^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 1) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 2) | ssin.sa 3.3 7/29/91
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 3) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 4) | The entry point sSIN computes the sine of an input argument
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 5) | sCOS computes the cosine, and sSINCOS computes both. The
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 6) | corresponding entry points with a "d" computes the same
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 7) | corresponding function values for denormalized inputs.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 8) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 9) | Input: Double-extended number X in location pointed to
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 10) | by address register a0.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 11) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 12) | Output: The function value sin(X) or cos(X) returned in Fp0 if SIN or
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 13) | COS is requested. Otherwise, for SINCOS, sin(X) is returned
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 14) | in Fp0, and cos(X) is returned in Fp1.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 15) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 16) | Modifies: Fp0 for SIN or COS; both Fp0 and Fp1 for SINCOS.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 17) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 18) | Accuracy and Monotonicity: The returned result is within 1 ulp in
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 19) | 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 20) | result is subsequently rounded to double precision. The
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 21) | result is provably monotonic in double precision.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 22) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 23) | Speed: The programs sSIN and sCOS take approximately 150 cycles for
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 24) | input argument X such that |X| < 15Pi, which is the usual
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 25) | situation. The speed for sSINCOS is approximately 190 cycles.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 26) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 27) | Algorithm:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 28) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 29) | SIN and COS:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 30) | 1. If SIN is invoked, set AdjN := 0; otherwise, set AdjN := 1.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 31) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 32) | 2. If |X| >= 15Pi or |X| < 2**(-40), go to 7.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 33) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 34) | 3. Decompose X as X = N(Pi/2) + r where |r| <= Pi/4. Let
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 35) | k = N mod 4, so in particular, k = 0,1,2,or 3. Overwrite
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 36) | k by k := k + AdjN.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 37) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 38) | 4. If k is even, go to 6.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 39) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 40) | 5. (k is odd) Set j := (k-1)/2, sgn := (-1)**j. Return sgn*cos(r)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 41) | where cos(r) is approximated by an even polynomial in r,
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 42) | 1 + r*r*(B1+s*(B2+ ... + s*B8)), s = r*r.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 43) | Exit.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 44) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 45) | 6. (k is even) Set j := k/2, sgn := (-1)**j. Return sgn*sin(r)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 46) | where sin(r) is approximated by an odd polynomial in r
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 47) | r + r*s*(A1+s*(A2+ ... + s*A7)), s = r*r.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 48) | Exit.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 49) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 50) | 7. If |X| > 1, go to 9.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 51) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 52) | 8. (|X|<2**(-40)) If SIN is invoked, return X; otherwise return 1.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 53) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 54) | 9. Overwrite X by X := X rem 2Pi. Now that |X| <= Pi, go back to 3.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 55) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 56) | SINCOS:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 57) | 1. If |X| >= 15Pi or |X| < 2**(-40), go to 6.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 58) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 59) | 2. Decompose X as X = N(Pi/2) + r where |r| <= Pi/4. Let
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 60) | k = N mod 4, so in particular, k = 0,1,2,or 3.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 61) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 62) | 3. If k is even, go to 5.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 63) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 64) | 4. (k is odd) Set j1 := (k-1)/2, j2 := j1 (EOR) (k mod 2), i.e.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 65) | j1 exclusive or with the l.s.b. of k.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 66) | sgn1 := (-1)**j1, sgn2 := (-1)**j2.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 67) | SIN(X) = sgn1 * cos(r) and COS(X) = sgn2*sin(r) where
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 68) | sin(r) and cos(r) are computed as odd and even polynomials
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 69) | in r, respectively. Exit
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 70) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 71) | 5. (k is even) Set j1 := k/2, sgn1 := (-1)**j1.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 72) | SIN(X) = sgn1 * sin(r) and COS(X) = sgn1*cos(r) where
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 73) | sin(r) and cos(r) are computed as odd and even polynomials
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 74) | in r, respectively. Exit
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 75) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 76) | 6. If |X| > 1, go to 8.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 77) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 78) | 7. (|X|<2**(-40)) SIN(X) = X and COS(X) = 1. Exit.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 79) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 80) | 8. Overwrite X by X := X rem 2Pi. Now that |X| <= Pi, go back to 2.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 81) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 82)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 83) | Copyright (C) Motorola, Inc. 1990
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 84) | All Rights Reserved
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 85) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 86) | For details on the license for this file, please see the
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 87) | file, README, in this same directory.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 88)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 89) |SSIN idnt 2,1 | Motorola 040 Floating Point Software Package
