832 lines
23 KiB
NASM
832 lines
23 KiB
NASM
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;---------------------------Module-Header------------------------------;
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; Module Name: math.asm
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;
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; Fast math routines.
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;
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; Created: 11/1/1996
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; Author: Otto Berkes [ottob]
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;
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; Copyright (c) 1996 Microsoft Corporation
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;----------------------------------------------------------------------;
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.386
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.model small,pascal
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assume cs:FLAT,ds:FLAT,es:FLAT,ss:FLAT
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assume fs:nothing,gs:nothing
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.xlist
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include gli386.inc
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.list
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PROFILE = 0
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include profile.inc
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;
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;
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; We're trying to solve:
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;
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; 1/sqrt(x)
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;
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; which in IEEE float is:
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;
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; 1/sqrt(M * 2^[E-127])
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;
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; To simplify, substitute e = [E-127]
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;
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; We can simplify this by pulling a large portion of the exponent out
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; by using only that portion of the exponent divisible by two (so we can
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; pull it out of the sqrt term):
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;
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; 1/sqrt(M * 2^(2*[e div 2]) * 2^[e MOD 2])
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;
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; which is:
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;
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; 1/ (2^[e div 2] * sqrt(M * 2^[e MOD 2]))
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;
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; or
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;
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; (2^[e div 2])^(-1) * 1/sqrt(M * 2^[e MOD 2])
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;
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; =
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; 2^-[e div 2] * 1/sqrt(M * 2^[e MOD 2])
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;
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; substitute back for e = [E-127]:
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;
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; 2^-[(E - 127) div 2] * 1/sqrt(M * 2^[(E - 127) MOD 2])
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;
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; =
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; 2^-[(E div 2) - 63] * 1/sqrt(M * 2^[(E - 1) MOD 2])
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;
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; =
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; 2^[63 - (E div 2)] * 1/sqrt(M * 2^[(E - 1) MOD 2])
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;
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; As a floating-point number, 2^[63 - (E div 2)] is just the exponent value:
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;
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; [63 - (E div 2)] + 127
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;
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; or
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; [(127+63) - (E div 2)]
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;
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; Remembering to account for the implicit '1' im the mantissa of IEEE floating-
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; point numbers, the range of (M * 2^[(E - 1) MOD 2]) is 0.800000 to
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; 0.ffffff*2, which is the interval [0.5, 2.0). We can use the fact that this
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; is a relatively small range, and therefore can use a table lookup near the
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; actual value. The table will contain values for the piece-wise approximation
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; to the curve 1/sqrt(M * 2^[(E - 1) MOD 2]) using an acceptable interval.
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; These values can then be used to approximate the desired inverse square root
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; value. At this point, all that remains is to apply the correct exponent
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; for the number, which is simply [(127+63) - (E div 2)] from the above
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; equations.
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;
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; To do the piecewise-linear approximation, we can store a table of values at
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; the appropriate intervals, and the deltas between them. However, this
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; will require calculating the difference between the interval value and
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; x. We can do a bit better by using slope-intercept (y = mx + b)m so the
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; table will store (m, b).
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;
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; With a 512-entry table, we will get at least 16 bits of precision. This
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; result was obtined using simulations.
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.data
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; The following 'C' code generates the table below:
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;#define SQRT_TAB_SIZE_LOG2 9 // 512-entry table
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;
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;#define MANTISSA_SIZE 24
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;#define SQRT_TAB_SIZE (1 << SQRT_TAB_SIZE_LOG2)
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;#define SQRT_INC (1 << (MANTISSA_SIZE - SQRT_TAB_SIZE_LOG2))
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;#define CASTFIX(a) (*((LONG *)&(a)))
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;
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;void genTable()
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;{
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; int i;
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; float x;
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; float xNext;
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; float y;
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; float yNext;
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; float xInterval;
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;
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; // We will start our table with the case where the exponent is even.
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;
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; CASTFIX(x) = 0x3f000000;
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;
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; // We will use the current and next values to generate the piece-wise
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; // data for the curve. The interval between 'current' and 'next' is
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; // based on the smallest change possible in the floating-point value
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; // that also represents a difference of one table-lookup entry.
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;
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; // When we switch to the odd-exponent case (at 1.0), we have to adjust
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; // for the fact that effective interval between successive values
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; / is doubled.
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;
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; CASTFIX(xNext) = CASTFIX(x) + SQRT_INC;
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; y = (float)1.0 / sqrt((double)x);
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;
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; // Calculate 1.0 / (piece-wise approximation interval).
