.file "atanhf.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
// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
// 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
//==============================================================
// 05/22/01 Initial version
// 05/20/02 Cleaned up namespace and sf0 syntax
// 08/06/02 Improved Itanium 2 performance
// 02/06/03 Reordered header: .section, .global, .proc, .align
// 05/26/03 Improved performance, fixed to handle unorms
//
// API
//==============================================================
// float atanhf(float)
//
// Overview of operation
//==============================================================
// Background
//
//
// There are 7 paths:
// 1. x = +/-0.0
// Return atanhf(x) = +/-0.0
//
// 2. 0.0 < |x| <= MAX_DENORMAL_ABS
// Return atanhf(x) = x + sign(x)*x^2
//
// 3. MAX_DENORMAL_ABS < |x| < 2^(-20)
// Return atanhf(x) = Pol3(x), where Pol3(x) = x + x^3
//
// 4. 2^(-20) <= |x| < 1
// Return atanhf(x) = 0.5 * (log(1 + x) - log(1 - x))
// Algorithm description for log function see below.
//
// 5. |x| = 1
// Return atanhf(x) = sign(x) * +INF
//
// 6. 1 < |x| <= +INF
// Return atanhf(x) = QNaN
//
// 7. x = [S,Q]NaN
// Return atanhf(x) = QNaN
//
//==============================================================
// Algorithm Description for log(x) function
//
// Consider x = 2^N * 1.f1 f2 f3 f4...f63
// log(x) = log(x * frcpa(x) / frcpa(x))
// = log(x * frcpa(x)) + log(1/frcpa(x))
// = log(x * frcpa(x)) - log(frcpa(x))
//
// frcpa(x) = 2^(-N) * frcpa(1.f1 f2 ... f63)
//
// -log(frcpa(x)) = -log(C)
// = -log(2^(-N)) - log(frcpa(1.f1 f2 ... f63))
//
// -log(frcpa(x)) = -log(C)
// = N*log2 - log(frcpa(1.f1 f2 ... f63))
//
//
// log(x) = log(1/frcpa(x)) + log(frcpa(x) x)
//
// log(x) = N*log2 + log(1./frcpa(1.f1 f2 ... f63)) + log(x * frcpa(x))
// log(x) = N*log2 + T + log(frcpa(x) x)
//
// Log(x) = N*log2 + T + log(C * x)
//
// C * x = 1 + r
//
// log(x) = N*log2 + T + log(1 + r)
// log(x) = N*log2 + T + Series(r)
//
// 1.f1 f2 ... f8 has 256 entries.
// They are 1 + k/2^8, k = 0 ... 255
// These 256 values are the table entries.
//
// Implementation
//==============================================================
// C = frcpa(x)
// r = C * x - 1
//
// Form rseries = r + P1*r^2 + P2*r^3 + P3*r^4
//
// x = f * 2*N where f is 1.f_1f_2f_3...f_63
// Nfloat = float(n) where n is the true unbiased exponent
// pre-index = f_1f_2....f_8
// index = pre_index * 16
// get the dxt table entry at index + offset = T
//
// result = (T + Nfloat * log(2)) + rseries
//
// The T table is calculated as follows
// Form x_k = 1 + k/2^8 where k goes from 0... 255
// y_k = frcpa(x_k)
// log(1/y_k) in quad and round to double-extended
// Registers used
//==============================================================
// Floating Point registers used:
// f8, input
// f32 -> f59
// General registers used:
// r14 -> r29, r32 -> r39
// Predicate registers used:
// p6 -> p9
// p6 to filter out case when |x| >= 1
// p7 to filter out case when x = [Q,S]NaN or +/-0
