.file "libm_sincos.s"
// Copyright (c) 2002 - 2005, Intel Corporation
// All rights reserved.
//
// Contributed 2002 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
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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
//==============================================================
// 02/01/02 Initial version
// 02/18/02 Large arguments processing routine is excluded.
// External interface entry points are added
// 03/13/02 Corrected restore of predicate registers
// 03/19/02 Added stack unwind around call to __libm_cis_large
// 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
// 02/11/04 cis is moved to the separate file.
// 03/31/05 Reformatted delimiters between data tables
//
// API
//==============================================================
// 1) void sincos(double, double*s, double*c)
// 2) __libm_sincos - internal LIBM function, that accepts
// argument in f8 and returns cosine through f8, sine through f9
//
// 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) + C[m] 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] + S[m] rsq Q
// S[m] Cos(r) = S[m] + s_rsq Q
// Q = S[m] + s_rsq Q
//
// Then,
//
// Answer = Q + C[m] P
// Registers used
//==============================================================
// general input registers:
// r14 -> r39
// predicate registers used:
// p6 -> p14
//
// floating-point registers used
// f9 -> f15
// f32 -> f67
// Assembly macros
//==============================================================
cis_Arg = f8
cis_Sin_res = f9
cis_Cos_res = f8
cis_NORM_f8 = f10
cis_W = f11
cis_int_Nfloat = f12
cis_Nfloat = f13
cis_r = f14
cis_rsq = f15
cis_rcub = f32
cis_Inv_Pi_by_16 = f33
cis_Pi_by_16_hi = f34
cis_Pi_by_16_lo = f35
cis_Inv_Pi_by_64 = f36
cis_Pi_by_16_lowest = f37
cis_r_exact = f38
cis_P1 = f39
cis_Q1 = f40
cis_P2 = f41
cis_Q2 = f42
cis_P3 = f43
cis_Q3 = f44
cis_P4 = f45
cis_Q4 = f46
cis_P_temp1 = f47
cis_P_temp2 = f48
cis_Q_temp1 = f49
cis_Q_temp2 = f50
cis_P = f51
cis_SIG_INV_PI_BY_16_2TO61 = f52
cis_RSHF_2TO61 = f53
cis_RSHF = f54
cis_2TOM61 = f55
cis_NFLOAT = f56
cis_W_2TO61_RSH = f57
cis_tmp = f58
cis_Sm_sin = f59
cis_Cm_sin = f60
cis_Sm_cos = f61
cis_Cm_cos = f62
cis_srsq_sin = f63
cis_srsq_cos = f64
cis_Q_sin = f65
cis_Q_cos = f66
cis_Q = f67
/////////////////////////////////////////////////////////////
cis_pResSin = r33
cis_pResCos = r34
cis_GR_sig_inv_pi_by_16 = r14
cis_GR_rshf_2to61 = r15
cis_GR_rshf = r16
cis_GR_exp_2tom61 = r17
cis_GR_n = r18
cis_GR_n_sin = r19
cis_exp_limit = r20
cis_r_signexp = r21
cis_AD_1 = r22
cis_r_sincos = r23
cis_r_exp = r24
cis_r_17_ones = r25
cis_GR_m_sin = r26