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;
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; xInterval = xNext - x;
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;
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; xInterval = (float)1.0 / xInterval;
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;
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; // Now, generate the table:
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;
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; for (i = 0; i < SQRT_TAB_SIZE; i++) {
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; float m;
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; float b;
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;
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; // We increment our floating-point values using integer operations
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; // to ensure accuracy:
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;
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; CASTFIX(xNext) = CASTFIX(x) + SQRT_INC;
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;
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; // Find next point on curve:
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;
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; yNext = (float)1.0 / sqrt((double)xNext);
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;
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; // Test for odd-exponent case:
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;
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; if (CASTFIX(x) == 0x3f800000)
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; xInterval *= (float)0.5;
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;
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; m = (yNext - y) * xInterval;
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; b = y - (m * x);
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;
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; printf("\t\tdd\t0%8xh, 0%8xh\n", CASTFIX(m), CASTFIX(b));
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;
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; y = yNext;
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; x = xNext;
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; }
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;}
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invSqrtTab dd 0bfb47e00h, 04007a1fah
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dd 0bfb37000h, 040075e36h
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dd 0bfb26600h, 040071b31h
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dd 0bfb16000h, 04006d8ech
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dd 0bfb05800h, 0400695e4h
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dd 0bfaf5800h, 0400654a4h
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dd 0bfae5600h, 0400612a2h
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dd 0bfad5800h, 04005d165h
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dd 0bfac5e00h, 0400590f1h
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dd 0bfab6400h, 04005503eh
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dd 0bfaa6e00h, 040051058h
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dd 0bfa97800h, 04004d033h
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dd 0bfa88800h, 040049163h
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dd 0bfa79600h, 0400451d0h
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dd 0bfa6aa00h, 040041396h
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dd 0bfa5be00h, 04003d522h
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dd 0bfa4d400h, 0400396fah
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dd 0bfa3ee00h, 0400359a8h
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dd 0bfa30800h, 040031c1dh
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dd 0bfa22400h, 04002dee2h
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dd 0bfa14400h, 04002a282h
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dd 0bfa06600h, 040026674h
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dd 0bf9f8800h, 040022a30h
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dd 0bf9eae00h, 04001eecah
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dd 0bf9dd400h, 04001b32eh
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dd 0bf9cfc00h, 0400177e8h
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dd 0bf9c2800h, 040013d86h
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dd 0bf9b5400h, 0400102efh
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dd 0bf9a8400h, 04000c93fh
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dd 0bf99b400h, 040008f5bh
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dd 0bf98e600h, 0400055d2h
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dd 0bf981800h, 040001c16h
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dd 0bf975000h, 03fffc7abh
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dd 0bf968600h, 03fff55a6h
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dd 0bf95c000h, 03ffee580h
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dd 0bf94fc00h, 03ffe761ah
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dd 0bf943800h, 03ffe0652h
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dd 0bf937400h, 03ffd9628h
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dd 0bf92b600h, 03ffd290eh
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dd 0bf91f800h, 03ffcbb95h
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dd 0bf913a00h, 03ffc4dbdh
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dd 0bf907e00h, 03ffbe0afh
