s_cbrtl.s

glibc 2.9,最新版的C语言库函数

       data4 0x1d927875, 0x9f074faa, 0x1e9dc2c3, 0x1f13c0d2
       data4 0x1e3c9685, 0x9e6b6f75, 0x9db9cb31, 0x1ea5f3aa
       data4 0x9d992c61, 0x1f1015e4, 0x1f194f70, 0x9e19d2b3
       data4 0x9d89116c, 0x1f23cd35, 0x1e33d3a2, 0x1ee331b8
       data4 0x1d5ba7ec, 0x9f273788, 0x9e6907f4, 0x9ed5f912
       data4 0x9edd458d, 0x1e2ca7b2, 0x1ef81fe4, 0x1dc7ade6
       data4 0x1e876e51, 0x9f04ec89, 0x1f1da63a, 0x1ec02bd0
       data4 0x9e71326f, 0x1e7847b4, 0x1f0de618, 0x9e036cb6
       data4 0x1eec61e2, 0x1ef1758b, 0x9ee880a3, 0x1ed269d7
       data4 0x1e27edd3, 0x9e8a81a1, 0x1eacb84d, 0x9e1aad37
       data4 0x1f1aa8f7, 0x1e9bbd90, 0x1ea1b61f, 0x9ed41c2f
       data4 0x1dbb5dd6, 0x1f0ec733, 0x9df06b1b, 0x1e06fef1
       data4 0x9edede3a, 0x1edeb5e2, 0x1f0e63ee, 0x9db316bb
       data4 0x9efc1ad3, 0x1f01fbb5, 0x9cc0d078, 0x1ea28b36
       data4 0x9e9dd205, 0x9e791534, 0x1da1c8d5, 0x9e8195cc
       data4 0x1f0681a4, 0x1eeaf1e2, 0x9ef83b37, 0x9f22a92b
       data4 0x1eabc4ce, 0x1f10eefb, 0x1e06d9aa, 0x1e7cacd5
       data4 0x1f1ea087, 0x1eb21983, 0x9f100c78, 0x1e840abe
       data4 0x9efab66c, 0x1f183fa8, 0x9e84ee68, 0x9eea083d
       data4 0x9ee23a74, 0x1f1351d7, 0x9ec5d42a, 0x9f071f57
       data4 0x9ef578d9, 0x9f1aa7e7, 0x1eb02044, 0x1f151a2e
       data4 0x9c0dc8b2, 0x9ef4087a, 0x1ec12b93, 0x1c1a946b
       data4 0x1e89946f, 0x9dafe8c3, 0x1d295288, 0x9e8497ab
       data4 0x1ec000c6, 0x1e102f29, 0x1e542256, 0x1e67d44d
       data4 0x1ef688d8, 0x1f0e0f29, 0x1e67861f, 0x1e869748
       data4 0x1ee6aa6e, 0x9e4d228b, 0x9e50be5b, 0x1e9fe225
       data4 0x9ea34102, 0x9e628a3b, 0x9ed9fd83, 0x1ecd7109
       data4 0x1f1864ff, 0x1ea19b76, 0x1db0d1c9, 0x9dff519b
       data4 0x1e8fea71, 0x9ee82e9a, 0x9f08919b, 0x9ef5c8ae
       data4 0x9ee446a4, 0x1ea59444, 0x1eb74230, 0x1ea13fbf
       data4 0x9ea6a3ea, 0x1e5f2797, 0x9e0adb07, 0x9d3adadd
       data4 0x1ebf2ee2, 0x1da19bfa, 0x1e8dea6d, 0x1ec4fea9
       data4 0x1e669f22, 0x1dc5f919, 0x9ed25caa, 0x1ee475b1
       data4 0x1ed0603e, 0x9eacb35c, 0x1dc00b27, 0x1e2f9991
       data4 0x1e7b0406, 0x1eaa3387, 0x9d865bde, 0x1eb78a48
       data4 0x1c40ae2e, 0x1ee9838b, 0x9f0f0d7f, 0x1e3e5d26
       data4 0x1e99e7a6, 0x9e681ccf, 0x9e93ed65, 0x9eeb6a66
       data4 0x1e29e9af, 0x9e96f923, 0x9e74f11d, 0x9f1474da
       data4 0x1eec2ea7, 0x1ebf7aa3, 0x9c25dcca, 0x9f0553c2
       data4 0x9e599efd, 0x1d2ab490, 0x1e95d7cd, 0x9ee4b20e
       data4 0x9d988ce5, 0x9ef9787e, 0x9dbbba5b, 0x9f12c304
       data4 0x1e3b9d70, 0x1e7bcae8, 0x9d98bb6e, 0x9e8e6b01
       data4 0x9f07d03b, 0x9d67c822, 0x9f0ef69e, 0x1c7c0fe3