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 90)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 91) |section 8
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 92)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 93) #include "fpsp.h"
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 94)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 95) BOUNDS1: .long 0x3FD78000,0x4004BC7E
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 96) TWOBYPI: .long 0x3FE45F30,0x6DC9C883
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 97)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 98) SINA7: .long 0xBD6AAA77,0xCCC994F5
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 99) SINA6: .long 0x3DE61209,0x7AAE8DA1
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 100)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 101) SINA5: .long 0xBE5AE645,0x2A118AE4
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 102) SINA4: .long 0x3EC71DE3,0xA5341531
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 103)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 104) SINA3: .long 0xBF2A01A0,0x1A018B59,0x00000000,0x00000000
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 105)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 106) SINA2: .long 0x3FF80000,0x88888888,0x888859AF,0x00000000
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 107)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 108) SINA1: .long 0xBFFC0000,0xAAAAAAAA,0xAAAAAA99,0x00000000
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 109)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 110) COSB8: .long 0x3D2AC4D0,0xD6011EE3
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 111) COSB7: .long 0xBDA9396F,0x9F45AC19
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 112)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 113) COSB6: .long 0x3E21EED9,0x0612C972
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 114) COSB5: .long 0xBE927E4F,0xB79D9FCF
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 115)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 116) COSB4: .long 0x3EFA01A0,0x1A01D423,0x00000000,0x00000000
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 117)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 118) COSB3: .long 0xBFF50000,0xB60B60B6,0x0B61D438,0x00000000
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 119)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 120) COSB2: .long 0x3FFA0000,0xAAAAAAAA,0xAAAAAB5E
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 121) COSB1: .long 0xBF000000
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 122)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 123) INVTWOPI: .long 0x3FFC0000,0xA2F9836E,0x4E44152A
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 124)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 125) TWOPI1: .long 0x40010000,0xC90FDAA2,0x00000000,0x00000000
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 126) TWOPI2: .long 0x3FDF0000,0x85A308D4,0x00000000,0x00000000
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 127)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 128) |xref PITBL
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 129)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 130) .set INARG,FP_SCR4
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 131)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 132) .set X,FP_SCR5
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 133) .set XDCARE,X+2
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 134) .set XFRAC,X+4
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 135)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 136) .set RPRIME,FP_SCR1
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 137) .set SPRIME,FP_SCR2
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 138)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 139) .set POSNEG1,L_SCR1
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 140) .set TWOTO63,L_SCR1
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 141)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 142) .set ENDFLAG,L_SCR2
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 143) .set N,L_SCR2
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 144)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 145) .set ADJN,L_SCR3
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 146)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 147) | xref t_frcinx
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 148) |xref t_extdnrm
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 149) |xref sto_cos
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 150)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 151) .global ssind
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 152) ssind:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 153) |--SIN(X) = X FOR DENORMALIZED X
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 154) bra t_extdnrm
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 155)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 156) .global scosd
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 157) scosd:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 158) |--COS(X) = 1 FOR DENORMALIZED X
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 159)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 160) fmoves #0x3F800000,%fp0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 161) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 162) | 9D25B Fix: Sometimes the previous fmove.s sets fpsr bits
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 163) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 164) fmovel #0,%fpsr
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 165) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 166) bra t_frcinx
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 167)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 168) .global ssin
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 169) ssin:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 170) |--SET ADJN TO 0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 171) movel #0,ADJN(%a6)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 172) bras SINBGN
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 173)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 174) .global scos
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 175) scos:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 176) |--SET ADJN TO 1
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 177) movel #1,ADJN(%a6)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 178)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 179) SINBGN:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 180) |--SAVE FPCR, FP1. CHECK IF |X| IS TOO SMALL OR LARGE
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 181)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 182) fmovex (%a0),%fp0 | ...LOAD INPUT
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 183)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 184) movel (%a0),%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 185) movew 4(%a0),%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 186) fmovex %fp0,X(%a6)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 187) andil #0x7FFFFFFF,%d0 | ...COMPACTIFY X
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 188)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 189) cmpil #0x3FD78000,%d0 | ...|X| >= 2**(-40)?
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 190) bges SOK1
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 191) bra SINSM
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 192)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 193) SOK1:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 194) cmpil #0x4004BC7E,%d0 | ...|X| < 15 PI?