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dd 0bf8fc600h, 03ffb7597h
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dd 0bf8f0c00h, 03ffb08f8h
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dd 0bf8e5800h, 03ffa9f80h
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dd 0bf8da000h, 03ffa3354h
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dd 0bf8cee00h, 03ff9ca56h
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dd 0bf8c3c00h, 03ff960ffh
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dd 0bf8b8a00h, 03ff8f74fh
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dd 0bf8adc00h, 03ff88fa8h
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dd 0bf8a2e00h, 03ff827aah
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dd 0bf898000h, 03ff7bf55h
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dd 0bf88d600h, 03ff75911h
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dd 0bf882e00h, 03ff6f3adh
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dd 0bf878400h, 03ff68cbfh
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dd 0bf86de00h, 03ff627eah
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dd 0bf863600h, 03ff5c18ah
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dd 0bf859400h, 03ff55e81h
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dd 0bf84f000h, 03ff4f9edh
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dd 0bf845000h, 03ff4977dh
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dd 0bf83ae00h, 03ff43381h
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dd 0bf831000h, 03ff3d1aeh
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dd 0bf827200h, 03ff36f8ch
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dd 0bf81d400h, 03ff30d1bh
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dd 0bf813a00h, 03ff2acdbh
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dd 0bf809e00h, 03ff24b0dh
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dd 0bf800600h, 03ff1eb75h
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dd 0bf7edc00h, 03ff18b91h
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dd 0bf7db000h, 03ff12ca5h
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dd 0bf7c8400h, 03ff0cd6eh
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dd 0bf7b5c00h, 03ff06f32h
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dd 0bf7a3400h, 03ff010ach
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dd 0bf791000h, 03fefb324h
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dd 0bf77f000h, 03fef569ch
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dd 0bf76d000h, 03feef9cch
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dd 0bf75b000h, 03fee9cb4h
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dd 0bf749400h, 03fee40a0h
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dd 0bf737c00h, 03fede592h
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dd 0bf726800h, 03fed8b8ch
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dd 0bf714c00h, 03fed2ea3h
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dd 0bf704000h, 03fecd6b3h
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dd 0bf6f2800h, 03fec7a8dh
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dd 0bf6e1c00h, 03fec2217h
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dd 0bf6d1000h, 03febc95eh
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dd 0bf6c0400h, 03feb7062h
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dd 0bf6afc00h, 03feb1878h
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dd 0bf69f400h, 03feac04ch
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dd 0bf68ec00h, 03fea67deh
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dd 0bf67ec00h, 03fea11deh
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dd 0bf66e800h, 03fe9ba45h
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dd 0bf65e800h, 03fe963c5h
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dd 0bf64ec00h, 03fe90e60h
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dd 0bf63f000h, 03fe8b8bch
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dd 0bf62f400h, 03fe862d9h
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dd 0bf620000h, 03fe80f73h
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dd 0bf610400h, 03fe7b912h
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dd 0bf601000h, 03fe76532h
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dd 0bf5f2000h, 03fe71276h
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dd 0bf5e2c00h, 03fe6be1ch
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dd 0bf5d3c00h, 03fe66ae8h
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dd 0bf5c5000h, 03fe618dch
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dd 0bf5b6000h, 03fe5c530h
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dd 0bf5a7800h, 03fe57414h
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dd 0bf598c00h, 03fe52157h
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dd 0bf58a800h, 03fe4d12fh
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dd 0bf57c000h, 03fe47f65h
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dd 0bf56dc00h, 03fe42ecbh
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dd 0bf55f800h, 03fe3ddf8h
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dd 0bf551800h, 03fe38e58h
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dd 0bf543800h, 03fe33e80h
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dd 0bf535c00h, 03fe2efdeh
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dd 0bf527c00h, 03fe29f96h
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dd 0bf51a000h, 03fe25086h
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dd 0bf50c800h, 03fe202b0h
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dd 0bf4ff000h, 03fe1b4a4h
