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+/* Optimized sinf(). PowerPC64/POWER8 version.
+ Copyright (C) 2016-2018 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ The GNU C Library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with the GNU C Library; if not, see
+ <http://www.gnu.org/licenses/>. */
+
+#include <sysdep.h>
+#define _ERRNO_H 1
+#include <bits/errno.h>
+#include <libm-alias-float.h>
+
+#define FRAMESIZE (FRAME_MIN_SIZE+16)
+
+#define FLOAT_EXPONENT_SHIFT 23
+#define FLOAT_EXPONENT_BIAS 127
+#define INTEGER_BITS 3
+
+#define PI_4 0x3f490fdb /* PI/4 */
+#define NINEPI_4 0x40e231d6 /* 9 * PI/4 */
+#define TWO_PN5 0x3d000000 /* 2^-5 */
+#define TWO_PN27 0x32000000 /* 2^-27 */
+#define INFINITY 0x7f800000
+#define TWO_P23 0x4b000000 /* 2^27 */
+#define FX_FRACTION_1_28 0x9249250 /* 0x100000000 / 28 + 1 */
+
+ /* Implements the function
+
+ float [fp1] sinf (float [fp1] x) */
+
+ .machine power8
+ENTRY (__sinf, 4)
+ addis r9,r2,L(anchor)@toc@ha
+ addi r9,r9,L(anchor)@toc@l
+
+ lis r4,PI_4@h
+ ori r4,r4,PI_4@l
+
+ xscvdpspn v0,v1
+ mfvsrd r8,v0
+ rldicl r3,r8,32,33 /* Remove sign bit. */
+
+ cmpw r3,r4
+ bge L(greater_or_equal_pio4)
+
+ lis r4,TWO_PN5@h
+ ori r4,r4,TWO_PN5@l
+
+ cmpw r3,r4
+ blt L(less_2pn5)
+
+ /* Chebyshev polynomial of the form:
+ * x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))). */
+
+ lfd fp9,(L(S0)-L(anchor))(r9)
+ lfd fp10,(L(S1)-L(anchor))(r9)
+ lfd fp11,(L(S2)-L(anchor))(r9)
+ lfd fp12,(L(S3)-L(anchor))(r9)
+ lfd fp13,(L(S4)-L(anchor))(r9)
+
+ fmul fp2,fp1,fp1 /* x^2 */
+ fmul fp3,fp2,fp1 /* x^3 */
+
+ fmadd fp4,fp2,fp13,fp12 /* S3+x^2*S4 */
+ fmadd fp4,fp2,fp4,fp11 /* S2+x^2*(S3+x^2*S4) */
+ fmadd fp4,fp2,fp4,fp10 /* S1+x^2*(S2+x^2*(S3+x^2*S4)) */
+ fmadd fp4,fp2,fp4,fp9 /* S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4))) */
+ fmadd fp1,fp3,fp4,fp1 /* x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))) */
+ frsp fp1,fp1 /* Round to single precision. */
+
+ blr
+
+ .balign 16
+L(greater_or_equal_pio4):
+ lis r4,NINEPI_4@h
+ ori r4,r4,NINEPI_4@l
+ cmpw r3,r4
+ bge L(greater_or_equal_9pio4)
+
+ /* Calculate quotient of |x|/(PI/4). */
+ lfd fp2,(L(invpio4)-L(anchor))(r9)
+ fabs fp1,fp1 /* |x| */
+ fmul fp2,fp1,fp2 /* |x|/(PI/4) */
+ fctiduz fp2,fp2
+ mfvsrd r3,v2 /* n = |x| mod PI/4 */
+
+ /* Now use that quotient to find |x| mod (PI/2). */
+ addi r7,r3,1
+ rldicr r5,r7,2,60 /* ((n+1) >> 1) << 3 */
+ addi r6,r9,(L(pio2_table)-L(anchor))
+ lfdx fp4,r5,r6
+ fsub fp1,fp1,fp4
+
+ .balign 16
+L(reduced):