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 195) blts SINMAIN
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 196) bra REDUCEX
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 197)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 198) SINMAIN:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 199) |--THIS IS THE USUAL CASE, |X| <= 15 PI.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 200) |--THE ARGUMENT REDUCTION IS DONE BY TABLE LOOK UP.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 201) fmovex %fp0,%fp1
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 202) fmuld TWOBYPI,%fp1 | ...X*2/PI
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 203)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 204) |--HIDE THE NEXT THREE INSTRUCTIONS
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 205) lea PITBL+0x200,%a1 | ...TABLE OF N*PI/2, N = -32,...,32
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 206)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 207)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 208) |--FP1 IS NOW READY
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 209) fmovel %fp1,N(%a6) | ...CONVERT TO INTEGER
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 210)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 211) movel N(%a6),%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 212) asll #4,%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 213) addal %d0,%a1 | ...A1 IS THE ADDRESS OF N*PIBY2
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 214) | ...WHICH IS IN TWO PIECES Y1 & Y2
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 215)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 216) fsubx (%a1)+,%fp0 | ...X-Y1
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 217) |--HIDE THE NEXT ONE
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 218) fsubs (%a1),%fp0 | ...FP0 IS R = (X-Y1)-Y2
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 219)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 220) SINCONT:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 221) |--continuation from REDUCEX
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 222)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 223) |--GET N+ADJN AND SEE IF SIN(R) OR COS(R) IS NEEDED
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 224) movel N(%a6),%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 225) addl ADJN(%a6),%d0 | ...SEE IF D0 IS ODD OR EVEN
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 226) rorl #1,%d0 | ...D0 WAS ODD IFF D0 IS NEGATIVE
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 227) cmpil #0,%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 228) blt COSPOLY
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 229)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 230) SINPOLY:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 231) |--LET J BE THE LEAST SIG. BIT OF D0, LET SGN := (-1)**J.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 232) |--THEN WE RETURN SGN*SIN(R). SGN*SIN(R) IS COMPUTED BY
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 233) |--R' + R'*S*(A1 + S(A2 + S(A3 + S(A4 + ... + SA7)))), WHERE
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 234) |--R' = SGN*R, S=R*R. THIS CAN BE REWRITTEN AS
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 235) |--R' + R'*S*( [A1+T(A3+T(A5+TA7))] + [S(A2+T(A4+TA6))])
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 236) |--WHERE T=S*S.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 237) |--NOTE THAT A3 THROUGH A7 ARE STORED IN DOUBLE PRECISION
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 238) |--WHILE A1 AND A2 ARE IN DOUBLE-EXTENDED FORMAT.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 239) fmovex %fp0,X(%a6) | ...X IS R
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 240) fmulx %fp0,%fp0 | ...FP0 IS S
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 241) |---HIDE THE NEXT TWO WHILE WAITING FOR FP0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 242) fmoved SINA7,%fp3
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 243) fmoved SINA6,%fp2
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 244) |--FP0 IS NOW READY
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 245) fmovex %fp0,%fp1
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 246) fmulx %fp1,%fp1 | ...FP1 IS T
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 247) |--HIDE THE NEXT TWO WHILE WAITING FOR FP1
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 248)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 249) rorl #1,%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 250) andil #0x80000000,%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 251) | ...LEAST SIG. BIT OF D0 IN SIGN POSITION
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 252) eorl %d0,X(%a6) | ...X IS NOW R'= SGN*R
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 253)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 254) fmulx %fp1,%fp3 | ...TA7
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 255) fmulx %fp1,%fp2 | ...TA6
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 256)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 257) faddd SINA5,%fp3 | ...A5+TA7
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 258) faddd SINA4,%fp2 | ...A4+TA6
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 259)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 260) fmulx %fp1,%fp3 | ...T(A5+TA7)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 261) fmulx %fp1,%fp2 | ...T(A4+TA6)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 262)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 263) faddd SINA3,%fp3 | ...A3+T(A5+TA7)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 264) faddx SINA2,%fp2 | ...A2+T(A4+TA6)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 265)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 266) fmulx %fp3,%fp1 | ...T(A3+T(A5+TA7))
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 267)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 268) fmulx %fp0,%fp2 | ...S(A2+T(A4+TA6))
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 269) faddx SINA1,%fp1 | ...A1+T(A3+T(A5+TA7))
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 270) fmulx X(%a6),%fp0 | ...R'*S
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 271)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 272) faddx %fp2,%fp1 | ...[A1+T(A3+T(A5+TA7))]+[S(A2+T(A4+TA6))]
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 273) |--FP3 RELEASED, RESTORE NOW AND TAKE SOME ADVANTAGE OF HIDING
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 274) |--FP2 RELEASED, RESTORE NOW AND TAKE FULL ADVANTAGE OF HIDING
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 275)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 276)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 277) fmulx %fp1,%fp0 | ...SIN(R')-R'
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 278) |--FP1 RELEASED.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 279)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 280) fmovel %d1,%FPCR |restore users exceptions
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 281) faddx X(%a6),%fp0 |last inst - possible exception set
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 282) bra t_frcinx
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 283)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 284)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 285) COSPOLY:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 286) |--LET J BE THE LEAST SIG. BIT OF D0, LET SGN := (-1)**J.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 287) |--THEN WE RETURN SGN*COS(R). SGN*COS(R) IS COMPUTED BY
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 288) |--SGN + S'*(B1 + S(B2 + S(B3 + S(B4 + ... + SB8)))), WHERE
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 289) |--S=R*R AND S'=SGN*S. THIS CAN BE REWRITTEN AS
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 290) |--SGN + S'*([B1+T(B3+T(B5+TB7))] + [S(B2+T(B4+T(B6+TB8)))])