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dd 0bf4f1c00h, 03fe167d5h
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dd 0bf4e4400h, 03fe1195dh
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dd 0bf4d7000h, 03fe0cc24h
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dd 0bf4c9c00h, 03fe07eb6h
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dd 0bf4bcc00h, 03fe0328ah
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dd 0bf4afc00h, 03fdfe62ah
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dd 0bf4a3000h, 03fdf9b0fh
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dd 0bf496000h, 03fdf4e47h
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dd 0bf489800h, 03fdf0441h
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dd 0bf47c800h, 03fdeb711h
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dd 0bf470400h, 03fde6e24h
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dd 0bf463c00h, 03fde2388h
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dd 0bf457400h, 03fddd8bah
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dd 0bf44b000h, 03fdd8f3ah
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dd 0bf43ec00h, 03fdd4589h
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dd 0bf432800h, 03fdcfba7h
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dd 0bf426800h, 03fdcb317h
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dd 0bf41a800h, 03fdc6a57h
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dd 0bf40e800h, 03fdc2167h
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dd 0bf402c00h, 03fdbd9cdh
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dd 0bf3f6c00h, 03fdb907dh
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dd 0bf3eb400h, 03fdb4a0dh
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dd 0bf3dfc00h, 03fdb036fh
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dd 0bf3d4000h, 03fdabb19h
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dd 0bf3c8800h, 03fda741fh
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dd 0bf3bd400h, 03fda2e83h
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dd 0bf3b2000h, 03fd9e8bah
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dd 0bf3a6800h, 03fd9a136h
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dd 0bf39b400h, 03fd95b13h
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dd 0bf390800h, 03fd917e3h
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dd 0bf385000h, 03fd8cfd5h
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dd 0bf37a400h, 03fd88c4fh
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dd 0bf36f800h, 03fd8489eh
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dd 0bf364400h, 03fd8019ah
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dd 0bf359c00h, 03fd7bf28h
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dd 0bf34f000h, 03fd77af6h
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dd 0bf344400h, 03fd73699h
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dd 0bf339c00h, 03fd6f3a9h
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dd 0bf32f400h, 03fd6b08fh
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dd 0bf324c00h, 03fd66d4bh
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dd 0bf31a800h, 03fd62b78h
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dd 0bf310000h, 03fd5e7e0h
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dd 0bf305c00h, 03fd5a5bbh
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dd 0bf2fb800h, 03fd5636dh
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dd 0bf2f1800h, 03fd52295h
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dd 0bf2e7400h, 03fd4dff5h
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dd 0bf2dd800h, 03fd4a06eh
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dd 0bf2d3400h, 03fd45d7ch
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dd 0bf2a2800h, 03fd31ccfh
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dd 0bf285c00h, 03fd25de5h
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dd 0bf273000h, 03fd1e0a7h
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dd 0bf269800h, 03fd1a0f9h
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dd 0bf260400h, 03fd162d3h
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dd 0bf257000h, 03fd12488h
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dd 0bf24e000h, 03fd0e7c8h
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dd 0bf244c00h, 03fd0a933h
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dd 0bf23bc00h, 03fd06c2bh
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dd 0bf232800h, 03fd02d4ch
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dd 0bf229c00h, 03fcff1b0h
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dd 0bf220c00h, 03fcfb43ch
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dd 0bf218000h, 03fcf785ah
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dd 0bf20f400h, 03fcf3c55h
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dd 0bf1fdc00h, 03fcec3e3h
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dd 0bf1f4c00h, 03fce85bbh
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dd 0bf1ec800h, 03fce4ca0h
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dd 0bf1e3c00h, 03fce0fech
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dd 0bf1db400h, 03fcdd4d2h
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dd 0bf1d2c00h, 03fcd9996h
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dd 0bf1b9800h, 03fcce8d5h
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dd 0bf1b1800h, 03fccb095h
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dd 0bf1a9400h, 03fcc7672h
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dd 0bf1a0c00h, 03fcc3a6ah
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dd 0bf199000h, 03fcc038fh