+ /* Now we are in the range -PI/4 to PI/4. */
+
+ /* Work out if we are in a positive or negative primary interval. */
+ rldicl r4,r7,62,63 /* ((n+1) >> 2) & 1 */
+
+ /* We are operating on |x|, so we need to add back the original
+ sign. */
+ rldicl r8,r8,33,63 /* (x >> 31) & 1, ie the sign bit. */
+ xor r4,r4,r8 /* 0 if result should be positive,
+ 1 if negative. */
+
+ /* Load a 1.0 or -1.0. */
+ addi r5,r9,(L(ones)-L(anchor))
+ sldi r4,r4,3
+ lfdx fp0,r4,r5
+
+ /* Are we in the primary interval of sin or cos? */
+ andi. r4,r7,0x2
+ bne L(cos)
+
+ /* Chebyshev polynomial of the form:
+ x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))). */
+
+ lfd fp9,(L(S0)-L(anchor))(r9)
+ lfd fp10,(L(S1)-L(anchor))(r9)
+ lfd fp11,(L(S2)-L(anchor))(r9)
+ lfd fp12,(L(S3)-L(anchor))(r9)
+ lfd fp13,(L(S4)-L(anchor))(r9)
+
+ fmul fp2,fp1,fp1 /* x^2 */
+ fmul fp3,fp2,fp1 /* x^3 */
+
+ fmadd fp4,fp2,fp13,fp12 /* S3+x^2*S4 */
+ fmadd fp4,fp2,fp4,fp11 /* S2+x^2*(S3+x^2*S4) */
+ fmadd fp4,fp2,fp4,fp10 /* S1+x^2*(S2+x^2*(S3+x^2*S4)) */
+ fmadd fp4,fp2,fp4,fp9 /* S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4))) */
+ fmadd fp4,fp3,fp4,fp1 /* x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))) */
+ fmul fp4,fp4,fp0 /* Add in the sign. */
+ frsp fp1,fp4 /* Round to single precision. */
+
+ blr
+
+ .balign 16
+L(cos):
+ /* Chebyshev polynomial of the form:
+ 1.0+x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))). */
+
+ lfd fp9,(L(C0)-L(anchor))(r9)
+ lfd fp10,(L(C1)-L(anchor))(r9)
+ lfd fp11,(L(C2)-L(anchor))(r9)
+ lfd fp12,(L(C3)-L(anchor))(r9)
+ lfd fp13,(L(C4)-L(anchor))(r9)
+
+ fmul fp2,fp1,fp1 /* x^2 */
+ lfd fp3,(L(DPone)-L(anchor))(r9)
+
+ fmadd fp4,fp2,fp13,fp12 /* C3+x^2*C4 */
+ fmadd fp4,fp2,fp4,fp11 /* C2+x^2*(C3+x^2*C4) */
+ fmadd fp4,fp2,fp4,fp10 /* C1+x^2*(C2+x^2*(C3+x^2*C4)) */
+ fmadd fp4,fp2,fp4,fp9 /* C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4))) */
+ fmadd fp4,fp2,fp4,fp3 /* 1.0 + x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))) */
+ fmul fp4,fp4,fp0 /* Add in the sign. */
+ frsp fp1,fp4 /* Round to single precision. */
+
+ blr
+
+ .balign 16
+L(greater_or_equal_9pio4):
+ lis r4,INFINITY@h
+ ori r4,r4,INFINITY@l
+ cmpw r3,r4
+ bge L(inf_or_nan)
+
+ lis r4,TWO_P23@h
+ ori r4,r4,TWO_P23@l
+ cmpw r3,r4
+ bge L(greater_or_equal_2p23)
+
+ fabs fp1,fp1 /* |x| */
+
+ /* Calculate quotient of |x|/(PI/4). */
+ lfd fp2,(L(invpio4)-L(anchor))(r9)
+
+ lfd fp3,(L(DPone)-L(anchor))(r9)
+ lfd fp4,(L(DPhalf)-L(anchor))(r9)
+ fmul fp2,fp1,fp2 /* |x|/(PI/4) */
