| .file "asin.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 |
| //============================================================== |
| // 02/02/00 Initial version |
| // 08/17/00 New and much faster algorithm. |
| // 08/31/00 Avoided bank conflicts on loads, shortened |x|=1 path, |
| // fixed mfb split issue stalls. |
| // 12/19/00 Fixed small arg cases to force inexact, or inexact and underflow. |
| // 08/02/02 New and much faster algorithm II |
| // 02/06/03 Reordered header: .section, .global, .proc, .align |
| |
| // Description |
| //========================================= |
| // The asin function computes the principal value of the arc sine of x. |
| // asin(0) returns 0, asin(1) returns pi/2, asin(-1) returns -pi/2. |
| // A doman error occurs for arguments not in the range [-1,+1]. |
| // |
| // The asin function returns the arc sine in the range [-pi/2, +pi/2] radians. |
| // |
| // There are 8 paths: |
| // 1. x = +/-0.0 |
| // Return asin(x) = +/-0.0 |
| // |
| // 2. 0.0 < |x| < 0.625 |
| // Return asin(x) = 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 asin(x) = 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: |
| // asin(x) = sign(x) * (Pi/2 - S3*PolB(R)) |
| // |
| // But for optimization perposes the reconstruction step is slightly |
| // changed: |
| // asin(x) = sign(x)*(Pi/2 - PolB(R)*S2) + sign(x)*d2*S2*PolB(R) |
| // |
| // 4. |x| = 1.0 |
| // Return asin(x) = sign(x)*Pi/2 |
| // |
| // 5. 1.0 < |x| <= +INF |
| // A doman error occurs for arguments not in the range [-1,+1] |
| // |
| // 6. x = [S,Q]NaN |
| // Return asin(x) = QNaN |
| // |
| // 7. x is denormal |
| // Return asin(x) = x + x^3, |
| // |
| // 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 -> f63 |
| |
| // General registers used: |
| // r3, r21 -> r31, r32 -> r38 |
| |
| // Predicate registers used: |
| // p0, p6 -> p14 |
| |
| // |
| // Assembly macros |
| //========================================= |
| // 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 |
| // Data tables |
| //============================================================== |
| RODATA |
| .align 16 |
| LOCAL_OBJECT_START(asin_base_range_table) |
| // Ai: Polynomial coefficients for the asin(x), |x| < .625000 |
| // Bi: Polynomial coefficients for the asin(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(asin_base_range_table) |
| |
| |
| .section .text |
| GLOBAL_LIBM_ENTRY(asin) |
| asin_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(asin_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 |
| 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 |
| } |
| ;; |
| { .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 asin_special |
| } |
| ;; |
| { .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 |
| } |
| ;; |
| { .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 fB0 = [rTmpPtr1], 16 // B0 |
| nop.f 0 |
| nop.i 0 |
| } |
| { .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 asin_abs_1 |
| } |
| ;; |
| { .mfi |
| ldfe fA3 = [rTmpPtr2], 48 // A3 or B1 |
| nop.f 0 |
| adds rTmpPtr1 = 64, rTmpPtr3 |
| } |
| { .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 asin_abs_gt_1 |
| } |
| ;; |
| { .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 |
| ldfpd fA13, fA15 = [rTmpPtr3] // A13, A15 or B4, B5 |
| fma.s1 fXCube = fXSqr, f8, f0 // x^3 |
| nop.i 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 |
| 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 asin_base_range; |
| } |
| ;; |
| |
| { .mfi |
| nop.m 0 |
| (p9) fma.s1 fH = fHalf, f1mXRcp, f0 // H0 for x > 0 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| (p9) fma.s1 fS = f1mX, f1mXRcp, f0 // S0 for x > 0 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| (p8) fma.s1 fH = fHalf, f1pXRcp, f0 // H0 for x < 0 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| (p8) fma.s1 fS = f1pX, f1pXRcp, f0 // S0 for x > 0 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fRQuadr = fRSqr, fRSqr, f0 // R^4 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fB11 = fB11, fR, fB10 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 fB1 = fB1, fR, fB0 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fB5 = fB5, fR, fB4 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 fB7 = fB7, fR, fB6 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fB3 = fB3, fR, fB2 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fnma.s1 fD = fH, fS, fHalf // d0 = 1/2 - H0*S0 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fR8 = fRQuadr, fRQuadr, f0 // R^4 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 fB9 = fB9, fR, fB8 |