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dd 0bf190800h, 03fcbc743h
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dd 0bf159400h, 03fca3be4h
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dd 0bf151800h, 03fca03f2h
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dd 0bf142400h, 03fc99582h
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dd 0bf13a400h, 03fc95b62h
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dd 0bf133000h, 03fc92698h
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dd 0bf12b400h, 03fc8ee0bh
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dd 0bf123c00h, 03fc8b733h
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dd 0bf11c400h, 03fc8803dh
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dd 0bf114c00h, 03fc84929h
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dd 0bf10d800h, 03fc813ceh
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dd 0bf106400h, 03fc7de56h
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dd 0bf0fec00h, 03fc7a6e8h
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dd 0bf0f7800h, 03fc77136h
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dd 0bf0f0400h, 03fc73b67h
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dd 0bf0e9000h, 03fc7057bh
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dd 0bf0e2000h, 03fc6d14fh
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dd 0bf0dac00h, 03fc69b29h
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dd 0bf0d3c00h, 03fc666c5h
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dd 0bf0ccc00h, 03fc63245h
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dd 0bf0c5800h, 03fc5fbc8h
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dd 0bf0bec00h, 03fc5c8f2h
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dd 0bf0b7c00h, 03fc5941eh
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dd 0bf0b0c00h, 03fc55f2eh
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dd 0bf0aa000h, 03fc52c07h
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dd 0bf0a3000h, 03fc4f6dfh
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dd 0bf09c400h, 03fc4c382h
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dd 0bf095c00h, 03fc491f2h
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dd 0bf08ec00h, 03fc45c76h
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dd 0bf088000h, 03fc428c8h
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dd 0bf081800h, 03fc3f6eah
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dd 0bf07b000h, 03fc3c4f2h
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dd 0bf074000h, 03fc38f06h
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dd 0bf06dc00h, 03fc35ec8h
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dd 0bf067400h, 03fc32c82h
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dd 0bf060800h, 03fc2f832h
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dd 0bf05a400h, 03fc2c7a9h
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dd 0bf053c00h, 03fc29515h
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dd 0bf04d800h, 03fc2645ah
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dd 0bf047000h, 03fc23192h
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dd 0bf040800h, 03fc1feb0h
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dd 0bf03a800h, 03fc1cfa0h
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dd 0bf034000h, 03fc19c8ah
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dd 0bf02dc00h, 03fc16b52h
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dd 0bf027c00h, 03fc13bfah
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dd 0bf021800h, 03fc10a90h
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dd 0bf01b400h, 03fc0d90dh
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dd 0bf015000h, 03fc0a771h
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dd 0bf00f400h, 03fc079b6h
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dd 0bf009000h, 03fc047e8h
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dd 0bf003000h, 03fc01800h
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dd 0beff4000h, 03fbfd000h
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dd 0befdc400h, 03fbf70a1h
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dd 0befc4c00h, 03fbf11e5h
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dd 0befad800h, 03fbeb3ceh
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dd 0bef96400h, 03fbe555ah
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dd 0bef7f800h, 03fbdf893h
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dd 0bef68e00h, 03fbd9bf4h
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dd 0bef52600h, 03fbd3f7eh
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dd 0bef3c200h, 03fbce3b6h
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dd 0bef26200h, 03fbc889eh
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dd 0bef10600h, 03fbc2e38h
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dd 0beefac00h, 03fbbd400h
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dd 0beee5400h, 03fbb79f8h
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dd 0beed0200h, 03fbb212eh
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dd 0beebb200h, 03fbac896h
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dd 0beea6600h, 03fba70b9h
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dd 0bee91a00h, 03fba1889h
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dd 0bee7d400h, 03fb9c1a0h
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dd 0bee69000h, 03fb96aeeh
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dd 0bee54e00h, 03fb91474h
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dd 0bee41200h, 03fb8bf48h