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 291) |--WHERE T=S*S.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 292) |--NOTE THAT B4 THROUGH B8 ARE STORED IN DOUBLE PRECISION
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 293) |--WHILE B2 AND B3 ARE IN DOUBLE-EXTENDED FORMAT, B1 IS -1/2
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 294) |--AND IS THEREFORE STORED AS SINGLE PRECISION.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 295)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 296) fmulx %fp0,%fp0 | ...FP0 IS S
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 297) |---HIDE THE NEXT TWO WHILE WAITING FOR FP0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 298) fmoved COSB8,%fp2
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 299) fmoved COSB7,%fp3
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 300) |--FP0 IS NOW READY
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 301) fmovex %fp0,%fp1
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 302) fmulx %fp1,%fp1 | ...FP1 IS T
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 303) |--HIDE THE NEXT TWO WHILE WAITING FOR FP1
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 304) fmovex %fp0,X(%a6) | ...X IS S
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 305) rorl #1,%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 306) andil #0x80000000,%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 307) | ...LEAST SIG. BIT OF D0 IN SIGN POSITION
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 308)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 309) fmulx %fp1,%fp2 | ...TB8
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 310) |--HIDE THE NEXT TWO WHILE WAITING FOR THE XU
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 311) eorl %d0,X(%a6) | ...X IS NOW S'= SGN*S
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 312) andil #0x80000000,%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 313)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 314) fmulx %fp1,%fp3 | ...TB7
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 315) |--HIDE THE NEXT TWO WHILE WAITING FOR THE XU
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 316) oril #0x3F800000,%d0 | ...D0 IS SGN IN SINGLE
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 317) movel %d0,POSNEG1(%a6)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 318)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 319) faddd COSB6,%fp2 | ...B6+TB8
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 320) faddd COSB5,%fp3 | ...B5+TB7
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 321)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 322) fmulx %fp1,%fp2 | ...T(B6+TB8)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 323) fmulx %fp1,%fp3 | ...T(B5+TB7)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 324)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 325) faddd COSB4,%fp2 | ...B4+T(B6+TB8)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 326) faddx COSB3,%fp3 | ...B3+T(B5+TB7)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 327)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 328) fmulx %fp1,%fp2 | ...T(B4+T(B6+TB8))
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 329) fmulx %fp3,%fp1 | ...T(B3+T(B5+TB7))
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 330)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 331) faddx COSB2,%fp2 | ...B2+T(B4+T(B6+TB8))
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 332) fadds COSB1,%fp1 | ...B1+T(B3+T(B5+TB7))
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 333)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 334) fmulx %fp2,%fp0 | ...S(B2+T(B4+T(B6+TB8)))
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 335) |--FP3 RELEASED, RESTORE NOW AND TAKE SOME ADVANTAGE OF HIDING
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 336) |--FP2 RELEASED.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 337)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 338)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 339) faddx %fp1,%fp0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 340) |--FP1 RELEASED
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 341)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 342) fmulx X(%a6),%fp0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 343)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 344) fmovel %d1,%FPCR |restore users exceptions
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 345) fadds POSNEG1(%a6),%fp0 |last inst - possible exception set
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 346) bra t_frcinx
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 347)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 348)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 349) SINBORS:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 350) |--IF |X| > 15PI, WE USE THE GENERAL ARGUMENT REDUCTION.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 351) |--IF |X| < 2**(-40), RETURN X OR 1.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 352) cmpil #0x3FFF8000,%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 353) bgts REDUCEX
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 354)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 355)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 356) SINSM:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 357) movel ADJN(%a6),%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 358) cmpil #0,%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 359) bgts COSTINY
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 360)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 361) SINTINY:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 362) movew #0x0000,XDCARE(%a6) | ...JUST IN CASE
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 363) fmovel %d1,%FPCR |restore users exceptions
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 364) fmovex X(%a6),%fp0 |last inst - possible exception set
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 365) bra t_frcinx
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 366)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 367)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 368) COSTINY:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 369) fmoves #0x3F800000,%fp0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 370)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 371) fmovel %d1,%FPCR |restore users exceptions
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 372) fsubs #0x00800000,%fp0 |last inst - possible exception set
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 373) bra t_frcinx
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 374)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 375)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 376) REDUCEX:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 377) |--WHEN REDUCEX IS USED, THE CODE WILL INEVITABLY BE SLOW.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 378) |--THIS REDUCTION METHOD, HOWEVER, IS MUCH FASTER THAN USING
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 379) |--THE REMAINDER INSTRUCTION WHICH IS NOW IN SOFTWARE.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 380)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 381) fmovemx %fp2-%fp5,-(%a7) | ...save FP2 through FP5
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 382) movel %d2,-(%a7)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 383) fmoves #0x00000000,%fp1
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 384) |--If compact form of abs(arg) in d0=$7ffeffff, argument is so large that
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 385) |--there is a danger of unwanted overflow in first LOOP iteration. In this
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 386) |--case, reduce argument by one remainder step to make subsequent reduction
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 387) |--safe.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 388) cmpil #0x7ffeffff,%d0 |is argument dangerously large?
