.file "sincos.s"
// Copyright (c) 2000 - 2005, Intel Corporation
// All rights reserved.
//
// Contributed 2000 by the Intel Numerics Group, Intel Corporation
//
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// 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
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// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
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// 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 Work range is widened by reduction strengthen (3 parts of Pi/16)
// 02/10/03 Reordered header: .section, .global, .proc, .align
// 08/08/03 Improved performance
// 10/28/04 Saved sincos_r_sincos to avoid clobber by dynamic loader
// 03/31/05 Reformatted delimiters between data tables
// API
//==============================================================
// double sin( double x);
// double cos( double 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)) -
// nfloat * LOWEST(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 and LOW parts are rounded to zero values,
// and LOWEST is rounded to nearest one.
//
// 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 + r^6 q3 + ... = Series for Cos
// Sin(r) = r + r^3 p1 + r^5 p2 + r^7 p3 + ... = 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^2p2 + r^4p3 + r^6p4
// Q = q1 + r^2q2 + r^4q3 + r^6q4
//
// rcub = r * rsq
// Sin(r) = r + rcub * P
// = r + r^3p1 + r^5p2 + r^7p3 + r^9p4 + ... = 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 + rcub * P
//
// Answer = S[m] Cos(r) + [Cm] P
//
// Cos(r) = 1 + rsq Q
// Cos(r) = 1 + r^2 Q
// Cos(r) = 1 + r^2 (q1 + r^2q2 + r^4q3 + r^6q4)
// Cos(r) = 1 + r^2q1 + r^4q2 + r^6q3 + r^8q4 + ...
//
// S[m] Cos(r) = S[m](1 + rsq Q)
// S[m] Cos(r) = S[m] + Sm 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 -> r26
// r32 -> r35
// predicate registers used:
// p6 -> p11
// floating-point registers used
// f9 -> f15
// f32 -> f61
// Assembly macros
//==============================================================
sincos_NORM_f8 = f9
sincos_W = f10
sincos_int_Nfloat = f11
sincos_Nfloat = f12
sincos_r = f13
sincos_rsq = f14
sincos_rcub = f15
sincos_save_tmp = f15
sincos_Inv_Pi_by_16 = f32
sincos_Pi_by_16_1 = f33
sincos_Pi_by_16_2 = f34
sincos_Inv_Pi_by_64 = f35
sincos_Pi_by_16_3 = f36
sincos_r_exact = f37
sincos_Sm = f38
sincos_Cm = f39
sincos_P1 = f40
sincos_Q1 = f41
sincos_P2 = f42
sincos_Q2 = f43
sincos_P3 = f44
sincos_Q3 = f45
sincos_P4 = f46
sincos_Q4 = f47
sincos_P_temp1 = f48
sincos_P_temp2 = f49
sincos_Q_temp1 = f50
sincos_Q_temp2 = f51
sincos_P = f52
sincos_Q = f53
sincos_srsq = f54
sincos_SIG_INV_PI_BY_16_2TO61 = f55
sincos_RSHF_2TO61 = f56
sincos_RSHF = f57
sincos_2TOM61 = f58
sincos_NFLOAT = f59
sincos_W_2TO61_RSH = f60