cis_GR_32m_sin = r26
cis_GR_n_cos = r27
cis_GR_m_cos = r28
cis_GR_32m_cos = r28
cis_AD_2_sin = r29
cis_AD_2_cos = r30
cis_gr_tmp = r31
GR_SAVE_B0 = r35
GR_SAVE_GP = r36
rB0_SAVED = r37
GR_SAVE_PFS = r38
GR_SAVE_PR = r39
RODATA
.align 16
// Pi/16 parts
LOCAL_OBJECT_START(double_cis_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_cis_pi)
// Coefficients for polynomials
LOCAL_OBJECT_START(double_cis_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_cis_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
GLOBAL_IEEE754_ENTRY(sincos)
// cis_GR_sig_inv_pi_by_16 = significand of 16/pi
{ .mlx
getf.exp cis_r_signexp = cis_Arg
movl cis_GR_sig_inv_pi_by_16 = 0xA2F9836E4E44152A
}
// cis_GR_rshf_2to61 = 1.1000 2^(63+63-2)
{ .mlx
addl cis_AD_1 = @ltoff(double_cis_pi), gp
movl cis_GR_rshf_2to61 = 0x47b8000000000000
};;
{ .mfi
ld8 cis_AD_1 = [cis_AD_1]
fnorm.s1 cis_NORM_f8 = cis_Arg
cmp.eq p13, p14 = r0, r0 // p13 set for sincos
}
// cis_GR_exp_2tom61 = exponent of scaling factor 2^-61
{ .mib
mov cis_GR_exp_2tom61 = 0xffff-61
nop.i 0
br.cond.sptk _CIS_COMMON
};;
GLOBAL_IEEE754_END(sincos)
libm_alias_double_other (__sincos, sincos)
GLOBAL_LIBM_ENTRY(__libm_sincos)
// cis_GR_sig_inv_pi_by_16 = significand of 16/pi
{ .mlx
getf.exp cis_r_signexp = cis_Arg
movl cis_GR_sig_inv_pi_by_16 = 0xA2F9836E4E44152A
}
// cis_GR_rshf_2to61 = 1.1000 2^(63+63-2)
{ .mlx
addl cis_AD_1 = @ltoff(double_cis_pi), gp
movl cis_GR_rshf_2to61 = 0x47b8000000000000
};;
// p14 set for __libm_sincos and cis
{ .mfi
ld8 cis_AD_1 = [cis_AD_1]
fnorm.s1 cis_NORM_f8 = cis_Arg
cmp.eq p14, p13 = r0, r0
}
// cis_GR_exp_2tom61 = exponent of scaling factor 2^-61
{ .mib
mov cis_GR_exp_2tom61 = 0xffff-61
nop.i 0
nop.b 0
};;
_CIS_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
// fcmp used to set denormal, and invalid on snans
{ .mfi
setf.sig cis_SIG_INV_PI_BY_16_2TO61 = cis_GR_sig_inv_pi_by_16
fclass.m p6,p0 = cis_Arg, 0xe7 // if x=0,inf,nan
addl cis_gr_tmp = -1, r0
}
// 1.1000 2^63 for right shift
{ .mlx
setf.d cis_RSHF_2TO61 = cis_GR_rshf_2to61
movl cis_GR_rshf = 0x43e8000000000000
};;
// Form another constant
// 2^-61 for scaling Nfloat
// 0x1001a is register_bias + 27.
// So if f8 >= 2^27, go to large arguments routine
{ .mfi
alloc GR_SAVE_PFS = ar.pfs, 3, 5, 0, 0
fclass.m p11,p0 = cis_Arg, 0x0b // Test for x=unorm
mov cis_exp_limit = 0x1001a
}
{ .mib
setf.exp cis_2TOM61 = cis_GR_exp_2tom61
nop.i 0
(p6) br.cond.spnt _CIS_SPECIAL_ARGS
};;
// Load the two pieces of pi/16
// Form another constant
// 1.1000...000 * 2^63, the right shift constant
{ .mmb
ldfe cis_Pi_by_16_hi = [cis_AD_1],16
setf.d cis_RSHF = cis_GR_rshf
(p11) br.cond.spnt _CIS_UNORM // Branch if x=unorm
};;