// p8 to filter out case when |x| < 2^(-20)
// p9 to filter out case when x = denormal
// Assembly macros
//==============================================================
DataPtr = r14
RcpTablePtrM = r15
RcpTablePtrP = r16
rExpbMask = r17
rBias = r18
rNearZeroBound = r19
rArgSExpb = r20
rArgExpb = r21
rExpbm = r22
rExpbp = r23
rSigm = r24
rSigp = r25
rNm = r26
rNp = r27
rIndm = r28
rIndp = r29
GR_SAVE_B0 = r33
GR_SAVE_GP = r34
GR_SAVE_PFS = r35
GR_Parameter_X = r36
GR_Parameter_Y = r37
GR_Parameter_RESULT = r38
atanh_GR_tag = r39
//==============================================================
fOneMx = f33
fOnePx = f34
fRm2 = f35
fRm3 = f36
fRp2 = f37
fRp3 = f38
fRcpM = f39
fRcpP = f40
fRp = f41
fRm = f42
fN4CvtM = f43
fN4CvtP = f44
fNm = f45
fNp = f46
fLogTm = f47
fLogTp = f48
fLog2 = f49
fArgAbs = f50
fNormX = f50
fP32m = f51
fP32p = f52
fP10m = f53
fP10p = f54
fX2 = f55
fP3 = f56
fP2 = f57
fP1 = f58
fHalf = f59
// Data tables
//==============================================================
RODATA
.align 16
LOCAL_OBJECT_START(atanhf_data)
data8 0xbfc0001008f39d59 // P3*0.5
data8 0x3fc5556073e0c45a // P2*0.5
data8 0xbfcffffffffaea15 // P1*0.5
data8 0x3fe0000000000000 // 0.5
data8 0x3fd62e42fefa39ef // 0.5*ln(2)
data8 0x0000000000000000 // pad
LOCAL_OBJECT_END(atanhf_data)
LOCAL_OBJECT_START(atanhf_data2)
data8 0x3f50040155d5889e //log(1/frcpa(1+0/256))/2
data8 0x3f68121214586b54 //log(1/frcpa(1+1/256))/2
data8 0x3f741929f96832f0 //log(1/frcpa(1+2/256))/2
data8 0x3f7c317384c75f06 //log(1/frcpa(1+3/256))/2
data8 0x3f81a6b91ac73386 //log(1/frcpa(1+4/256))/2
data8 0x3f85ba9a5d9ac039 //log(1/frcpa(1+5/256))/2
data8 0x3f89d2a8074325f4 //log(1/frcpa(1+6/256))/2
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data8 0x3fa0ec139c5da601 //log(1/frcpa(1+17/256))/2
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data8 0x3fc335504b355a37 //log(1/frcpa(1+89/256))/2
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data8 0x3fd128a24f1d9aff //log(1/frcpa(1+181/256))/2
data8 0x3fd1365252bf0865 //log(1/frcpa(1+182/256))/2
data8 0x3fd14ae558b4a92d //log(1/frcpa(1+183/256))/2
data8 0x3fd15f85a19c765b //log(1/frcpa(1+184/256))/2
data8 0x3fd16d4d38c119fa //log(1/frcpa(1+185/256))/2
data8 0x3fd18203c20dd133 //log(1/frcpa(1+186/256))/2
data8 0x3fd196c7bc4b1f3b //log(1/frcpa(1+187/256))/2
data8 0x3fd1a4a738b7a33c //log(1/frcpa(1+188/256))/2
data8 0x3fd1b981c0c9653d //log(1/frcpa(1+189/256))/2
data8 0x3fd1ce69e8bb106b //log(1/frcpa(1+190/256))/2
data8 0x3fd1dc619de06944 //log(1/frcpa(1+191/256))/2
data8 0x3fd1f160a2ad0da4 //log(1/frcpa(1+192/256))/2
data8 0x3fd2066d7740737e //log(1/frcpa(1+193/256))/2
data8 0x3fd2147dba47a394 //log(1/frcpa(1+194/256))/2
data8 0x3fd229a1bc5ebac3 //log(1/frcpa(1+195/256))/2
data8 0x3fd237c1841a502e //log(1/frcpa(1+196/256))/2
data8 0x3fd24cfce6f80d9a //log(1/frcpa(1+197/256))/2
data8 0x3fd25b2c55cd5762 //log(1/frcpa(1+198/256))/2
data8 0x3fd2707f4d5f7c41 //log(1/frcpa(1+199/256))/2
data8 0x3fd285e0842ca384 //log(1/frcpa(1+200/256))/2