+ friz fp2,fp2 /* n = floor(|x|/(PI/4)) */
+
+ /* Calculate (n + 1) / 2. */
+ fadd fp2,fp2,fp3 /* n + 1 */
+ fmul fp3,fp2,fp4 /* (n + 1) / 2 */
+ friz fp3,fp3
+
+ lfd fp4,(L(pio2hi)-L(anchor))(r9)
+ lfd fp5,(L(pio2lo)-L(anchor))(r9)
+
+ fmul fp6,fp4,fp3
+ fadd fp6,fp6,fp1
+ fmadd fp1,fp5,fp3,fp6
+
+ fctiduz fp2,fp2
+ mfvsrd r7,v2 /* n + 1 */
+
+ b L(reduced)
+
+ .balign 16
+L(inf_or_nan):
+ bne L(skip_errno_setting) /* Is a NAN? */
+
+ /* We delayed the creation of the stack frame, as well as the saving of
+ the link register, because only at this point, we are sure that
+ doing so is actually needed. */
+
+ stfd fp1,-8(r1)
+
+ /* Save the link register. */
+ mflr r0
+ std r0,16(r1)
+ cfi_offset(lr, 16)
+
+ /* Create the stack frame. */
+ stdu r1,-FRAMESIZE(r1)
+ cfi_adjust_cfa_offset(FRAMESIZE)
+
+ bl JUMPTARGET(__errno_location)
+ nop
+
+ /* Restore the stack frame. */
+ addi r1,r1,FRAMESIZE
+ cfi_adjust_cfa_offset(-FRAMESIZE)
+ /* Restore the link register. */
+ ld r0,16(r1)
+ mtlr r0
+
+ lfd fp1,-8(r1)
+
+ /* errno = EDOM */
+ li r4,EDOM
+ stw r4,0(r3)
+
+L(skip_errno_setting):
+ fsub fp1,fp1,fp1 /* x - x */
+ blr
+
+ .balign 16
+L(greater_or_equal_2p23):
+ fabs fp1,fp1
+
+ srwi r4,r3,FLOAT_EXPONENT_SHIFT
+ subi r4,r4,FLOAT_EXPONENT_BIAS
+
+ /* We reduce the input modulo pi/4, so we need 3 bits of integer
+ to determine where in 2*pi we are. Index into our array
+ accordingly. */
+ addi r4,r4,INTEGER_BITS
+
+ /* To avoid an expensive divide, for the range we care about (0 - 127)
+ we can transform x/28 into:
+
+ x/28 = (x * ((0x100000000 / 28) + 1)) >> 32
+
+ mulhwu returns the top 32 bits of the 64 bit result, doing the
+ shift for us in the same instruction. The top 32 bits are undefined,
+ so we have to mask them. */
+
+ lis r6,FX_FRACTION_1_28@h
+ ori r6,r6,FX_FRACTION_1_28@l
+ mulhwu r5,r4,r6
+ clrldi r5,r5,32
+
+ /* Get our pointer into the invpio4_table array. */
+ sldi r4,r5,3
+ addi r6,r9,(L(invpio4_table)-L(anchor))
+ add r4,r4,r6
+
+ lfd fp2,0(r4)
+ lfd fp3,8(r4)
+ lfd fp4,16(r4)
+ lfd fp5,24(r4)
+
+ fmul fp6,fp2,fp1
+ fmul fp7,fp3,fp1
+ fmul fp8,fp4,fp1
+ fmul fp9,fp5,fp1
+
+ /* Mask off larger integer bits in highest double word that we don't
+ care about to avoid losing precision when combining with smaller
+ values. */
+ fctiduz fp10,fp6
+ mfvsrd r7,v10
+ rldicr r7,r7,0,(63-INTEGER_BITS)
+ mtvsrd v10,r7
+ fcfidu fp10,fp10 /* Integer bits. */
+
+ fsub fp6,fp6,fp10 /* highest -= integer bits */
+
+ /* Work out the integer component, rounded down. Use the top two
+ limbs for this. */