_CIS_COMMON2:
// Return here if x=unorm
// Create constant inexact set
{ .mmi
ldfe cis_Pi_by_16_lo = [cis_AD_1],16
setf.sig cis_tmp = cis_gr_tmp
nop.i 0
};;
// Select exponent (17 lsb)
{ .mfi
ldfe cis_Pi_by_16_lowest = [cis_AD_1],16
nop.f 0
dep.z cis_r_exp = cis_r_signexp, 0, 17
};;
// Start loading P, Q coefficients
// p10 is true if we must call routines to handle larger arguments
// p10 is true if f8 exp is > 0x1001a
{ .mmb
ldfpd cis_P4,cis_Q4 = [cis_AD_1],16
cmp.ge p10, p0 = cis_r_exp, cis_exp_limit
(p10) br.cond.spnt _CIS_LARGE_ARGS // go to |x| >= 2^27 path
};;
// cis_W = x * cis_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 cis_P3,cis_Q3 = [cis_AD_1],16
fma.s1 cis_W_2TO61_RSH = cis_NORM_f8,cis_SIG_INV_PI_BY_16_2TO61,cis_RSHF_2TO61
nop.i 0
};;
// get N = (int)cis_int_Nfloat
// cis_NFLOAT = Round_Int_Nearest(cis_W)
{ .mmf
getf.sig cis_GR_n = cis_W_2TO61_RSH
ldfpd cis_P2,cis_Q2 = [cis_AD_1],16
fms.s1 cis_NFLOAT = cis_W_2TO61_RSH,cis_2TOM61,cis_RSHF
};;
// cis_r = -cis_Nfloat * cis_Pi_by_16_hi + x
{ .mfi
ldfpd cis_P1,cis_Q1 = [cis_AD_1], 16
fnma.s1 cis_r = cis_NFLOAT,cis_Pi_by_16_hi,cis_NORM_f8
nop.i 0
};;
// Add 2^(k-1) (which is in cis_r_sincos) to N
{ .mmi
add cis_GR_n_cos = 0x8, cis_GR_n
;;
//Get M (least k+1 bits of N)
and cis_GR_m_sin = 0x1f,cis_GR_n
and cis_GR_m_cos = 0x1f,cis_GR_n_cos
};;
{ .mmi
nop.m 0
nop.m 0
shl cis_GR_32m_sin = cis_GR_m_sin,5
};;
// Add 32*M to address of sin_cos_beta table
// cis_r = cis_r -cis_Nfloat * cis_Pi_by_16_lo
{ .mfi
add cis_AD_2_sin = cis_GR_32m_sin, cis_AD_1
fnma.s1 cis_r = cis_NFLOAT, cis_Pi_by_16_lo, cis_r
shl cis_GR_32m_cos = cis_GR_m_cos,5
};;
// Add 32*M to address of sin_cos_beta table
{ .mmf
ldfe cis_Sm_sin = [cis_AD_2_sin],16
add cis_AD_2_cos = cis_GR_32m_cos, cis_AD_1
fclass.m.unc p10,p0 = cis_Arg,0x0b // den. input - uflow
};;
{ .mfi
ldfe cis_Sm_cos = [cis_AD_2_cos], 16
nop.i 0
};;
{ .mfi
ldfe cis_Cm_sin = [cis_AD_2_sin]
fma.s1 cis_rsq = cis_r, cis_r, f0 // get r^2
nop.i 0
}
// fmpy forces inexact flag
{ .mfi
nop.m 0
fmpy.s0 cis_tmp = cis_tmp,cis_tmp
nop.i 0
};;
{ .mfi
nop.m 0
fnma.s1 cis_r_exact = cis_NFLOAT, cis_Pi_by_16_lowest, cis_r
nop.i 0
};;
{ .mfi
ldfe cis_Cm_cos = [cis_AD_2_cos]
fma.s1 cis_P_temp1 = cis_rsq, cis_P4, cis_P3
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 cis_Q_temp1 = cis_rsq, cis_Q4, cis_Q3
nop.i 0
};;
{ .mfi
nop.m 0
fmpy.s1 cis_srsq_sin = cis_Sm_sin, cis_rsq
nop.i 0
}
{ .mfi
nop.m 0
fmpy.s1 cis_srsq_cos = cis_Sm_cos,cis_rsq
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 cis_Q_temp2 = cis_rsq, cis_Q_temp1, cis_Q2
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 cis_P_temp2 = cis_rsq, cis_P_temp1, cis_P2
nop.i 0
};;
{ .mfi