data8 0x3fd294294708b773 //log(1/frcpa(1+201/256))/2
data8 0x3fd2a9a2670aff0c //log(1/frcpa(1+202/256))/2
data8 0x3fd2b7fb2c8d1cc1 //log(1/frcpa(1+203/256))/2
data8 0x3fd2c65a6395f5f5 //log(1/frcpa(1+204/256))/2
data8 0x3fd2dbf557b0df43 //log(1/frcpa(1+205/256))/2
data8 0x3fd2ea64c3f97655 //log(1/frcpa(1+206/256))/2
data8 0x3fd3001823684d73 //log(1/frcpa(1+207/256))/2
data8 0x3fd30e97e9a8b5cd //log(1/frcpa(1+208/256))/2
data8 0x3fd32463ebdd34ea //log(1/frcpa(1+209/256))/2
data8 0x3fd332f4314ad796 //log(1/frcpa(1+210/256))/2
data8 0x3fd348d90e7464d0 //log(1/frcpa(1+211/256))/2
data8 0x3fd35779f8c43d6e //log(1/frcpa(1+212/256))/2
data8 0x3fd36621961a6a99 //log(1/frcpa(1+213/256))/2
data8 0x3fd37c299f3c366a //log(1/frcpa(1+214/256))/2
data8 0x3fd38ae2171976e7 //log(1/frcpa(1+215/256))/2
data8 0x3fd399a157a603e7 //log(1/frcpa(1+216/256))/2
data8 0x3fd3afccfe77b9d1 //log(1/frcpa(1+217/256))/2
data8 0x3fd3be9d503533b5 //log(1/frcpa(1+218/256))/2
data8 0x3fd3cd7480b4a8a3 //log(1/frcpa(1+219/256))/2
data8 0x3fd3e3c43918f76c //log(1/frcpa(1+220/256))/2
data8 0x3fd3f2acb27ed6c7 //log(1/frcpa(1+221/256))/2
data8 0x3fd4019c2125ca93 //log(1/frcpa(1+222/256))/2
data8 0x3fd4181061389722 //log(1/frcpa(1+223/256))/2
data8 0x3fd42711518df545 //log(1/frcpa(1+224/256))/2
data8 0x3fd436194e12b6bf //log(1/frcpa(1+225/256))/2
data8 0x3fd445285d68ea69 //log(1/frcpa(1+226/256))/2
data8 0x3fd45bcc464c893a //log(1/frcpa(1+227/256))/2
data8 0x3fd46aed21f117fc //log(1/frcpa(1+228/256))/2
data8 0x3fd47a1527e8a2d3 //log(1/frcpa(1+229/256))/2
data8 0x3fd489445efffccc //log(1/frcpa(1+230/256))/2
data8 0x3fd4a018bcb69835 //log(1/frcpa(1+231/256))/2
data8 0x3fd4af5a0c9d65d7 //log(1/frcpa(1+232/256))/2
data8 0x3fd4bea2a5bdbe87 //log(1/frcpa(1+233/256))/2
data8 0x3fd4cdf28f10ac46 //log(1/frcpa(1+234/256))/2
data8 0x3fd4dd49cf994058 //log(1/frcpa(1+235/256))/2
data8 0x3fd4eca86e64a684 //log(1/frcpa(1+236/256))/2
data8 0x3fd503c43cd8eb68 //log(1/frcpa(1+237/256))/2
data8 0x3fd513356667fc57 //log(1/frcpa(1+238/256))/2
data8 0x3fd522ae0738a3d8 //log(1/frcpa(1+239/256))/2
data8 0x3fd5322e26867857 //log(1/frcpa(1+240/256))/2
data8 0x3fd541b5cb979809 //log(1/frcpa(1+241/256))/2
data8 0x3fd55144fdbcbd62 //log(1/frcpa(1+242/256))/2
data8 0x3fd560dbc45153c7 //log(1/frcpa(1+243/256))/2
data8 0x3fd5707a26bb8c66 //log(1/frcpa(1+244/256))/2
data8 0x3fd587f60ed5b900 //log(1/frcpa(1+245/256))/2
data8 0x3fd597a7977c8f31 //log(1/frcpa(1+246/256))/2
data8 0x3fd5a760d634bb8b //log(1/frcpa(1+247/256))/2
data8 0x3fd5b721d295f10f //log(1/frcpa(1+248/256))/2
data8 0x3fd5c6ea94431ef9 //log(1/frcpa(1+249/256))/2
data8 0x3fd5d6bb22ea86f6 //log(1/frcpa(1+250/256))/2
data8 0x3fd5e6938645d390 //log(1/frcpa(1+251/256))/2
data8 0x3fd5f673c61a2ed2 //log(1/frcpa(1+252/256))/2
data8 0x3fd6065bea385926 //log(1/frcpa(1+253/256))/2
data8 0x3fd6164bfa7cc06b //log(1/frcpa(1+254/256))/2
data8 0x3fd62643fecf9743 //log(1/frcpa(1+255/256))/2
LOCAL_OBJECT_END(atanhf_data2)
.section .text
GLOBAL_LIBM_ENTRY(atanhf)
{ .mfi
getf.exp rArgSExpb = f8
fclass.m p9,p0 = f8, 0x0b // is arg denormal ?
