ .mfi
- nop.m 999
- fma.s1 acos_z = acos_l3,acos_T6,acos_z
- nop.i 999;;
-}
-
-{ .mfi
- nop.m 999
- fma.s1 acos_series_t = acos_t11,acos_poly_p11,acos_poly_p0
- nop.i 999
-}
-{ .mfi
- nop.m 999
-(p11) fma.s1 acos_const_add = acos_const_piby2, f1, acos_const_piby2
- nop.i 999
+;;
+{.mfi
+ nop.m 0
+ fnma.s1 fD = fH, fS, fHalf // d2 = 1/2 - H2*S2
+ nop.i 0
}
;;
-
{ .mfi
- nop.m 999
-(p12) fma.s1 acos_const_add = f1,f0,f0
- nop.i 999
+ nop.m 0
+ // Cpi + signum(x)*PolB*S2
+ fnma.s1 fCpi = fSignedS, fCloseTo1Pol, fCpi
+ nop.i 0
+}
+{ .mfi
+ nop.m 0
+ // signum(x)*PolB * S2
+ fnma.s1 fCloseTo1Pol = fSignedS, fCloseTo1Pol, f0
+ nop.i 0
}
;;
-
-{ .mfi
- nop.m 999
- fma.s1 acos_1poly_p0 = acos_tx4,acos_1poly_p4,acos_1poly_p0
- nop.i 999
-}
-{ .mfi
- nop.m 999
- fma.s1 acos_1poly_p11 = acos_tx4,acos_1poly_p15,acos_1poly_p11
- nop.i 999;;
+{ .mfb
+ nop.m 0
+ // final result for 0.625 <= |x| < 1
+ fma.d.s0 f8 = fCloseTo1Pol, fD, fCpi
+ // exit here for 0.625 <= |x| < 1
+ br.ret.sptk b0
}
+;;
-
-{ .mfi
- nop.m 999
- fma.s1 acos_tx11 = acos_tx8,acos_tx3,f0
- nop.i 999;;
-}
-
-{ .mfi
- nop.m 999
-//(acos_pred_GTsqrt2by2) fnma.s1 answer2 = acos_z,acos_series_t,acos_const_piby2
-(p8) fnma.s1 answer2 = acos_z,acos_series_t,f0
- nop.i 999;;
-}
-
-{ .mfi
- nop.m 999
- fma.s1 acos_series_tx = acos_tx11,acos_1poly_p11,acos_1poly_p0
- nop.i 999;;
-}
-
-{ .mfi
- nop.m 999
-//(acos_pred_GTsqrt2by2) fnma.d f8 = acos_sgn_x,answer2,acos_const_piby2
-(p8) fnma.d f8 = acos_sgn_x,answer2,acos_const_add
- nop.i 999;;
-}
-
-{ .mfb
- nop.m 999
-//(acos_pred_LEsqrt2by2) fnma.d f8 = f8,acos_series_tx,acos_const_piby2
-(p7) fnma.d f8 = f8,acos_series_tx,acos_const_piby2
- br.ret.sptk b0 ;;
-}
+// here if |x| < 0.625
+.align 32
+acos_base_range:
+{ .mfi
+ ldfe fCpi = [rPiBy2Ptr] // Pi/2
+ fma.s1 fA33 = fA33, fXSqr, fA31
+ nop.i 0
+}
+{ .mfi
+ nop.m 0
+ fma.s1 fA15 = fA15, fXSqr, fA13
+ nop.i 0
+}
+;;
+{ .mfi
+ nop.m 0
+ fma.s1 fA29 = fA29, fXSqr, fA27
+ nop.i 0
+}
+{ .mfi
+ nop.m 0
+ fma.s1 fA25 = fA25, fXSqr, fA23
+ nop.i 0
+}
+;;
+{ .mfi
+ nop.m 0
+ fma.s1 fA21 = fA21, fXSqr, fA19
+ nop.i 0
+}
+{ .mfi
+ nop.m 0
+ fma.s1 fA9 = fA9, fXSqr, fA7
+ nop.i 0
+}
+;;
+{ .mfi
+ nop.m 0
+ fma.s1 fA5 = fA5, fXSqr, fA3
+ nop.i 0
+}
+;;
+{ .mfi
+ nop.m 0
+ fma.s1 fA35 = fA35, fXQuadr, fA33
+ nop.i 0
+}
+{ .mfi
+ nop.m 0
+ fma.s1 fA17 = fA17, fXQuadr, fA15
+ nop.i 0
+}
+;;
+{ .mfi
+ nop.m 0
+ fma.s1 fX8 = fXQuadr, fXQuadr, f0 // x^8
+ nop.i 0
+}
+{ .mfi
+ nop.m 0
+ fma.s1 fA25 = fA25, fXQuadr, fA21