nop.m 0
fmpy.s1 cis_rcub = cis_r_exact, cis_rsq // get r^3
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 cis_Q = cis_rsq, cis_Q_temp2, cis_Q1
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 cis_P = cis_rsq, cis_P_temp2, cis_P1
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 cis_Q_sin = cis_srsq_sin,cis_Q, cis_Sm_sin
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 cis_Q_cos = cis_srsq_cos,cis_Q, cis_Sm_cos
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 cis_P = cis_rcub,cis_P, cis_r_exact // final P
nop.i 0
};;
// If den. arg, force underflow to be set
{ .mfi
nop.m 0
(p10) fmpy.d.s0 cis_tmp = cis_Arg,cis_Arg
nop.i 0
};;
{ .mfi
nop.m 0
fma.d.s0 cis_Sin_res = cis_Cm_sin,cis_P,cis_Q_sin//Final sin
nop.i 0
}
{ .mfb
nop.m 0
fma.d.s0 cis_Cos_res = cis_Cm_cos,cis_P,cis_Q_cos//Final cos
(p14) br.ret.sptk b0 // common exit for __libm_sincos and cis main path
};;
{ .mmb
stfd [cis_pResSin] = cis_Sin_res
stfd [cis_pResCos] = cis_Cos_res
br.ret.sptk b0 // common exit for sincos main path
};;
_CIS_SPECIAL_ARGS:
// sin(+/-0) = +/-0
// sin(Inf) = NaN
// sin(NaN) = NaN
{ .mfi
nop.m 999
fma.d.s0 cis_Sin_res = cis_Arg, f0, f0 // sinf(+/-0,NaN,Inf)
nop.i 999
};;
// cos(+/-0) = 1.0
// cos(Inf) = NaN
// cos(NaN) = NaN
{ .mfb
nop.m 999
fma.d.s0 cis_Cos_res = cis_Arg, f0, f1 // cosf(+/-0,NaN,Inf)
(p14) br.ret.sptk b0 //spec exit for __libm_sincos and cis main path
};;
{ .mmb
stfd [cis_pResSin] = cis_Sin_res
stfd [cis_pResCos] = cis_Cos_res
br.ret.sptk b0 // common exit for sincos main path
};;
_CIS_UNORM:
// Here if x=unorm
{ .mfb
getf.exp cis_r_signexp = cis_NORM_f8 // Get signexp of x
fcmp.eq.s0 p11,p0 = cis_Arg, f0 // Dummy op to set denorm
br.cond.sptk _CIS_COMMON2 // Return to main path
};;
GLOBAL_LIBM_END(__libm_sincos)
//// |x| > 2^27 path ///////
.proc _CIS_LARGE_ARGS
_CIS_LARGE_ARGS:
.prologue
{ .mfi
nop.m 0
nop.f 0
.save ar.pfs, GR_SAVE_PFS
mov GR_SAVE_PFS = ar.pfs
}
;;
{ .mfi
mov GR_SAVE_GP = gp
nop.f 0
.save b0, GR_SAVE_B0
mov GR_SAVE_B0 = b0
};;
.body
// Call of huge arguments sincos
{ .mib
nop.m 0
mov GR_SAVE_PR = pr
br.call.sptk b0 = __libm_sincos_large
};;
{ .mfi
mov gp = GR_SAVE_GP
nop.f 0
mov pr = GR_SAVE_PR, 0x1fffe
}
;;
{ .mfi
nop.m 0
nop.f 0
mov b0 = GR_SAVE_B0
}
;;
{ .mfi
nop.m 0
fma.d.s0 cis_Cos_res = cis_Cos_res, f1, f0
mov ar.pfs = GR_SAVE_PFS
}
{ .mfb
nop.m 0
fma.d.s0 cis_Sin_res = cis_Sin_res, f1, f0
(p14) br.ret.sptk b0 // exit for |x| > 2^27 path (__libm_sincos and cis)
};;
{ .mmb
stfd [cis_pResSin] = cis_Sin_res
stfd [cis_pResCos] = cis_Cos_res
br.ret.sptk b0 // exit for sincos |x| > 2^27 path
};;
.endp _CIS_LARGE_ARGS
.type __libm_sincos_large#,@function
.global __libm_sincos_large#