| nop.i 0 |
| } |
| ;; |
| {.mfi |
| nop.m 0 |
| fma.s1 fB12 = fB12, fRSqr, fB11 |
| nop.i 0 |
| } |
| {.mfi |
| nop.m 0 |
| fma.s1 fB7 = fB7, fRSqr, fB5 |
| nop.i 0 |
| } |
| ;; |
| {.mfi |
| nop.m 0 |
| fma.s1 fB3 = fB3, fRSqr, fB1 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fH = fH, fD, fH // H1 = H0 + H0*d0 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 fS = fS, fD, fS // S1 = S0 + S0*d0 |
| nop.i 0 |
| } |
| ;; |
| {.mfi |
| nop.m 0 |
| fma.s1 fPiBy2 = fPiBy2, fSignX, f0 // signum(x)*Pi/2 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fB12 = fB12, fRSqr, fB9 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 fB7 = fB7, fRQuadr, fB3 |
| nop.i 0 |
| } |
| ;; |
| {.mfi |
| nop.m 0 |
| fnma.s1 fD = fH, fS, fHalf // d1 = 1/2 - H1*S1 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fnma.s1 fSignedS = fSignX, fS, f0 // -signum(x)*S1 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fCloseTo1Pol = fB12, fR8, fB7 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| fma.s1 fH = fH, fD, fH // H2 = H1 + H1*d1 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 fS = fS, fD, fS // S2 = S1 + S1*d1 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| // -signum(x)* S2 = -signum(x)*(S1 + S1*d1) |
| fma.s1 fSignedS = fSignedS, fD, fSignedS |
| nop.i 0 |
| } |
| ;; |
| {.mfi |
| nop.m 0 |
| fnma.s1 fD = fH, fS, fHalf // d2 = 1/2 - H2*S2 |
| nop.i 0 |
| } |
| ;; |
| { .mfi |
| nop.m 0 |
| // signum(x)*(Pi/2 - PolB*S2) |
| fma.s1 fPiBy2 = fSignedS, fCloseTo1Pol, fPiBy2 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| // -signum(x)*PolB * S2 |
| fma.s1 fCloseTo1Pol = fSignedS, fCloseTo1Pol, f0 |
| nop.i 0 |
| } |
| ;; |
| { .mfb |
| nop.m 0 |
| // final result for 0.625 <= |x| < 1 |
| fma.d.s0 f8 = fCloseTo1Pol, fD, fPiBy2 |
| // exit here for 0.625 <= |x| < 1 |
| br.ret.sptk b0 |
| } |
| ;; |
| |
| |
| // here if |x| < 0.625 |
| .align 32 |
| asin_base_range: |
| { .mfi |
| nop.m 0 |
| 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 |
| 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 |
| fma.d.s0 f8 = fBaseP, fXCube, f8 |
| // exit here for |x| < 0.625 path |
| br.ret.sptk b0 |
| } |
| ;; |
| |
| // here if |x| = 1 |
| // asin(x) = sign(x) * Pi/2 |
| .align 32 |
| asin_abs_1: |
| { .mfi |
| ldfe fPiBy2 = [rPiBy2Ptr] // Pi/2 |
| nop.f 0 |
| nop.i 0 |
| } |
| ;; |
| {.mfb |
| nop.m 0 |
| // result for |x| = 1.0 |
| fma.d.s0 f8 = fPiBy2, fSignX, f0 |
| // exit here for |x| = 1.0 |
| br.ret.sptk b0 |
| } |
| ;; |
| |
| // here if x is a NaN, denormal, or zero |
| .align 32 |
| asin_special: |
| { .mfi |
| nop.m 0 |
| // 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 |
| nop.m 0 |
| // 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 |
| } |
| ;; |
| { .mfb |
| nop.m 0 |
| nop.f 0 |
| // 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 |
| // absolute value of normalized x |
| fmerge.s fNormX = f1, fNormX |
| nop.i 0 |
| } |
| ;; |
| { .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 asin_unnormal_back |
| } |
| ;; |
| // if we still here it means that input is "true" denormal |
| { .mfb |
| nop.m 0 |
| // final result if x is denormal |
| fma.d.s0 f8 = f8, fXSqr, f8 |
| // exit here if x is denormal |
| br.ret.sptk b0 |
| } |
| ;; |
| |
| // here if |x| > 1.0 |
| // error handler should be called |
| .align 32 |
| asin_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 = 61 // error code |
| frcpa.s0 FR_RESULT, p0 = f0,f0 |
| // call error handler routine |
| br.cond.sptk __libm_error_region |
| } |
| ;; |
| GLOBAL_LIBM_END(asin) |
| |
| |
| |
| 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 |
| 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 |
| { .mib |
| 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] = 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 |
| 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 |
| };; |
| { .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# |
