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; Copyright 2001-2010 - Mersenne Research, Inc. All rights reserved
; Author: George Woltman
; Email: woltman@alum.mit.edu
;
; These macros implement Pentium 4 optimized versions of macros found
; in hg.mac.
x6r_fft MACRO r1, r2, r3, r4, r5, r6, t1, t2
xcopy t1, r3
addpd r3, r5 ;; T4 = R3 + R5
xcopy t2, r2
addpd r2, r6 ;; T2 = R2 + R6
subpd t1, r5 ;; T3 = R3 - R5
subpd t2, r6 ;; T1 = R2 - R6
xload r5, XMM_HALF
mulpd r5, r3 ;; 0.5 * (R3 + R5)
addpd r3, r1 ;; new R1 = R1 + R3 + R5
xload r6, XMM_HALF
mulpd r6, r2 ;; 0.5 * (R2 + R6)
addpd r2, r4 ;; new R3 = R2 + R4 + R6
mulpd t1, XMM_P866 ;; new I2 = 0.866 * (R3 - R5)
subpd r1, r5 ;; new R2 = R1 - 0.5 * (R3 + R5)
mulpd t2, XMM_P866 ;; new I4 = 0.866 * (R2 - R6)
subpd r6, r4 ;; new R4 = 0.5 * (R2 + R6) - R4
subpd r3, r2 ;; R1 = R1 - R3 (final R2)
multwo r2
addpd r2, r3 ;; R3 = R1 + R3 (final R1)
subpd t1, t2 ;; I2 = I2 - I4 (final R6)
multwo t2
addpd t2, t1 ;; I4 = I2 + I4 (final R4)
subpd r1, r6 ;; R2 = R2 - R4 (final R5)
multwo r6
addpd r6, r1 ;; R4 = R2 + R4 (final R3)
ENDM
x6r_unfft MACRO r1, r2, r3, r4, r5, r6, t1, t2
subpd r3, r5 ;; R3 - R5 (new R4)
multwo r5
addpd r5, r3 ;; R3 + R5 (new R2)
subpd r4, r6 ;; R4 - R6 (new I4)
multwo r6
addpd r6, r4 ;; R4 + R6 (new I2)
xload t2, XMM_HALF
mulpd t2, r3 ;; 0.5 * R4
subpd r1, r2 ;; R1 - R2 (new R3)
multwo r2
addpd r2, r1 ;; R1 + R2 (new R1)
xload t1, XMM_HALF
mulpd t1, r5 ;; 0.5 * R2
mulpd r4, XMM_P866 ;; 0.866 * I4
mulpd r6, XMM_P866 ;; 0.866 * I2
addpd t2, r1 ;; R3 + 0.5 * R4
addpd r5, r2 ;; final R1 = R1 + R2
subpd r2, t1 ;; R1 - 0.5 * R2
subpd r1, r3 ;; final R4 = R3 - R4
subpd t2, r4 ;; final R6 = R3 + 0.5 * R4 - 0.866 * I4
multwo r4
addpd r4, t2 ;; final R2 = R3 + 0.5 * R4 + 0.866 * I4
subpd r2, r6 ;; final R5 = R1 - 0.5 * R2 - 0.866 * I2
multwo r6
addpd r6, r2 ;; final R3 = R1 - 0.5 * R2 + 0.866 * I2
ENDM
x7r_fft MACRO r1, r2, r3, r4, r5, r6, r7, t1, memr1
subpd r2, r7 ;; R2-R7
multwo r7
addpd r7, r2 ;; T1 = R2+R7
subpd r3, r6 ;; R3-R6
multwo r6
addpd r6, r3 ;; T2 = R3+R6
subpd r4, r5 ;; R4-R5
multwo r5