       data4 0x9e9bfbb9, 0x9e83b84b, 0x1efbf15e, 0x9ecfa6a6
       data4 0x9c91158e, 0x9ecf6770, 0x1ee1e3a8, 0x9dc95ec0
       data4 0x1ef603f7, 0x1d5e52ba, 0x1c477d1b, 0x9e955cd8
       data4 0x1ed665b0, 0x9e8376c4, 0x9c0ee88e, 0x1e8c989e
       data4 0x1ea2df29, 0x9d961e5c, 0x1e101813, 0x1e7fffff
       data4 0x9e5abff4, 0x1dbddd71, 0x1eb69100, 0x1e71f114
       data4 0x1e9ca798, 0x1ef62c8d, 0x9db4e55a, 0x1dbe69ce
       data4 0x9ef1c01f, 0x1f044a2a, 0x9eb9e0d7, 0x9ee59745
       data4 0x9e874803, 0x1ea0b418, 0x9e13572a, 0x1ddbb3a2
       data4 0x9ec0e391, 0x1e89fba1, 0x1ee8b261, 0x9e5d25f0
       data4 0x9ef222cb, 0x9ef135ec, 0x1ea04b9a, 0x9f04291f
       data4 0x9e969254, 0x9ee32f08, 0x9ed909d3, 0x9e362640
       data4 0x9ec20735, 0x1e50131b, 0x9ed4e049, 0x1ee8e817
       data4 0x1e1e09c0, 0x9ea643c5, 0x9e5a1ab6, 0x9e389059
       data4 0x1e560947, 0x1d02b877, 0x1e4475ab, 0x9ea9aaf6
       data4 0x1e95bc5e, 0x1eaf6afd, 0x1d43067d, 0x9d043821
       data4 0x9e97baa9, 0x1de5c4f9, 0x9e9a0069, 0x9e1b9944
       data4 0x1eb13686, 0x9eb907eb, 0x1e059589, 0x1cbd0f93
       data4 0x9eb7e6ae, 0x1e9fa175, 0x1ee5bdf4, 0x1e8052f7
       data4 0x9c80d1e3, 0x1bfbe28e, 0x9e672b3b, 0x9ecacf19
       data4 0x9e3c04be, 0x1dfe8c5c, 0x1e1ba9cb, 0x1eb40b1e
       data4 0x1ec7e7f6, 0x9d0d45b3, 0x1ef0113b, 0x9a155fa3
       data4 0x1e28ec3b, 0x1e7ca8df, 0x9d2f91b4, 0x1eccd9ed
       data4 0x9ed943bc, 0x9ccaab19, 0x9e8a5c58, 0x1ec3bca8
       data4 0x1ed78dc7, 0x9ed391a8, 0x9e938f6e, 0x9ec4a030
       data4 0x9e80346e, 0x1e7a4686, 0x9e284315, 0x9e39584c
       data4 0x1ebdc9b4, 0x9e9cfce5, 0x9ef55c65, 0x1e2941e7
       data4 0x9efbe59f, 0x1d87c41b, 0x1e40befc, 0x1e3d05b5
       data4 0x1de9ea67, 0x1ec9a21c, 0x1decb69a, 0x1df6e75a
       data4 0x9e8030ab, 0x9db20540, 0x9ef1e977, 0x1e3cdc43
       data4 0x1e0492b0, 0x9e91d872, 0x1e775346, 0x9e939978
       data4 0x1eb2714e, 0x1e49a203, 0x9e10195a, 0x1ef1ffc3
       data4 0x9ea8b709, 0x9e832e27, 0x1ed5ac3b, 0x1edb20a6
       data4 0x1e4dbd4e, 0x1efbb932, 0x1d8170ec, 0x1e6c4849
       data4 0x1f008e17, 0x1e8000c4, 0x1d855ecf, 0x9e37cb85
       data4 0x1ecffdf5, 0x1eba6519, 0x9edbe600, 0x1ea3e5e7
       data4 0x1ed4fb39, 0x1f00be77, 0x1e6f4484, 0x9e9e7107
       data4 0x9e30b29d, 0x9ee6e174, 0x1e3a2656, 0x9dd72f3f
       data4 0x9ee12138, 0x1ed16fed, 0x9ece8a02, 0x9ca5b249
       data4 0x9eafd508, 0x9ef0e9fc, 0x1d1307ac, 0x1eecee20
       data4 0x1cf60c6f, 0x9d556216, 0x9eaed175, 0x9ec919f4
       data4 0x1ec2c988, 0x1cd82772, 0x9dc99456, 0x1eab0467
       data4 0x1e89b36f, 0x1c757944, 0x1eef9abd, 0x9e98664d
LOCAL_OBJECT_END(D_table)