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 389) bnes LOOP
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 390) movel #0x7ffe0000,FP_SCR2(%a6) |yes
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 391) | ;create 2**16383*PI/2
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 392) movel #0xc90fdaa2,FP_SCR2+4(%a6)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 393) clrl FP_SCR2+8(%a6)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 394) ftstx %fp0 |test sign of argument
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 395) movel #0x7fdc0000,FP_SCR3(%a6) |create low half of 2**16383*
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 396) | ;PI/2 at FP_SCR3
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 397) movel #0x85a308d3,FP_SCR3+4(%a6)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 398) clrl FP_SCR3+8(%a6)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 399) fblt red_neg
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 400) orw #0x8000,FP_SCR2(%a6) |positive arg
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 401) orw #0x8000,FP_SCR3(%a6)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 402) red_neg:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 403) faddx FP_SCR2(%a6),%fp0 |high part of reduction is exact
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 404) fmovex %fp0,%fp1 |save high result in fp1
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 405) faddx FP_SCR3(%a6),%fp0 |low part of reduction
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 406) fsubx %fp0,%fp1 |determine low component of result
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 407) faddx FP_SCR3(%a6),%fp1 |fp0/fp1 are reduced argument.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 408)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 409) |--ON ENTRY, FP0 IS X, ON RETURN, FP0 IS X REM PI/2, |X| <= PI/4.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 410) |--integer quotient will be stored in N
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 411) |--Intermediate remainder is 66-bit long; (R,r) in (FP0,FP1)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 412)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 413) LOOP:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 414) fmovex %fp0,INARG(%a6) | ...+-2**K * F, 1 <= F < 2
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 415) movew INARG(%a6),%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 416) movel %d0,%a1 | ...save a copy of D0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 417) andil #0x00007FFF,%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 418) subil #0x00003FFF,%d0 | ...D0 IS K
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 419) cmpil #28,%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 420) bles LASTLOOP
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 421) CONTLOOP:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 422) subil #27,%d0 | ...D0 IS L := K-27
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 423) movel #0,ENDFLAG(%a6)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 424) bras WORK
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 425) LASTLOOP:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 426) clrl %d0 | ...D0 IS L := 0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 427) movel #1,ENDFLAG(%a6)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 428)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 429) WORK:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 430) |--FIND THE REMAINDER OF (R,r) W.R.T. 2**L * (PI/2). L IS SO CHOSEN
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 431) |--THAT INT( X * (2/PI) / 2**(L) ) < 2**29.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 432)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 433) |--CREATE 2**(-L) * (2/PI), SIGN(INARG)*2**(63),
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 434) |--2**L * (PIby2_1), 2**L * (PIby2_2)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 435)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 436) movel #0x00003FFE,%d2 | ...BIASED EXPO OF 2/PI
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 437) subl %d0,%d2 | ...BIASED EXPO OF 2**(-L)*(2/PI)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 438)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 439) movel #0xA2F9836E,FP_SCR1+4(%a6)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 440) movel #0x4E44152A,FP_SCR1+8(%a6)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 441) movew %d2,FP_SCR1(%a6) | ...FP_SCR1 is 2**(-L)*(2/PI)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 442)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 443) fmovex %fp0,%fp2
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 444) fmulx FP_SCR1(%a6),%fp2
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 445) |--WE MUST NOW FIND INT(FP2). SINCE WE NEED THIS VALUE IN
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 446) |--FLOATING POINT FORMAT, THE TWO FMOVE'S FMOVE.L FP <--> N
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 447) |--WILL BE TOO INEFFICIENT. THE WAY AROUND IT IS THAT
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 448) |--(SIGN(INARG)*2**63 + FP2) - SIGN(INARG)*2**63 WILL GIVE
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 449) |--US THE DESIRED VALUE IN FLOATING POINT.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 450)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 451) |--HIDE SIX CYCLES OF INSTRUCTION
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 452) movel %a1,%d2
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 453) swap %d2
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 454) andil #0x80000000,%d2
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 455) oril #0x5F000000,%d2 | ...D2 IS SIGN(INARG)*2**63 IN SGL
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 456) movel %d2,TWOTO63(%a6)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 457)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 458) movel %d0,%d2
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 459) addil #0x00003FFF,%d2 | ...BIASED EXPO OF 2**L * (PI/2)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 460)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 461) |--FP2 IS READY
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 462) fadds TWOTO63(%a6),%fp2 | ...THE FRACTIONAL PART OF FP1 IS ROUNDED
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 463)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 464) |--HIDE 4 CYCLES OF INSTRUCTION; creating 2**(L)*Piby2_1 and 2**(L)*Piby2_2