addpd r5, r4 ;; T3 = R4+R5
xcopy t1, r1 ;; R1
addpd t1, r7 ;; R1+T1
addpd t1, r6 ;; R1+T1+T2
addpd t1, r5 ;; R1+T1+T2+T3 (final R1)
xstore memr1, t1
mulpd r7, XMM_P623 ;; T1 = T1 * .623
mulpd r6, XMM_P623 ;; T2 = T2 * .623
mulpd r5, XMM_P623 ;; T3 = T3 * .623
xstore XMM_TMP1, r2
xcopy r2, r1
xcopy t1, r1
addpd r1, r7 ;; newR2 = R1 + T1
addpd r2, r5 ;; newR3 = R1 + T3
addpd t1, r6 ;; newR4 = R1 + T2
mulpd r7, XMM_M358 ;; T1 = T1 * (-.223/.623)
mulpd r6, XMM_M358 ;; T2 = T2 * (-.223/.623)
mulpd r5, XMM_M358 ;; T3 = T3 * (-.223/.623)
addpd r1, r6 ;; newR2 = newR2 + T2
addpd r2, r7 ;; newR3 = newR3 + T1
addpd t1, r5 ;; newR4 = newR4 + T3
mulpd r7, XMM_P404 ;; T1 = T1 * (-.901/-.223)
mulpd r6, XMM_P404 ;; T2 = T2 * (-.901/-.223)
mulpd r5, XMM_P404 ;; T3 = T3 * (-.901/-.223)
addpd r1, r5 ;; newR2 = newR2 + T3 (final R2)
addpd r2, r6 ;; newR3 = newR3 + T2 (final R3)
addpd t1, r7 ;; newR4 = newR4 + T1 (final R4)
xload r7, XMM_TMP1 ;; T1 = R2-R7
mulpd r7, XMM_P975 ;; T1 = T1 * .975
mulpd r3, XMM_P975 ;; T2 = T2 * .975
mulpd r4, XMM_P975 ;; T3 = T3 * .975
xstore XMM_TMP2, r2 ;; final R3
xcopy r2, r3 ;; newI2 = T2
xcopy r6, r7 ;; newI3 = T1
xcopy r5, r4 ;; newI4 = T3
mulpd r7, XMM_P445 ;; T1 = T1 * (.434/.975)
mulpd r3, XMM_P445 ;; T2 = T2 * (.434/.975)
mulpd r5, XMM_P445 ;; T3 = T3 * (.434/.975)
addpd r2, r5 ;; newI2 = newI2 + T3
subpd r6, r3 ;; newI3 = newI3 - T2
addpd r4, r7 ;; newI4 = newI4 + T1
mulpd r7, XMM_P180 ;; T1 = T1 * (.782/.434)
mulpd r3, XMM_P180 ;; T2 = T2 * (.782/.434)
mulpd r5, XMM_P180 ;; T3 = T3 * (.782/.434)
addpd r2, r7 ;; newI2 = newI2 + T1 (final I2)
subpd r6, r5 ;; newI3 = newI3 - T3 (final I3)
subpd r4, r3 ;; newI4 = newI4 - T2 (final I4)
xload r5, XMM_TMP2 ;; final R3
ENDM
x7r_unfft_mem MACRO r1, r2, r3, r4, r5, r6, r7, t1, memr3, memr7, outmemr1
xcopy t1, r1 ;; R1
addpd t1, r2 ;; R1 + R2
addpd t1, r4 ;; R1 + R2 + R3
addpd t1, r6 ;; R1 + R2 + R3 + R4 (final R1)
xstore outmemr1, t1 ;; Save final R1
xcopy r7, r1 ;; A2 = R1
xcopy t1, r1 ;; A3 = R1
mulpd r2, XMM_P623 ;; S2 = R2 * .623
mulpd r4, XMM_P623 ;; S3 = R3 * .623
mulpd r6, XMM_P623 ;; S4 = R4 * .623