fp_tmp = f61
/////////////////////////////////////////////////////////////
sincos_GR_sig_inv_pi_by_16 = r14
sincos_GR_rshf_2to61 = r15
sincos_GR_rshf = r16
sincos_GR_exp_2tom61 = r17
sincos_GR_n = r18
sincos_GR_m = r19
sincos_GR_32m = r19
sincos_GR_all_ones = r19
sincos_AD_1 = r20
sincos_AD_2 = r21
sincos_exp_limit = r22
sincos_r_signexp = r23
sincos_r_17_ones = r24
sincos_r_sincos = r25
sincos_r_exp = r26
GR_SAVE_PFS = r33
GR_SAVE_B0 = r34
GR_SAVE_GP = r35
GR_SAVE_r_sincos = r36
RODATA
// Pi/16 parts
.align 16
LOCAL_OBJECT_START(double_sincos_pi)
data8 0xC90FDAA22168C234, 0x00003FFC // pi/16 1st part
data8 0xC4C6628B80DC1CD1, 0x00003FBC // pi/16 2nd part
data8 0xA4093822299F31D0, 0x00003F7A // pi/16 3rd part
LOCAL_OBJECT_END(double_sincos_pi)
// Coefficients for polynomials
LOCAL_OBJECT_START(double_sincos_pq_k4)
data8 0x3EC71C963717C63A // P4
data8 0x3EF9FFBA8F191AE6 // Q4
data8 0xBF2A01A00F4E11A8 // P3
data8 0xBF56C16C05AC77BF // Q3
data8 0x3F8111111110F167 // P2
data8 0x3FA555555554DD45 // Q2
data8 0xBFC5555555555555 // P1
data8 0xBFDFFFFFFFFFFFFC // Q1
LOCAL_OBJECT_END(double_sincos_pq_k4)
// Sincos table (S[m], C[m])
LOCAL_OBJECT_START(double_sin_cos_beta_k4)
data8 0x0000000000000000 , 0x00000000 // sin( 0 pi/16) S0
data8 0x8000000000000000 , 0x00003fff // cos( 0 pi/16) C0
//
data8 0xc7c5c1e34d3055b3 , 0x00003ffc // sin( 1 pi/16) S1
data8 0xfb14be7fbae58157 , 0x00003ffe // cos( 1 pi/16) C1
//
data8 0xc3ef1535754b168e , 0x00003ffd // sin( 2 pi/16) S2
data8 0xec835e79946a3146 , 0x00003ffe // cos( 2 pi/16) C2
//
data8 0x8e39d9cd73464364 , 0x00003ffe // sin( 3 pi/16) S3
data8 0xd4db3148750d181a , 0x00003ffe // cos( 3 pi/16) C3
//
data8 0xb504f333f9de6484 , 0x00003ffe // sin( 4 pi/16) S4
data8 0xb504f333f9de6484 , 0x00003ffe // cos( 4 pi/16) C4
//
data8 0xd4db3148750d181a , 0x00003ffe // sin( 5 pi/16) C3
data8 0x8e39d9cd73464364 , 0x00003ffe // cos( 5 pi/16) S3
//
data8 0xec835e79946a3146 , 0x00003ffe // sin( 6 pi/16) C2
data8 0xc3ef1535754b168e , 0x00003ffd // cos( 6 pi/16) S2
//
data8 0xfb14be7fbae58157 , 0x00003ffe // sin( 7 pi/16) C1
data8 0xc7c5c1e34d3055b3 , 0x00003ffc // cos( 7 pi/16) S1
//
data8 0x8000000000000000 , 0x00003fff // sin( 8 pi/16) C0
data8 0x0000000000000000 , 0x00000000 // cos( 8 pi/16) S0
//
data8 0xfb14be7fbae58157 , 0x00003ffe // sin( 9 pi/16) C1
data8 0xc7c5c1e34d3055b3 , 0x0000bffc // cos( 9 pi/16) -S1
//
data8 0xec835e79946a3146 , 0x00003ffe // sin(10 pi/16) C2
data8 0xc3ef1535754b168e , 0x0000bffd // cos(10 pi/16) -S2
//
data8 0xd4db3148750d181a , 0x00003ffe // sin(11 pi/16) C3
data8 0x8e39d9cd73464364 , 0x0000bffe // cos(11 pi/16) -S3
//
data8 0xb504f333f9de6484 , 0x00003ffe // sin(12 pi/16) S4
data8 0xb504f333f9de6484 , 0x0000bffe // cos(12 pi/16) -S4
//