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dd 0bee2d400h, 03fb86942h
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dd 0bee19e00h, 03fb8151ah
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dd 0bee06600h, 03fb7c018h
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dd 0bedf3400h, 03fb76c6ch
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dd 0bede0400h, 03fb71900h
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dd 0bedcd600h, 03fb6c5d4h
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dd 0bedbac00h, 03fb67379h
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dd 0beda8400h, 03fb62161h
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dd 0bed95e00h, 03fb5cf8eh
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dd 0bed83a00h, 03fb57e00h
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dd 0bed71a00h, 03fb52d48h
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dd 0bed5fc00h, 03fb4dcd8h
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dd 0bed4e000h, 03fb48cb0h
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dd 0bed3c800h, 03fb43d64h
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dd 0bed2b000h, 03fb3edd2h
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dd 0bed19c00h, 03fb39f1eh
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dd 0bed08a00h, 03fb350b8h
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dd 0becf7c00h, 03fb30333h
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dd 0bece6c00h, 03fb2b4d7h
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dd 0becd6200h, 03fb267f3h
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dd 0becc5a00h, 03fb21b61h
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dd 0becb5200h, 03fb1ce8dh
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dd 0beca4e00h, 03fb182a2h
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dd 0bec94c00h, 03fb1370ch
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dd 0bec84a00h, 03fb0eb36h
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dd 0bec74e00h, 03fb0a0e4h
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dd 0bec65200h, 03fb05652h
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dd 0bec55800h, 03fb00c1ah
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dd 0bec45e00h, 03fafc1a4h
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dd 0bec36a00h, 03faf78bah
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dd 0bec27600h, 03faf2f93h
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dd 0bec18400h, 03faee6c9h
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dd 0bec09600h, 03fae9ef8h
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dd 0bebfa600h, 03fae5650h
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dd 0bebeba00h, 03fae0ea2h
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dd 0bebdd000h, 03fadc756h
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dd 0bebce800h, 03fad806ch
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dd 0bebc0000h, 03fad3948h
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dd 0bebb1e00h, 03facf3c3h
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dd 0beba3a00h, 03facad67h
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dd 0beb95800h, 03fac6770h
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dd 0beb87a00h, 03fac2280h
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dd 0beb79c00h, 03fabdd57h
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dd 0beb6c000h, 03fab9897h
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dd 0beb5e600h, 03fab5440h
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dd 0beb50e00h, 03fab1054h
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dd 0beb43600h, 03faacc32h
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dd 0beb36200h, 03faa891eh
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dd 0beb28e00h, 03faa45d6h
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dd 0beb1bc00h, 03faa02fah
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dd 0beb0ec00h, 03fa9c08eh
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dd 0beb01e00h, 03fa97e92h
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dd 0beaf5000h, 03fa93c63h
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dd 0beadba00h, 03fa8b959h
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dd 0beacf400h, 03fa87927h
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dd 0beac2a00h, 03fa83776h
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dd 0beab6600h, 03fa7f788h
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dd 0beaaa200h, 03fa7b76ah
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dd 0bea9e000h, 03fa777c2h
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dd 0bea91e00h, 03fa737e9h
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dd 0bea85e00h, 03fa6f889h
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dd 0bea7a000h, 03fa6b9a2h
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dd 0bea6e400h, 03fa67b36h
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dd 0bea62800h, 03fa63c9ch
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dd 0bea56e00h, 03fa5fe7ch
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dd 0bea4b400h, 03fa5c02fh
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dd 0bea3fe00h, 03fa5830bh
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dd 0bea34600h, 03fa5450dh
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dd 0bea29400h, 03fa508e8h
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dd 0bea1de00h, 03fa4cb3ch
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dd 0bea12c00h, 03fa48ebeh
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dd 0bea07c00h, 03fa452c2h
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dd 0be9fcc00h, 03fa4169ah