addpd r7, r2 ;; A2 = A2 + S2
addpd t1, r6 ;; A3 = A3 + S4
addpd r1, r4 ;; A4 = A4 + S3
mulpd r2, XMM_M358 ;; S2 = S2 * (-.223/.623)
mulpd r4, XMM_M358 ;; S3 = S3 * (-.223/.623)
mulpd r6, XMM_M358 ;; S4 = S4 * (-.223/.623)
addpd r7, r4 ;; A2 = A2 + S3
addpd t1, r2 ;; A3 = A3 + S2
addpd r1, r6 ;; A4 = A4 + S4
mulpd r2, XMM_P404 ;; S2 = S2 * (-.901/-.223)
mulpd r4, XMM_P404 ;; S3 = S3 * (-.901/-.223)
mulpd r6, XMM_P404 ;; S4 = S4 * (-.901/-.223)
addpd r7, r6 ;; A2 = A2 + S4
addpd t1, r4 ;; A3 = A3 + S3
addpd r1, r2 ;; A4 = A4 + S2
xstore XMM_TMP2, r7 ;; Save A2
xload r3, memr3 ;; Load I2
xload r7, memr7 ;; Load I3
mulpd r3, XMM_P975 ;; T2 = I2*.975
mulpd r5, XMM_P975 ;; T3 = I3*.975
mulpd r7, XMM_P975 ;; T4 = I4*.975
xcopy r6, r5 ;; B2 = T3
xcopy r2, r3 ;; B3 = T2
xcopy r4, r7 ;; B4 = T4
mulpd r3, XMM_P445 ;; T2 = T2 * (.434/.975)
mulpd r5, XMM_P445 ;; T3 = T3 * (.434/.975)
mulpd r7, XMM_P445 ;; T4 = T4 * (.434/.975)
addpd r6, r7 ;; B2 = B2 + T4
subpd r2, r5 ;; B3 = B3 - T3
addpd r4, r3 ;; B4 = B4 + T2
mulpd r3, XMM_P180 ;; T2 = T2 * (.782/.434)
mulpd r5, XMM_P180 ;; T3 = T3 * (.782/.434)
mulpd r7, XMM_P180 ;; T4 = T4 * (.782/.434)
addpd r6, r3 ;; B2 = B2 + T2
subpd r2, r7 ;; B3 = B3 - T4
subpd r4, r5 ;; B4 = B4 - T3
xload r3, XMM_TMP2 ;; Reload A2
subpd r3, r6 ;; A2 = A2 - B2 (final R7)
multwo r6 ;; B2 = B2 * 2
addpd r6, r3 ;; B2 = A2 + B2 (final R2)
subpd t1, r2 ;; A3 = A3 - B3 (final R6)
multwo r2 ;; B3 = B3 * 2
addpd r2, t1 ;; B3 = A3 + B3 (final R3)
subpd r1, r4 ;; A4 = A4 - B4 (final R5)
multwo r4 ;; B4 = B4 * 2
addpd r4, r1 ;; B4 = A4 + B4 (final R4)
ENDM
x7r_unfft MACRO r1, r2, r3, r4, r5, r6, r7, t1, memr1
xcopy t1, r1 ;; R1
addpd t1, r2 ;; R1 + R2
addpd t1, r4 ;; R1 + R2 + R3
addpd t1, r6 ;; R1 + R2 + R3 + R4 (final R1)
mulpd r3, XMM_P975 ;; T2 = I2*.975
mulpd r5, XMM_P975 ;; T3 = I3*.975
mulpd r7, XMM_P975 ;; T4 = I4*.975
xstore memr1, t1 ;; Save final R1
xstore XMM_TMP2, r2 ;; Save R2
xstore XMM_TMP3, r4 ;; Save R3
xcopy t1, r5 ;; B2 = T3
xcopy r2, r3 ;; B3 = T2
xcopy r4, r7 ;; B4 = T4
mulpd r3, XMM_P445 ;; T2 = T2 * (.434/.975)
mulpd r5, XMM_P445 ;; T3 = T3 * (.434/.975)