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 465) movew %d2,FP_SCR2(%a6)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 466) clrw FP_SCR2+2(%a6)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 467) movel #0xC90FDAA2,FP_SCR2+4(%a6)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 468) clrl FP_SCR2+8(%a6) | ...FP_SCR2 is 2**(L) * Piby2_1
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 469)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 470) |--FP2 IS READY
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 471) fsubs TWOTO63(%a6),%fp2 | ...FP2 is N
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 472)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 473) addil #0x00003FDD,%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 474) movew %d0,FP_SCR3(%a6)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 475) clrw FP_SCR3+2(%a6)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 476) movel #0x85A308D3,FP_SCR3+4(%a6)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 477) clrl FP_SCR3+8(%a6) | ...FP_SCR3 is 2**(L) * Piby2_2
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 478)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 479) movel ENDFLAG(%a6),%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 480)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 481) |--We are now ready to perform (R+r) - N*P1 - N*P2, P1 = 2**(L) * Piby2_1 and
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 482) |--P2 = 2**(L) * Piby2_2
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 483) fmovex %fp2,%fp4
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 484) fmulx FP_SCR2(%a6),%fp4 | ...W = N*P1
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 485) fmovex %fp2,%fp5
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 486) fmulx FP_SCR3(%a6),%fp5 | ...w = N*P2
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 487) fmovex %fp4,%fp3
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 488) |--we want P+p = W+w but |p| <= half ulp of P
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 489) |--Then, we need to compute A := R-P and a := r-p
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 490) faddx %fp5,%fp3 | ...FP3 is P
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 491) fsubx %fp3,%fp4 | ...W-P
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 492)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 493) fsubx %fp3,%fp0 | ...FP0 is A := R - P
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 494) faddx %fp5,%fp4 | ...FP4 is p = (W-P)+w
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 495)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 496) fmovex %fp0,%fp3 | ...FP3 A
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 497) fsubx %fp4,%fp1 | ...FP1 is a := r - p
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 498)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 499) |--Now we need to normalize (A,a) to "new (R,r)" where R+r = A+a but
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 500) |--|r| <= half ulp of R.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 501) faddx %fp1,%fp0 | ...FP0 is R := A+a
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 502) |--No need to calculate r if this is the last loop
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 503) cmpil #0,%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 504) bgt RESTORE
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 505)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 506) |--Need to calculate r
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 507) fsubx %fp0,%fp3 | ...A-R
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 508) faddx %fp3,%fp1 | ...FP1 is r := (A-R)+a
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 509) bra LOOP
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 510)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 511) RESTORE:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 512) fmovel %fp2,N(%a6)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 513) movel (%a7)+,%d2
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 514) fmovemx (%a7)+,%fp2-%fp5
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 515)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 516)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 517) movel ADJN(%a6),%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 518) cmpil #4,%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 519)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 520) blt SINCONT
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 521) bras SCCONT
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 522)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 523) .global ssincosd
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 524) ssincosd:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 525) |--SIN AND COS OF X FOR DENORMALIZED X
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 526)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 527) fmoves #0x3F800000,%fp1
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 528) bsr sto_cos |store cosine result
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 529) bra t_extdnrm
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 530)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 531) .global ssincos
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 532) ssincos:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 533) |--SET ADJN TO 4
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 534) movel #4,ADJN(%a6)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 535)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 536) fmovex (%a0),%fp0 | ...LOAD INPUT
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 537)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 538) movel (%a0),%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 539) movew 4(%a0),%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 540) fmovex %fp0,X(%a6)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 541) andil #0x7FFFFFFF,%d0 | ...COMPACTIFY X
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 542)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 543) cmpil #0x3FD78000,%d0 | ...|X| >= 2**(-40)?
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 544) bges SCOK1
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 545) bra SCSM
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 546)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 547) SCOK1:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 548) cmpil #0x4004BC7E,%d0 | ...|X| < 15 PI?