+ nop.i 0
+}
+;;
+{ .mfi
+ nop.m 0
+ fma.s1 fA9 = fA9, fXQuadr, fA5
+ nop.i 0
+}
+;;
+{ .mfi
+ nop.m 0
+ fms.s1 fCpi = fCpi, f1, f8 // Pi/2 - x
+ nop.i 0
+}
+;;
+{ .mfi
+ nop.m 0
+ fma.s1 fA35 = fA35, fXQuadr, fA29
+ nop.i 0
+}
+{ .mfi
+ nop.m 0
+ fma.s1 fA17 = fA17, fXSqr, fA11
+ nop.i 0
+}
+;;
+{ .mfi
+ nop.m 0
+ fma.s1 fX16 = fX8, fX8, f0 // x^16
+ nop.i 0
+}
+;;
+{ .mfi
+ nop.m 0
+ fma.s1 fA35 = fA35, fX8, fA25
+ nop.i 0
+}
+{ .mfi
+ nop.m 0
+ fma.s1 fA17 = fA17, fX8, fA9
+ nop.i 0
+}
+;;
+{ .mfi
+ nop.m 0
+ fma.s1 fBaseP = fA35, fX16, fA17
+ nop.i 0
+}
+;;
+{ .mfb
+ nop.m 0
+ // final result for |x| < 0.625
+ fnma.d.s0 f8 = fBaseP, fXCube, fCpi
+ // exit here for |x| < 0.625 path
+ br.ret.sptk b0
+}
+;;
-L(ACOS_ZERO):
-// Here if x=0
-{ .mfb
- nop.m 999
- fma.d f8 = acos_const_piby2,f1,f0
- br.ret.sptk b0 ;;
-}
+// here if |x| = 1
+// acos(1) = 0
+// acos(-1) = Pi
+.align 32
+acos_abs_1:
+{ .mfi
+ ldfe fPiBy2 = [rPiBy2Ptr] // Pi/2
+ nop.f 0
+ nop.i 0
+}
+;;
+.pred.rel "mutex", p8, p9
+{ .mfi
+ nop.m 0
+ // result for x = 1.0
+(p9) fma.d.s0 f8 = f1, f0, f0 // 0.0
+ nop.i 0
+}
+{.mfb
+ nop.m 0
+ // result for x = -1.0
+(p8) fma.d.s0 f8 = fPiBy2, f1, fPiBy2 // Pi
+ // exit here for |x| = 1.0
+ br.ret.sptk b0
+}
+;;
+// here if x is a NaN, denormal, or zero
+.align 32
+acos_special:
+{ .mfi
+ // point to Pi/2
+ adds rPiBy2Ptr = 272, rTblAddr
+ // set p12 = 1 if x is a NaN
+ fclass.m p12, p0 = f8, 0xc3
+ nop.i 0
+}
+{ .mlx
+ nop.m 0
+ // smallest positive DP normalized number
+ movl rDenoBound = 0x0010000000000000
+}
+;;
+{ .mfi
+ ldfe fPiBy2 = [rPiBy2Ptr] // Pi/2
+ // set p13 = 1 if x = 0.0
+ fclass.m p13, p0 = f8, 0x07
+ nop.i 0
+}
+{ .mfi
+ nop.m 0
+ fnorm.s1 fNormX = f8
+ nop.i 0
+}
+;;
+{ .mfb
+ // load smallest normal to FP reg
+ setf.d fDenoBound = rDenoBound
+ // answer if x is a NaN
+(p12) fma.d.s0 f8 = f8,f1,f0
+ // exit here if x is a NaN
+(p12) br.ret.spnt b0
+}
+;;
+{ .mfi
+ nop.m 0
+ // absolute value of normalized x
+ fmerge.s fNormX = f1, fNormX
+ nop.i 0
+}
+;;
+{ .mfb
+ nop.m 0
+ // final result for x = 0
+(p13) fma.d.s0 f8 = fPiBy2, f1, f8
+ // exit here if x = 0.0
+(p13) br.ret.spnt b0
+}
+;;
+// if we still here then x is denormal or unnormal
+{ .mfi
+ nop.m 0
+ // set p14 = 1 if normalized x is greater than or
+ // equal to the smallest denormalized value
+ // So, if p14 is set to 1 it means that we deal with
+ // unnormal rather than with "true" denormal
+ fcmp.ge.s1 p14, p0 = fNormX, fDenoBound
+ nop.i 0