mulpd r7, XMM_P445 ;; T4 = T4 * (.434/.975)
addpd t1, r7 ;; B2 = B2 + T4
subpd r2, r5 ;; B3 = B3 - T3
addpd r4, r3 ;; B4 = B4 + T2
mulpd r3, XMM_P180 ;; T2 = T2 * (.782/.434)
mulpd r5, XMM_P180 ;; T3 = T3 * (.782/.434)
mulpd r7, XMM_P180 ;; T4 = T4 * (.782/.434)
addpd t1, r3 ;; B2 = B2 + T2
subpd r2, r7 ;; B3 = B3 - T4
subpd r4, r5 ;; B4 = B4 - T3
xload r3, XMM_TMP2 ;; Reload R2
xload r5, XMM_TMP3 ;; Reload R3
xstore XMM_TMP2, t1 ;; Save B2
xcopy r7, r1 ;; A2 = R1
xcopy t1, r1 ;; A3 = R1
mulpd r3, XMM_P623 ;; S2 = R2 * .623
mulpd r5, XMM_P623 ;; S3 = R3 * .623
mulpd r6, XMM_P623 ;; S4 = R4 * .623
addpd r7, r3 ;; A2 = A2 + S2
addpd t1, r6 ;; A3 = A3 + S4
addpd r1, r5 ;; A4 = A4 + S3
mulpd r3, XMM_M358 ;; S2 = S2 * (-.223/.623)
mulpd r5, XMM_M358 ;; S3 = S3 * (-.223/.623)
mulpd r6, XMM_M358 ;; S4 = S4 * (-.223/.623)
addpd r7, r5 ;; A2 = A2 + S3
addpd t1, r3 ;; A3 = A3 + S2
addpd r1, r6 ;; A4 = A4 + S4
mulpd r3, XMM_P404 ;; S2 = S2 * (-.901/-.223)
mulpd r5, XMM_P404 ;; S3 = S3 * (-.901/-.223)
mulpd r6, XMM_P404 ;; S4 = S4 * (-.901/-.223)
addpd r7, r6 ;; A2 = A2 + S4
addpd t1, r5 ;; A3 = A3 + S3
addpd r1, r3 ;; A4 = A4 + S2
xload r3, XMM_TMP2 ;; Reload B2
subpd r7, r3 ;; A2 = A2 - B2 (final R7)
multwo r3 ;; B2 = B2 * 2
addpd r3, r7 ;; B2 = A2 + B2 (final R2)
subpd t1, r2 ;; A3 = A3 - B3 (final R6)
multwo r2 ;; B3 = B3 * 2
addpd r2, t1 ;; B3 = A3 + B3 (final R3)
subpd r1, r4 ;; A4 = A4 - B4 (final R5)
multwo r4 ;; B4 = B4 * 2
addpd r4, r1 ;; B4 = A4 + B4 (final R4)
ENDM
x8r2_fft MACRO r1, r2, r3, r4, r5, r6, r7, r8, mem6, mem8, dest1
subpd r1, r3 ;; new R3 = R1 - R3 (final R3)
multwo r3
addpd r3, r1 ;; new R1 = R1 + R3
subpd r2, r4 ;; new R4 = R2 - R4 (final R4)
multwo r4
addpd r4, r2 ;; new R2 = R2 + R4
subpd r3, r4 ;; R1 = R1 - R2 (final R2)
multwo r4
addpd r4, r3 ;; R2 = R1 + R2 (final R1)
xload r8, mem8
xload r6, mem6
subpd r6, r8 ;; R2 - I2
addpd r8, mem6 ;; R2 + I2
mulpd r6, XMM_SQRTHALF ;; newR2
xstore dest1, r4
mulpd r8, XMM_SQRTHALF ;; newI2
subpd r7, r8 ;; I1 = I1 - I2 (new I2)
multwo r8
addpd r8, r7 ;; I2 = I1 + I2 (new I1)
subpd r5, r6 ;; R1 = R1 - R2 (new R2)