data8 0x8e39d9cd73464364 , 0x00003ffe // sin(13 pi/16) S3
data8 0xd4db3148750d181a , 0x0000bffe // cos(13 pi/16) -C3
//
data8 0xc3ef1535754b168e , 0x00003ffd // sin(14 pi/16) S2
data8 0xec835e79946a3146 , 0x0000bffe // cos(14 pi/16) -C2
//
data8 0xc7c5c1e34d3055b3 , 0x00003ffc // sin(15 pi/16) S1
data8 0xfb14be7fbae58157 , 0x0000bffe // cos(15 pi/16) -C1
//
data8 0x0000000000000000 , 0x00000000 // sin(16 pi/16) S0
data8 0x8000000000000000 , 0x0000bfff // cos(16 pi/16) -C0
//
data8 0xc7c5c1e34d3055b3 , 0x0000bffc // sin(17 pi/16) -S1
data8 0xfb14be7fbae58157 , 0x0000bffe // cos(17 pi/16) -C1
//
data8 0xc3ef1535754b168e , 0x0000bffd // sin(18 pi/16) -S2
data8 0xec835e79946a3146 , 0x0000bffe // cos(18 pi/16) -C2
//
data8 0x8e39d9cd73464364 , 0x0000bffe // sin(19 pi/16) -S3
data8 0xd4db3148750d181a , 0x0000bffe // cos(19 pi/16) -C3
//
data8 0xb504f333f9de6484 , 0x0000bffe // sin(20 pi/16) -S4
data8 0xb504f333f9de6484 , 0x0000bffe // cos(20 pi/16) -S4
//
data8 0xd4db3148750d181a , 0x0000bffe // sin(21 pi/16) -C3
data8 0x8e39d9cd73464364 , 0x0000bffe // cos(21 pi/16) -S3
//
data8 0xec835e79946a3146 , 0x0000bffe // sin(22 pi/16) -C2
data8 0xc3ef1535754b168e , 0x0000bffd // cos(22 pi/16) -S2
//
data8 0xfb14be7fbae58157 , 0x0000bffe // sin(23 pi/16) -C1
data8 0xc7c5c1e34d3055b3 , 0x0000bffc // cos(23 pi/16) -S1
//
data8 0x8000000000000000 , 0x0000bfff // sin(24 pi/16) -C0
data8 0x0000000000000000 , 0x00000000 // cos(24 pi/16) S0
//
data8 0xfb14be7fbae58157 , 0x0000bffe // sin(25 pi/16) -C1
data8 0xc7c5c1e34d3055b3 , 0x00003ffc // cos(25 pi/16) S1
//
data8 0xec835e79946a3146 , 0x0000bffe // sin(26 pi/16) -C2
data8 0xc3ef1535754b168e , 0x00003ffd // cos(26 pi/16) S2
//
data8 0xd4db3148750d181a , 0x0000bffe // sin(27 pi/16) -C3
data8 0x8e39d9cd73464364 , 0x00003ffe // cos(27 pi/16) S3
//
data8 0xb504f333f9de6484 , 0x0000bffe // sin(28 pi/16) -S4
data8 0xb504f333f9de6484 , 0x00003ffe // cos(28 pi/16) S4
//
data8 0x8e39d9cd73464364 , 0x0000bffe // sin(29 pi/16) -S3
data8 0xd4db3148750d181a , 0x00003ffe // cos(29 pi/16) C3
//
data8 0xc3ef1535754b168e , 0x0000bffd // sin(30 pi/16) -S2
data8 0xec835e79946a3146 , 0x00003ffe // cos(30 pi/16) C2
//
data8 0xc7c5c1e34d3055b3 , 0x0000bffc // sin(31 pi/16) -S1
data8 0xfb14be7fbae58157 , 0x00003ffe // cos(31 pi/16) C1
//
data8 0x0000000000000000 , 0x00000000 // sin(32 pi/16) S0
data8 0x8000000000000000 , 0x00003fff // cos(32 pi/16) C0
LOCAL_OBJECT_END(double_sin_cos_beta_k4)
.section .text
////////////////////////////////////////////////////////
// There are two entry points: sin and cos
// If from sin, p8 is true
// If from cos, p9 is true
GLOBAL_IEEE754_ENTRY(sin)
{ .mlx
getf.exp sincos_r_signexp = f8
movl sincos_GR_sig_inv_pi_by_16 = 0xA2F9836E4E44152A // signd of 16/pi
}
{ .mlx