+ fadd fp10,fp6,fp7 /* highest + higher */
+
+ fctiduz fp10,fp10
+ mfvsrd r7,v10
+ andi. r0,r7,1
+ fcfidu fp10,fp10
+
+ /* Subtract integer component from highest limb. */
+ fsub fp12,fp6,fp10
+
+ beq L(even_integer)
+
+ /* Our integer component is odd, so we are in the -PI/4 to 0 primary
+ region. We need to shift our result down by PI/4, and to do this
+ in the mod (4/PI) space we simply subtract 1. */
+ lfd fp11,(L(DPone)-L(anchor))(r9)
+ fsub fp12,fp12,fp11
+
+ /* Now add up all the limbs in order. */
+ fadd fp12,fp12,fp7
+ fadd fp12,fp12,fp8
+ fadd fp12,fp12,fp9
+
+ /* And finally multiply by pi/4. */
+ lfd fp13,(L(pio4)-L(anchor))(r9)
+ fmul fp1,fp12,fp13
+
+ addi r7,r7,1
+ b L(reduced)
+
+L(even_integer):
+ lfd fp11,(L(DPone)-L(anchor))(r9)
+
+ /* Now add up all the limbs in order. */
+ fadd fp12,fp12,fp7
+ fadd fp12,r12,fp8
+ fadd fp12,r12,fp9
+
+ /* We need to check if the addition of all the limbs resulted in us
+ overflowing 1.0. */
+ fcmpu 0,fp12,fp11
+ bgt L(greater_than_one)
+
+ /* And finally multiply by pi/4. */
+ lfd fp13,(L(pio4)-L(anchor))(r9)
+ fmul fp1,fp12,fp13
+
+ addi r7,r7,1
+ b L(reduced)
+
+L(greater_than_one):
+ /* We did overflow 1.0 when adding up all the limbs. Add 1.0 to our
+ integer, and subtract 1.0 from our result. Since that makes the
+ integer component odd, we need to subtract another 1.0 as
+ explained above. */
+ addi r7,r7,1
+
+ lfd fp11,(L(DPtwo)-L(anchor))(r9)
+ fsub fp12,fp12,fp11
+
+ /* And finally multiply by pi/4. */
+ lfd fp13,(L(pio4)-L(anchor))(r9)
+ fmul fp1,fp12,fp13
+
+ addi r7,r7,1
+ b L(reduced)
+
+ .balign 16
+L(less_2pn5):
+ lis r4,TWO_PN27@h
+ ori r4,r4,TWO_PN27@l
+
+ cmpw r3,r4
+ blt L(less_2pn27)
+
+ /* A simpler Chebyshev approximation is close enough for this range:
+ x+x^3*(SS0+x^2*SS1). */
+
+ lfd fp10,(L(SS0)-L(anchor))(r9)
+ lfd fp11,(L(SS1)-L(anchor))(r9)
+
+ fmul fp2,fp1,fp1 /* x^2 */
+ fmul fp3,fp2,fp1 /* x^3 */
+
+ fmadd fp4,fp2,fp11,fp10 /* SS0+x^2*SS1 */
+ fmadd fp1,fp3,fp4,fp1 /* x+x^3*(SS0+x^2*SS1) */
+
+ frsp fp1,fp1 /* Round to single precision. */
+
+ blr
+
+ .balign 16
+L(less_2pn27):
+ cmpwi r3,0
+ beq L(zero)
+
+ /* Handle some special cases:
+
+ sinf(subnormal) raises inexact/underflow
+ sinf(min_normalized) raises inexact/underflow
+ sinf(normalized) raises inexact. */
+
+ lfd fp2,(L(small)-L(anchor))(r9)
+
+ fmul fp2,fp1,fp2 /* x * small */
+ fsub fp1,fp1,fp2 /* x - x * small */
+
+ frsp fp1,fp1
+
+ blr
+
+ .balign 16
+L(zero):
+ blr
+
+END (__sinf)
+
+ .section .rodata, "a"
+
+ .balign 8
+
+L(anchor):
+