multwo r6
addpd r6, r5 ;; R2 = R1 + R2 (new R1)
ENDM
x8r2_unfft MACRO r1, r2, r3, r4, r5, r6, r7, r8, mem8, dest1
subpd r1, r2 ;; new R2 = R1 - R2
multwo r2
addpd r2, r1 ;; new R1 = R1 + R2
subpd r1, r4 ;; R2 = R2 - R4 (final R4)
multwo r4
addpd r4, r1 ;; R4 = R2 + R4 (final R2)
subpd r2, r3 ;; R1 = R1 - R3 (final R3)
multwo r3
addpd r3, r2 ;; R3 = R1 + R3 (final R1)
xload r8, mem8
addpd r8, r6 ;; new I1 = I1 + I2
xstore dest1, r3
subpd r6, mem8 ;; new I2 = I1 - I2
subpd r5, r7 ;; new R2 = R1 - R2
multwo r7
addpd r7, r5 ;; new R1 = R1 + R2
xload r3, XMM_SQRTHALF
mulpd r6, r3 ;; B2 = I2 * sine
mulpd r5, r3 ;; A2 = R2 * sine
xcopy r3, r6 ;; Save B2 (C2 = B2)
subpd r6, r5 ;; C2 = C2 - A2 (new I2)
addpd r5, r3 ;; A2 = A2 + B2 (new R2)
ENDM
x8r2_half_fft MACRO r1, r2, r3, r4, t1, t2, t3
subpd r1, r3 ;; new R3 = R1 - R3 (final R3)
multwo r3
addpd r3, r1 ;; new R1 = R1 + R3
subpd r2, r4 ;; new R4 = R2 - R4 (final R4)
multwo r4
addpd r4, r2 ;; new R2 = R2 + R4
subpd r3, r4 ;; R1 = R1 - R2 (final R2)
multwo r4
addpd r4, r3 ;; R2 = R1 + R2 (final R1)
ENDM
x8r2_half_unfft MACRO r1, r2, r3, r4, t1, t2, t3
subpd r1, r2 ;; new R2 = R1 - R2
multwo r2
addpd r2, r1 ;; new R1 = R1 + R2
subpd r1, r4 ;; R2 = R2 - R4 (final R4)
multwo r4
addpd r4, r1 ;; R4 = R2 + R4 (final R2)
subpd r2, r3 ;; R1 = R1 - R3 (final R3)
multwo r3
addpd r3, r2 ;; R3 = R1 + R3 (final R1)
ENDM
half_x4r_fft MACRO r1, r2, r3, r4, t1
subpd r1, r2 ;; R1 - R2 (final R2)
multwo r2
addpd r2, r1 ;; R1 + R2 (final R1)
;; Nop R3
;; Nop R4
ENDM
x4r_fft MACRO r1, r2, r3, r4, r5, r6, r7, r8
subpd r1, r2 ;; R1 - R2 (final R2)
multwo r2
addpd r2, r1 ;; R1 + R2 (final R1)
;; Nop R3
;; Nop R4
subpd r6, r8 ;; R2 - I2
multwo r8
addpd r8, r6 ;; R2 + I2
mulpd r6, XMM_SQRTHALF ;; newR2
mulpd r8, XMM_SQRTHALF ;; newI2
subpd r7, r8 ;; I1 = I1 - I2 (new I2)
multwo r8
addpd r8, r7 ;; I2 = I1 + I2 (new I1)
subpd r5, r6 ;; R1 = R1 - R2 (new R2)
multwo r6
addpd r6, r5 ;; R2 = R1 + R2 (new R1)
ENDM
; These macros implement 64-bit Pentium 4 optimized versions of macros found
; in hg.mac. We make use of the 8 extra registers.