addl sincos_AD_1 = @ltoff(double_sincos_pi), gp
movl sincos_GR_rshf_2to61 = 0x47b8000000000000 // 1.1 2^(63+63-2)
}
;;
{ .mfi
ld8 sincos_AD_1 = [sincos_AD_1]
fnorm.s0 sincos_NORM_f8 = f8 // Normalize argument
cmp.eq p8,p9 = r0, r0 // set p8 (clear p9) for sin
}
{ .mib
mov sincos_GR_exp_2tom61 = 0xffff-61 // exponent of scale 2^-61
mov sincos_r_sincos = 0x0 // sincos_r_sincos = 0 for sin
br.cond.sptk _SINCOS_COMMON // go to common part
}
;;
GLOBAL_IEEE754_END(sin)
libm_alias_double_other (__sin, sin)
GLOBAL_IEEE754_ENTRY(cos)
{ .mlx
getf.exp sincos_r_signexp = f8
movl sincos_GR_sig_inv_pi_by_16 = 0xA2F9836E4E44152A // signd of 16/pi
}
{ .mlx
addl sincos_AD_1 = @ltoff(double_sincos_pi), gp
movl sincos_GR_rshf_2to61 = 0x47b8000000000000 // 1.1 2^(63+63-2)
}
;;
{ .mfi
ld8 sincos_AD_1 = [sincos_AD_1]
fnorm.s1 sincos_NORM_f8 = f8 // Normalize argument
cmp.eq p9,p8 = r0, r0 // set p9 (clear p8) for cos
}
{ .mib
mov sincos_GR_exp_2tom61 = 0xffff-61 // exp of scale 2^-61
mov sincos_r_sincos = 0x8 // sincos_r_sincos = 8 for cos
nop.b 999
}
;;
////////////////////////////////////////////////////////
// All entry points end up here.
// If from sin, sincos_r_sincos is 0 and p8 is true
// If from cos, sincos_r_sincos is 8 = 2^(k-1) and p9 is true
// We add sincos_r_sincos to N
///////////// Common sin and cos part //////////////////
_SINCOS_COMMON:
// Form two constants we need
// 16/pi * 2^-2 * 2^63, scaled by 2^61 since we just loaded the significand
// 1.1000...000 * 2^(63+63-2) to right shift int(W) into the low significand
{ .mfi
setf.sig sincos_SIG_INV_PI_BY_16_2TO61 = sincos_GR_sig_inv_pi_by_16
fclass.m p6,p0 = f8, 0xe7 // if x = 0,inf,nan
mov sincos_exp_limit = 0x1001a
}
{ .mlx
setf.d sincos_RSHF_2TO61 = sincos_GR_rshf_2to61
movl sincos_GR_rshf = 0x43e8000000000000 // 1.1 2^63
} // Right shift
;;
// Form another constant
// 2^-61 for scaling Nfloat
// 0x1001a is register_bias + 27.
// So if f8 >= 2^27, go to large argument routines
{ .mfi
alloc r32 = ar.pfs, 1, 4, 0, 0
fclass.m p11,p0 = f8, 0x0b // Test for x=unorm
mov sincos_GR_all_ones = -1 // For "inexect" constant create
}
{ .mib
setf.exp sincos_2TOM61 = sincos_GR_exp_2tom61
nop.i 999
(p6) br.cond.spnt _SINCOS_SPECIAL_ARGS
}
;;
// Load the two pieces of pi/16
// Form another constant
// 1.1000...000 * 2^63, the right shift constant
{ .mmb
ldfe sincos_Pi_by_16_1 = [sincos_AD_1],16
setf.d sincos_RSHF = sincos_GR_rshf
(p11) br.cond.spnt _SINCOS_UNORM // Branch if x=unorm
}
;;
_SINCOS_COMMON2:
// Return here if x=unorm
// Create constant used to set inexact
{ .mmi
ldfe sincos_Pi_by_16_2 = [sincos_AD_1],16
setf.sig fp_tmp = sincos_GR_all_ones
nop.i 999
};;
// Select exponent (17 lsb)
{ .mfi
ldfe sincos_Pi_by_16_3 = [sincos_AD_1],16
nop.f 999
dep.z sincos_r_exp = sincos_r_signexp, 0, 17