mov rExpbMask = 0x1ffff
}
{ .mfi
addl DataPtr = @ltoff(atanhf_data), gp
fnma.s1 fOneMx = f8, f1, f1 // 1 - x
mov rBias = 0xffff
}
;;
{ .mfi
nop.m 0
fclass.m p7,p0 = f8, 0xc7 // is arg NaN or +/-0 ?
mov rNearZeroBound = 0xffeb // 2^(-20)
}
{ .mfi
ld8 DataPtr = [DataPtr]
fma.s1 fOnePx = f8, f1, f1 // 1 + x
nop.i 0
}
;;
{ .mfb
nop.m 0
fnorm.s1 fNormX = f8 // Normalize x
(p9) br.cond.spnt ATANH_UNORM // Branch if x=unorm
}
;;
ATANH_COMMON:
// Return here if x=unorm and not denorm
{ .mfi
ldfpd fP3, fP2 = [DataPtr], 16
fma.s1 fX2 = f8, f8, f0 // x^2
nop.i 0
}
{ .mfb
nop.m 0
(p7) fma.s.s0 f8 = f8,f1,f8 // NaN or +/-0
(p7) br.ret.spnt b0
}
;;
{ .mfi
ldfpd fP1, fHalf = [DataPtr], 16
frcpa.s1 fRcpM, p9 = f1, fOneMx // rcpm = frcpa(1 - x)
nop.i 0
}
;;
{ .mfi
getf.exp rExpbm = fOneMx
frcpa.s1 fRcpP, p0 = f1, fOnePx // rcpp = frcpa(1 + x)
// biased exponent
and rArgExpb = rArgSExpb, rExpbMask
}
;;
{ .mmi
getf.exp rExpbp = fOnePx
// is |x| < 2^(-20) ?
cmp.gt p8,p0 = rNearZeroBound, rArgExpb
cmp.ge p6,p0 = rArgExpb, rBias // is |x| >= 1 ?
}
;;
{ .mmb
getf.sig rSigm = fOneMx
nop.m 0
(p6) br.cond.spnt atanhf_ge_one
}
;;
{ .mfb
getf.sig rSigp = fOnePx
(p8) fma.s.s0 f8 = fX2, f8, f8 // x + x^3
(p8) br.ret.spnt b0 // Exit for MAX_DENORM_ABS < |x| < 2^-20
}
;;
{ .mfi
ldfd fLog2 = [DataPtr], 16
fms.s1 fRm = fRcpM, fOneMx, f1 // rm = rcpm * (1 - x) - 1
nop.i 0
}
;;
{ .mmf
// (1 - x) is always positive here and we need not mask sign bit
sub rNm = rExpbm, rBias
// (1 + x) is always positive here and we need not mask sign bit
sub rNp = rExpbp, rBias
fms.s1 fRp = fRcpP, fOnePx, f1 // rp = rcpp * (1 + x) - 1
}
;;
{ .mmi
setf.sig fN4CvtM = rNm
setf.sig fN4CvtP = rNp
extr.u rIndm = rSigm,55,8 // Extract 8 bits
}
;;
{ .mmi
shladd RcpTablePtrM = rIndm, 3, DataPtr
nop.m 0
extr.u rIndp = rSigp,55,8 // Extract 8 bits
}
;;
{ .mmi
ldfd fLogTm = [RcpTablePtrM]
shladd RcpTablePtrP = rIndp, 3, DataPtr
nop.i 0
}
;;
{ .mfi
ldfd fLogTp = [RcpTablePtrP]
fma.s1 fRm2 = fRm, fRm, f0 // rm^2
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 fP32m = fP3, fRm, fP2 // P3*rm + P2
nop.i 0
}
;;
{ .mfi
nop.m 0
fma.s1 fRp2 = fRp, fRp, f0 // rp^2
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 fP10m = fP1, fRm, fHalf // P1*rm + 1
nop.i 0
}
;;
{ .mfi
nop.m 0
fma.s1 fP32p = fP3, fRp, fP2 // P3*rp + P2
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 fP10p = fP1, fRp, fHalf // P1*rp + 1
nop.i 0
}
;;
{ .mfi
nop.m 0
fcvt.xf fNm = fN4CvtM
nop.i 0
}
{ .mfi
nop.m 0
fcvt.xf fNp = fN4CvtP
nop.i 0
}
;;
{ .mfi
nop.m 0
// (P3*rm + P2)*rm^2 + (P1*rm + 1)