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dd 0be9f1e00h, 03fa3daf5h
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dd 0be9e7000h, 03fa39f25h
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dd 0be9dc400h, 03fa363dah
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dd 0be9d1a00h, 03fa32915h
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dd 0be9c7000h, 03fa2ee26h
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dd 0be9bc800h, 03fa2b3beh
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dd 0be9b2000h, 03fa2792ch
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dd 0be9a7a00h, 03fa23f22h
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dd 0be99d600h, 03fa205a4h
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dd 0be993200h, 03fa1cbfch
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dd 0be989000h, 03fa192dfh
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dd 0be97ec00h, 03fa158e5h
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dd 0be974e00h, 03fa120e2h
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dd 0be96ae00h, 03fa0e802h
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dd 0be961000h, 03fa0afb1h
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dd 0be957200h, 03fa07738h
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dd 0be94d800h, 03fa04006h
|
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dd 0be943a00h, 03fa0073eh
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dd 0be93a200h, 03f9fd078h
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dd 0be930a00h, 03f9f998ch
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dd 0be927000h, 03f9f61c1h
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dd 0be91da00h, 03f9f2b43h
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dd 0be914400h, 03f9ef4a0h
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dd 0be90b000h, 03f9ebe92h
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dd 0be901a00h, 03f9e87a3h
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dd 0be8f8a00h, 03f9e52c3h
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dd 0be8ef600h, 03f9e1c46h
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dd 0be8e6600h, 03f9de71eh
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dd 0be8dd600h, 03f9db1d2h
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dd 0be8d4600h, 03f9d7c62h
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dd 0be8cb800h, 03f9d478ch
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dd 0be8c2c00h, 03f9d1352h
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dd 0be8b9e00h, 03f9cde36h
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dd 0be8b1400h, 03f9caa76h
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dd 0be8a8a00h, 03f9c7694h
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dd 0be8a0000h, 03f9c428eh
|
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dd 0be897600h, 03f9c0e67h
|
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dd 0be88f000h, 03f9bdba1h
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dd 0be886800h, 03f9ba7f7h
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dd 0be87e200h, 03f9b74eeh
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dd 0be875e00h, 03f9b4287h
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dd 0be86d800h, 03f9b0f3bh
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dd 0be865600h, 03f9add56h
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dd 0be85d200h, 03f9aaa8ch
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dd 0be855200h, 03f9a792ch
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dd 0be84d000h, 03f9a46e6h
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dd 0be844e00h, 03f9a1480h
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dd 0be83d000h, 03f99e387h
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dd 0be835200h, 03f99b26eh
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dd 0be82d400h, 03f998136h
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dd 0be825600h, 03f994fdfh
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dd 0be81da00h, 03f991f31h
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dd 0be816000h, 03f98ef2eh
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dd 0be80e400h, 03f98be42h
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dd 0be7ef400h, 03f982ebch
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dd 0be76b800h, 03f9686b6h
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dd 0be725800h, 03f95a193h
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|
|
dd 0be5b5400h, 03f90bc62h
|
||
|
|
dd 0be5a9800h, 03f9092fbh
|
||
|
|
dd 0be59e000h, 03f906a5fh
|
||
|
|
dd 0be592800h, 03f9041ach
|
||
|
|
dd 0be587000h, 03f9018e2h
|
||
|
|
dd 0be57b800h, 03f8ff001h
|
||
|
|
dd 0be570400h, 03f8fc7edh
|
||
|
|
dd 0be565000h, 03f8f9fc2h
|
||
|
|
dd 0be559c00h, 03f8f7782h
|
||
|
|
dd 0be54e800h, 03f8f4f2ah
|
||
|
|
dd 0be543800h, 03f8f27a2h
|
||
|
|
dd 0be538800h, 03f8f0004h
|
||
|
|
dd 0be52d800h, 03f8ed850h
|
||
|
|
dd 0be522c00h, 03f8eb16eh
|
||
|
|
dd 0be517c00h, 03f8e898eh
|
||
|
|
dd 0be50d000h, 03f8e6280h
|
||
|
|
dd 0be502400h, 03f8e3b5dh
|
||
|
|
dd 0be4f7800h, 03f8e1424h
|
||
|
|
dd 0be4ecc00h, 03f8decd6h
|
||
|
|
dd 0be4e2800h, 03f8dc748h
|
||
|
|
dd 0be4d7c00h, 03f8d9fcfh
|
||
|
|
dd 0be4cd800h, 03f8d7a18h
|
||
|
|
dd 0be4c3000h, 03f8d5360h
|
||
|
|
dd 0be4b8800h, 03f8d2c92h
|
||
|
|
dd 0be4ae800h, 03f8d078ah
|
||
|
|
dd 0be4a4000h, 03f8ce094h
|
||
|
|
dd 0be49a000h, 03f8cbb64h
|
||
|
|
dd 0be48fc00h, 03f8c9531h
|
||
|
|
dd 0be485c00h, 03f8c6fd9h
|
||
|
|
dd 0be47bc00h, 03f8c4a6dh
|
||
|
|
dd 0be471c00h, 03f8c24edh
|
||
|
|
dd 0be467c00h, 03f8bff59h
|
||
|
|
dd 0be45e000h, 03f8bdaa2h
|
||
|
|
dd 0be454000h, 03f8bb4e6h
|
||
|
|