};;
// Polynomial coefficients (Q4, P4, Q3, P3, Q2, Q1, P2, P1) loading
// p10 is true if we must call routines to handle larger arguments
// p10 is true if f8 exp is >= 0x1001a (2^27)
{ .mmb
ldfpd sincos_P4,sincos_Q4 = [sincos_AD_1],16
cmp.ge p10,p0 = sincos_r_exp,sincos_exp_limit
(p10) br.cond.spnt _SINCOS_LARGE_ARGS // Go to "large args" routine
};;
// sincos_W = x * sincos_Inv_Pi_by_16
// Multiply x by scaled 16/pi and add large const to shift integer part of W to
// rightmost bits of significand
{ .mfi
ldfpd sincos_P3,sincos_Q3 = [sincos_AD_1],16
fma.s1 sincos_W_2TO61_RSH = sincos_NORM_f8,sincos_SIG_INV_PI_BY_16_2TO61,sincos_RSHF_2TO61
nop.i 999
};;
// get N = (int)sincos_int_Nfloat
// sincos_NFLOAT = Round_Int_Nearest(sincos_W)
// This is done by scaling back by 2^-61 and subtracting the shift constant
{ .mmf
getf.sig sincos_GR_n = sincos_W_2TO61_RSH
ldfpd sincos_P2,sincos_Q2 = [sincos_AD_1],16
fms.s1 sincos_NFLOAT = sincos_W_2TO61_RSH,sincos_2TOM61,sincos_RSHF
};;
// sincos_r = -sincos_Nfloat * sincos_Pi_by_16_1 + x
{ .mfi
ldfpd sincos_P1,sincos_Q1 = [sincos_AD_1],16
fnma.s1 sincos_r = sincos_NFLOAT, sincos_Pi_by_16_1, sincos_NORM_f8
nop.i 999
};;
// Add 2^(k-1) (which is in sincos_r_sincos) to N
{ .mmi
add sincos_GR_n = sincos_GR_n, sincos_r_sincos
;;
// Get M (least k+1 bits of N)
and sincos_GR_m = 0x1f,sincos_GR_n
nop.i 999
};;
// sincos_r = sincos_r -sincos_Nfloat * sincos_Pi_by_16_2
{ .mfi
nop.m 999
fnma.s1 sincos_r = sincos_NFLOAT, sincos_Pi_by_16_2, sincos_r
shl sincos_GR_32m = sincos_GR_m,5
};;
// Add 32*M to address of sin_cos_beta table
// For sin denorm. - set uflow
{ .mfi
add sincos_AD_2 = sincos_GR_32m, sincos_AD_1
(p8) fclass.m.unc p10,p0 = f8,0x0b
nop.i 999
};;
// Load Sin and Cos table value using obtained index m (sincosf_AD_2)
{ .mfi
ldfe sincos_Sm = [sincos_AD_2],16
nop.f 999
nop.i 999
};;
// get rsq = r*r
{ .mfi
ldfe sincos_Cm = [sincos_AD_2]
fma.s1 sincos_rsq = sincos_r, sincos_r, f0 // r^2 = r*r
nop.i 999
}
{ .mfi
nop.m 999
fmpy.s0 fp_tmp = fp_tmp,fp_tmp // forces inexact flag
nop.i 999
};;
// sincos_r_exact = sincos_r -sincos_Nfloat * sincos_Pi_by_16_3
{ .mfi
nop.m 999
fnma.s1 sincos_r_exact = sincos_NFLOAT, sincos_Pi_by_16_3, sincos_r
nop.i 999
};;
// Polynomials calculation
// P_1 = P4*r^2 + P3
// Q_2 = Q4*r^2 + Q3
{ .mfi
nop.m 999
fma.s1 sincos_P_temp1 = sincos_rsq, sincos_P4, sincos_P3
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 sincos_Q_temp1 = sincos_rsq, sincos_Q4, sincos_Q3
nop.i 999
};;
// get rcube = r^3 and S[m]*r^2
{ .mfi
nop.m 999
fmpy.s1 sincos_srsq = sincos_Sm,sincos_rsq
nop.i 999
}
{ .mfi
nop.m 999
fmpy.s1 sincos_rcub = sincos_r_exact, sincos_rsq
nop.i 999
};;
// Polynomials calculation
// Q_2 = Q_1*r^2 + Q2
// P_1 = P_1*r^2 + P2