IFDEF X86_64
xfive_reals_fft_preload MACRO
movapd xmm8, XMM_P618 ;; (.588/.951)
movapd xmm9, XMM_P309 ;; .309
movapd xmm10, XMM_P951 ;; .951
movapd xmm11, XMM_P588 ;; .588
movapd xmm12, XMM_M809 ;; -.809
movapd xmm13, XMM_M262 ;; (-.809/.309)
movapd xmm14, XMM_M162 ;; (-.951/.588)
movapd xmm15, XMM_M382 ;; (.309/-.809)
ENDM
x5r_fft MACRO r1, r2, r3, r4, r5, t1, t2, t3
movapd t1, r5 ;; 0-5 Copy R5
addpd r5, r2 ;; 1-4 T1 = R2 + R5
movapd t2, r4 ;; 2-7 Copy R4
addpd r4, r3 ;; 3-5 T2 = R3 + R4
movapd t3, r1 ;; 4-9 newR2 = R1
subpd r2, t1 ;; 6-9 T3 = R2 - R5
movapd t1, r1 ;; 7-12 newR3 = R1
subpd r3, t2 ;; 8-11 T4 = R3 - R4
movapd t2, xmm8 ;; 9-14 const (.588/.951)
addpd r1, r5 ;; 10-13 newR1 = R1 + T1
mulpd r5, xmm9 ;; 11-16 T1 = T1 * .309
mulpd r2, xmm10 ;; 13-18 T3 = T3 * .951 (new I2)
addpd r1, r4 ;; 14-17 newR1 = newR1 + T2
mulpd r3, xmm11 ;; 15-20 T4 = T4 * .588
addpd t3, r5 ;; 17-20 newR2 = newR2 + T1
mulpd r4, xmm12 ;; 18-23 T2 = T2 * -.809
mulpd r5, xmm13 ;; 20-25 T1 = T1 * (-.809/.309)
mulpd t2, r2 ;; 22-27 T3 = T3 * (.588/.951)
addpd r2, r3 ;; 23-26 newI2 = newI2 + T4
mulpd r3, xmm14 ;; 24-29 T4 = T4 * (-.951/.588)
addpd t3, r4 ;; 25-28 newR2 = newR2 + T2
mulpd r4, xmm15 ;; 26-31 T2 = T2 * (.309/-.809)
addpd t1, r5 ;; 27-30 newR3 = newR3 + T1
addpd t2, r3 ;; 30-33 T3 = T3 + T4 (final I3)
addpd t1, r4 ;; 32-35 newR3 = newR3 + T2
ENDM
xfive_reals_unfft_preload MACRO
movapd xmm8, XMM_P309 ;; Load .309
movapd xmm9, XMM_M809 ;; Load -.809
movapd xmm10, XMM_P951 ;; Load 0.951
movapd xmm11, XMM_P588 ;; Load 0.588
ENDM
x5r_unfft MACRO r1, r2, r3, r4, r5, t1, t2, t3, mem1
movapd t1, xmm8 ;; Load .309
mulpd t1, r2 ;; 1-6 R2*.309
movapd t2, xmm9 ;; Load -.809
mulpd t2, r2 ;; 3-8 R2*-.809
addpd r2, r4 ;; 4-7 R2+R3
movapd t3, xmm9 ;; Load -.809
mulpd t3, r4 ;; 5-10 R3*-.809
addpd r2, r1 ;; 6-9 R1+R2+R3 (final R1)
mulpd r4, xmm8 ;; 7-12 R3*.309
addpd t1, r1 ;; 8-11 R1 + R2*.309
movapd mem1, r2 ;; Save final R1
movapd r2, xmm10 ;; Load 0.951
mulpd r2, r3 ;; 9-14 I2*.951
addpd t2, r1 ;; 10-13 R1 + R2*-.809
movapd r1, xmm11 ;; Load 0.588
mulpd r1, r5 ;; 11-16 I3*.588
addpd t1, t3 ;; 12-15 R1 + R2*.309 - R3*.809
mulpd r3, xmm11 ;; 13-18 I2*.588
addpd t2, r4 ;; 14-17 R1 - R2*.809 + R3*.309
mulpd r5, xmm10 ;; 15-20 I3*-.951
movapd t3, t1 ;; 16-21 R1 + R2*.309 - R3*.809
addpd r2, r1 ;; 17-20 I2*.951 + I3*.588
movapd r4, t2 ;; 18-23 R1 - R2*.809 + R3*.309
subpd r3, r5 ;; 21-24 I2*.588 - I3*.951
addpd t1, r2 ;; 23-26 final R2
subpd t3, r2 ;; 25-28 final R5
addpd t2, r3 ;; 27-30 final R3
subpd r4, r3 ;; 29-31 final R4
ENDM
ENDIF