.section .text
GLOBAL_LIBM_ENTRY(cbrtl)

{ .mfi
       getf.sig GR_ARGSIG = f8
       // will continue on main path only for normal/denormal numbers
       // all other values will be filtered out and will exit early
       fclass.nm.unc p12, p7 = f8, 0x1b
       // GR_ADDR = pointer to C_1...C_6 followed by T_table
       addl GR_ADDR = @ltoff(poly_coeffs), gp
}
{ .mfi
       // GR_BIAS23 = 2/3*bias -63 = 0xaaaa-0x3f = 0xaa6b
       mov GR_BIAS23 = 0xaa6b
       // normalize a
       fma.s1 FR_XNORM = f8, f1, f0
       // GR_D_ADDR = pointer to D table
       addl GR_D_ADDR = @ltoff(D_table), gp
}
;;

{ .mmf
       // load start address for C_1...C_6 followed by T_table
       ld8 GR_C_START = [ GR_ADDR ]
       // load start address of D table
       ld8 GR_D_START = [ GR_D_ADDR ]
       // y = frcpa(a)
       frcpa.s1 FR_RCP, p6 = f1, f8
}
;;

{ .mmi
        // get normalized significand
       getf.sig GR_NORMSIG = FR_XNORM
        // get exponent
       getf.exp GR_NORMEXPSGN = FR_XNORM
 (p7)  cmp.eq p12, p0 = GR_ARGSIG, r0
}
;;

{ .mii
       // load C_1
       ldfe FR_C1 = [ GR_C_START ], 16
       mov GR_SGNMASK = 0x20000
       nop.i 0
}
;;

{ .mfb
       // load C_2
       ldfe FR_C2 = [ GR_C_START ], 16
 (p12) fma.s0 f8 = f8, f1, f0
       // NaN/Infinities exit early
 (p12) br.ret.spnt b0
}
;;

{ .mfi
       // load C_3, C_4
       ldfpd FR_C3, FR_C4 = [ GR_C_START ], 16
       // y = frcpa(a), set flags and result when argument is 0
       // only used when p6=0
       frcpa.s0 f8, p0 = f1, f8
       nop.i 0
}
;;

{ .mii
       // get GR_SIGN = sign
       and GR_SIGN = GR_NORMEXPSGN, GR_SGNMASK
       // eliminate leading 1 from GR_NORMSIG = 2nd table index
       shl GR_INDEX2 = GR_NORMSIG, 1
       // eliminate sign from exponent 
       andcm GR_NORMEXP = GR_NORMEXPSGN, GR_SGNMASK
}
;;

{ .mfi
       // load C_5, C_6
 (p6)  ldfpd FR_C5, FR_C6 = [ GR_C_START ], 16
       // r = 1-a*y
 (p6)  fnma.s1 FR_R = FR_RCP, FR_XNORM, f1
       // Start computation of floor(exponent/3) by
       // computing (2^20+2)/3*exponent = exponent*0x55556
       // 1: exponent* = 5; 
       // (2^{16}-1)/3 = 0x5555: 
       // will form 0x5555*exponent by using shladd's
       shladd GR_EXP5 = GR_NORMEXP, 2, GR_NORMEXP
}
;;

{ .mib
       // Next several integer steps compute floor(exponent/3)
       // GR_TMP1 = (5*expon)*16
       shladd GR_TMP1 = GR_EXP5, 4, r0
       // GR_EXP3 = 3*exponent
       shladd GR_EXP3 = GR_NORMEXP, 1, GR_NORMEXP
       nop.b 0
}
;;