fma.s1 fP32m = fP32m, fRm2, fP10m
nop.i 0
}
{ .mfi
nop.m 0
// (P3*rp + P2)*rp^2 + (P1*rp + 1)
fma.s1 fP32p = fP32p, fRp2, fP10p
nop.i 0
}
;;
{ .mfi
nop.m 0
// Nm*ln(2)/2 + Tm/2
fma.s1 fLogTm = fNm, fLog2, fLogTm
nop.i 0
}
{ .mfi
nop.m 0
// Np*ln(2)/2 + Tp/2
fma.s1 fLogTp = fNp, fLog2, fLogTp
nop.i 0
}
;;
{ .mfi
nop.m 0
// ((P3*rm + P2)*rm^2 + (P3*rm + 1))*0.5*rm + (Nm*ln(2)/2 + Tm/2)
fma.d.s1 fP32m = fP32m, fRm, fLogTm
nop.i 0
}
{ .mfi
nop.m 0
// ((P3*rp + P2)*rp^2 + (P3*rp + 1))*0.5*rp + (Np*ln(2)/2 + Tp/2)
fma.d.s1 fP32p = fP32p, fRp, fLogTp
nop.i 0
}
;;
{ .mfb
nop.m 0
// atanhf(x) = 0.5 * (log(1 + x) - log(1 - x))
fnma.s.s0 f8 = fP32m, f1, fP32p
br.ret.sptk b0 // Exit for 2^(-20) <= |x| < 1.0
}
;;
ATANH_UNORM:
// Here if x=unorm
{ .mfi
getf.exp rArgSExpb = fNormX // Recompute if x unorm
fclass.m p0,p9 = fNormX, 0x0b // Test x denorm
nop.i 0
}
;;
{ .mfb
nop.m 0
fcmp.lt.s0 p10,p11 = f8, f0 // Set denormal flag
(p9) br.cond.sptk ATANH_COMMON // Continue if x unorm and not denorm
}
;;
.pred.rel "mutex",p6,p7
{ .mfi
nop.m 0
(p6) fnma.s.s0 f8 = f8,f8,f8 // Result x-x^2 if x=-denorm
nop.i 0
}
{ .mfb
nop.m 0
(p7) fma.s.s0 f8 = f8,f8,f8 // Result x+x^2 if x=+denorm
br.ret.spnt b0 // Exit if denorm
}
;;
// Here if |x| >= 1.0
atanhf_ge_one:
{ .mfi
alloc r32 = ar.pfs,1,3,4,0
fmerge.s fArgAbs = f0, f8 // Form |x|
nop.i 0
}
;;
{ .mfi
nop.m 0
fmerge.s f10 = f8, f8 // Save input for error call
nop.i 0
}
;;
{ .mfi
nop.m 0
fcmp.eq.s1 p6,p7 = fArgAbs, f1 // Test for |x| = 1.0
nop.i 0
}
;;
// Set error tag and result, and raise invalid flag if |x| > 1.0
{ .mfi
(p7) mov atanh_GR_tag = 133
(p7) frcpa.s0 f8, p0 = f0, f0 // Get QNaN, and raise invalid
nop.i 0
}
;;
// Set error tag and result, and raise Z flag if |x| = 1.0
{ .mfi
nop.m 0
(p6) frcpa.s0 fRm, p0 = f1, f0 // Get inf, and raise Z flag
nop.i 0
}
;;
{ .mfb
(p6) mov atanh_GR_tag = 134
(p6) fmerge.s f8 = f8, fRm // result is +-inf
br.cond.sptk __libm_error_region // Exit if |x| >= 1.0
}
;;
GLOBAL_LIBM_END(atanhf)
libm_alias_float_other (atanh, atanh)
LOCAL_LIBM_ENTRY(__libm_error_region)
.prologue
{ .mfi
add GR_Parameter_Y=-32,sp // Parameter 2 value
nop.f 0
.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
{ .mib
stfs [GR_Parameter_X] = f10 // STORE Parameter 1 on stack
// Parameter 3 address
add GR_Parameter_RESULT = 0,GR_Parameter_Y
nop.b 0
}
{ .mib
stfs [GR_Parameter_Y] = f8 // 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
add GR_Parameter_RESULT = 48,sp
nop.m 0
nop.i 0
};;
{ .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#