+}
+;;
+{ .mfi
+ nop.m 0
+(p14) fcmp.eq.s0 p6, p0 = f8, f0 // Set D flag if x unnormal
+ nop.i 0
+}
+{ .mfb
+ nop.m 0
+ // normalize unnormal input
+(p14) fnorm.s1 f8 = f8
+ // return to the main path
+(p14) br.cond.sptk acos_unnormal_back
+}
+;;
+// if we still here it means that input is "true" denormal
+{ .mfb
+ nop.m 0
+ // final result if x is denormal
+ fms.d.s0 f8 = fPiBy2, f1, f8 // Pi/2 - x
+ // exit here if x is denormal
+ br.ret.sptk b0
+}
+;;
-L(ACOS_ABS_ONE):
-.pred.rel "mutex",p11,p12
-// Here if |x|=1
-{ .mfi
- nop.m 999
-(p11) fma.d f8 = acos_const_piby2,f1,acos_const_piby2 // acos(-1)=pi
- nop.i 999
-}
-{ .mfb
- nop.m 999
-(p12) fma.d f8 = f1,f0,f0 // acos(1)=0
- br.ret.sptk b0 ;;
-}
+// here if |x| > 1.0
+// error handler should be called
+.align 32
+acos_abs_gt_1:
+{ .mfi
+ alloc r32 = ar.pfs, 0, 3, 4, 0 // get some registers
+ fmerge.s FR_X = f8,f8
+ nop.i 0
+}
+{ .mfb
+ mov GR_Parameter_TAG = 58 // error code
+ frcpa.s0 FR_RESULT, p0 = f0,f0
+ // call error handler routine
+ br.cond.sptk __libm_error_region
+}
+;;
+GLOBAL_LIBM_END(acos)
-.endp acos
-ASM_SIZE_DIRECTIVE(acos)
-.proc __libm_error_region
-__libm_error_region:
+LOCAL_LIBM_ENTRY(__libm_error_region)
.prologue
{ .mfi
add GR_Parameter_Y=-32,sp // Parameter 2 value
- nop.f 999
+ nop.f 0
.save ar.pfs,GR_SAVE_PFS
mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
}
@@ -879,28 +840,29 @@ __libm_error_region:
mov GR_SAVE_GP=gp // Save gp
};;
{ .mmi
- stfs [GR_Parameter_Y] = f1,16 // Store Parameter 2 on stack
+ stfd [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
- frcpa.s0 f9,p0 = f0,f0
-;;
-
{ .mib
- stfd [GR_Parameter_X] = f8 // Store Parameter 1 on stack
- add GR_Parameter_RESULT = 0,GR_Parameter_Y
- nop.b 0 // Parameter 3 address
+ stfd [GR_Parameter_X] = FR_X // STORE Parameter 1 on stack
+ add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
+ nop.b 0
}
{ .mib
- stfd [GR_Parameter_Y] = f9,-16 // Store Parameter 3 on stack
- adds r32 = 48,sp
- br.call.sptk b0=__libm_error_support# // Call error handling function
+ stfd [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
- ldfd f8 = [r32] // Get return result off stack
+ add GR_Parameter_RESULT = 48,sp
+ nop.m 0
+ nop.i 0
+};;
+{ .mmi
+ ldfd 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
@@ -909,11 +871,8 @@ __libm_error_region:
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
+LOCAL_LIBM_END(__libm_error_region)
+.type __libm_error_support#,@function
+.global __libm_error_support#