{ .mmi
       // GR_EXP6 = 6*exponent
       shladd GR_EXP6 = GR_EXP3, 1, r0
       // GR_EXP17 = 17*expon
       add GR_EXP17 = GR_EXP5, GR_TMP1
       // GR_IX2 = 2nd table index (8 bits)
       shr.u GR_IX2 = GR_INDEX2, 56
}
;;

{ .mmi
       // adjust T_table pointer by 2nd index
       shladd GR_T_INDEX = GR_IX2, 3, GR_C_START
       // adjust D_table pointer by 2nd index
       shladd GR_D_INDEX = GR_IX2, 2, GR_D_START
       // GR_TMP2 = (17*expon)*16^2
       shl GR_TMP2 = GR_EXP17, 8
}
;;

{ .mmi
       // GR_TMP3 = expon*(2^16-1)/3
       add GR_TMP3 = GR_EXP17, GR_TMP2
;;
       // GR_TMP4 = expon*(2^20+2)/3 = expon*0x55556
       shladd GR_TMP4 = GR_TMP3, 4, GR_EXP6
       nop.i 0
}
;;

{ .mii
       nop.m 0
       // GR_EXP_RES = floor(expon/3)
       shr.u GR_EXP_RES = GR_TMP4, 20
       nop.i 0
}
;;

{ .mmi
       nop.m 0
       // r16 = 3*exponent
       shladd r16 = GR_EXP_RES, 1, GR_EXP_RES
       // bias exponent
       add GR_EXPBIAS = GR_BIAS23, GR_EXP_RES
}
;;

{ .mmi
       // get remainder of exponent/3
       sub GR_EXP_MOD_3 = GR_NORMEXP, r16
;;
       // add sign to exponent
       or GR_EXPSIGNRES = GR_EXPBIAS, GR_SIGN
       // remainder << = 8
       shl GR_REMTMP = GR_EXP_MOD_3, 8
}
;;

{ .mfi
       // adjust D_table pointer by 1st index
       shladd GR_IX_D = GR_REMTMP, 2, GR_D_INDEX
       // P_1 = C_1+C_2*r
 (p6)  fma.s1 FR_P1 = FR_C2, FR_R, FR_C1
       // adjust T_table pointer by 1st index
       shladd GR_IX_T = GR_REMTMP, 3, GR_T_INDEX
}
{ .mfi
       // FR_SGNEXP = sign*2^{exponent/3}
 (p6)  setf.exp FR_SGNEXP = GR_EXPSIGNRES
       // r^2 = r*r
 (p6)  fma.s1 FR_R2 = FR_R, FR_R, f0
       nop.i 0
}
;;

{ .mfi
       // load D
 (p6)  ldfs FR_D = [ GR_IX_D ]
       // P_2 = C_3+C_4*r
 (p6)  fma.s1 FR_P2 = FR_C4, FR_R, FR_C3
       nop.i 0
}
{ .mfi
       // load T
 (p6)  ldf8 FR_T = [ GR_IX_T ]
       // P_3 = C_5+C_6*r
 (p6)  fma.s1 FR_P3 = FR_C6, FR_R, FR_C5
       nop.i 0
}
;;

{ .mfi
       nop.m 0
       // P_4 = D-r*P_1
 (p6)  fnma.s1 FR_P4 = FR_R, FR_P1, FR_D
       nop.i 0
}
{ .mfi
       nop.m 0
       // r^3 = r*r^2
 (p6)  fma.s1 FR_R3 = FR_R, FR_R2, f0
       nop.i 0
}
;;

{ .mfi
       nop.m 0
       // P_5 = P_2+r2*P_3
 (p6)  fma.s1 FR_P5 = FR_R2, FR_P3, FR_P2
       nop.i 0
}
;;

{ .mfi
       nop.m 0
       // T = T*(sign*2^{exponent/3})
 (p6)  fma.s1 FR_TF = FR_T, FR_SGNEXP, f0
       nop.i 0
}
{ .mfi
       nop.m 0
       // P = P_4-r3*P_5
 (p6)  fnma.s1 FR_P = FR_R3, FR_P5, FR_P4
       nop.i 0
}
;;

{ .mfb
       nop.m 0
       // result = T+T*p
 (p6)  fma.s0 f8 = FR_TF, FR_P, FR_TF
       br.ret.sptk b0
}
;;

GLOBAL_LIBM_END(cbrtl)