{ .mfi
nop.m 999
fma.s1 sincos_Q_temp2 = sincos_rsq, sincos_Q_temp1, sincos_Q2
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 sincos_P_temp2 = sincos_rsq, sincos_P_temp1, sincos_P2
nop.i 999
};;
// Polynomials calculation
// Q = Q_2*r^2 + Q1
// P = P_2*r^2 + P1
{ .mfi
nop.m 999
fma.s1 sincos_Q = sincos_rsq, sincos_Q_temp2, sincos_Q1
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 sincos_P = sincos_rsq, sincos_P_temp2, sincos_P1
nop.i 999
};;
// Get final P and Q
// Q = Q*S[m]*r^2 + S[m]
// P = P*r^3 + r
{ .mfi
nop.m 999
fma.s1 sincos_Q = sincos_srsq,sincos_Q, sincos_Sm
nop.i 999
}
{ .mfi
nop.m 999
fma.s1 sincos_P = sincos_rcub,sincos_P, sincos_r_exact
nop.i 999
};;
// If sin(denormal), force underflow to be set
{ .mfi
nop.m 999
(p10) fmpy.d.s0 fp_tmp = sincos_NORM_f8,sincos_NORM_f8
nop.i 999
};;
// Final calculation
// result = C[m]*P + Q
{ .mfb
nop.m 999
fma.d.s0 f8 = sincos_Cm, sincos_P, sincos_Q
br.ret.sptk b0 // Exit for common path
};;
////////// x = 0/Inf/NaN path //////////////////
_SINCOS_SPECIAL_ARGS:
.pred.rel "mutex",p8,p9
// sin(+/-0) = +/-0
// sin(Inf) = NaN
// sin(NaN) = NaN
{ .mfi
nop.m 999
(p8) fma.d.s0 f8 = f8, f0, f0 // sin(+/-0,NaN,Inf)
nop.i 999
}
// cos(+/-0) = 1.0
// cos(Inf) = NaN
// cos(NaN) = NaN
{ .mfb
nop.m 999
(p9) fma.d.s0 f8 = f8, f0, f1 // cos(+/-0,NaN,Inf)
br.ret.sptk b0 // Exit for x = 0/Inf/NaN path
};;
_SINCOS_UNORM:
// Here if x=unorm
{ .mfb
getf.exp sincos_r_signexp = sincos_NORM_f8 // Get signexp of x
fcmp.eq.s0 p11,p0 = f8, f0 // Dummy op to set denorm flag
br.cond.sptk _SINCOS_COMMON2 // Return to main path
};;
GLOBAL_IEEE754_END(cos)
libm_alias_double_other (__cos, cos)
//////////// x >= 2^27 - large arguments routine call ////////////
LOCAL_LIBM_ENTRY(__libm_callout_sincos)
_SINCOS_LARGE_ARGS:
.prologue
{ .mfi
mov GR_SAVE_r_sincos = sincos_r_sincos // Save sin or cos
nop.f 999
.save ar.pfs,GR_SAVE_PFS
mov GR_SAVE_PFS = ar.pfs
}
;;
{ .mfi
mov GR_SAVE_GP = gp
nop.f 999
.save b0, GR_SAVE_B0
mov GR_SAVE_B0 = b0
}
.body
{ .mbb
setf.sig sincos_save_tmp = sincos_GR_all_ones// inexact set
nop.b 999
(p8) br.call.sptk.many b0 = __libm_sin_large# // sin(large_X)
};;
{ .mbb
cmp.ne p9,p0 = GR_SAVE_r_sincos, r0 // set p9 if cos
nop.b 999
(p9) br.call.sptk.many b0 = __libm_cos_large# // cos(large_X)
};;
{ .mfi
mov gp = GR_SAVE_GP
fma.d.s0 f8 = f8, f1, f0 // Round result to double
mov b0 = GR_SAVE_B0
}
// Force inexact set
{ .mfi
nop.m 999
fmpy.s0 sincos_save_tmp = sincos_save_tmp, sincos_save_tmp
nop.i 999
};;
{ .mib
nop.m 999
mov ar.pfs = GR_SAVE_PFS
br.ret.sptk b0 // Exit for large arguments routine call
};;
LOCAL_LIBM_END(__libm_callout_sincos)
.type __libm_sin_large#,@function
.global __libm_sin_large#
.type __libm_cos_large#,@function
.global __libm_cos_large#