dd 0be44a800h, 03f8b90fah
|
||
|
|
dd 0be440800h, 03f8b6b16h
|
||
|
|
dd 0be437000h, 03f8b4704h
|
||
|
|
dd 0be42d800h, 03f8b22dfh
|
||
|
|
dd 0be423c00h, 03f8afdb3h
|
||
|
|
dd 0be41a400h, 03f8ad968h
|
||
|
|
dd 0be410c00h, 03f8ab50ah
|
||
|
|
dd 0be407800h, 03f8a918eh
|
||
|
|
dd 0be3fe000h, 03f8a6d0ah
|
||
|
|
dd 0be3f4c00h, 03f8a496ah
|
||
|
|
dd 0be3eb400h, 03f8a24c0h
|
||
|
|
dd 0be3e2400h, 03f8a01f2h
|
||
|
|
dd 0be3d9000h, 03f89de1ah
|
||
|
|
dd 0be3d0000h, 03f89bb28h
|
||
|
|
dd 0be3c6c00h, 03f89972bh
|
||
|
|
dd 0be3bd800h, 03f89731ch
|
||
|
|
dd 0be3b4c00h, 03f8950eeh
|
||
|
|
dd 0be3abc00h, 03f892db4h
|
||
|
|
dd 0be3a3000h, 03f890b62h
|
||
|
|
dd 0be399c00h, 03f88e709h
|
||
|
|
dd 0be391400h, 03f88c591h
|
||
|
|
dd 0be388400h, 03f88a20fh
|
||
|
|
dd 0be37fc00h, 03f888075h
|
||
|
|
dd 0be377000h, 03f885dcch
|
||
|
|
dd 0be36e400h, 03f883b12h
|
||
|
|
dd 0be365800h, 03f881847h
|
||
|
|
dd 0be35d400h, 03f87f768h
|
||
|
|
dd 0be354800h, 03f87d47ah
|
||
|
|
|
||
|
|
.code
|
||
|
|
|
||
|
|
SQRT_TAB_LOG2 equ 9 ;; log2 of the lookup-table
|
||
|
|
MANTISSA_SIZE equ 24 ;; number if mantissa bits in fp value
|
||
|
|
;; number of represented mantissa bits
|
||
|
|
;; (one less than total due to hidden
|
||
|
|
;; leading one).
|
||
|
|
MANTISSA_BITS equ (MANTISSA_SIZE - 1)
|
||
|
|
ELEMENT_SIZE_LOG2 equ 3 ;; log2 of each table entry (8 bytes)
|
||
|
|
;; shift required to get bits in value
|
||
|
|
;; in the correct place to use as an
|
||
|
|
;; index for the table lookup
|
||
|
|
EXPONENT_SHIFT equ (MANTISSA_BITS - (SQRT_TAB_LOG2 - 1)\
|
||
|
|
- ELEMENT_SIZE_LOG2)
|
||
|
|
;; mask value for clamping to [.5..2)
|
||
|
|
CLAMP_MASK equ ((1 SHL (MANTISSA_BITS+1)) - 1)
|
||
|
|
;; mask for sign/exponent bits
|
||
|
|
MANTISSA_MASK equ ((1 SHL MANTISSA_BITS) - 1)
|
||
|
|
;; mask for sign/exponent bits
|
||
|
|
EXPONENT_MASK equ (-1 AND (NOT MANTISSA_MASK))
|
||
|
|
;; mask for table lookup
|
||
|
|
TABLE_MASK equ ((1 SHL (SQRT_TAB_LOG2 + ELEMENT_SIZE_LOG2)) - 1) \
|
||
|
|
AND (NOT((1 SHL ELEMENT_SIZE_LOG2) - 1))
|
||
|
|
;; bias used to represent clamped value
|
||
|
|
EXPONENT_BIAS_EVEN equ 3f000000h
|
||
|
|
;; bias value used for final exponent
|
||
|
|
;; computation
|
||
|
|
LARGE_EXPONENT_BIAS equ (((127 + 127/2) SHL (MANTISSA_BITS+1)) OR CLAMP_MASK)
|
||
|
|
|
||
|
|
|
||
|
|
x equ DWORD PTR 8[ebp]
|
||
|
|
num equ DWORD PTR -8[ebp]
|
||
|
|
|
||
|
|
@__FastInvSqrt@4 PROC NEAR
|
||
|
|
|
||
|
|
push ebp
|
||
|
|
mov ebp, esp
|
||
|
|
sub esp, 8
|
||
|
|
push ecx
|
||
|
|
|
||
|
|
mov eax, x
|
||
|
|
mov ecx, eax
|
||
|
|
shr ecx, EXPONENT_SHIFT ;; ecx is table index (8 frac. bits)
|
||
|
|
and eax, CLAMP_MASK ;; clamp number to [0.5, 2.0]
|
||
|
|
and ecx, TABLE_MASK ;; (8 bytes)/(table entry)
|
||
|
|
or eax, EXPONENT_BIAS_EVEN ;; re-adjust exponent for clamped number
|
||
|
|
mov num, eax
|
||
|
|
fld num
|
||
|
|
fmul [invSqrtTab+ecx] ;; find mx
|
||
|
|
mov eax, LARGE_EXPONENT_BIAS;; (127+63)<<23 to re-adjust exponent
|
||
|
|
sub eax, x ;; divide exponent by 2
|
||
|
|
fadd [invSqrtTab+ecx+4] ;; get mx + b
|
||
|
|
shr eax, 1
|
||
|
|
and eax, EXPONENT_MASK ;; mask exponent
|
||
|
|
mov num, eax
|
||
|
|
fmul num ;; now adjust for exponent
|
||
|
|
|
||
|
|
pop ecx
|
||
|
|
mov esp, ebp
|
||
|
|
pop ebp
|
||
|
|
ret 4
|
||
|
|
|
||
|
|
@__FastInvSqrt@4 endp
|
||
|
|
|
||
|
|
len equ DWORD PTR -4[ebp]
|
||
|
|
num equ DWORD PTR -8[ebp]
|
||
|
|
|
||
|
|
@__glNormalize@8 PROC NEAR
|
||
|
|
|
||
|
|
push ebp
|
||
|
|
mov ebp, esp
|
||
|
|
sub esp, 8
|
||
|
|
fld DWORD PTR [edx]
|
||
|
|
fmul DWORD PTR [edx] ;; x
|
||
|
|
fld DWORD PTR [edx+4]
|
||
|
|
fmul DWORD PTR [edx+4] ;; y x
|
||
|
|
fld DWORD PTR [edx+8]
|
||
|
|
fmul DWORD PTR [edx+8] ;; z y x
|
||
|
|
fxch ST(2) ;; x y z
|
||
|
|
faddp ST(1), ST ;; xy z
|
||
|
|
faddp ST(1), ST ;; xyz
|
||
|
|
fstp len
|
||
|
|
mov eax, len
|
||
|
|
test eax, eax
|
||
|
|
jne notZeroLen
|
||
|
|
|
||
|
|
mov [ecx], eax
|
||
|
|
mov [ecx+4], eax
|
||
|
|
mov [ecx+8], eax
|
||
|
|
mov esp, ebp
|
||
|
|
pop ebp
|
||
|
|
ret 0
|
||
|
|
|
||
|
|
notZeroLen:
|
||
|
|
|
||
|
|
cmp eax, __FLOAT_ONE
|
||
|
|
jne notOneLen
|
||
|
|
cmp ecx, edx
|
||
|
|
je normExit
|
||
|
|
mov eax, [edx]
|
||
|
|
mov [ecx], eax
|
||
|
|
mov eax, [edx+4]
|
||
|
|
mov [ecx+4], eax
|
||
|
|
mov eax, [edx+8]
|
||
|
|
mov [ecx+8], eax
|
||
|
|
mov esp, ebp
|
||
|
|
pop ebp
|
||
|
|
ret 0
|
||
|
|
|
||
|
|
notOneLen:
|
||
|
|
|
||
|
|
;; eax already has length
|
||
|
|
|
||
|
|
push edi
|
||
|
|
mov edi, eax
|
||
|
|
shr edi, EXPONENT_SHIFT ;; edi is table index (8 frac. bits)
|
||
|
|
and eax, CLAMP_MASK ;; clamp number to [0.5, 2.0]
|
||
|
|
and edi, TABLE_MASK ;; (8 bytes)/(table entry)
|
||
|
|
or eax, EXPONENT_BIAS_EVEN ;; re-adjust exponent for clamped number
|
||
|
|
mov num, eax
|
||
|
|
fld num
|
||
|
|
fmul [invSqrtTab+edi] ;; find mx
|
||
|
|
mov eax, LARGE_EXPONENT_BIAS;; (127+63)<<23 to re-adjust exponent
|
||
|
|
sub eax, len ;; divide exponent by 2
|
||
|
|
fadd [invSqrtTab+edi+4] ;; get mx + b
|
||
|
|
shr eax, 1
|
||
|
|
and eax, EXPONENT_MASK ;; mask exponent
|
||
|
|
mov num, eax
|
||
|
|
fmul num ;; now adjust for exponent
|
||
|
|
|
||
|
|
fld DWORD PTR [edx] ;; 1/sqrt(len) on stack
|
||
|
|
fmul ST, ST(1)
|
||
|
|
fld DWORD PTR [edx+4]
|
||
|
|
fmul ST, ST(2)
|
||
|
|
fld DWORD PTR [edx+8]
|
||
|
|
fmul ST, ST(3) ;; z y x len
|
||
|
|
fxch ST(2) ;; x y z len
|
||
|
|
fstp DWORD PTR [ecx]
|
||
|
|
fstp DWORD PTR [ecx+4]
|
||
|
|
fstp DWORD PTR [ecx+8]
|
||
|
|
fstp ST(0) ;; pop len
|
||
|
|
|
||
|
|
pop edi
|
||
|
|
mov esp, ebp
|
||
|
|
pop ebp
|
||
|
|
ret 0
|
||
|
|
|
||
|
|
normExit:
|
||
|
|
|
||
|
|
mov esp, ebp
|
||
|
|
pop ebp
|
||
|
|
ret 0
|
||
|
|
|
||
|
|
@__glNormalize@8 ENDP
|
||
|
|
|
||
|
|
END
|