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 549) blts SCMAIN
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 550) bra REDUCEX
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 551)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 552)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 553) SCMAIN:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 554) |--THIS IS THE USUAL CASE, |X| <= 15 PI.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 555) |--THE ARGUMENT REDUCTION IS DONE BY TABLE LOOK UP.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 556) fmovex %fp0,%fp1
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 557) fmuld TWOBYPI,%fp1 | ...X*2/PI
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 558)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 559) |--HIDE THE NEXT THREE INSTRUCTIONS
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 560) lea PITBL+0x200,%a1 | ...TABLE OF N*PI/2, N = -32,...,32
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 561)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 562)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 563) |--FP1 IS NOW READY
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 564) fmovel %fp1,N(%a6) | ...CONVERT TO INTEGER
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 565)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 566) movel N(%a6),%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 567) asll #4,%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 568) addal %d0,%a1 | ...ADDRESS OF N*PIBY2, IN Y1, Y2
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 569)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 570) fsubx (%a1)+,%fp0 | ...X-Y1
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 571) fsubs (%a1),%fp0 | ...FP0 IS R = (X-Y1)-Y2
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 572)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 573) SCCONT:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 574) |--continuation point from REDUCEX
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 575)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 576) |--HIDE THE NEXT TWO
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 577) movel N(%a6),%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 578) rorl #1,%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 579)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 580) cmpil #0,%d0 | ...D0 < 0 IFF N IS ODD
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 581) bge NEVEN
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 582)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 583) NODD:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 584) |--REGISTERS SAVED SO FAR: D0, A0, FP2.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 585)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 586) fmovex %fp0,RPRIME(%a6)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 587) fmulx %fp0,%fp0 | ...FP0 IS S = R*R
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 588) fmoved SINA7,%fp1 | ...A7
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 589) fmoved COSB8,%fp2 | ...B8
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 590) fmulx %fp0,%fp1 | ...SA7
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 591) movel %d2,-(%a7)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 592) movel %d0,%d2
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 593) fmulx %fp0,%fp2 | ...SB8
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 594) rorl #1,%d2
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 595) andil #0x80000000,%d2
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 596)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 597) faddd SINA6,%fp1 | ...A6+SA7
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 598) eorl %d0,%d2
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 599) andil #0x80000000,%d2
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 600) faddd COSB7,%fp2 | ...B7+SB8
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 601)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 602) fmulx %fp0,%fp1 | ...S(A6+SA7)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 603) eorl %d2,RPRIME(%a6)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 604) movel (%a7)+,%d2
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 605) fmulx %fp0,%fp2 | ...S(B7+SB8)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 606) rorl #1,%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 607) andil #0x80000000,%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 608)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 609) faddd SINA5,%fp1 | ...A5+S(A6+SA7)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 610) movel #0x3F800000,POSNEG1(%a6)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 611) eorl %d0,POSNEG1(%a6)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 612) faddd COSB6,%fp2 | ...B6+S(B7+SB8)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 613)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 614) fmulx %fp0,%fp1 | ...S(A5+S(A6+SA7))
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 615) fmulx %fp0,%fp2 | ...S(B6+S(B7+SB8))
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 616) fmovex %fp0,SPRIME(%a6)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 617)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 618) faddd SINA4,%fp1 | ...A4+S(A5+S(A6+SA7))
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 619) eorl %d0,SPRIME(%a6)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 620) faddd COSB5,%fp2 | ...B5+S(B6+S(B7+SB8))
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 621)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 622) fmulx %fp0,%fp1 | ...S(A4+...)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 623) fmulx %fp0,%fp2 | ...S(B5+...)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 624)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 625) faddd SINA3,%fp1 | ...A3+S(A4+...)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 626) faddd COSB4,%fp2 | ...B4+S(B5+...)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 627)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 628) fmulx %fp0,%fp1 | ...S(A3+...)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 629) fmulx %fp0,%fp2 | ...S(B4+...)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 630)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 631) faddx SINA2,%fp1 | ...A2+S(A3+...)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 632) faddx COSB3,%fp2 | ...B3+S(B4+...)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 633)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 634) fmulx %fp0,%fp1 | ...S(A2+...)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 635) fmulx %fp0,%fp2 | ...S(B3+...)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 636)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 637) faddx SINA1,%fp1 | ...A1+S(A2+...)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 638) faddx COSB2,%fp2 | ...B2+S(B3+...)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 639)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 640) fmulx %fp0,%fp1 | ...S(A1+...)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 641) fmulx %fp2,%fp0 | ...S(B2+...)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 642)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 643)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 644)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 645) fmulx RPRIME(%a6),%fp1 | ...R'S(A1+...)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 646) fadds COSB1,%fp0 | ...B1+S(B2...)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 647) fmulx SPRIME(%a6),%fp0 | ...S'(B1+S(B2+...))