+ /* Chebyshev constants for sin, range -PI/4 - PI/4. */
+L(S0): .8byte 0xbfc5555555551cd9
+L(S1): .8byte 0x3f81111110c2688b
+L(S2): .8byte 0xbf2a019f8b4bd1f9
+L(S3): .8byte 0x3ec71d7264e6b5b4
+L(S4): .8byte 0xbe5a947e1674b58a
+
+ /* Chebyshev constants for sin, range 2^-27 - 2^-5. */
+L(SS0): .8byte 0xbfc555555543d49d
+L(SS1): .8byte 0x3f8110f475cec8c5
+
+ /* Chebyshev constants for cos, range -PI/4 - PI/4. */
+L(C0): .8byte 0xbfdffffffffe98ae
+L(C1): .8byte 0x3fa55555545c50c7
+L(C2): .8byte 0xbf56c16b348b6874
+L(C3): .8byte 0x3efa00eb9ac43cc0
+L(C4): .8byte 0xbe923c97dd8844d7
+
+L(invpio2):
+ .8byte 0x3fe45f306dc9c883 /* 2/PI */
+
+L(invpio4):
+ .8byte 0x3ff45f306dc9c883 /* 4/PI */
+
+L(invpio4_table):
+ .8byte 0x0000000000000000
+ .8byte 0x3ff45f306c000000
+ .8byte 0x3e3c9c882a000000
+ .8byte 0x3c54fe13a8000000
+ .8byte 0x3aaf47d4d0000000
+ .8byte 0x38fbb81b6c000000
+ .8byte 0x3714acc9e0000000
+ .8byte 0x3560e4107c000000
+ .8byte 0x33bca2c756000000
+ .8byte 0x31fbd778ac000000
+ .8byte 0x300b7246e0000000
+ .8byte 0x2e5d2126e8000000
+ .8byte 0x2c97003248000000
+ .8byte 0x2ad77504e8000000
+ .8byte 0x290921cfe0000000
+ .8byte 0x274deb1cb0000000
+ .8byte 0x25829a73e0000000
+ .8byte 0x23fd1046be000000
+ .8byte 0x2224baed10000000
+ .8byte 0x20709d338e000000
+ .8byte 0x1e535a2f80000000
+ .8byte 0x1cef904e64000000
+ .8byte 0x1b0d639830000000
+ .8byte 0x1964ce7d24000000
+ .8byte 0x17b908bf16000000
+
+L(pio4):
+ .8byte 0x3fe921fb54442d18 /* PI/4 */
+
+/* PI/2 as a sum of two doubles. We only use 32 bits of the upper limb
+ to avoid losing significant bits when multiplying with up to
+ (2^22)/(pi/2). */
+L(pio2hi):
+ .8byte 0xbff921fb54400000
+
+L(pio2lo):
+ .8byte 0xbdd0b4611a626332
+
+L(pio2_table):
+ .8byte 0
+ .8byte 0x3ff921fb54442d18 /* 1 * PI/2 */
+ .8byte 0x400921fb54442d18 /* 2 * PI/2 */
+ .8byte 0x4012d97c7f3321d2 /* 3 * PI/2 */
+ .8byte 0x401921fb54442d18 /* 4 * PI/2 */
+ .8byte 0x401f6a7a2955385e /* 5 * PI/2 */
+ .8byte 0x4022d97c7f3321d2 /* 6 * PI/2 */
+ .8byte 0x4025fdbbe9bba775 /* 7 * PI/2 */
+ .8byte 0x402921fb54442d18 /* 8 * PI/2 */
+ .8byte 0x402c463abeccb2bb /* 9 * PI/2 */
+ .8byte 0x402f6a7a2955385e /* 10 * PI/2 */
+
+L(small):
+ .8byte 0x3cd0000000000000 /* 2^-50 */
+
+L(ones):
+ .8byte 0x3ff0000000000000 /* +1.0 */
+ .8byte 0xbff0000000000000 /* -1.0 */
+
+L(DPhalf):
+ .8byte 0x3fe0000000000000 /* 0.5 */
+
+L(DPone):
+ .8byte 0x3ff0000000000000 /* 1.0 */
+
+L(DPtwo):
+ .8byte 0x4000000000000000 /* 2.0 */
+
+libm_alias_float (__sin, sin)
generated by cgit v1.2.3 (git 2.39.1) at 2024-04-30 20:20:40 +0000