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 648)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 649) movel %d1,-(%sp) |restore users mode & precision
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 650) andil #0xff,%d1 |mask off all exceptions
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 651) fmovel %d1,%FPCR
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 652) faddx RPRIME(%a6),%fp1 | ...COS(X)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 653) bsr sto_cos |store cosine result
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 654) fmovel (%sp)+,%FPCR |restore users exceptions
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 655) fadds POSNEG1(%a6),%fp0 | ...SIN(X)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 656)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 657) bra t_frcinx
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 658)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 659)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 660) NEVEN:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 661) |--REGISTERS SAVED SO FAR: FP2.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 662)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 663) fmovex %fp0,RPRIME(%a6)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 664) fmulx %fp0,%fp0 | ...FP0 IS S = R*R
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 665) fmoved COSB8,%fp1 | ...B8
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 666) fmoved SINA7,%fp2 | ...A7
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 667) fmulx %fp0,%fp1 | ...SB8
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 668) fmovex %fp0,SPRIME(%a6)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 669) fmulx %fp0,%fp2 | ...SA7
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 670) rorl #1,%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 671) andil #0x80000000,%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 672) faddd COSB7,%fp1 | ...B7+SB8
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 673) faddd SINA6,%fp2 | ...A6+SA7
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 674) eorl %d0,RPRIME(%a6)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 675) eorl %d0,SPRIME(%a6)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 676) fmulx %fp0,%fp1 | ...S(B7+SB8)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 677) oril #0x3F800000,%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 678) movel %d0,POSNEG1(%a6)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 679) fmulx %fp0,%fp2 | ...S(A6+SA7)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 680)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 681) faddd COSB6,%fp1 | ...B6+S(B7+SB8)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 682) faddd SINA5,%fp2 | ...A5+S(A6+SA7)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 683)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 684) fmulx %fp0,%fp1 | ...S(B6+S(B7+SB8))
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 685) fmulx %fp0,%fp2 | ...S(A5+S(A6+SA7))
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 686)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 687) faddd COSB5,%fp1 | ...B5+S(B6+S(B7+SB8))
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 688) faddd SINA4,%fp2 | ...A4+S(A5+S(A6+SA7))
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 689)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 690) fmulx %fp0,%fp1 | ...S(B5+...)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 691) fmulx %fp0,%fp2 | ...S(A4+...)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 692)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 693) faddd COSB4,%fp1 | ...B4+S(B5+...)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 694) faddd SINA3,%fp2 | ...A3+S(A4+...)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 695)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 696) fmulx %fp0,%fp1 | ...S(B4+...)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 697) fmulx %fp0,%fp2 | ...S(A3+...)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 698)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 699) faddx COSB3,%fp1 | ...B3+S(B4+...)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 700) faddx SINA2,%fp2 | ...A2+S(A3+...)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 701)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 702) fmulx %fp0,%fp1 | ...S(B3+...)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 703) fmulx %fp0,%fp2 | ...S(A2+...)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 704)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 705) faddx COSB2,%fp1 | ...B2+S(B3+...)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 706) faddx SINA1,%fp2 | ...A1+S(A2+...)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 707)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 708) fmulx %fp0,%fp1 | ...S(B2+...)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 709) fmulx %fp2,%fp0 | ...s(a1+...)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 710)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 711)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 712)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 713) fadds COSB1,%fp1 | ...B1+S(B2...)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 714) fmulx RPRIME(%a6),%fp0 | ...R'S(A1+...)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 715) fmulx SPRIME(%a6),%fp1 | ...S'(B1+S(B2+...))
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 716)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 717) movel %d1,-(%sp) |save users mode & precision
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 718) andil #0xff,%d1 |mask off all exceptions
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 719) fmovel %d1,%FPCR
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 720) fadds POSNEG1(%a6),%fp1 | ...COS(X)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 721) bsr sto_cos |store cosine result
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 722) fmovel (%sp)+,%FPCR |restore users exceptions
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 723) faddx RPRIME(%a6),%fp0 | ...SIN(X)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 724)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 725) bra t_frcinx
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 726)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 727) SCBORS:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 728) cmpil #0x3FFF8000,%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 729) bgt REDUCEX
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 730)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 731)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 732) SCSM:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 733) movew #0x0000,XDCARE(%a6)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 734) fmoves #0x3F800000,%fp1
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 735)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 736) movel %d1,-(%sp) |save users mode & precision
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 737) andil #0xff,%d1 |mask off all exceptions
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 738) fmovel %d1,%FPCR
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 739) fsubs #0x00800000,%fp1
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 740) bsr sto_cos |store cosine result
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 741) fmovel (%sp)+,%FPCR |restore users exceptions
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 742) fmovex X(%a6),%fp0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 743) bra t_frcinx
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 744)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 745) |end
Orange Pi5 kernel
Deprecated Linux kernel 5.10.110 for OrangePi 5/5B/5+ boards
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